Integer is either a composite number or a prime number. Therefore, detecting composite numbers is important for solving prime numbers. The study of prime numbers, apart from satisfying human curiosity, can be very important. In this article, the order of composite numbers has been detected. And explained with a simple method and a simple function. And, a method has been developed in which all composite numbers and therefore prime numbers can be determined by using the specified methods, functions and formulas.

Prime number-related issues can be viewed from drastically different perspectives by examining the close connections between prime numbers and composite numbers. We think that multiple perspectives are the pillars on the path to solutions so we have created this study. As a result of the study, we proposed two new formulas by presenting three theorems and one proof for each theorem, a total of three proofs. We proved that the formula p · n + p returns a composite number in the first of the theorems, which is the preliminary theorem. Our first theorem except the preliminary theorem is that the formula p · n + p returns all composite numbers, and we proved that too. Finally, we created Theorem II using Theorem I to use in our other work and proved that the formula 2 · n · p + p returns all odd composite numbers, which is Theorem II. Afterward, we presented the similarities of the 2 · n · p + p formula we put forth with another known formula.

Precision agriculture (PA) is a holistic, sustainable, innovative systems approach that assists farmers in production management. Adopting PA could improve sustainable food security and community economic sustainability. Developing an understanding of PA adoption attributes is needed to assist extension practitioners to promote adoption and better understand the innovation adoption phenomena. A systematic review of literature was conducted to investigate PA adoption. Thirty-three publications were examined, and four themes were found among the reviewed publications. The results were interpreted using Rogers’ diffusion of innovations framework to address the research objectives. Of the reviewed literature, we found relative advantage and compatibility were two dominant attributes to strengthen the adoption of PA, and the complexity attribute was rarely used to promote the adoption of PA. This study shows that change agents do not fully use five attributes of innovation when they promote PA technology to stakeholders to adopt. Thus, we recommend studies from the agricultural extension specialists’ perspectives in the future may determine contributions to motivate farmers’ adoption of PA, in particular related to complexity.

It is highly likely that the wearing of face masks reduces the rate of respiratory infections (e.g. SARS-CoV-2), to protect both the user and those around them. This paper sets out to review the areas that effect the efficacy of masks, the materials, design, hygiene and fit testing, in order to make recommendations as to how to make mask from resources found in most homes for when commercial models are unavailable. This paper finds that a mask constructed with a filter made from high thread count cotton is likely to provide a reasonable level of protection (~70% filtration) and that if a layers of other materials such as chiffon or silk is added the filtration may be much higher (~90%). There is also some promise in less available materials such as vacuum cleaner bags and air conditioner filters. Examples of fabric and rigid designs are reviewed but most are limited by the fit to the users which is hard to determine in a home setting. It would be extremely helpful if a method was devised for people to test or be tested for the fit of home made masks. In the mean time careful thought should be given to whether the user judges a good fit. Users should also be careful to practice other means of hygiene and distancing.

This theoretical article reviews the model describing processes in social systems based on the analysis of their resource base. Application of the system theory can help to explain why some systems are aimed at prevention of type I errors, while other seek to decrease quantity of type II errors. Such differences are manifested in investment of resources either into deep interaction or into wide coverage. Some examples of such strategies in economic, market and production systems are provided in the article. The article introduces some provisions of the system theory in the context of the resource flows. The main indicators that are considered in this article are the characteristics of the sources of the exchanging flows of resources. Their relative frequency and quality are investigated, on the basis of which the most effective strategy of the system is derived, as a mechanism for redistributing resources. The rigor of the system's strategy depends on the magnitude of the difference in characteristics. It is explained how exactly it influences the exchange processes, that in reality systems do not interact simultaneously, and one of the opposite resource flows is always delayed. It is shown how the system strategy depends on the risks linked with interactions. Also, there are grounds for the need to accumulate resources, including in the situation of their surplus. The model helps also explain shift of economic centers throughout history. Additionally, there is an analogy between systems strategies and the competitive strategies described by M. Porter, and outsourcing versus integration.

This article presents description of social structures such as, for example, states, in the context of their consideration as systems. Moreover, it seeks to develop K. Marx’s model in terms of systematic approach, as well as to justify the application of the Fibonacci sequence to systems in general and, in particular, to social systems. The description covers a wide range of issues, ranging from the assertion of the basic principle of living systems as patterns in resources flows to description of functions of various aspects of states and their economics in terms of objective needs of such structures. In addition, this article justifies synergetic effect based on proposed model, and the way this effect is applied to state systems. Moreover, it includes the description of main changes of socio-economic formations throughout the history as a natural development of social systems, including possible modern stages. The fundamental tool of this description is description of essence of the mechanism of property rights and its formation options. The differences of two extreme directions of such development are also described on the basis of the objective factor of resource provision. Special attention is given to the concept of surplus value as a feature of social production systems.

This theoretical article provides a brief description of the model of living systems' functioning by defining them as resource flows patterns. It reviews the living systems growth limitation between their development cycles by the Fibonacci sequence. Besides, there are presented systems resource base criteria, necessary for accumulating the resources and their investment. The article also considers the conditions for the formation of various systems strategies. Then we reviewed the principles of elemental analysis of information by a person as a living system according to the considered model. The study also shows the possibility of forming priorities in analyzing information for 16 combinations as maximum. At that, it remains crucial to divide a human's information analysis between the two hemispheres of the brain. The described combinations of priorities in a person's information analysis are compared with the existing differential personality models, such as the big five personality traits, the Myers-Briggs type indicator, temperaments model and Honey and Mumford Learning styles.

This article presents the results of the consideration of the Bertrand paradox in terms of geometric probability theory. Although the method and conclusions of this article are straightforward, no equivalent studies were found when reviewing the relevant literature. This could be conditioned by the fact that the hypotheses presented in this research have low intuitive obviousness and, in contrast, could be due to the historically established agreement regarding the issue. This article shows that out of three classical solutions to the problem described by Bertrand, two methods are inconsistent with the claimed relative objectivity. Although the remaining solution (1/4) seems to be the most correct, we cannot claim that we have exhaustively ruled out all aspects that could reduce its adequacy to solve the problem.

The two main strategies used in this study are the binary representation and the decomposition of a natural number into many compound functions of odd function and even function. The Collatz conjecture regarding odd even numbers in number theory can be examined and discussed using them in this way: The sequence created by the finite iterations of the Collatz function becomes the ultimately periodic sequence if any natural number is the beginning value, proving the conjecture that has been held for 85 years.

The Rho guanine nucleotide exchange factor (RGNEF) protein encoded by the ARHGEF28 gene has been implicated in the neurodegenerative disease amyotrophic lateral sclerosis (ALS). Biochemical and pathological studies have shown that RGNEF is a component of the hallmark neuronal cytoplasmic inclusions in ALS-affected neurons. Additionally, a heterozygous mutation in ARHGEF28 has been identified in a number of familial ALS (fALS) cases that may give rise to one of two truncated variants of the protein. Little is known about the normal biological function of RGNEF or how it contributes to ALS pathogenesis. To further explore RGNEF biology we have established and characterized a yeast model and characterized RGNEF expression in several mammalian cell lines. We demonstrate that RGNEF is toxic when overexpressed and forms inclusions. We also found that the fALS-associated mutation in ARGHEF28 gives rise to an inclusion-forming and toxic protein. Additionally, through unbiased screening using the split-ubiquitin system, we have identified RGNEF interacting proteins, including two ALS-associated proteins. Functional characterization of other RGNEF interactors identified in our screen suggest that RGNEF functions as a microtubule regulator. Our findings indicate that RGNEF misfolding and toxicity may cause impairment of the microtubule network and contribute to ALS pathogenesis.

A prime number is a natural number with no divisors other than itself and the number 1. There are many unsolved problems related to prime numbers. One such problem is finding a general method for identifying prime numbers. Although it is known that all prime numbers fall under the categories of 2, 3, or 6n±1 (where n≥1), a formalized method for eliminating composite numbers (non-prime numbers) from these categories has yet to be developed. This paper aims to explore a possible method for such elimination, which involves checking whether there exists an n that satisfies n = 6km+k+m or n = 6km+k-m (where k and m are non-zero integers). This method is expected to be a major step forward in the derivation of prime numbers.

In our recent publications, based on strong and electroweak interactions, we have developed a completely new formula for estimating nuclear binding energy. With reference to currently believed Semi Empirical Mass Formula (SEMF), we call our formula as ‘Strong and Electroweak Mass Formula’ (SEWMF). Our formula constitutes 4 simple terms and only one energy coefficient of magnitude 10.1 MeV. First term is a volume term, second term seems to be a representation of free nucleons associated with electroweak interaction, third term is a radial term and fourth one is an asymmetry term about the mean stable mass number. In this paper, we make an attempt to understand and estimate the maximum binding energy associated with any mass number. It can be expressed as, for A > 4, $\left(BE\right)_A\cong \left[A-0.000935A^2-A^{1/3}-A^{-1/2}\right]$ MeV. We are working on refining the 4^th term with even-odd corrections, shell corrections and other microscopic corrections. Proceeding further, stable mass numbers and super heavy mass numbers can be understood with a relation of the form, $\left[\textrm{RoundOff}\left(\left(Z+2.9464\right)^{1.2}-1.7165\right)\right]\pm\left[0,1\right]\pm\left(2n\right)$ where $n \cong 0,1,2$. It needs a review with respect to even-odd proton numbers and other microscopic corrections.Very interesting point to be noted is that based on the concept of “binding energy per nucleon”, the most complicated Avogadro number and Unified atomic mass unit can be estimated in a unified approach.

Electron beam treatment of ZnS:Cu,Br (Cu activator content 0…0.6%wt.) radioluminescent phosphors as well as charge mixture with the electron energy 900 keV and absorbed dose of 600 kGy resulted in a enhancement of brightness up to 80%. The increased brightness is due to increase of content of wurtzite phase relative to sphalerite one with formation of wurtzite/sphalerite nanocomposite structure. Transformation of crystal structure is accompanied with corresponding change in content of active surface centers characteristic for sphalerite and wurtzite phases. A model describing surface centers of ZnS:Cu,Br radioluminescent phosphor is suggested.

Tack is one of the most important factors affecting the operability of prepregs, but it is still very difficult to obtain the change of prepreg tack with time at different temperatures. In this paper, a newly designed T-peel device is used to test the tack decay rate of prepregs at different temperatures. The obtained decay rate deviates less than 8.9% from the manufacturer's data. The maximum deviation of the ratio of tack decay speeds calculated by the Arrhenius equation from the experiments is not higher than -9.7%. It is proved that the present method can obtain the decay rate of tack of prepregs at different temperatures. This method is also applicable to the other two types of prepregs. The article proposes the handling life unit, an operational life measurement unit for prepregs, and establishes that the relationship between tack and remaining shelf life reduces prepreg management costs.

With reference to our earlier published views on large nuclear gravitational constant , nuclear elementary charge and strong coupling constant , in this paper, we present simple relations for nuclear stability range, binding energy of isotopes and magic proton numbers.

Land use and cover change (LUCC) is an important method to investigate the causes of global environment change. We utilized the emergy ecological footprint (EEF) model to construct a land-use change model to be used as a systematic measuring tool for monitoring sustainable development trends. In particular, we estimated the eco-security of the Cing-jing region as a case study so that responsible agencies can use it to maintain a balance between ecological preservation and tourism development. The results indicated the following: First, the ecological environment of the Cing-jing region satisfied the safety standard in 2008–2014; however, the related indices increased considerably. Second, the grey model predicted a decrease in 2015–2024 ecological carrying capacities of Cing-jing and a large increase in capita EFs, resulting in a larger ecological deficit and higher EFI. The eco-security from 2015–2024 was higher compared to 7 years ago and is predicted to reach the Grade 2 intermediate level in 2022; thus the Cing-jing region is gradually becoming ecologically unsustainable. Strengths of our study included the use of EEF theory in a quantitative analysis of slope lands for the effective evaluation of ecological security. Finally, we expanded our research to include ecological security issues.

In the paper, the authors discover several series identities involving the Catalan numbers, the Catalan function, the Riemanian zeta function, and the alternative Hurwitz zeta function.

The SARS-CoV-2 nucleocapsid protein (N protein) is critical to viral replication by undergoing liquid-liquid phase separation to seed the formation of a ribonucleoprotein (RNP) complex to drive viral genomic RNA (gRNA) translation and in also suppressing both stress granules and processing bodies which is postulated to increase uncoated gRNA availability. The N protein can also form biomolecular condensates with a broad range of host endogenous proteins including RNA binding proteins (RBPs). Amongst these RBPs are proteins that are associated with pathological neuronal and glial cytoplasmic inclusions across several adult-onset neurodegenerative disorders, including TAR DNA binding protein 43 kDa (TDP-43) which forms pathological inclusions in over 95% of amyotrophic lateral sclerosis cases. In this study, we demonstrate that the N protein can form biomolecular condensates with TDP-43 and that this is dependant on the N protein C-terminus domain (N-CTD) and the intrinsically disordered C-terminus domain of TDP-43. This process is markedly accelerated in the presence of RNA. In silico modelling suggests that the biomolecular condensate that formed in the presence of RNA is composed of a N protein quadriplex in which the intrinsically disordered TDP-43 C terminus domain is incorporated.

Nanomaterials have shown significant promise for enhancing the performance of composite materials and increasing their functionality for various industrial applications. This review explores the unique properties of nanomaterials, particularly carbon-based nanomaterials, and provides key findings in utilizing them to enhance composite performance. It highlights specific nano-based composite materials and their significant potential in advancing the field of nanocomposites. Challenges associated with nanocomposite production and utilization are also discussed, along with possible solutions to address them. Finally, the study provides recommendations for continued research and innovation in nanocomposites to fully unlock the benefits of these advanced materials for broader future applications.

A low-cost bio-mass-derived carbon substrate has been employed to synthesize MoS₂@carbon composites through a hydrothermal method. Carbon fibers derived from natural cotton provide a three-dimensional and open framework for the uniform growth of MoS₂ nanosheets, thus constructing hierarchically coaxial architecture. The unique structure could synergistically benefit fast Li-ion and electron transport from the conductive carbon scaffold and porous MoS₂ nanostructures. As a result, the MoS₂@carbon composites, when served as anodes for Li-ion batteries, exhibit a high reversible specific capacity of 820 mAh g^-1, high-rate capability (457 mAh g^-1 at 2 A g^-1), and excellent cycling stability. The superior electrochemical performance makes the MoS₂@carbon composites to be low-cost and promising anode materials for Li-ion batteries.

With reference to electromagnetic interaction and Abdus Salam’s strong (nuclear) gravity, 1) Square root of ‘reciprocal’ of the strong coupling constant can be considered as the strength of nuclear elementary charge. 2) ‘Reciprocal’ of the strong coupling constant can be considered as the maximum strength of nuclear binding energy. 3) In deuteron, strength of nuclear binding energy is around unity and there exists no strong interaction in between neutron and proton. $G_s\cong 3.32688\times {10}^{28}{\mathrm{m}}^3{\mathrm{kg}}^{-1}{\sec }^{-2}$ being the nuclear gravitational constant, nuclear charge radius can be shown to be, $R_0\cong \frac{2G_s{m}_p}{c^2}\cong 1.24\mathrm{fm}.$ $e_s\cong \left(\frac{G_s{m}_p^2}{\hslash c}\right)e\cong 4.716785\times {10}^{-19}\mathrm{C}$ being the nuclear elementary charge, proton magnetic moment can be shown to be, ${\mu }_p\cong \frac{e_s\hslash }{2m_p}\cong \frac{e{G}_s{m}_p}{2c}\cong 1.48694\times {10}^{-26}\mathrm{J}{.\mathrm{T}}^{-1}.$ ${\alpha }_s\cong {\left(\frac{\hslash c}{G_s{m}_p^2}\right)}^2\cong 0.1153795$ being the strong coupling constant, strong interaction range can be shown to be proportional to $\exp \left(\frac{1}{{\alpha }_s^2}\right).$ Interesting points to be noted are: An increase in the value of ${\alpha }_s$ helps in decreasing the interaction range indicating a more strongly bound nuclear system. A decrease in the value of ${\alpha }_s$ helps in increasing the interaction range indicating a more weakly bound nuclear system. From $Z\cong 30$ onwards, close to stable mass numbers, nuclear binding energy can be addressed with, ${\left(B\right)}_{A_s}\cong Z\times \left\{\left(\frac{1}{{\alpha }_s}+1\right)+\sqrt{\sqrt{30\times 31}}\right\}\left(m_n-m_p\right)c^2\approx Z\times 19.66\mathrm{MeV}.$ With further study, magnitude of the Newtonian gravitational constant can be estimated with nuclear elementary physical constants. One sample relation is, $\left(\frac{G_N}{G_s}\right)\cong \frac{1}{2}{\left(\frac{m_e}{m_p}\right)}^{10}\left[\sqrt{\frac{G_F}{\hslash c}}/\left(\frac{\hslash }{m_{e}c}\right)\right]$ where $G_N$ represents the Newtonian gravitational constant and $G_F$ represents the Fermi’s weak coupling constant. Two interesting coincidences are, ${\left(m_p/m_e\right)}^{10}\cong \exp \left(1/{\alpha }_s^2\right)$ and $2G_s{m}_e/c^2\cong \sqrt{G_F/\hslash c}.$

As a member of smart materials, electrorheological elastomers (EREs) formed by pre-treating active electrorheological particles are attracting more and more attention. In this work, four Mg-doped strontium titanate particles with spherical, dendritic, flake-like and pinecone-like morphorlogies were obtained by hydrothermal and low-temperature co-precipitation. XRD, SEM, Raman and FT-IR were used to characterize the obtained products. The results showed that the sizes of Mg-doped strontium titanates are about 1.5‒2.0 μm, and the phase structure are dominated by cubic crystal. These Mg-doped strontium titanates were dispersed in a hydrogel composite elastic medium. Then, Mg-doped strontium titanate/glycerol/gelatin electrorheological composite hydrophilic elastomers were obtained with or without electric field. The electric field response properties of Mg-doped strontium titanate composite elastomers were investigated. It concluded that dendritic Mg-doped strontium titanate composite elastomers is high-performance EREs. And the maximum value of energy storage modulus of Mg-doped strontium titanate composite elastomers has achieved 8.70 MPa. This high electrorheological performance of the products is helpful for their applications in vibration control, force transducers, smart structures, dampers, and other fields.

The theory of harmonic based function is discussed here within the framework of umbral operational methods. We derive a number of results based on elementary notions relying on the properties of Gaussian integrals.

Aluminium matrix composite’s overall quality is impacted by the friction stir process parameters, which have a major impact on the microstructure, soundness, and particle dispersion inside the stir zone. Although it requires a lot of experimentation, optimizing these factors is vital. For the purpose of optimizing the ultimate tensile strength and microhardness of the AA5083/Silicon carbide and AA5083/Coal composites fabricated by FSP, this work used the Taguchi L9 design of experiments. Three process parameters were investigated at three levels each. For the AA5083/Silicon carbide composite, the results of the ANOVA analysis showed rotational speed has a larger impact on ultimate tensile strength while forAA5083/coal tilt angle has a larger impact on ultimate tensile strength. On the other hand, rotating speed had a greater effect on microhardness and percentage elongation of the AA5083/Coal and AA5083/Silicon carbide composite joints, according to ANOVA analysis. The need for specific process optimization for each composite was highlighted by the fact that different combinations of parameters were best for obtaining the necessary attributes in the AA5083/Silicon carbide and AA5083/Coal composites.

The neuroglial extracellular matrix (ECM) provides critical support and physiological cues for the proper growth, differentiation, and function of neuronal cells in the brain. However, in most in vitro settings that study neural physiology, cells are grown as monolayers on stiff surfaces that maximize adhesion and proliferation, and therefore lack the physiological cues that ECM in native neuronal tissues provides. Macromolecular crowding (MMC) is a biophysical phenomenon based on the principle of excluded volume that can be harnessed to induce native ECM deposition by cells in culture. Here, we show that MMC using two species of Ficoll with vitamin C supplementation significantly boosts deposition of relevant brain ECM by cultured human astrocytes. Dopaminergic neurons co-cultured on this astrocyte-ECM bed prepared under MMC treatment showed longer and denser neuronal extensions, a higher number of pre ad post synaptic contacts, and increased physiological activity as evidenced by higher frequency calcium oscillation, compared to standard co-culture conditions. When the pharmacological activity of various compounds was tested on MMC-treated co-cultures, their responses were enhanced, and for apomorphine, a D2-receptor agonist, it was inverted in comparison to control cell culture conditions, thus emulating responses observed in in vivo settings. These results indicate that macromolecular crowding can harness the ECM-building potential of human astrocytes in vitro forming an ultra-flat 3D microenvironment that makes neural cultures more physiological and pharmacological relevant.

Wear-resistant steel/carbon steel composite plate not only has the double performance advantage of high strength and wear-resistance, but also can reduce energy consumption and production cost. Based on 50% reduction rate, the wear resistance of BTW1/Q345 composite was studied at different annealing temperatures, and the dry friction and wear tests of BTW1/Q345 composite at different annealing temperatures were carried out by using RETC MFT-5000. The macro-micro morphology and wear mechanism of wear marks at different annealing temperatures were analyzed by using white light interference three-dimensional surface profiler, Scanning electron microscope scanning electron microscope (SEM) and backscatter electron diffraction (EBSD) . The results show that with the increase of annealing temperature, the grain size near the scratch of BTW1 in the wear-resistant layer of the composite plate is refined, and the wear-resistant property is higher than that of the original sample.When the annealing temperature is 860℃,the wear resistance is the best.

In the paper, the authors find closed forms for derangement numbers in terms of the Hessenberg determinants, discover a recurrence relation of derangement numbers, present a formula for any higher order derivative of the exponential generating function of derangement numbers, and compute some related Hessenberg and tridiagonal determinants.

In polymer-based dental composites, wear is a three-body wear system mainly abrasive, because of the food particles and wear products suspended in the oral cavity, which are transferred to the microcavities of the surface of the replacements. Due to this fact, the incorporation of nanodiamond as reinforcement in these polymer matrix composites, which promotes the creation of a solid lubricant tribofilm surface could be advantageous. When nanodiamond is added in contents of 0.8, 1.6 and 3.2 wt %, an increase in microhardness from 95 up to 420 %, compared to the one of neat BisGMA/TEGDMA, is observed. Additionally, the incorporation of a content of 1.6 wt % is enough to cause a diminution of ~78 % in the friction coefficient and a reduction of the specific wear rate and Archard’s coefficient of ~50 %. Nevertheless, the addition of relatively high contents reduces the effectiveness of photoinitiation and UV-curing, which is related to the scattering and absorption of UV radiation by ND.

There are various types of charged particles in the space environment, which can cause different types of radiation damage to materials and devices, leading to on-orbit failures and even accidents of spacecraft. Developing lightweight and efficient radiation shielding materials is an effective approach to improve the inherent protection of spacecraft. The protective performance of different materials against proton and electron spectra in the Earth’s radiation belts is evaluated by Geant4 simulation. Based on the simulation results, suitable hardening components are selected to design composite materials, and B4C/PEEK composites with different B4C content were successfully prepared. Experimental results demonstrate that the simulated and experimental results for the electron, proton and neutron shielding performance of B4C/PEEK composites are consistent. These composites exhibit excellent radiation shielding capabilities against electrons, protons and neutrons, and the radiation protection performance improves with increasing B4C content in the B4C/PEEK composite materials.

This study outlines a 3-step production process for Ti-TiC Metal Matrix Composite (MMC) employing powder Mechanical Blending, Laser Powder Bed Fusion (LPBF), and a heat treatment. A TiC fraction of more than 20 vol% was formed in-situ through the reaction of titanium with carbon during the LPBF process. The manufactured MMC pieces showed a record stiffness and fracture strain combination. The LPBF energy density impacted strongly porosity type. The as-built microstructure displayed an homogeneous distribution of sub-stoichiometric TiC dendrites which were fully converted into equiaxed TiC grains during the heat treatment. The TiC C/Ti ratio was found to be close to 0.5, resulting in an effective reinforcement content nearly twice the one expected for stoichiometric TiC, leading to stronger reinforcement. The mechanical analysis revealed a Young’s modulus of up to 149 GPa and an ultimate tensile strength of up to 770 MPa, indicating a 27% and 34% improvement, respectively, compared to commercially pure Titanium produced by LPBF and heat treated in the same conditions. A fracture strain of up to 2.8% was achieved. The combination of in-situ formation of defect-free TiC reinforcement and subsequent heat treatment enables to reach an exceptional ductility, considering the 20 vol% reinforcement content.

Hybrid reinforcement in a composite material (CM), in many situations, allows better govern material mechanical properties. Polymer matrix CM plate is reinforced with small particles and macro-fibers. Particles are oil shale ash (OSA) powder, macro-fibers – basalt fiber threads im-pregnated by matrix material. With the goal to find out elastic properties of the matrix- polymer with OSA, samples with its different concentrations were experimentally fabricated and their elastic properties were experimentally measured. Obtained data were used in numerical model-ling. Was observed polymer matrix composite slab, reinforced with OSA and three-dimensional (3D) basalt fiber fabric. Fabric are forming threads impregnated by matrix (polymer resin mixed with OSA particles). Damage accumulation in the stretched slab was modelled. Impregnated thread, in the modelling, is observed as a macro-fiber (MF) with averaged elastic properties. With the load increase MF in the material began to break. At first, appeared isolated single breaks. A probabilistic sequential MF rupture accumulation model was accepted and numerical-ly realized. The geometry of the reinforcing knitted fabric was modeled using the Leaf and Glaskin approach. In the knitted fabric highly, stressed MF cross-sections are observed as po-tential location where thread breakage can occur. If one thread breaks, the cross-sections of the adjacent threads experience the overload caused by this rupture. More overloaded crossection in the adjacent overloaded thread breaks and we obtain two adjacent broken MF designated as a defect with the size j=2. The probabilities of obtaining defect consisting of at least 2, 3, … j adjacent broken MF in the plate were calculated. The calculations continued until the rupture process becomes unstable (j→∞). The overstresses on adjacent threads in the CM were calculat-ed using the FEM three-dimensional numerical approach. Analytical and stochastic methods were used for the load-carrying capacity determination and different size defects accumulation in the hybrid composite material (HCM) plate. Also, was calculated the probability of the plate rupture.

This study assessed the acute effects of oral methylliberine (DynamineTM) supplementation on cognitive function and indices of well-being. This was a double-blind, randomized, within-subject crossover trial. 25 healthy men and women (33.5±10.7yr, 172.7±8.6cm, 73.3±11.0kg) underwent pretesting before ingesting methylliberine (100mg) or placebo (PLA) for 3 days. On the fourth day participants were tested before their 4th dose (baseline) and every hour post-ingestion for 3 hours. After a one-week washout period, participants repeated testing with the alternate investigational product. The testing battery consisted of vitals, Stroop test and Trail Making Test-B, and visual analog scales that assessed various indices of well-being. Mixed factorial ANOVA with repeated measures were used to assess all variables. There were significant (p≤0.050) interactions in concentration, motivation, and mood. Methylliberine improved concentration 1- and 3-hours, motivation 3 hours, and mood 1-, 2-, and 3 hours (p≤0.050). Methylliberine improved energy, sustained energy, and mood in all participants to a greater extent than PLA at 1-hour and 3-hours relative to baseline (p≤0.050). PLA improved motivation at 1- and 2-hours and mood at 2-hours (p≤0.050). Methylliberine improved concentration, well-being, and the ability to tolerate stress to a greater extent than PLA at 3-hours relative to baseline (p≤0.050). Women observed elevations in sustained energy 1- and 3-hours (p≤0.050) in methylliberine vs. PLA. Methylliberine had negligible influence on cognitive function, vitals (p>0.050), and no adverse events were reported. Methylliberine significantly improved subjective feelings of energy, concentration, motivation, and mood, but not cognitive function. PLA improved motivation and mood at hours 1 and 2, while methylliberine sustained benefits for longer. Methylliberine also improved concentration, well-being, and the ability to tolerate stress to a greater degree than PLA while having no detrimental effects on vital signs. Methylliberine also seems to have a positive impact on sustained energy in women.

The details of the solar flare production mechanisms are not yet completely understood. One of the standing questions is the anisotropy of the X-ray flux, especially in strong flares. It can be studied indirectly by analysing the characteristics of flares at different positions on the visible disc. In this paper, the durations, peak and integral fluxes of strong (X-class) solar flares from cycles 22--25 are considered with respect to their apparent position on the Sun. It is found that there exists a significant north--south asymmetry in all three parameters, which also varies depending on the phase of the solar cycle (with general predominance of the south). This confirms the results of previous studies. A weaker and less significant east--west asymmetry is found as well, partly supported by literature. A previously undetected centre-to-limb asymmetry is reported (in favour of the limb) in all three parameters. All three asymmetries are enhanced during the solar minimum, which could hint at their connection to the large scale magnetic structuring of the Sun. The prevalence of strong solar flares near the limb at the solar minimum has clear space weather warning implications.

Since 1742, the year in which the Prussian Christian Goldbach wrote a letter to Leonhard Euler with his Conjecture in the weak version, mathematicians have been working on the problem. The tools in number theory become the most sophisticated thanks to the resolution solutions. Euler himself said he was unable to prove it. The weak guess in the modern version states the following: any odd number greater than 5 can be written as the sum of 3 primes. In response to Goldbach's letter, Euler reminded him of a conversation in which he proposed what is now known as Goldbach's strong conjecture: any even number greater than 2 can be written as a sum of 2 prime numbers. The most interesting result came in 2013, with proof of weak version by the Peruvian Mathematician Harald Helfgott, however the strong version remained without a definitive proof. The weak version can be demonstrated without major difficulties and will not be described in this article, as it becomes a corollary of the strong version. Despite the enormous intellectual baggage that great mathematicians have had over the centuries, the Conjecture in question has not been validated or refuted until today.

This paper addresses a new micromechanical model to predict biaxial tensile moduli of plain weave fabric (PWF) composites by considering the interaction between the orthogonal interlacing strands. The two orthogonal yarns in micromechanical unit cell (UC) were idealized as the curved beams with a path depicted by using sinusoidal shape functions. The biaxial tensile moduli of PWF composites were derived by means of the minimum total complementary potential energy principle founded on micromechanics. The biaxial tensile tests were respectively conducted on the RTM-made EW220/5284 PWF composites at five biaxial loading ratios of 0, 1, 2, 3 and ∞ to validate the new model. The predictions from the new model were compared with experimental data and good correlation was achieved between the predictions and actual experiments, demonstrating the practical and effective use of the proposed model. Using the new model, the biaxial tensile moduli of plain weave fabric (PWF) composites could be predicted based only on the properties of basic woven fabric.

In this article, many experimental similarities between electromagnetic fields (which are applied in systems of electrons, atoms, and liquids) and strong interaction fields (which are applied in systems of quarks, nucleons, and nuclei) are reviewed. The currently accepted theories describing electromagnetic fields differ fundamentally from those describing strong fields. Therefore, the many similarities are quite surprising, and some are not adequately explained even today. Several such unexplained similarities are listed among the top open problems in particle physics, such as the “EMC effect,” the “proton spin crisis,” and the “strong CP problem.” This paper highlights, for the first time, the underlying common characteristics of these problems, potentially offering valuable contribution to future explanations.

The aim of this study was to investigate the physicochemical characterization and biological activities of chitosan (CH) based composite films with the incorporation of chestnut flower essential oil (CFEO). The composite films were prepared by casting method and characterized in terms of structural, morphological and mechanical properties via FT-IR, XRD, UV, SEM and TGA. The results proved the significantly increased water vapor permeability (WVP), heat resistance, antibacterial and antioxidant capabilities of CH-CFEO films. The incorporation of CH and CFEO enhanced the UV blocking, which made the film shield almost all UV light. Films with the tensile strength of 6.37 ± 0.41 MPa and elongation at break of 22.57 ± 0.35% were got with 6 mg mL-1 CFEO. Subsequently, the fruit preservation experiments also confirmed that the composite films could effectively extend the shelf life of bananas through their excellent water vapor and oxygen barrier. These desirable performances enable our newly developed composite films to be a remarkable packaging material to solve the fresh fruit preservation dilemma.

In this paper, we define and investigate modified p-Leonardo, p-Leonardo-Lucas and p-Leonardo sequences as special cases of the generalized Leonardo sequence. We present Binet's formulas, generating functions, Simson formulas, and the summation formulas for these sequences. Moreover, we give some identities and matrices related with these sequences. Furthermore, we show that there are close relations between modified p-Leonardo, p-Leonardo-Lucas, p-Leonardo numbers and Fibonacci, Lucas numbers.

The aim of this paper is to establish a valid procedure for better understanding all the phenomena associated with the high-speed machining of Glass Fibre Reinforced Plastic (GFRP) composites. Both rectangular and circular specimens were machined at high speeds (up to 50 m/min) in order to understand what occurred for all values of fiber orientation angles during machining operations. An innovative testing methodology was proposed and studied to investigate the phenomenon of burr formation and thus understand how to avoid it during machining operations. To this end, the forces arising during the machining process and the roughness of the resulting surface, were carefully studied and correlated with the cutting angle. Additionally, the cutting surface and chip morphology formed during cutting tests were examined using a high-speed camera. Close correlations are found between the variations of the cutting forces' signals and the trends of the roughness and the morphology of the machined surface.

Gymnema sylvestre is a pharmacological plant which has a rich source of bioactive compounds specifically gymnemic acid (GA) and phenolic compounds (PC) that used for pharmaceutical industries. Sources for naturally occurring bioactive compounds are limited, due to geographical and seasonal variations; on the other hand, it is commercially in demand. Biosynthesis of G. sylvestre phytochemicals through in vitro culture often enhanced by elicitation. The use of cell suspension cultures (CSC) has interested serious attention on the production of essential phytochemicals. The current study is aimed at improving the contents of GA and PC in G. sylvestre CSC using the copper oxide nanoparticles (CuO NPs). Callus was obtained on MS medium with 2.0 mg/L 2,4-dichlorophenoxyacetic acid (2,4-D), 0.1 mg/L kinetin (KIN), phytoagar (8.0 g/L), and sucrose (30 g/L). The above medium devoid of agar was used for the initiation of CSC. The CSC was treated with three levels of CuO NPs (1, 3 or 5 mg/L) to enhance the production of GA and PC. The greatest amount of GA (89.25 mg/g dry cell mass, DCM), total phenolic (245.10 mg/g), and flavonoid (4.57 mg/g) in CSC were achieved when G. sylvestre cells were treated for 48 h with 3 mg/L CuO NPs. Also, the biomedical potential (antioxidant, antidiabetic, anti-inflammatory, antibacterial, antifungal and anticancer activities) were also high in the CuO NPs (3 mg/L) treated CSC extracts of G. sylvestre. CuO NPs elicitation of CSC significantly increased production of GA (9-fold), and PC than non-elicited CSC in G. sylvestre.

In this paper, we investigate the generalized Padovan sequences and we deal with, in detail, four special cases, namely, Padovan, Perrin, Padovan-Perrin and modified Padovan sequences. We present Binet's formulas, generating functions, Simson formulas, and the summation formulas for these sequences. Moreover, we give some identities and matrices related with these sequences.

Number is based in special edges, is introduced. The kind of natural extension from edges toward vertex and the set of vertices in the way that, the final notion is number, is studied. The result is obtained which is about the study on the classes of graphs in the matter of new notions. There is the extended notion about having edge amid two vertices toward having some edges in the word of neighbor and in another stage going into the atmosphere of having consecutive edges in the terminology of path and in the upper vision going on the notion about path with jargon and buzzword of distance as if the minimal vertices has concluded the new notions with the word, number.

New setting is introduced to study “closing numbers” and “super-closing numbers” as optimal-super-resolving number, optimal-super-coloring number and optimal-super-dominating number. In this way, some approaches are applied to get some sets from (Neutrosophic)n-SuperHyperGraph and after that, some ideas are applied to get different types of super-closing numbers which are called by optimal-super-resolving number, optimal-super-coloring number and optimal-super-dominating number. The notion of dual is another new idea which is covered by these notions and results. In the setting of dual, the set of super-vertices is exchanged with the set of super-edges. Thus these results and definitions hold in the setting of dual. Setting of neutrosophic n-SuperHyperGraph is used to get some examples and solutions for two applications which are proposed. Both setting of SuperHyperGraph and neutrosophic n-SuperHyperGraph are simultaneously studied but the results are about the setting of n-SuperHyperGraphs. Setting of neutrosophic n-SuperHyperGraph get some examples where neutrosophic hypergraphs as special case of neutrosophic n-SuperHyperGraph are used. The clarifications use neutrosophic n-SuperHyperGraph and theoretical study is to use n-SuperHyperGraph but these results are also applicable into neutrosophic n-SuperHyperGraph. Special usage from different attributes of neutrosophic n-SuperHyperGraph are appropriate to have open ways to pursue this study. Different types of procedures including optimal-super-set, and optimal-super-number alongside study on the family of (neutrosophic)n-SuperHyperGraph are proposed in this way, some results are obtained. General classes of (neutrosophic)n-SuperHyperGraph are used to obtains these closing numbers and super-closing numbers and the representatives of the optimal-super-coloring sets, optimal-super-dominating sets and optimal-super-resolving sets. Using colors to assign to the super-vertices of n-SuperHyperGraph and characterizing optimal-super-resolving sets and optimal-super-dominating sets are applied. Some questions and problems are posed concerning ways to do further studies on this topic. Using different ways of study on n-SuperHyperGraph to get new results about closing numbers and super-closing numbers alongside sets in the way that some closing numbers super-closing numbers get understandable perspective. Family of n-SuperHyperGraph are studied to investigate about the notions, super-resolving and super-coloring alongside super-dominating in n-SuperHyperGraph. In this way, sets of representatives of optimal-super-colors, optimal-super-resolving sets and optimal-super-dominating sets have key role. Optimal-super sets and optimal-super numbers have key points to get new results but in some cases, there are usages of sets and numbers instead of optimal-super ones. Simultaneously, three notions are applied into (neutrosophic)n-SuperHyperGraph to get sensible results about their structures. Basic familiarities with n-SuperHyperGraph theory and neutrosophic n-SuperHyperGraph theory are proposed for this article.

Modern day construction is widely influenced using concrete-steel composite columns. A lot of research on concrete-steel composite columns is being carried out around the world. The rapid growth in concrete-steel composite construction has widely decreased the use of conventional reinforced cement concrete construction (R.C.C), and the steel construction practices. The concrete-steel composite construction has obtained an extensive receiving around the globe. As Pakistan is a developing country, so, it is relatively a new concept for its construction industry when compared with the developed countries around the globe. Although, the R.C.C construction is suitable and economical for construction of framing systems of low-rise buildings, however, the increased dead load, span restrictions, less stiffness and risky formwork makes it uneconomical and unviable when it comes across the construction of intermediate to high-rise buildings. This research is an effort to learn the cost effectiveness, increased or decreased stiffness, and change on the functionality of the composite construction for intermediate to high-rise buildings constructed in Pakistan. A Base + Ground + 11 storey commercial building is selected for this study. A comparison is made between conventional R.C.C columns structure and concrete-encased composite columns structure. The equivalent static nonlinear analysis is performed using ETABS 2017 software. Although, for Base + Ground + 11 storey building, the construction cost of concrete-encased composite structure is 7.7% more than the conventional R.C.C columns structure, but the concrete-encased composite structure will have 13.013% more constructed floor area. This increased floor area helps to settle the cost difference between the two structures.

The combination of micro- or nanofluidics and strong light–matter coupling has gained much interest in the past decade, which has led to the development of advanced systems and devices with numerous potential applications in different fields, such as chemistry, biosensing, and material science. Strong light–matter coupling is achieved by placing a dipole (e.g. an atom or a molecule) into a confined electromagnetic field, with molecular transitions being in resonance with the field and the coupling strength exceeding the average dissipation rate. Despite intense research and encouraging results in this field, some challenges still need to be overcome, related to the fabrication of nano- and microscale optical cavities, stability, scaling up and production, sensitivity, signal-to-noise ratio, and real-time control and monitoring. The goal of this paper is to summarize recent developments of micro- and nanofluidic systems employing strong light–matter coupling. An overview of various methods and techniques used to achieve strong light–matter coupling in micro- or nanofluidic systems is presented, preceded by a brief outline of the fundamentals of strong light–matter coupling and optofluidics operating in the strong coupling regime. The potential applications of these integrated systems in sensing, optofluidics, and quantum technologies are explored. The challenges and prospects in this rapidly developing field are discussed.

Here we analyze three well-known conjectures: (i) the existence of infinitely-many twin primes, (ii) Goldbach’s strong conjecture, and (iii) Polignac’s conjecture. We show that the three conjectures are related to each other. In particular, we see that in analysing the validity of the Goldbach’s strong conjecture, one must consider also the existence of an infinite number of twin primes. As a consequence of how we approach this analysis, we also observe that if this conjecture is true, then so is Polignac’s conjecture. Our first step is an analysis of the existence of infinitely-many twin primes numbers. For this, using the formula 4((n−1)!+1) ≡ −n (mod n(n + 2)) – satisfied if and only if (n, n + 2) are twin primes –, together with Wilson’s theorem, we obtain conditions that must be met for two numbers to be twin primes. Our results, obtained from an analytic and functional study, lead us to conclude that there may exist infinitely-many twin primes. Next, we consider the validity of the Goldbach’s strong conjecture. After showing that the conjecture is true for the first even numbers, we notice a pattern that we analyze for any even number, reducing it to three cases: (i) when the even number 2n is two times a prime number n; (ii) when the even number 2n is such that n = 2m, with 2m − 1 and 2m + 1 twin primes; (iii) all other cases, i.e., for any 2n even number ∀n ∈ N with n > 1, n prime or not, with independence of n = 2m being 2m−1 and 2m+1 twin primes or not. In this last case we show that one can always find a certain r ∈ N such that 1 < r < n satisfying that n−r and n+r are primes, so that their sum is 2n. In this case we use the reduction to absurd method, and our results lead us to conclude that Goldbach’s strong conjecture is true to the best of our calculations, as well as the Polignac’s conjecture.

There are gravitational field and baryonic matter (star, planet, gases etc.) in our world; gravitational field is much more fundamental for that the relativistic mass of the gravitational field of a neutron star is almost 10²¹ times the mass of the neutron star. And, it is astonishing that the relativistic mass density of the gravitational field on the surface of a neutron star can be larger than the mass density of the neutron star. It is well known that, in the weak gravitational field a light line appears a straight line while in the strong field it is a curved line. It is stressed that the result measured in the strong field is more fundamental for that in a galaxy the measurable object is generally with strong field. It results in that the way that the result measured on the Earth with weak field is used as the universal standard need be revised as gravity is studied in the scale of a galaxy. It seems that a new theory of gravity need be developed for the new observations.

This paper is given to the investigation of warm inflation using Modified Chaplygin gas in the background of locally rotationally symmetric Bianchi Identity type I. We find out the field equations and perturbations parameters such as; scalar power spectrum, scalar spectral index, scalar potential and tensor to scalar ratio under slow roll approximation. We find out these parameters in directional of Hubble parameter during the Logamediate inflationary regime in weak and strong case. These comological parameters shows that the anisotropic model is also compatible WMAP$7$ with recent observational data Planck $2018$.

Composite fiber materials are superior materials due to their high strength and light weight. Composites reflect the properties of their constituents, which is proportional to the volume fraction of each phase. There are different fiber reinforcement types and each affects it’s flexural, tensile and compression strength. When selecting a composite for a specific application, the forces excreted on the composite must be known in order to determine the reinforcement type. Unidirectional fiber reinforcement will allow very strong load resistance but only in one direction where as a random orientated fiber reinforcement can resist less load but can maintain this quota in all directions. These materials are said to be anisotropic. Certain composite fibers, taking into consideration there weights, are physically stronger than conventional metals. This research deals with the analysis of three composite materials with different reinforcement types, volume fraction and phase content. It was found that material A (glass epoxy) was the strongest in the longitudinal direction with a flexural strength of 534 MPa in the longitudinal and 420 MPa in the transverse direction. The flexural stresses of material B (glass silicone) and material C (glass polyester) where both found in the 120 to 135 MPa range. Differences were due to their differences in matrix composition and reinforcement type.

The risk classification of barrier lake is the key to conducting emergency treatment in a scientific manner. Such difficulties are faced as short time for risk evaluation, complex evaluation indicators, difficulty in obtaining information quickly and quantifying index weights. Based on this, this paper constructs a quantitative risk classification model for barrier lakes based on D-AHP. On the basis of studies on nearly 100 cases of barrier lakes, an 8-factor evaluation index system and quantitative classification are proposed. The methods of rapid calculation of reservoir capacity curve of barrier lake and intelligent identification of particles on the surface of barrier body were developed, which realized the rapid acquisition of 8-factor evaluation index information in emergency environment. The D-AHP method dealt with inconsistent weight assignment to evaluation factors by experts, which helped achieve weight quantification of 8 factors. The risk assessment on15 barrier lakes such as Tangjiashan barrier lake show that the conclusion drawn with risk classification method proposed in this paper is basically consistent with that of the traditional table-lookup method. However, the table-lookup method ignores cumulative loss’s impacts on the risk level of barrier lakes, and considers the extremely severe loss of barrier lakes as a sufficient condition for the evaluation level to be grade I, and thus a deviation in the evaluation. The risk classification method proposed in this paper is more reasonable and reliable.

Currently, there is a high interest in smart sensors and integrated composite materials in various industries such as construction, aviation, automobile, medical, information technology, communication, and manufacturing. Here, a new conceptual design for a force and temperature sensor system is developed by integrating fiber optic Bragg grating sensors embedded within composite materials, and a mathematical model is proposed that allows one to estimate strain and temperature based on signals obtained from optical Bragg gratings. This is important for understanding the behaviors of sensors under different conditions and for creating effective monitoring systems. Describing the strain gradient distribution, especially considering different materials with different values of Young's modulus, provides insight into how different materials respond to applied forces and temperature changes. The shape of the strain gradient distribution was obtained, which is a quadratic function with a maximum value of 1500 µ, with a maximum value at the center of the lattice and a symmetrically decreasing strain value with distance from the central part of the fiber Bragg grating. With axial strain at the installation site of the Bragg grating sensor under applied force values ranging from 10 to 11 N, the change in strain was linear. As a result of theoretical research, it was found that the developed system with fiber-optic sensors based on Bragg gratings embedded in composite materials is resistant to external influences and temperature changes.

Polyamides (PAs) are one of the most important engineering polymers; however, the difficulty in dissolving them hinders their applications. Formic acid (FA) is the most common solvent for PAs, but it has industrial limitations. In this contribution, we proposed a new solvent system for PAs by replacing a portion of the FA with urea and calcium chloride (FAUCa). Urea imparts the hydrogen bonding and calcium ion from the calcium chloride, as a Lewis acid was added to the system to compensate for the pH decrease due to the addition of urea. The results showed that the proposed solvent (FAUCa) could readily dissolve PAs, resulting in less decrease in the mechanical properties during the dissolution. The composite prepared using the FAUCa has almost the same properties like the one prepared using the FA solution. The solution was applied on a polyamide 66 fabric to make an all-polyamide composite coated-fabric, which then was characterized. The FAUCa solution had a higher viscosity than the one prepared using the neat FA solvent, which can be an advantage in the applications which needs higher viscosity like preparing the all-polyamide composite coated-fabric. A more viscouse solution makes a denser coating which will increase the water-/gas-tightness. In conclusion, using the FAUCa solvent has two merits: 1. replacement of 40 % of the FA with less harmful and environmentally-friendly chemicals and 2. enabling for the preparation of more viscouse solutions, which makes denser coating.

Polypyrrole (PPy)-capped caped silver nanowire (Ag NW) nanomaterials (core–shell rod-shaped Ag NW@PPy) were synthesized suing a one–port suspension polymerization technique. The thickness of PPy layer on the 50-nm-thickness/15-μm-length Ag NW was effectively controlled to 10, 40, 50, and 60 nm. Thin films cast from one-dimensional conductive Ag NW@PPy formed a three-dimensional (3-D) conductive porous network structure and provided excellent electrochemical performance. The 3-D Ag NW@PPy network can significantly reduce the internal resistance of the electrode and maintain structural stability. As a result, a high specific capacitance of 625 F/g at a scan rate of 1 mV/s was obtained from the 3-D porous Ag NW@PPy composite film. The cycling performance over a long period exceeding 10,000 cycles was also evaluated. We expect that our core–shell-structured Ag NW@PPy composites and their 3-D porous structure network films can be applied as electrochemical materials for the design and manufacture of supercapacitors and other energy storage devices.

This paper reports results of analysis of field ion emission mechanism from tungsten-epoxy composite emitters that are compared to tungsten nano-field emitters. In this context, the mechanism of emission from this type of emitters is described based on a theory of induced conductive channels. The tungsten emitters were prepared using the electrochemical polishing technique and coated with a layer of the epoxy resin. Field ion microscope (FIM) analyses are reported including the study of the emission-ion density distributions from both the uncoated and coated emitters. Two forms of emission patterns have been observed in the ion emission microscopy technique describing the differences in the emission mechanism of both types of emitters. The observed results show: (a) the expected crystalline surface atomic distribution images of the field ion microscopy in the case of uncoated tungsten tips, and (b) randomly distributed emission spots that describe the locations of the induced conductive channels inside the resin coating layer.

Culex quinquefasciatus is an important target for vector control because of its ability to transmit pathogens that cause disease. Most populations are resistant to pyrethroids and often to organophosphates, the two most common classes of active ingredients used by public health agencies. A knockdown resistance (kdr) mutation, resulting in a change from a leucine to phenylalanine in the voltage gated sodium channel, is one mechanism contributing to the pyrethroid resistant phenotype. Enzymatic resistance has also been shown to play a very important role. Recent studies have shown strong resistance in populations even when kdr is relatively low which indicates factors other than kdr may be larger contributors to resistance. In this study, we examined on a statewide scale (over 70 populations), the strength of the correlation between resistance in the CDC bottle bioassay and the kdr genotypes and allele frequencies. Spearman correlation analysis showed only moderate (-0.51) and weak (-0.29) correlation between the kdr genotype and permethrin and deltamethrin respectively. The frequency of the kdr allele was an even weaker correlate. These results indicate, in contrast to Aedes aegypti, assessing kdr in populations of Culex quinquefasciatus is not a good surrogate for phenotypic resistance testing.

The article shows materials to the question about algebraic features of the genetic code and about the dictatorial influence of the DNA and RNA molecules on the whole organism. Presented results testify in favor that the genetic code is an algebraic code related with a wide class of algebraic codes, which are a basis of noise-immune coding of information in communication technologies. Structural features of the genetic systems are associated with hypercomplex double (or hyperbolic) numbers and with bisymmetric doubly stochastic matrices. The received results confirm that represented matrix approaches are effective for modeling genetic phenomena and revealing the interconnections of structures of biological bodies at various levels of their organization. This allows one to think that living organisms are algebraically encoded entities where structures of genetic molecules have the dictatorial influence on inherited structures of the whole organism. New described algebraic approaches and results are discussed.

In this paper, we define Tetranacci and Tetranacci-Lucas matrix sequences and investigate their properties.

In this paper, we present Binet's formulas, generating functions, and the summation formulas for generalized Pentanacci numbers, and as special cases, we investigate Pentanacci and Pentanacci-Lucas numbers with their properties. Also, we define Gaussian generalized Pentanacci numbers and as special cases, we investigate Gaussian Pentanacci and Gaussian Pentanacci-Lucas numbers with their properties. Moreover, we give some identities for these numbers. Furthermore, we present matrix formulations of generalized Pentanacci numbers and Gaussian generalized Pentanacci numbers.

In this paper, we introduce the partially degenerate Changhee-Genocchi polynomials and numbers and investigated some identities of these polynomials. Furthermore, we investigate some explicit identities and properties of the partially degenerate Changhee-Genocchi arising from the nonlinear dierential equations.

In the paper, the authors survey integral representations of the Catalan numbers and the Catalan–Qi function, discuss equivalent relations between these integral representations, supply alternative and new proofs of several integral representations, collect applications of some integral representations, and present sums of several power series whose coefficients involve the Catalan numbers.

The Riemann hypothesis is the assertion that all non-trivial zeros are complex numbers with real part $\frac{1}{2}$. It is considered by many to be the most important unsolved problem in pure mathematics. There are several statements equivalent to the famous Riemann hypothesis. Robin's criterion states that the Riemann hypothesis is true if and only if the inequality $\sigma(n) < e^{\gamma} \cdot n \cdot \log \log n$ holds for all natural numbers $n > 5040$, where $\sigma(n)$ is the sum-of-divisors function of $n$, $\gamma \approx 0.57721$ is the Euler-Mascheroni constant and $\log$ is the natural logarithm. We require the properties of superabundant numbers, that is to say left to right maxima of $n \mapsto \frac{\sigma(n)}{n}$. In this note, using Robin's criterion on superabundant numbers, we prove that the Riemann hypothesis is true.

When presenting special relativity, it is customary to single out the so-called paradoxes. One of these paradoxes is the formal occurrence of speeds exceeding the speed of light. An essential part of such paradoxes arises from the incompleteness of the relativistic calculus of velocities. In special relativity, the additive group is used for velocities. However, the use of only group operations imposes artificial restrictions on possible computations. Naive expansion to vector space is usually done by using non-relativistic operations. We propose to consider arithmetic operations in the special theory of relativity in the framework of the Cayley–Klein model for projective spaces. We show that such paradoxes do not arise in the framework of the proposed relativistic extension of algebraic operations.

Elliptic scator algebra is possible in 1+n dimensions, n∈N. It is isomorphic to complex algebra in 1+1 dimensions, when the real part and any one hypercomplex component are considered. It is endowed with two representations: an additive one, where the scator components are represented as a sum; and a polar representation, where the scator components are represented as products of exponentials. Within the scator framework, De Moivre’s formula is generalized to 1+n dimensions in the so called victoria equation. This novel formula is then used to obtain compact expressions for the integer powers of scator elements. A scator in S1+n can be factored into a product of n scators that are geometrically represented as its projections onto n two dimensional planes. A geometric interpretation of scator multiplication in terms of rotations with respect to the scalar axis is expounded. The powers of scators, when the ratio of their director components is a rational number, lie on closed curves. For 1+2 dimensional scators, twisted curves in a three dimensional space are obtained. Collecting previous results, it is possible to evaluate the exponential of a scator element in 1+2 dimensions.

The importance and near ubiquity of the Golden Ratio in disciplines like chemistry and biology is well known, but only recently has it come to light in areas pertaining to the Quantum domain. By using a modified tool-kit of hyper-complex numbers (known as Dimensional Gate Operators) and numerical analysis, we uncover a connection between hyper-dimensional objects, the Fibonacci sequence and that of quasiparticles and excitations. The results show that dimensionality increases in step with the Fibonacci sequence.

At nuclear scale, we present three heuristic relations pertaining to strong and electroweak coupling constants. With these relations, close to beta stability line, it is possible to study nuclear binding energy with a single energy coefficient of magnitude $\left(\frac{1}{{\alpha }_s}\right)\left[\frac{e^2}{4\pi {\epsilon }_0{R}_0}\right]\approx 10.0\text{MeV}\text{.}$ With reference to up and down quark masses, it is also possible to interpret that, nuclear binding energy is proportional to the mean mass of $\left[\left(2m_u+m_d\right)\text{and}\left(m_u+2m_d\right)\right]\approx 10.0\text{MeV}.$

New setting is introduced to study the global powerful alliance. Global powerful alliance is about a set of vertices which are applied into the setting of neutrosophic graphs. Neighborhood has the key role to define this notion. Also, neighborhood is defined based on strong edges. Strong edge gets a framework as neighborhood and after that, too close vertices have key role to define global powerful alliance based on strong edges. The structure of set is studied and general results are obtained. Also, some classes of neutrosophic graphs excluding empty, path, star, and wheel and containing complete, cycle and r-regular-strong are investigated in the terms of set, minimal set, number, and neutrosophic number. Neutrosophic number is used in this way. It’s applied to use the type of neutrosophic number in the way that, three values of a vertex are used and they’ve same share to construct this number. It’s called “modified neutrosophic number”. Summation of three values of vertex makes one number and applying it to a set makes neutrosophic number of set. This approach facilitates identifying minimal set and optimal set which forms minimal-global-powerful-alliance number and minimal-global-powerful-alliance-neutrosophic number. Two different types of sets namely global-powerful alliance and minimal-global-powerful alliance are defined. Global-powerful alliance identifies the sets in general vision but minimal-global-powerful alliance takes focus on the sets which deleting a vertex is impossible. Minimal-global-powerful-alliance number is about minimum cardinality amid the cardinalities of all minimal-global-powerful alliances in a given neutrosophic graph. New notions are applied in the settings both individual and family. Family of neutrosophic graphs has an open avenue, in the way that, the family only contains same classes of neutrosophic graphs. The results are about minimal-global-powerful alliance, minimal-global-powerful-alliance number and its corresponded sets, minimal-global-powerful-alliance-neutrosophic number and its corresponded sets, and characterizing all minimal-global-powerful alliances, minimal-t-powerful alliance, minimal-t-powerful-alliance number and its corresponded sets, minimal-t-powerful-alliance-neutrosophic number and its corresponded sets, and characterizing all minimal-t-powerful alliances. The connections amid t-powerful-alliances are obtained. The number of connected components has some relations with this new concept and it gets some results. Some classes of neutrosophic graphs behave differently when the parity of vertices are different and in this case, cycle, and complete illustrate these behaviors. Two applications concerning complete model as individual and family, under the titles of time table and scheduling conclude the results and they give more clarifications and closing remarks. In this study, there’s an open way to extend these results into the family of these classes of neutrosophic graphs. The family of neutrosophic graphs aren’t study deeply and with more results but it seems that analogous results are determined. Slight progress is obtained in the family of these models but there are open avenues to study family of other models as same models and different models. There’s a question. How can be related to each other, two sets partitioning the vertex set of a graph? The ideas of neighborhood and neighbors based on strong edges illustrate open way to get results. A set is global powerful alliance when two sets partitioning vertex set have uniform structure. All members of set have more amount of neighbors in the set than out of set and reversely for non-members of set with less members in the way that the set is simultaneously t-offensive and(t-2)-defensive. A set is global if t=0. It leads us to the notion of global powerful alliance. Different edges make different neighborhoods but it’s used one style edge titled strong edge. These notions are applied into neutrosophic graphs as individuals and family of them. Independent set as an alliance is a special set which has no neighbor inside and it implies some drawbacks for these notions. Finding special sets which are well-known, is an open way to purse this study. Special set which its members have only one neighbor inside, characterize the connected components where the cardinality of its complement is the number of connected components. Some problems are proposed to pursue this study. Basic familiarities with graph theory and neutrosophic graph theory are proposed for this article.

New setting is introduced to study the global offensive alliance. Global offensive alliance is about a set of vertices which are applied into the setting of neutrosophic graphs. Neighborhood has the key role to define this notion. Also, neighborhood is defined based on strong edges. Strong edge gets a framework as neighborhood and after that, too close vertices have key role to define global offensive alliance based on strong edges. The structure of set is studied and general results are obtained. Also, some classes of neutrosophic graphs containing complete, empty, path, cycle, star, and wheel are investigated in the terms of set, minimal set, number, and neutrosophic number. Neutrosophic number is defined in new way. It’s first time to define this type of neutrosophic number in the way that, three values of a vertex are used and they’ve same share to construct this number. It’s called “modified neutrosophic number”. Summation of three values of vertex makes one number and applying it to a set makes neutrosophic number of set. This approach facilitates identifying minimal set and optimal set which forms minimal-global-offensive-alliance number and minimal-global-offensive-alliance-neutrosophic number. Two different types of sets namely global-offensive alliance and minimal-global-offensive alliance are defined. Global-offensive alliance identifies the sets in general vision but minimal-global-offensive alliance takes focus on the sets which deleting a vertex is impossible. Minimal-global-offensive-alliance number is about minimum cardinality amid the cardinalities of all minimal-global-offensive alliances in a given neutrosophic graph. New notions are applied in the settings both individual and family. Family of neutrosophic graphs is studied in the way that, the family only contains same classes of neutrosophic graphs. Three types of family of neutrosophic graphs including m-family of neutrosophic stars with common neutrosophic vertex set, m-family of odd complete graphs with common neutrosophic vertex set, and m-family of odd complete graphs with common neutrosophic vertex set are studied. The results are about minimal-global-offensive alliance, minimal-global-offensive-alliance number and its corresponded sets, minimal-global-offensive-alliance-neutrosophic number and its corresponded sets, and characterizing all minimal-global-offensive alliances. The connection of global-offensive-alliances with dominating set and chromatic number are obtained. The number of connected components has some relations with this new concept and it gets some results. Some classes of neutrosophic graphs behave differently when the parity of vertices are different and in this case, path, cycle, and complete illustrate these behaviors. Two applications concerning complete model as individual and family, under the titles of time table and scheduling conclude the results and they give more clarifications. In this study, there’s an open way to extend these results into the family of these classes of neutrosophic graphs. The family of neutrosophic graphs aren’t study deeply and with more results but it seems that analogous results are determined. Slight progress is obtained in the family of these models but there are open avenues to study family of other models as same models and different models. There’s a question. How can be related to each other, two sets partitioning the vertex set of a graph? The ideas of neighborhood and neighbors based on strong edges illustrate open way to get results. A set is global offensive alliance when two sets partitioning vertex set have uniform structure. All members of set have more amount of neighbors in the set than out of set. It leads us to the notion of global offensive alliance. Different edges make different neighborhoods but it’s used one style edge titled strong edge. These notions are applied into neutrosophic graphs as individuals and family of them. Independent set as an alliance is a special set which has no neighbor inside and it implies some drawbacks for these notions. Finding special sets which are well-known, is an open way to purse this study. Special set which its members have only one neighbor inside, characterize the connected components where the cardinality of its complement is the number of connected components. Some problems are proposed to pursue this study. Basic familiarities with graph theory and neutrosophic graph theory are proposed for this article.

We report the use of Einstein rings to reveal the quantized and dynamical states of space-time in a region of impressed gravitational field as predicted by the Nexus Paradigm of quantum gravity. This in turn reveals the orbital speeds of objects found therein and the radius of curvature of the quantized space-time. Similarities between the Nexus graviton and the singular isothermal sphere (SIS) in the Cold Dark Matter (CDM) paradigm are highlighted. However unlike the singular isothermal sphere, the Nexus graviton does not contain singularities or divergent integrals. This solves the core cusp problem. In this work, data from a sample of fifteen Einstein rings published on the Cfa-Arizona Space Telescope Lens Survey (CASTLES) website is used to probe the quantized properties of space-time.

Cognitive Computing has become somewhat of a rallying call in the technology world, with the promise of new smart services offered by industry giants like IBM and Microsoft. The recent technological advances in Artificial Intelligence (AI) have thrown into the public sphere some old questions about the relationship between machine computation and human intelligence. Much of the industry and media hype suggests that many traditional challenges have been overcome. On the contrary, our simple examples from language processing demonstrate that present day Cognitive Computing still struggles with fundamental, long-standing problems in AI. An alternative interpretation of cognitive computing is presented, following Licklider's lead in adopting man-computer symbiosis as a metaphor for designing software systems that enhance human cognitive performance. A survey of existing proposals on this view suggests a distinction between weak and strong versions of symbiosis. We propose a Strong Cognitive Symbiosis which dictates an interdependence rather than simply cooperation between human and machine functioning, and introduce new software systems which were designed for cognitive symbiosis. We conclude that strong symbiosis presents a viable new perspective for the design of cognitive computing systems.

Natural and sustainable plant-based antioxidants and antimicrobials are highly desirable for improving food quality and safety. The present investigation assessed the antimicrobial and antioxidant properties of active components from Alkanna tinctoria (herb) roots, also known as Ratanjot root. Two methods were used to extract active components: microwave-assisted hot water (MAHW) and ethanol and air-dried. MAHW extract yielded 6.29% while the ethanol yielded 18.27%, suggesting superior Ratanjot root extract powder (RRP) solubility in ethanol over water. The ethanol extract showed significantly higher antioxidant activity than the MAHW extract. Gas chromatography and mass-spec analysis revealed three major phenolic compounds: Butanoic acid, 3-hydroxy-3-methyl-; Arnebin 7, and Diisooctylpthalate. The color attributes (L*, a*, b*, hab, C*ab) for the ethanolic and MAHW extracts revealed significant differences (P < 0.05) in all the above parameters for both types of extracts, except for yellowness (b*) and chroma (C*ab) values. The ethanol extract exhibited antimicrobial activity against 14 bacterial species, with a signifi-cantly higher inhibitory effect against Gram-positive bacteria (Listeria monocytogenes and Staphylococcus aureus) than the Gram-negative bacteria (Salmonella enterica serovar Typhimurium and Escherichia coli). The minimum inhibitory concentration (MIC) and minimum bactericidal concentration (MBC) were both 25 mg/ml for the Gram-negative bacteria, while the MIC and MBC concentrations varied for Gram-positive bacteria (0.049 - 0.098 mg/ml and 0.098 - 0.195 mg/ml) and the antimicrobial effect was bactericidal. The antimicrobial activities of RRP extract remained stable under broad temperature (37-100°C) and pH (2-6) conditions, as well as during refrigerated storage for 30 days. Application of RRP at 1% (10 mg/g) and 2.5% (25 mg/g) levels in a cooked chicken meatball model system prevented lipid oxidation and improved sensory attributes and retarded microbial growth during refrigerated (4°C) storage for 20 days. Furthermore, the RRP extract was non-toxic when tested with sheep erythrocytes and did not inhibit the growth of probiotics, Lacticaseibacillus casei, and Lactiplantibacillus plantarum. In conclusion, the study suggests that RRP possesses excellent antimicrobial and antioxidant activities, thus making it suitable for food preservation.

A co-curing resin system consisting of 9368 epoxy resin for prepreg and 6808 epoxy resin for resin transfer molding (RTM) was developed. A corresponding preparation method of novel polymer composite bolted T-joint with internal skeleton and external skin was proposed based on prepreg-RTM co-curing process, and novel T-joints were fabricated. A series of conventional configuration T-joints based on RTM process and T-joints made of 2A12 aluminum alloy were prepared simultaneously. Bending performances were studied on these T-joints experimentally. The results indicate that 9368 epoxy resin and 6808 epoxy resin exhibit good compatibility in rheological and thermophysical properties. The novel T-joints prepared with prepreg-RTM co-curing process show no obvious fiber local winding or resin-rich regions inside, and the interface quality between internal skeleton and external skin is excellent. The main failure modes of the novel T-joint under bending load include separation of skin and skeleton and fracture along the thickness on the base panel; the skeleton carries the main bending load, but there is still load transfer between external skin and internal skeleton through their interface. The internal damages of the novel T-joint are highly consistent with surface damages observed visually, facilitating the detection and timely discovery of damages. The initial stiffness, damage initiation load, and ultimate load of the novel T-joint are 1.65 times, 5.89 times, and 3.45 times that of conventional T-joint, respectively. When considering the influence of density, the relative initial stiffness and relative ultimate load of the novel T-joint are 1.44 times and 2.07 times that of aluminum alloy T-joint, respectively.

Preventing the occurrence of secondary caries serves as one of the significant issues in dental clinic, thus make it indispensable to improving the properties of conventional composite resin (CR) by developing a novel CR. In present study, two groups of experimental CRs loaded with different contents of fluoride-doped nano-zirconia fillers (25 wt% and 50 wt%) were fabricated. The surface topography, mechanical performance, fluoride release, antibacterial effect, aging property and cytotoxicity of the experimental CRs were evaluated subsequently. A uniform distribution of the F-zirconia fillers over the whole surface of resin matrix could be observed. The experimental CRs showed continuous fluoride release within 28 days, which was positively correlated with the content of F-zirconia fillers. Moreover, the amount of fluoride release increased in the acidic buffer. Addition of F-zirconia fillers could improve the color stability, wear resistance and microhardness of the experimental CRs, without reducing the flexure strength. Furtherly, the fluoride ions released continuously from the experimental CRs resulted in effective contact and antibacterial properties, while they showed no cytotoxicity. As a consequence, considerations can be made to employ this new kind of composite resin loaded with fluoride-doped nano-zirconia fillers to meet clinical requirements when the antimicrobial benefits are desired.

This review is focused on current state-of-the-art research on electroactive-based materials and their synthesis, as well as their physicochemical and biological properties. Special attention is paid to pristine intrinsically conducting polymers (ICPs) and their composites with other organic and inorganic components, well-defined micro- and nanostructures, and enhanced surface areas compared with those of conventionally prepared ICPs. Hydrogels, due to their defined porous structures and being filled with aqueous solution, offer the ability to increase the amount of immobilized chemical, biological or biochemical molecules. When other components are incorporated into ICPs, the materials form composites; in this particular case, they form conductive composites. The design and synthesis of conductive composites result in the inheritance of the advantages of each component and offer new features because of the synergistic effects between the components. The resulting structures of ICPs, conducting polymer hydrogels and their composites, as well as the unusual physicochemical properties, biocompatibility and multi-functionality of these materials, facilitate their bioapplications. The synergistic effects between constituents have made these materials particularly attractive as sensing elements for biological agents, and they also enable the immobilization of bioreceptors such as enzymes, antigen–antibodies, and nucleic acids onto their surfaces for the detection of an array of biological agents. Currently, these materials have unlimited applicability in biomedicine. In this review, we have limited discussion to three areas in which it seems that the use of ICPs and materials, including their different forms, are particularly interesting, namely, biosensors, delivery of drugs and tissue engineering.

In this paper, the distribution of prime numbers is expressed based on proving the Riemann hypothesis. The relationship between three numbers, three, six, and nine, and the modality to the distribution of prime numbers, is one of the results of Riemann's zeta function. Prime numbers are classified into six groups of single-digit numbers. There are no prime numbers in groups of three, six, and nine. The groups are made based on the sum of the internal digits. And for each set, there is an angle in the complex plane. The distance between the prime numbers in each group has a regular pattern. This pattern is a multiple of the numbers three, six, and nine. According to Euler's number, for an angle of 60 degrees, the real part of the cosine is 1/2. Accordingly, all prime numbers are related to angles greater than 60 degrees to 90 degrees. As a result, based on the relationship between the golden spiral and the complex conjugate of the zeta function, the function in The 1/2 point becomes zero based on the prime numbers.

In the paper, by virtue of the Faá di Bruno formula and two identities for the Bell polynomial of the second kind, the authors find a closed form for the Stirling polynomials in terms of the Stirling numbers of the first and second kinds.

(1) Background The SKT is a short cognitive performance test designed to assess impairments in memory and cognitive abilities such as attention and speed of information processing. In 2019, new regression-based norms for the English version of the SKT were calculated applying data from older cognitively healthy adults living in the US, Ireland and Australia (the norming sample) The study has two aims: to establish valid cut-offs for distinguishing between no cognitive impairment, mild cognitive impairment (MCI) and dementia (1), and to cross-validate the new norms for detecting MCI and dementia (2) in a community sample of older adults with clinical diagnoses; (2)Methods: The validation sample included 142 older adults (mean age=87.7, SD=3.55) from the Sydney Memory and Aging Study (MAS Study). Participants were classified as having normal cognition, MCI, or dementia through a consensus diagnosis as well as by the SKT; (3)Results: The sensitivity of the SKT for the differentiation of cognitive impairment (MCI or dementia) from normal cognition was 80.6%. The convergence between the SKT and the consensus diagnoses was 60.1% for all three diagnostic groups. The correlation between the SKT and the Addenbrooke’s Cognitive Examination III (ACE-III), a well validated measure of cognitive ability in older adults, was r = 0.3;. (4) Conclusions: In sum, it can be stated that the SKT is a valid tool for detecting early stages of cognitive impairment, performing very well in discriminating between no cognitive impairment and cognitive impairment (MCI or dementia).

Grape pomace is a winery byproduct rich in polyphenols with antioxidant capacity, which makes it an attractive product for use in pig diets. The study aimed to investigate the effect of 0, 5, and 10% inclusion of dehydrated grape pomace (DGP) in finishing pig diets. Including 10% of DGP in the diets increased (P&lt;0.05) daily feed intake, backfat thickness at the first rib, P2 backfat thickness, fat area, and fat to meat ratio and decreased (P&lt;0.05) the percentage of lean meat. Grape pomace did not affect TBARS and fresh meat quality characteristics, except for intramuscular fat. When 10% DGP was included in the diet, intramuscular fat, ΣSFA, ΣMUFA, and Σω-3 increased and ω-6:ω-3 ratio was reduced. In conclusion including up to 10% of DGP in the diet of finishing pigs did not affect growth performance, and the oxidative stability of processed meat, but increased the adiposity of the carcasses. Meat quality was improved through an increase in intramuscular fat and ω-3 fatty acids at 10% inclusion. It is feasible to include DGP in pig diets at a level of at least 10%, which would contribute to the rational use and reduction of environmental liability of by-products from the winery industry.

In the paper, the authors present unified generalizations for the Bell numbers and polynomials, establish explicit formulas and inversion formulas for these generalizations in terms of the Stirling numbers of the first and second kinds with the help of the Faà di Bruno formula, properties of the Bell polynomials of the second kind, and the inversion theorem connected with the Stirling numbers of the first and second kinds, construct determinantal and product inequalities for these generalizations with aid of properties of the completely monotonic functions, and derive the logarithmic convexity for the sequence of these generalizations.

A new generalized definition of Mersenne numbers is proposed of the form (a^n - (a-1)^n), called Global Generalized Mersenne numbers, or simply Generalized Mersenne numbers and noted GM_{a,n} where a is the base and n is the exponent, both being positive integers. The properties are investigated for prime exponents n and several theorems on Mersenne numbers regarding their congruence properties are generalized and demonstrated. In particular, it is found that, for any base a, Generalized Mersenne numbers are in general such that (GM_{a,n} - 1) are even and divisible by n, a and (a-1) for any odd prime exponent n and by (a(a-1)+1) for any prime exponent n > 5. The remaining factor is a function of triangular numbers of (a-1), specific to each prime exponent n. Four theorems on Mersenne numbers are generalized and four new theorems are demonstrated, allowing to show first, that (GM_{a,n} - 1) are divisible by 6, and more precisely GM_{a,n} are congruent to 1(mod 12) or 7(mod 12) depending on the congruence of the base a(mod 4); second, that (GM_{a,n} - 1) are divisible by 10 if n == 1(mod 4) and, if n == 3(mod 4), GM_{a,n} == 1(mod 10), or 7(mod 10) or 9(mod 10) depending on the congruence of the base a(mod 5); third, that all factors c_{i} of GM_{a,n} are of the form (2nf_{i}+1) with f_{i} natural integers such that c_{i} is prime itself or the product of primes of the form (2nj+1) with j natural integer; fourth, that for odd prime exponents n, all GM_{a,n} are periodically congruent to either +/-1\(mod 8) or +/-3(mod 8) depending on the congruence of the base a(mod 8); and fifth, that the factors of a composite GM_{a,n} is of the form (2nf_{i}+1) with f_{i} == u(mod 4) and u being either 0, 1, 2 or 3 depending on the congruence of the exponent n(mod 4) and on the congruence of the base a(mod 8). The potential use of Generalized Mersenne primes in cryptography is shortly addressed.

Cognitive linguistics is founded on the assumption that language is a reflection of universal cognitive principles, implying that all cognitive processes share a common origin. This assumption is known as the 'Cognitive Commitment.' The present article examines the sensory schema hypothesis, which traces all forms of expression back to sensations. This theoretical framework integrates the physicality of the body with sensations that underlie human experiences and their linguistic and non-linguistic expressions. By challenging the traditional dichotomy between mind and body, it provides a more integrated understanding.

We consider an $N$ fermion system at low temperature $T$ in which we encounter special particle number values $N_m$ exhibiting special traits. These values arise in focusing attention upon the degree of mixture (DM) of the pertinent quantum states. Given the coupling constant of the Hamiltonian, the DMs stay constant for all $N$-values, but experience sudden jumps at the $N_m$. For a quantum state described by the matrix $\rho$, its purity is expressed by $Tr \rho^2$ and then the degree of mixture is given by $1 - Tr \rho^2$, a quantity that coincides with the entropy $S_q$ for $q=2$. Thus, Tsallis entropy of index two faithfully represents the degree of mixing of a state, that is, it measures the extent to which the state departs from maximal purity . Macroscopic manifestations of the degree of mixing can be observed through various physical quantities. Our present study is closely related to properties of many-fermion systemsn that are usually manipulated at zero temperature. Here we wish to study the subject at finite temperature. Gibbs' ensemble is appealed to. Some interesting insights are thereby gained.

In this paper, we introduce hybrid numbers with Fibonacci and Lucas hybrid number coefficients. We give the Binet formulas, generating functions, exponential generating functions for these numbers. Then we define an associate matrix for these numbers. In addition, using this matrix, we present two different versions of Cassini identitiy of these numbers.

In this paper, we introduce a new class of degenerate Hermite-Fubini numbers and polynomials and investigate some properties of these polynomials. We establish summation formulas of these polynomials by summation techniques series. Furthermore, we derive symmetric identities of degenerate Hermite-Fubini numbers and polynomials by using generating functions.

The main purpose of this paper is to introduce a new class of $q$-Hermite-Fubini numbers and polynomials by combining the $q$-Hermite polynomials and $q$-Fubini polynomials. By using generating functions for these numbers and polynomials, we derive some alternative summation formulas including powers of consecutive $q$-integers. Also, we establish some relationships for $q$-Hermite-Fubini polynomials associated with $q$-Bernoulli polynomials, $q$-Euler polynomials and $q$-Genocchi polynomials and $q$-Stirling numbers of the second kind.

In this paper, we investigate a new $q$-analogue of the higher order degenerate Changhee polynomials and numbers, which are called the Witt-type formula for the $q$-analogue of degenerate Changhee polynomials of order $r$. We can derive some new interesting identities related to the degenerate $(h,q)$-Changhee polynomials and numbers.

In this paper, we investigate a new $q$-analogue of the higher order degenerate Changhee polynomials and numbers, which are called the Witt-type formula for the $q$-analogue of degenerate Changhee polynomials of order $r$. We can derive some new interesting identities related to the degenerate $(h,q)$-Changhee polynomials and numbers.

Bringing toghether mathematical and philosophical ideas related to transcendental numbers, this paper begins with a survey on transcendence and transcendental numbers, it then presents several properties of the transcendental numbers e and π, and then it gives the proof of a new inequality for transcendental numbers. Also, in relationship with these topics, we study solutions to the Yang-Baxter equation from hyperbolic functions and from logical implication.

In the present paper, we introduce (p, q)-extension of Apostol type Frobenius-Euler polynomials and numbers and investigate some basic identities and properties for these polynomials and numbers, including addition theorems, difference equations, derivative properties, recurrence relations and so on. Then, we provide integral representations, explicit formulas and relations for these polynomials and numbers. Moreover, we discover (p, q)-extensions of Carlitz's result [L. Carlitz, Mat. Mag., 32 (1959), 247–260] and Srivastava and Pintér addition theorems in [H. M. Srivastava, A. Pinter, Appl. Math. Lett., 17 (2004), 375–380].

Thorium is a weak radioactive element, but the control of its concentration in natural aqueous systems is of great interest for health, because it is a toxic heavy metal. The present paper presents the recovery of thorium from diluted synthetic aqueous systems by nanofiltration. The membranes used for nanofiltration of systems containing thorium species are composites containing 4′-Aminobenzo-15-crown-5 ether (ABCE) and sulfonated poly–ether–ether–ketone (sPEEK). The composite membranes (ABCE–sPEEK) were characterized by scanning electron microscopy (SEM), energy dispersive X–ray spectroscopy EDAX, thermal analysis (TG and DSC) and from the perspective of thorium removal performance. To determine the process performances, the variables were: the nature of the composite membrane, the concentration of thorium in the aqueous systems, the rotation speed of the stirrer, the pressure and the pH of the thorium aqueous system. When using pure water, a permeate flux value of 12 L·m⁻2 h⁻1 was obtained for sPEEK membrane, and up to 15 L·m⁻2 h⁻1 for the ABCE–sPEEK composite membrane. The use of mechanical stirring, with a propeller stirrer, leads to an increase in the permeate flux of pure water by about 20 % for each of the studied membrane. Depending on the concentration of thorium and the pH of the feed solution, retentions between 84.9 % and 98.4 % were obtained. An important observation is the retention jump at pH 2 for the ABCE–sPEEK composite membrane. In the paper, a thorium ion retention mechanism is proposed for the sPEEK membrane and the ABCE–sPEEK composite membrane.

The importance of a properly regulated immune response has been explored through various research-oriented methods. It has proved that having an effective and well-regulated immune response helps prevent many minors and serious diseases. Any kind of dysregulation in the working of the immune system may lead to severe consequences. An autoimmune disorder is one such consequence in which the component of the immune system starts targeting self-cells of the body, treating them as self-antigen producing autoantibodies and immune complexes resulting from the failure of immune responses both at a central and peripheral level. Currently, many autoimmune disorders are prevailing across the world, and new diseases need attention.In this review, we have written about the functions of T cell, LncRNAs and also some interactions between the LncRNAs and miRNAs in the pathogenesis of Multiple sclerosis (MS), Systemic lupus erythematosus (SLE), Type 1 diabetes (T1D), Rheumatoid arthritis (RA). To find the functions of these autoimmune disorders we have done intensive literature search during this we also found that GAS5 and MALAT are common in MS, SLE, T1D, RA. And finally, we have also mentioned the therapeutic drugs which neutralizes the different cluster of differentiation (CDs) and also suppresses the T cell differentiation in MS, SLE and RA. For T1D therapeutic strategies and various types of insulin are mentioned.

New setting is introduced to study the alliances. Alliances are about a set of vertices which are applied into the setting of neutrosophic graphs. Neighborhood has the key role to define these notions. Also, neighborhood is defined based on the edges, strong edges and some edges which are coming from connectedness. These three types of edges get a framework as neighborhood and after that, too close vertices have key role to define offensive alliance, defensive alliance, t-offensive alliance, and t-defensive alliance based on three types of edges, common edges, strong edges and some edges which are coming from connectedness. The structure of set is studied and general results are obtained. Also, some classes of neutrosophic graphs containing complete, empty, path, cycle, bipartite, t-partite, star and wheel are investigated in the terms of set, minimal set, number, and neutrosophic number. In this study, there’s an open way to extend these results into the family of these classes of neutrosophic graphs. The family of neutrosophic graphs aren’t study but it seems that analogous results are determined. There’s a question. How can be related to each other, two sets partitioning the vertex set of a graph? The ideas of neighborhood and neighbors based on different edges illustrate open way to get results. A set is alliance when two sets partitioning vertex set have uniform structure. All members of set have different amount of neighbors in the set and out of set. It leads us to the notion of offensive and defensive. New ideas, offensive alliance, defensive alliance, t-offensive alliance, t-defensive alliance, strong offensive alliance, strong defensive alliance, strong t-offensive alliance, strong t-defensive alliance, connected offensive alliance, connected defensive alliance, connected t-offensive alliance, and connected t-defensive alliance are introduced. Two numbers concerning cardinality and neutrosophic cardinality of alliances are introduced. A set is alliance when its complement make a relation in the terms of neighborhood. Different edges make different neighborhoods. Three types of edges are applied to define three styles of neighborhoods. General edges, strong edges and connected edges are used where connected edges are the edges arising from connectedness amid two endpoints of the edges. These notions are applied into neutrosophic graphs as individuals and family of them. Independent set as an alliance is a special set which has no neighbor inside and it implies some drawbacks for this notions. Finding special sets which are well-known, is an open way to purse this study. Special set which its members have only one neighbor inside, characterize the connected components where the cardinality of its complement is the number of connected components. Some problems are proposed to pursue this study. Basic familiarities with graph theory and neutrosophic graph theory are proposed for this article.

We report the strong coupling between plasmonic surface lattice resonances (SLRs) and photonic Fabry-Pérot (F-P) resonances in a microcavity embedded with two-dimensional periodic array of metal-insulator-metal nanopillars. For such a plasmonic-photonic system, we show that the SLR can be strongly coupled to the F-P resonances of both the odd- and even orders, and that the splitting energy reaches as high as 138 meV in the visible regime. We expect that this work will provide a new scheme for strong coupling between plasmonic and photonic modes.

In this short communication, we conducted first-principles calculations to explore the stability of boron monochalcogenides (BX, X=S, Se or Te), as a new class of two-dimensional (2D) materials. We predicted BX monolayers with two different atomic stacking sequences of ABBA and ABBC, referred in this work to 2H and 1T, respectively. Analysis of phonon dispersions confirm the dynamical stability of BX nanosheets with the both 2H and 1T atomic lattices. Ab-initio molecular dynamics simulations reveal the outstanding thermal stability of all predicted monolayers at high temperatures over 1500 K. BX structures were found to exhibit high elastic modulus and tensile strengths. It was found that BS and BTe nanosheets can show high stretchability, comparable to that of the graphene. It was found that all predicted monolayers exhibit semiconducting electronic character, in which 2H structures present lower band-gaps as compared with 1T lattices. The band-gap values were found to decrease from BS to BTe. According to the HSE06 results, 1T-BS and 2H-BTe show respectively, the maximum (4.0 eV) and minimum (2.06 eV) electronic band-gaps. This investigation introduces boron monochalcogenides as a novel class of 2D semiconductors with remarkable thermal, dynamical and mechanical stability.

Intermediate temperature solid oxide fuel cell (SOFC) operation provides numerous advantages such as high combined heat and power (CHP) efficiency, potentially long-term materials stability, and the use of low-cost materials. However, due to the sluggish kinetics of the oxygen reduction reaction at intermediate temperature, the cathode of SOFC requires an efficient and stable catalyst. Significant progress in the development of cathode materials has been made over recent years. In this article, multiple strategies for improving the performance of cathode materials have been extensively reviewed such as A and B site doping of perovskites, infiltration of catalytic active materials, the use of core-shell composites, etc. Emphasis has been given to intrinsic properties such as thermal expansion compatibility, chemical and thermal stability, and oxygen transport number. Furthermore, to avoid any insulating phase formation at the cathode/electrolyte interface, strategies for interfacial layer modifications have also been extensively reviewed and summarized. Based on major technical challenges, future research directions have been proposed for efficient and stable intermediate temperature solid oxide fuel cell (SOFC) operation.

With the rapid development of intelligent logistics and network environment, it has become an urgent problem to efficiently and accurately handle and analyse the huge amount of uncertain decision information. Traditional decision making methods often fail to make the best use of complex and incomplete information, especially in the field of cyber defence. To address these problems, this paper introduces a new mathematical tool, discrete multidimensional Z-numbers (MZs), for expressing and dealing with uncertainty and reliability in network defence decisions. In this paper, we first introduce the synthesis method of discrete multidimensional Z-numbers, which allows us to consider the uncertainty and reliability of multi-source information in network defence strategy. Then, the hidden probability of MZs is calculated by using the hidden probability model, and the multidimensional Z+−number is proposed, which improves the expressiveness of the model in dealing with information uncertainty. Based on MZs, we define a variety of utility functions and build a multi-attribute group decision framework for network defence around these functions. The MZs provides a novel perspective for analysing and designing response strategies, especially against highly adaptive and covert attacks. The method in this paper is verified by a case of network security assessment of an intelligent logistics company. The results show that this method can significantly improve the accuracy and efficiency of decision making, demonstrating its unique advantages and wide application potential in network defence. This integrated discrete multidimensional Z-number group decision method is not only suitable for intelligent logistics decision making, but also provides an efficient decision support tool for network defence, which helps to improve the intelligence and adaptability of network security defence.

Soft pneumatic actuators/robotics have received significant interest in the medical and health fields, due to their intrinsic elasticity and simple control strategies enabling desired interaction. However, current soft hand pneumatic exoskeletons often exhibit uniform deformation, mismatch the profile of the interacted objects, and seldom quantify the assistive effects during activities of daily life (ADL), such as extension angle and joint stiffness predicted. The lack of quantification poses challenges to the effective and sustainable advancement of rehabilitation technology. This paper introduces the design, modeling, and testing of pneumatic bioinspired Segmented Composite Proprioceptive Bending Actuators (SCPBAs) for hand rehabilitation in ADL tasks. The actuator’s soft-joint/rigid-bone segmented structure, inspired by the human finger anatomy, provides a superior fit compared to traditional continuous structures. A quasi-static model is established to predict the bending angles based on geometrical parameters. The SCPBAs also include a quantitative evaluation of joint stiffness and extension angle utilizing proprioceptive bending information. Additionally, a soft under-actuated hand exoskeleton equipped with SCPBAs demonstrates its potential in ADL rehabilitation scenarios.

The article is devoted to applications of 2-dimensional hyperbolic numbers and their algebraic 2ⁿ-dimensional extensions in modeling some genetic and cultural phenomena. Mathematical properties of hyperbolic numbers and their bisymmetric matrix representations are described in a connection with their application to analyze the following structures: alphabets of DNA nucleobases; inherited phyllotaxis phenomena; Punnett squares in Mendelian genetics; the psychophysical Weber-Fechner law; long literary Russian texts (in their special binary representations). New methods of algebraic analysis of the harmony of musical works are proposed, taking into account the innate predisposition of people to music. The hypothesis is put forward that sets of eigenvectors of matrix representations of basis units of 2ⁿ-dimensional hyperbolic numbers play an important role in transmitting biological information. A general hyperbolic rule regarding the oligomer cooperative organization of different genomes is described jointly with its quantum-information model. Besides, the hypothesis about some analog of the Weber-Fechner law for sequences of spikes in single nerve fibers is formulated. The proposed algebraic approach is connected with the theme of the grammar of biology and applications of bisymmetric doubly stochastic matrices. Applications of hyperbolic numbers reveal hidden interrelations between structures of different biological and physical phenomena. They lead to new approaches in mathematical modeling genetic phenomena and innate biological structures.

In this paper, we introduce the generalized dual hyperbolic Fibonacci numbers. As special cases, we deal with dual hyperbolic Fibonacci and dual hyperbolic Lucas numbers. We present Binet's formulas, generating functions and the summation formulas for these numbers. Moreover, we give Catalan's, Cassini's, d'Ocagne's, Gelin-Cesàro's, Melham's identities and present matrices related with these sequences.

We suggest a new solution to the strong CP problem. The solution is based on the proper use of the boundary conditions for the QCD generating functional integral. It obeys the principle of renormalizability of Quantum Field Theory and does not involve new particles like axions.

Nickel electrodeposition is a widely utilized method for creating thin films on various substrates with various desirable attributes. Recently, there has been a growing interest in developing nickel composite coatings that incorporate additional elements or particles into the nickel matrix to enhance their properties. These composite coatings offer superior wear resistance, corrosion resistance, hardness, and other functional benefits compared to pure nickel coatings. Some of the recent advancements in electrodeposited nickel composite coatings include improved wear resistance, enhanced mechanical properties and better corrosion resistance. Researchers have discovered that adding Al, Si, Zr, C, W, and Ti particles to nickel coatings can significantly enhance wear resistance. The uniform distribution of these particles within the nickel matrix acts as a barrier to wear and tear. Studies have also shown that nickel composite coatings with Al, Si, Zr, C, W, and Ti particles exhibit superior mechanical properties, including increased hardness. These particles refine the grain size of the nickel matrix and hinder defect movement, leading to greater mechanical strength. Moreover, nickel composite coatings offer improved protection against corrosion compared to pure nickel coatings. This review provides a detail discussion of nickel composite coatings with regard to their comparative advantaged compared to pure nickel coatings on different substrates.