The objective of this work was to evaluate the roast time, weight loss and quality of coffee grain at four different roasting degrees, aiming to recognize and develop sustainable patterns to industrialize specialty coffees. Coffee (Coffea arabica L.), from eight producers, with scores between 80 and 83 from SCA classification, were used. Samples of 300 g were roasted in a cylindric rotative roaster, until the grains reached four different roasting profiles (Agtron scale 22.36, #33.64, #40.05, #59.92). Afterwards, analysis of roasting time, gas pressure, weight loss, and sensorial grades were accomplished. It was observed that samples roasted at #22.36 led to significant differences, regarding roasting time and weight loss. Furthermore, there is a significant difference at the sensorial grades of the coffee beverage. Comparing the roast degree #40.05 (standard used for specialty coffee) with the roast degree #22.36 (most used for commodities coffee), the first one has a gas consumption of 0.34 kg per coffee kg, whilst the second presented a gas consumption of 0.41 kg per coffee kg. Thus, from gas consumption, roast degree # 40.05 is the more sustainable option, along with the remaining parameters analyzed.

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.

We introduce a full binary directed tree structure to represent the set of natural numbers, further categorizing them into three distinct subsets: pure odd numbers, pure even numbers, and mixed numbers. We adopt a binary string representation for natural numbers and elaborate on the composite methodology encompassing odd- and even-number functions. Our analysis focuses on examining the iteration sequence (or composition) of the Collatz function and its reduced variant, which serves as an analog to the inverse function, to scrutinize the validity of the Collatz conjecture. To substantiate this conjecture, we incorporate binary strings into an algebraic formula that captures the essence of the Collatz sequence. By this means, we transform discrete powers of 2 into continuous counterparts, ultimately culminating in the smallest natural number, 1. Consequently, the sequence generated through infinite iterations of the Collatz function emerges as an eventually periodic sequence, thereby validating an enduring 87-year-old conjecture.

We use binary string to represent a natural number and show the composite procedure of odd-number and even-number functions, thus we propose full binary directed tree to represent the set of natural numbers and give another partition the natural number set to three sets: pure odd, pure even and mixed number. For the Collatz conjecture we make use of the parity of a natural number to analyse the sequence of iteration (or composite) of Collatz function and reduced Collatz function analog to the inverse function. We give tabular and binary strings to the algebra expression to state the sequence of Collatz, this is the key topic to proof the conjecture: the discrete powers of 2 can be changed to ultimately continuous powers of 2, finally get to pure even number and to the smallest number 1. The sequence created by the infinite 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 87 years.

Tungsten fibre-reinforced tungsten composites (Wf/W) have been in development to overcome the inherent brittleness of tungsten as one of the most promising candidate for the first wall and divertor armour material in a future fusion power plant. As the development of Wf/W continues, the fracture toughness of the composite is one of the main design drivers. In this contribution the efforts on size upscaling of Wf/W based on Chemical Vapour Deposition (CVD) is shown together with fracture mechanical tests of two different size samples of Wf/W produced by CVD. Three-point bending tests according to ASTM E399 for brittle materials were used to get a first estimation of the toughness. A provisional fracture toughness value of up to 346MPam1/2 was calculated for the as-fabricated material. As the material does not show a brittle fracture in the as-fabricated state, the J-Integral approach based on the ASTM E1820 was additionally applied for this state. A maximum value of the J-integral of 41kJ/m2 (134,8MPam1/2) was determined for the largest samples. Post mortem investigations were employed to detail the active mechanisms and crack propagation.

Identifying anti-spike antibodies that exhibit strong neutralizing activity against current dominant circulating variants and antibodies that are escaped by these variants have important implications in the development of therapeutic and diagnostic solutions as well as in improving understanding of the humoral response to SARS-CoV-2 infection. We characterized seven anti-RBD monoclonal antibodies for their binding activity, pairing capability and neutralization activity to SARS-CoV-2 and three variant RBDs (UK, SA and BR P.1) via lateral flow immunoassays. The results allowed us to group these antibodies into three distinct epitope bins. Our studies showed that two antibodies had broadly potent neutralizing activity against SARS-CoV-2 and these variant RBDs and that one antibody did not neutralize the SA and BR P.1 RBDs. The antibody escaped by the SA and BR P.1 RBDs retained binding activity to SA and BR P.1 RBDs but was unable to induce neutralization. Further, we demonstrated that the lateral flow immunoassay can be a rapid and effective tool for antibody characterization, including epitope classification and antibody neutralization kinetics. From these studies, the potential contributions of the mutations (N501Y, E484K and K417N/T) contained in these variants’ RBDs on antibody pairing capability, neutralization activity and therapeutic antibody targeting strategy are discussed.

This paper first explains the theory of the origin of force from a new perspective, explaining that the origin of all forces is caused by the "missing of energy in the time dimension" (non-conservation in a certain period of time), and constructs a unified theory of force on this basis. Then, through the unified theory of force, the following phenomena are reinterpreted: (1) The common origin of the inverse square law of gravitation and electromagnetic force; (2) The origin of the repulsive force of electrons and protons at small distances; (3) The mystery of the rotation curve of galaxies and the new explanation of "dark matter"; (4) explain the origin of the magnetic field; (5) Predict that moving magnets have the same radiation effect as charged particles (electron magnetic moments also have radiation effects); (6) Reinterpret Maxwell's displacement current; (7) Reinterpret synchrotron radiation and bremsstrahlung; (8) Explain that the strong and weak forces are short-range forces; (9) Predict the true structure of black holes and the origin of gravitational waves;(10) Possible explanation for the origin of the speed of light.

The existence of palindrome numbers of arbitrary length greater than 2 that are divisible by the prime number 37 is proven in this paper. The method to construct such a palindrome is also described. It turns out that a palindrome number divisible by 37 is also divisible by 3 and, consequently, divisible by 111.

Recently, a paper was written to reformulate and strengthen the theory of semi-structured complex numbers H (a new number set invented to enable division by zero). Whilst the paper had profound results, the application of this number set in many areas of engineering and science has not been fully explored. Consequently, the aim of this paper was to establish the number set H as a useful mathematical tool by providing an amalgam of results arising from its application in several areas of engineering and science. In the process, this paper makes four major contributions: these are (1) determining the product of the gradients of a horizontal and vertical line; (2) developing new Euler formulas relating exponential, trigonometric and hyperbolic functions in the 3D semi-structured complex number Euclidean space; (3) establishing semi-structured complex numbers as a better extension of the complex number set than quaternions; (4) resolving singularities that may arise in engineering and science equations (because of division by zero) to develop reasonable conclusions in the absence of experimental data. These results and their applications provide a firm foundation to advance the number set H as a useful mathematical tool.

Motivated by Kim-Kim [19] introduced the new type of degenerate poly- Bernoulli polynomials by means of the degenerate polylogarithm function. In this paper, we define the degenerate poly-Frobenius-Euler polynomials, called the new type of degenerate poly-Frobenius-Euler polynomials, by means of the degenerate polylogarithm function. Then, we derive explicit expressions and some identities of those numbers and polynomials.

Recently, Kim-Kim [13] have introduced polyexponential functions as an inverse to the polylogarithm functions, and constructed type 2 poly-Bernoulli polynomials. They have also introduced unipoly functions attached to each suitable arithmetic function as a universal concept. Inspired by their work, in this paper, we introduce a new class of the Frobenius-Genocchi polynomials. We derive the diverse formulas and identities covering some summation formulas, derivative formula and correlations with Bernoulli polynomials and numbers, Stirling numbers of the both kinds, degenerate Frobenius-Genocchi polynomials and degenerate Frobenius-Euler polynomials. Moreover, by using the unipoly function as following Kim-Kim's work in <cite>Kim1</cite>, we consider degenerate unipoly-Frobenius-Genocchi polynomials and investigate some formulas and relationships with Daehee numbers, degenerate Frobenius-Genocchi numbers and Stirling numbers of the first kind. Finally, we obtain an Gaussian integral representation of the Frobenius-Genocchi polynomials in terms of the 2-variable Hermite polynomials.

In the paper, the authors establish two identities, which can be regarded as nonlinear differential equations, for the generating function of Eulerian polynomials, find two identities for the Stirling numbers of the second kind, and present two identities for Eulerian polynomials and higher order Eulerian polynomials, pose two open problems about summability of two finite sums involving the Stirling numbers of the second kind. Some of these conclusions meaningfully and significantly simplify several known results.

In the paper, the authors find two explicit formulas and recover a recursive formula for the generalized Motzkin numbers. Consequently, the authors deduce two explicit formulas and a recursive formula for the Motzkin numbers, the Catalan numbers, and the restricted hexagonal numbers respectively.

Hereditary cancer syndromes caused by germline mutations account for 5-10% of all cancers. The finding of a genetic mutation could have far-reaching consequences for pharmaceutical therapy, personalized prevention strategies, and cascade testing. According to the National Comprehensive Cancer Network’s (NCCN) and the Italian Association of Medical Oncology (AIOM) guidelines, unaffected family members should be tested only if the affected one is unavailable. This article explores whether germline genetic testing may be offered to high-risk families for hereditary cancer even if a living affected relative is missing. A retrospective study was carried out on 103 healthy subjects tested from 2017 to 2023. We enrolled all subjects with at least two first or second-degree relatives affected by breast, ovarian, pancreatic, gastric, prostate, or colorectal cancer. All subjects were tested by Next Generation Sequencing (NGS) multi-gene panel of 27 cancer-associated genes. In the study population, 5 (about 5%) pathogenic/likely pathogenic variants (PVs/LPVs) were found while 40 (42%) had a Variant of Uncertain Significance (VUS). This study highlights the importance of genetic testing for individuals with a strong family history of hereditary malignancies. This approach would allow women who tested positive to receive tailored treatment and prevention strategies based on their personal mutation status.

In recent years the yield of fruits and vegetables have been decreasing in Colombia, threatening national food security. Analysis of crop production data may lead to identifying cropping systems that have shown better adaptability to changes in climatic and non-climatic factors associated with agricultural production. The open database AGRONET keeps data of the agricultural activities conducted in Colombia, allowing to find the information organized by crops, regions and years; each row of the database registers farm information in Colombia. Aiming to identify resilient crops systems, agricultural data of fruits and vegetables were analyzed. First, trends in crop production were studied by year and locations, detecting the regions and crops with highest yields in the period from 2006 until 2020. Then, mixed linear regression and principal components analysis were applied to elucidate the relation between non-climatic factors and crop yield. In Colombia, vegetable production was more efficient than fruits, observing yields of 10.23 and 13.33 t ha^-1, respectively. On the other hand, the Colombian central region showed high yields for vegetables, while for fruits this was exhibited in northern and eastern locations. In the present study, yield variation responded to changes in the location of crop systems, while years had no effect on vegetable production. Furthermore, the price of the agricultural product and the cost of fertilizers were associated with the yield of the analyzed crops systems. In Colombia, carrot, cabbage, tomato papaya and pineapple are resilient crops whose yield increases especially by the regions where they are cultivated.

We examine data assimilation coupling between meteorology and chemistry in the stratosphere from both weak and strong coupling strategies. The study was performed with the Canadian operational weather prediction Global Environmental Multiscale (GEM) model coupled online with the photochemical stratospheric chemistry developed at the Belgian Institute for Space Aeronomy, described in Part I. Here, the Canadian Meteorological Centre’s operational variational assimilation system was extended to include errors of chemical variables and cross-covariances between meteorological and chemical variables in a 3D-Var configuration, and we added the adjoint of tracer advection in the 4D-Var configuration. Our results show that the assimilation of limb sounding observations from the MIPAS instrument on board Envisat can be used to anchor the AMSU-A radiance bias correction scheme. Also, the added value of limb sounding temperature observations on meteorology and transport is shown to be significant. Weak coupling data assimilation with ozone-radiation interaction is shown to give comparable on meteorology whether a simplified linearized or comprehensive ozone chemistry scheme is used. Strong coupling data assimilation, using static error cross-covariances between ozone and temperature in a 3D-Var context, produced inconclusive results with the approximations we used. We have also conducted the assimilation of long-lived species observations using 4D-Var to infer winds. Our results showed the added value of assimilating several long-lived species, and an improvement in the zonal wind in the Tropics within the troposphere and lower stratosphere. 4D-Var assimilation also induced a correction of zonal wind in the surf zone and a temperature bias in the lower tropical stratosphere

POH (Peri Orbital Hyperpigmentation) represents a minor clinical entity that attracts immense aesthetic damages and it generates social integration difficulties. This review focuses on the etiopathogenic causes of this entity, differentiating and reclassifying this defect as having, on the one hand, genetic causes of melanic hyperproduction – for Fitzpatrick cutaneous phototypes IV and V – and, on the other hand, both genetic and acquired vascular causes, in individuals with light-coloured skin phototypes. Hence, there is a big difference in the field of pathogenic treatment, for the two entities. In addition, this study notes the direct relationship between skin aging and POH, especially for aquired vascular causes. In this reasoning, other aesthetic deficiencies of the skin in the palpebral area should be also considered, like: blepharochalasis, wrinkles, the anatomical causes of the lower eyelid shading, symmetrical or asymmetric suborbital oedema. All of these issues will complicate the therapeutic decision and subsidiary, the pharmaceutical advice. In this context, the review shows the guidelines for a honest councelling of the patients, pointing the efficiency limit for the topical pharmaceutical medication (depigmentants, exfoliants) versus the necessity of minimally invasive or/ and surgical treatments (in blefarochalasis).

This work presents the results of optimizing the physicochemical properties of composite briquettes based on microsilica for metallurgical-grade silicon production. Microsilica, a waste product of silicon production, contains a sufficiently high amount of silicon dioxide (96-97%). This fact makes microsilica a promising composite material for metallurgical processing. However, its granulometric composition limits its direct use. The method of briquetting on an industrial briquetting press was used. The influence of the granulometric composition of the composite mixture on the heat tolerance and strength of the finished briquettes was studied. The methods of obtaining and testing the briquettes, their composition, and the briquetting and drying process are described. The obtained briquettes were tested for the smelting of metallurgical silicon. The silicon recovery rate in the metal with the standard charge was 71%, while the recovery rate with the briquetted monocharge was 85%. The results of silicon smelting from the briquettes demonstrated the high quality of the obtained metal, corresponding to the standards of metallurgical-grade silicon. The implementation of these technologies not only improves the quality of the final product but also addresses environmental issues related to the disposal of microsilica, reducing its accumulation and minimizing its impact on the environment.

We report on the role of synergistic polarization of Ba0.9Sr0.1TiO3 (BST) nanoparticles in sulfur cathodes to enhance the redox kinetics of polysulfides for high-capacity Li-S batteries. Ferroelectric nanoparticles are known to significantly improve the electrochemical performance of Li-S batteries due to their inherent self-polarization and high adsorption capacity towards polysulfides. X-ray diffraction spectra confirmed the tetragonal symmetry (c/a=1.0073), while Raman spectroscopic analysis validated the presence of tetragonal orientation Raman modes in BST-modified composites. Scanning electron microscope (SEM) images showed a homogeneous distribution of BST in the sulfur cathode system, with grain sizes ranging from 1 to 1.5 μm. Notably, the BST-coupled S50BST30CB10PVDF10 composite cathode achieved a capacity of approximately 820 mAh/g at 100 mA/g, maintaining stability over 100 cycles, demonstrating improved electrochemical performance. Two distinct plateaus between 2.3 V to 2.0 V and 2.0 V to 1.5 V further underscore the superior performance of BST ferroelectric nanoparticles in enhancing the redox kinetics of Li-S batteries. By leveraging the favourable affinity of polar substances towards polysulfides, we aimed to create a more stable reactive environment within the cathodic site, effectively trapping polysulfide intermediates through the synergistic polarization of BST nanoparticles. The synergistic polarization induced by the asymmetric crystal structure of ferroelectrics is anticipated to generate internal electric fields, enhancing chemisorption with heteropolar reactive. The observed high cyclic stability further validates the efficacy of these composite cathodes in mitigating the polysulfide shuttle effect, offering promising prospects for advancing Li-S battery technology.

In this research first, a sequence of properties called delta is assigned to each prime number and then examined. Deltas are only dependent on the distribution of prime numbers, so the results obtained for the delta distribution can be considered as a proxy for the distribution of prime numbers. The first observation was that these properties are not unique and different prime numbers may have the same value of delta of a given order. It was found that a small number of deltas cover a large portion of prime numbers, so by recognizing repetitive deltas, the next prime numbers can be predicted with a certain probability, but the most important observation of this study is the normal distribution of deltas. This research has not tried to justify the obtained observations and instead of answering the questions, it seeks to ask the right question.

Creative thinking is increasingly recognised as an essential ability that should be part of school curricula. Given the move towards online learning and assessment, we investigate whether mathematical creativity can be assessed at-scale in the Numbers game, an arithmetic game in Math Garden, a popular online math practice platform. In the Numbers game, a generalisation of the 24 Game, children are asked to figure out how to compute a target number using basic arithmetic operations and a given set of numbers. We argue that creative thinking is required when the search space is complex, and propose that the base-pattern, i.e., the sequence of the operations needed to solve a Numbers game item, indicates search space complexity. We then demonstrate that items with disordered base-patterns are more likely to require mathematical creativity to figure out. Specifically, our analysis shows that for items with only one solution sequence, those with disordered base-patterns are more difficult and take longer to solve compared to items with ordered base-patterns. For items where multiple solution sequences are possible, nine times out of ten children choose ordered over disordered base-patterns. We conclude that the Numbers game has potential for assessing mathematical creativity at-scale.

In this paper, we define new kind of Daehee numbers, the degenerate Daehee numbers of the third kind, using degenerate log function as generating function. We obtain some identities for the degenerate Daehee numbers of the third kind associated with the Daehee, degenerate Daehee and degenerate Daehee numbers of the second kind. In addition, we derive a differential equation associated with the degenerate log function. We deduce some identities from the differential equation.

In the paper, the authors express the Fuss–Catalan numbers as several forms in terms of the Catalan–Qi function, find some analytic properties, including the monotonicity, logarithmic convexity, complete monotonicity, and minimality, of the Fuss–Catalan numbers, and derive a double inequality for bounding the Fuss–Catalan numbers.

Decades ago, when computational was expensive and limited, the structural design was mostly performed by hand calculations using simple mathematical models. For example, it was a common practice to design a structure as complex as the wing of an aircraft by simple beam analysis. However, ever since the classic paper by Turner et al., due to a rapid increase in computational, more complex mathematical models are being used to simulate the physical behavior of complex structural components. To solve intractable problems unsolvable by hand calculations, numerical techniques like Finite Element Analysis (FEA), Computational Fluid Dynamics (CFD), Finite Difference Method etc. are being employed. In fact, the availability of these methods has led to the development of an entirely new area of research known as Multidisciplinary Design Optimization (MDO) where various disciplines are considered in an optimization problem. The most important question while using a mathematical model to represent practical industrial problems is to what extent these models represent the real-life situation. Computational models are always built on upon assumptions. Simply at looking at the simulation outcomes i.e. the graphical and numerical results, it is often very difficult to ensure if the underlying assumption holds and that the results are reliable. This has led to the development of another field of research known as Verification and Validation (called V&V in short).

We prove a quasi-pseudometric version of the strong Ekeland principle proved by P. Georgiev and T. Suzuki.

To understand the mystery of final unification, in our earlier publications, we proposed that, 1) There exist three atomic gravitational constants associated with electroweak, strong and electromagnetic interactions; and 2) There exists a strong interaction elementary charge (e_s) in such a way that, it's squared ratio with normal elementary charge is close to inverse of the strong coupling constant. In this context, starting from lepton rest masses to stellar masses, we have developed many interesting and workable relations. We noticed that, electroweak field seems to be operated by a primordial massive fermion of rest energy 585 GeV. It can be considered as the zygote of all elementary particles and galactic dark matter. Proceeding further, with a characteristic fermion-boson mass ratio of 2.27, quarks can be classified into quark fermions and quark bosons. Considering strong charge conservation and electromagnetic charge conservation, fractional charge quark fermions and quark bosons can be understood. Quark fermions that generate observable massive baryons can be called as Fluons. Quark bosons that generate observable mesons can be called as Bluons. By considering a new hadronic fermion of rest energy 103.4 GeV, rest masses of fluons and bluons can be estimated and there by baryon masses and meson masses can be estimated.

The literature analysis did not indicate any studies on fluorination tests of carbon nanocomposite coatings doped with transition metals of the nc-MeC/a-C type. This was the motivation for undertaking research in this area. As a model coating to investigate the effect of fluorination in a tetrafluoromethane (CF4) atmosphere, a nano-composite carbon coating doped with chromium nc-CrC/a-C produced by magnetron sputtering from graphite targets and the use of a Pulse-DC type medium frequency power supply was chosen [6]. After deposition of the gradient CrCN adhesive sublayer, fluorination of the main coating was conducted in a reactive mode in an (Ar+CF4) atmosphere at various CF4 contents. It was observed that the presence of CF4 in the atmosphere resulted in a reduced amount of chromium carbides formed in favor of chromium fluorides. So far, this is an observation that seems unnoticed by the carbon coatings researchers. Fluorine was assumed to bond much more readily to carbon than to chromium, due to the stability of tetrafluoromethane (CF4). The opposite seems to be true. The mechanical properties (nano-hardness and Young's modulus) and tribological properties in the 'pin-on-disc' friction pair are presented, along with the analysis of bonds occurring between chromium, carbon, and fluorine (XPS).

In the present work, a predictive modelling and optimization with the adaptive network based fuzzy inference system(ANFIS) modelling of mechanical properties of laser-coated NB/SiC/Ni welds was studied based on Taguchi design by laser cladding. An ANFIS model based on a Sugeno type fuzzy inference system was developed for predicting the hardness properties of SiC/BN/Ni welds by laser cladding with experimental data required for network training and prediction. Based on analysis of variance, three important factors were taken as inputs for the fuzzy logic inferences, while the hardness properties was taken as the output of the ANFIS. The microstructure of welds were analysed using scanning electron microscopy with an energy dispersive X-Ray spectrometer. Highly developed leaf-like dendrites and eutectic crystals were found in some areas of the melting zone for the BN/SiC/Ni weld, which was significantly hardened. The ANFIS model based on Taguchi's design provides a better pattern of response because the predicted and experimental values were highly similar. As a result, a satisfactory result was achieved between the predicted and experimental values of hardness in laser-coated NB/SiC/Ni welds, whereby the success and validity of the method was verified.

We demonstrate a new quantitative method to the sieve of Eratosthenes, which is an alternative to the sieve of Legendre. In this method, every element of a given set is sifted out once only, and therefore, this method is free of the Mobius function and of the parity barrier. Using this method, we prove that every sufficiently large even number is the sum of two primes, and that every even number is the difference of two primes in infinitely many ways.

In this paper, we introduce a new type of degenerate poly-Fubini polynomials and numbers, are called degenerate poly-Fubini polynomials and numbers, by using the degenerate polylogarithm function and derive several properties on the degenerate poly-Fubini polynomials and numbers. In the last section, we also consider the degenerate unipoly-Fubini polynomials attached to an arithmetic function, by using the degenerate polylogarithm function and investigate some identities of those polynomials. In particular, we give some new explicit expressions and identities of degenerate unipoly polynomials related to special numbers and polynomials.

In this paper, we construct the degenerate poly-Fubini polynomials, called the type 2 degenerate poly-Fubini polynomials, by using the modified degenerate polyexponential function and derive several properties on the degenerate poly-Fubini polynomials and numbers. In the last section, we introduce type 2 degenerate unipoly- Fubini polynomials attached to an arithmetic function, by using the modified degenerate polyexponential function and investigate some identities for those polynomials. Furthermore, we give some new explicit expressions and identities of degenerate unipoly polynomials related to special numbers and polynomials.

In this paper, we introduce a new class of Laguerre-based 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 Laguerre-based Hermite-Fubini numbers and polynomials by using generating functions.

Optical power splitters play a crucial role as the fundamental building blocks for many integrated optical devices. They should have low losses, broad bandwidth, and a high tolerance to fabrication errors. Adiabatic optical power splitters inherently possess these qualities while being compatible with foundry processes well-suited for mass-production. The long device lengths of adiabatic power splitters, however, are a limiting factor to achieve compact device sizes, which must be reduced. Here, we use a polynomial taper profile optimization algorithm to design 1×2 and 2×2 adiabatic power splitters with significantly shorter lengths than their adiabatic counterparts. The best performing 1×2 and 2×2 power splitters have 20 μm and 16 μm coupling lengths, respectively. Our designs have minimum feature sizes ranging from 140 nm to 200 nm, and our measurements averaged across 9 different chips show excellent consistency in performance for devices with 180 nm and 200 nm minimum features. Both the 1×2 and 2×2 adiabatic optical power splitters have excess losses less than 0.7 dB over a 100 nm bandwidth, with a standard deviation lower than 0.3 dB. Furthermore, our measurements show greater than 20 dB extinction ratios over 130 nm bandwidth. We also demonstrate the design of 1×2 power splitters with arbitrary splitting ratios, where splitting ratios ranging from 50:50 to 94:6 were achieved with standard deviations between 2% and 6%.

Surface initiated atom transfer radical polymerization (SI-ATRP) is one of the most versatile technique to modify the surface properties of material. Recent developed metal free SI-ATRP makes such technique more widely applicable. Herein photo-induced metal-free SI-ATRP of methacrylates, such as methyl methacrylate, N-isopropanyl acrylamide, and N,N- dimethylaminoethyl methacrylate, on the surface of SBA-15 was reported to fabricate organic-inorganic hybrid materials. SBA-15 based polymeric composite with adjustable graft ratio was obtained. The structure evolution during the SI-ATRP modification of SBA-15 was monitored and verified by FT-IR, XPS, TGA, BET, and TEM. The obtained polymeric composite showed enhanced adsorption ability for the model compound toluene in aqueous. This procedure provides a low cost, ready availability, and facile modification way to synthesize the polymeric composites without the contamination of metal.

One century ago, ferroelectricity and then piezoelectricity were discovered using Rochelle salt crystals. Today, modern societies are invited to switch towards a resilient and circular economy model. In this context, this work proposes a method to manufacture piezoelectric devices made from agro-resources such as tartric acid and polylactide significantly reducing the energy budget without requiring any sophisticated equipement. These piezoelectric devices are manufactured by liquid phase epitaxy grown Rochelle salt (RS) crystals into a 3D printed poly(Lactic acid) (PLA) matrix being the artificial squared meshes which mimic the natural wood anatomy. This composite material can easily be produced in any fablab with renewable materials and at low processsing temperatures, reducing then the total energy consumed. Manufactured biodegradable samples are fully recyclable and have good piezoelectric properties without any pooling step. The measured piezoelectric coefficients of manufactured samples are higher than many piezoelectric polymers such as PVDF-TrFE.

Hydrogen sulfide is present in active or extinct volcanic areas (mofettas). The habitable premises in these areas are affected by the presence of hydrogen sulfide, which, even in low concentrations, gives off a bad to unbearable smell. If the living spaces considered are closed enclosures, then a system can be designed to reduce the concentration of hydrogen sulfide. This paper presents a membrane way to reduce the hydrogen sulfide concentration to acceptable limits using a cellulosic derivative-propylene hollow fiber based composite membrane module. The cellulosic derivatives considered were carboxymethyl–cellulose (NaCMC), cellulose acetate (CA), methyl 2–hydroxyethyl–cellulose (MHEC), and 2–hydroxyethyl–cellulose (HEC). In the permeation module, hydrogen sulfide is captured with a solution of cadmium that forms cadmium sulfide, usable as a luminescent substance. The composite membranes were characterized by SEM, EDAX, FTIR, FTIR 2D maps, thermal analysis (TG and DSC) and from the perspective of hydrogen sulfide air removal performance. To determine the process performances, the variables were: the nature of the cellulosic derivative–polypropylene hollow fiber composite membrane, the concentration of hydrogen sulfide in the polluted air, the flow rate of polluted air, and the pH of the cadmium nitrate solution. Pertraction efficiency was maximum for the sodium carboxymethyl–cellulose (NaCMC)-polypropylene hollow fiber membrane, a hydrogen sulfide concentration in the polluted air of 20 ppm, polluted air flow rate of 50 L/min, and a pH of 2 and 4.

This study fabricated piezoelectric fibers of polyvinylidene fluoride (PVDF) with graphene using near-field electrospinning (NFES) technology. A uniform experimental design table U*7 (7^4 ) was applied, considering weight percentage (1-13 wt%), distance between needle and disk collector (2.1-3.9 mm), and applied voltage (14.5-17.5 kV). We optimized the parameters using electrical property measurements and the Kriging response surface method. Adding 13 wt% graphene significantly improved electrical conductivity, increasing from 17.7 μS/cm for pure PVDF to 187.5 μS/cm. The fiber diameter decreased from 21.4 μm in PVDF/1% graphene to 9.1 μm in PVDF/13% graphene. Adding 5 wt% graphene increased the β-phase content by 6.9%, reaching 65.4% compared to pure PVDF fibers. Material characteristics were investigated using scanning electron microscopy (SEM), Fourier-transform infrared spectroscopy (FTIR), X-ray diffraction analysis (XRD), contact angle measurements, and tensile testing. Optimal parameters included 3.47 wt% graphene, yielding 15.82 mV voltage at 5 Hz and 5 N force (2.04 times pure PVDF). Force testing showed a sensitivity (S) of 7.67493 log(mV/N). Fibers were attached to electrodes for piezoelectric sensor applications. Results affirmed enhanced electrical conductivity, piezoelectric performance, and mechanical strength. The optimized piezoelectric sensor could be applied to measure physiological signals, such as attaching it to the throat under different conditions to measure the output voltage. The force-to-voltage conversion facilitated subsequent analysis.

False news refers to false, fake, or misleading information presented as real news. In recent years, there has been a noticeable increase in false news on the Internet. The goal of this paper was to study the automatic detection of such false news using machine learning and natural language processing techniques and to determine which techniques work the most effectively. This article first studies what constitutes false news, and how it differs from other types of misleading information. We also study the results achieved by other researchers on the same topic. After building a foundation to understand false news, and the various ways of automatically detecting it, this article provides its own experiments. These experiments were done on four different datasets, one that was made just for this article, and using 10 different machine learning methods. The results of this article were satisfactory and provided answers to the original research questions set up at the beginning of this article. This article could determine from the experiments that passive-aggressive algorithms, support vector machines, and random forests are the most efficient methods for automatic false news detection. This article also concluded that more complex experiments, such as using multiple levels of identifying false news or detecting computer-generated false news, require more complex machine learning models.

This paper presents a new proof of the infinite nature of prime numbers. Grounded in fundamental Set theory and Analysis, the proof uses the method of contradiction to demonstrate the absurdity of assuming the set of all prime numbers to be finite.

This work is divided into two parts. In the first one the combinatorics of a new class of randomly generated objects, exhibiting the same properties as the distribution of prime numbers, is solved and the probability distribution of the combinatorial counterpart of the n-th prime number is derived, together with an estimate of the prime-counting function π(x). A proposition equivalent to the Prime Number Theorem (PNT) is proved to hold, while the equivalent of the Riemann Hypothesis (RH) is proved to be false with probability 1 (w.p. 1) for this model. Many identities involving Stirling numbers of the second kind and harmonic numbers are found, some of which appear to be new. The second part is dedicated to generalizing the model to investigate the conditions enabling both PNT and RH. A model representing a general class of random integer sequences is found, for which RH holds w.p. 1. The prediction of the number of consecutive prime pairs, as a function of the gap d, is derived from this class of models and the results are in agreement with empirical data for large gaps. A heuristic version of the model, directly related to the sequence of primes, is discussed and new integral lower and upper bounds of π(x) are found.

Herein, we report results of the study of the composite ferroelectric scaffolds based on vinylidene fluoride-tetrafluoroethylene copolymer (VDF-TeFE) and polyvinylpyrrolidone (PVP) produced by electrospinning and their application as a wound-healing material. The physicochemical properties of ferroelectric composite polymer scaffolds depending on the content of PVP (in the range from 0 to 50 wt %) including morphology, composition and crystalline structure were studied. The cytotoxicity of materials and the proliferative activity of cells during their cultivation on the surface of formed scaffolds are reported. It has been found that the optimal PVP content in the VDF-TeFE composite scaffolds is 15 wt%. On a model of a full-thickness contaminated wound in vivo, it was shown that piezoelectric scaffolds based on VDF-TeFE copolymer containing 15 wt% PVP provide better wound healing results in comparison with standard gauze dressings impregnated with a solution of an antibacterial agent.

Solid polymer electrolytes and composite polymer electrolytes serve as crucial components in all-solid-state energy storage devices. Structural batteries and supercapacitors present a promising alternative for electric vehicles, integrating structural functionality with energy storage capability. However, despite their potential, these applications are hampered by various challenges, particularly in the realm of developing new solid polymer electrolytes that require more investigations. In this study, novel solid polymer electrolytes and composite polymer electrolytes were synthesized using epoxy resin blends, ionic liquid, lithium salt, and alumina nanoparticles, and subsequently characterized. Among the formulations tested, the optimal system, designated as L70P30ILE40Li1MAl2 and containing 40 wt.% of ionic liquid and 5.7 wt.% of lithium salt, exhibited exceptional mechanical properties. It displayed a remarkable storage modulus of 1.2 GPa and reached ionic conductivities of 0.085 mS/cm at 60°C. Furthermore, a proof-of-concept supercapacitor was fabricated, demonstrating the practical application of the developed electrolyte system.

In this preliminary investigation, a concise molecular docking study using the Pyrx program screened thousands of compounds against the active site of HIV-1 reverse transcriptase. The Virtual Screening library was employed to assess binding energetics scores, focusing on identifying candidates with high Vina Scores. Eight compounds, including Tetrophan, Imatinib, Amentoflavone, Alprazolam, Bilobetin, Bafetinib, Nilotinib, and Ginketin, emerged as promising candidates with significant binding energies.Recognizing compounds that strongly bind to HIV-1 reverse transcriptase holds potential for antiretroviral drug development in the fight against HIV infection. Subsequently, the study evaluated the toxicity properties of these candidates using pKCSM. Amentoflavone, a natural biflavonoid found in Ginkgo biloba and Nilotinib, a tyrosine kinase inhibitor, demonstrated lower overall toxicity profiles compared to other candidates. Further toxicity analysis using Pro-Tox-II revealed Amentoflavone's higher predictive LD50, lower toxicity class, and reduced probabilities of hepatotoxicity, carcinogenicity, mutagenicity, and moderate immunotoxicity compared to Nilotinib. While Nilotinib, a pharmaceutical drug, exhibited higher probabilities of adverse effects in these categories. In summary, Amentoflavone and Nilotinib present as promising candidates with lower toxicity concerns. Amentoflavone, as a natural substance, showcases a more favorable toxicity profile than Nilotinib, offering valuable insights for potential therapeutic applications.

Gamba grass (Andropogon gayanus Kunth) is a tussock-forming forage species adapted to acid soils of Brazilian savannas and cultivated for grazing pastures. Four decades since its releasing, Planaltina prevails as the most commercialized cultivar of the species, even though the new cultivar BRS Sarandi could be a better alternative for Gamba grass-based farms by presenting greater leaf:stem ratio. The objective of this study was to evaluate the average daily live weight gain (ADG) of Nellore bulls (Bos indicus) for two Gamba grass cultivars – Planaltina and Sarandi. The experiment was conducted in Planaltina, Federal District, Brazil, during 3 years, namely 2018, 2018-2019 and 2020. The experimental design was completely randomized block with two treatments and three replicates, each one continuously stocked at three stocking rates (SR) - 1.3, 2.6 and 4 young bulls/ha. Canopy height (CH), forage mass (FM), plant-part proportion (leaf, stem and dead material) and nutritive value were evaluated. In 2018, mean ADG for Sarandi pastures was greater (0.690 kg/bull/d) than Planaltina (0.490 kg/bull/d) (P=0.0839). In the subsequent year (2018-2019), there was no effect of cultivar (P = 0.4089), while in 2020 the ADG was again affected by cultivar (P=0.0412), confirming the advantage of Sarandi (0.790 kg/bull/d) over Planaltina (0.650 kg/bull/d). In 2018 and 2020, the percentage of stems for Sarandi was about 3-6 pp lesser than for Planaltina (P

In this paper, we investigate p-adic q-integral (q-Volkenborn integral) on Z_p of p-adic gamma function via their Mahler expansions. We also derived two q-Volkenborn integrals of p-adic gamma function in terms of q-Daehee polynomials and numbers and q-Daehee polynomials and numbers of the second kind. Moreover, we discover q-Volkenborn integral of the derivative of p-adic gamma function. We acquire the relationship between the p-adic gamma function and Stirling numbers of the first kind. We finally develop a novel and interesting representation for the p-adic Euler constant by means of the q-Daehee polynomials and numbers.

This paper presents the results of laboratory tests of CFRP (carbon fibre-reinforced polymer) laminates, which allowed the development of numerical material models. The obtained data were used in a further stage to perform numerical simulations of four variants of medical tabletops differing, among other features, in the shape of the cross-section. Maximum deflections and effort in the composite material were analyzed. The final step was to perform a laboratory test for one of the tabletop versions, the results of which confirmed the correctness of the numerical calculations. This work is aimed at both researchers and designers involved in the practical application of fibre-reinforced polymer matrix composites.

This work is a natural extension of the author’s previous work: “Multiple scattering theory for heterogeneous elastic continua with strong property fluctuation: theoretical fundamentals and applications” (arXiv:1706.09137 [physics.geo-ph]), which established the foundation for developing multiple scattering model for heterogeneous elastic continua with either weak or strong fluctuations in mass density and elastic stiffness. Polycrystalline material is another type of heterogeneous materials that widely exists in nature and extensively used in industry. In this work, the corresponding multiple scattering theory for polycrystalline materials with randomly oriented anisotropic crystallites is developed. To validate the theory, the theoretical results for a series of materials such as OFHC copper, 304 stainless steel, and Inconel 600 are compared to experimental measurements and the numerical results obtained using finite element simulations. Detailed analysis shows that the new theory is capable of predicting the dispersion and attenuation of polycrystals with satisfactory accuracy. The results also show the new model can give an estimate on the average grain size with a relative error equal to or less than ten percent. As applications in ultrasonic nondestructive evaluation, we calculated the dispersion and attenuation coefficient of one of the most important polycrystalline materials in aeronautics engineering: high-temperature titanium alloys. The effects of grain symmetry, grain size, and alloying elements on the dispersion and attenuation behaviors are examined. Key information is obtained which has significant implications for quantitatively evaluating the average grain size, monitoring the phase transition, and even estimating gradual change in chemical composition of titanium components in gas turbine engines. For applications in seismology, the velocities and Q-factors for both hexagonal and cubic polycrystalline iron models for the Earth’s uppermost inner core are obtained in the whole frequency range. Using the realistic material parameters of iron under the high temperature and high-pressure conditions calculated from ab initio simulations, the numerical results show that the Q-factors range from 0.001 to 0.05, which shows good agreement with that inferred from real seismic data. The new model predicts the velocity of longitudinal waves varies between ± 1% to ± 5 % relative to the Voight average velocity, while the velocity of transverse waves varies from ± 10% to ± 20%, which gives promising explanation to the abnormally slow transverse velocity observed in practical measurements. The numerical results support the conjecture that the Earth’s uppermost inner core is a solid polycrystalline medium. The comprehensive numerical examples show the new model is capable of capturing the most important scattering features of both ultrasonic and seismic waves with satisfactory accuracy. This work provides a universal, quantitative model for characterization of a large variety of polycrystalline materials. It also can be extended to incorporate more complicated microstructures, including ellipsoidal grains with or without textures, and even multi-phase polycrystalline materials. The new model demonstrates great potential of applications in ultrasonic nondestructive evaluation and inspection of aerospace and aeronautic structures. It also provides a theoretical framework for quantitative seismic data explanation and inversion for the material composition and structural formations of the Earth’s inner core.

We present simple relations for nuclear stability and nuclear binding energy with respect to three gravitational constants associated with electroweak, strong and electromagnetic interactions.

The parts obtained by FFF technology are anisotropic in any direction; while the whole part constitutes out of layers, each of the layers include one or more perimeters of shell and the infill with density from 0 to 100%. Mechanical performance of FFF parts depends on its shape, orientation, constitution and 3D printing parameters. A classification for shapes of parts obtained by FFF and stressed during its operation is provided. For the most questionable class (parts with interrupted shell critically stressed on interlayer boundaries) a representative sample and testing apparatus is developed. Different approaches to the sample shape modification were applied and tested. The part shape optimization resulted in increment of the force, required to fracture the part from 483 to 1096 N.

In this paper we investigate some properties of square-free numbers. In particular, we study a function that counts the number of square-free numbers no larger than the given number n. We show that this function has asymptotics consistent with the predictions of the Riemann hypothesis and use this to obtain new and better estimates of the density of square-free numbers. Finally, we present a well-known generalization of the concept of a square-free number to monoids and research on square-free factorizations.

Motivation by the definition of the type 2 poly-Bernoulli polynomials introduced by Kim-Kim [9], in the present paper, we consider a new class of new generating function for the Fubini polynomials, called the type 2 poly-Fubini polynomials by means of the polyexponential function. Then, we derive some useful relations and properties. We show that the type 2 poly-Fubini polynomials equal a linear combination of the classical of the Fubini polynomials and Stirling numbers of the first kind. In a special case, we give a relation between the type 2 poly-Fubini polynomials and Bernoulli polynomials of order r. Moreover, inspired by the definition of the unipoly-Bernoulli polynomials introduced by Kim-Kim [9]. We introduce the type 2 unipoly-Fubini polynomials by means of unipoly function and give multifarious properties including derivative and integral properties. Furthermore, we provide a correlation between the unipoly-Fubini polynomials and the classical Fubini polynomials.

In this paper, we consider a new class of polynomials which is called the multi-poly-Euler polynomials. Then, we investigate their some properties and relations. We provide that the type 2 degenerate multi-poly-Euler polynomials equals a linear combination of the degenerate Euler polynomials of higher order and the degenerate Stirling numbers of the first kind. Moreover, we provide an addition formula and a derivative formula. Furthermore, in a special case, we acquire a correlation between the type 2 degenerate multi-poly-Euler polynomials and degenerate Whitney numbers.

Inspired by the definition of degenerate multi-poly-Genocchi polynomials given by using the degenerate multi-polyexponential functions. In this paper, we consider a class of new generating function for the degenerate multi-poly-Bernoulli polynomials, called the type 2 degenerate multi-poly-Bernoulli polynomials by means of the degenerate multiple polyexponential functions. Then, we investigate their some properties and relations. We show that the type 2 degenerate multi-poly-Bernoulli polynomials equals a linear combination of the weighted degenerate Bernoulli polynomials and Stirling numbers of the first kind. Moreover, we provide an addition formula and a derivative formula. Furthermore, in a special case, we acquire a correlation between the type 2 degenerate multi-poly-Bernoulli numbers and degenerate Whitney numbers.

Mathematical modelling of bioprocesses has a long and notable history, with eminent contributions from fields including microbiology, ecology, biophysics, chemistry, statistics, control theory and mathematical theory. This richness of ideas and breadth of concepts provide great motivation for inquisitive engineers and intrepid scientists to try their hand at modelling, and this collaboration of disciplines has also delivered significant milestones in the quality and application of models for both theoretical and practical interrogation of engineered biological systems. The focus of this review is the anaerobic digestion process, which, as a technology that has come in and out of fashion, still remains a fundamental process for addressing the global climate emergency. Whether with conventional anaerobic digestion systems, biorefineries, or other anaerobic technologies, mathematical models are important tools that are used to design, monitor, control and optimise the process. Both highly structured, mechanistic models and data-driven approaches have been used extensively over half a decade, but recent advances in computational capacity, scientific understanding and diversity and quality of process data, presents an opportunity for the development of new modelling paradigms, augmentation of existing methods, or even incorporation of tools from other disciplines, to ensure that anaerobic digestion research can remain resilient and relevant in the face of emerging and future challenges.

In this paper, we investigate p-adic q-integral (q-Volkenborn integral) on ℤ_{p} of p-adic gamma function via their Mahler expansions. We also derived two q-Volkenborn integrals of p-adic gamma function in terms of q-Daehee polynomials and numbers and q-Daehee polynomials and numbers of the second kind. Moreover, we discover q-Volkenborn integral of the derivative of p-adic gamma function. We acquire the relationship between the p-adic gamma function and Stirling numbers of the first kind. We finally develop a novel and interesting representation for the p-adic Euler constant by means of the q-Daehee polynomials and numbers.

In this paper, we introduce a new class of $(p,q)$-analogue type of Fubini numbers and polynomials and investigate some properties of these polynomials. We establish summation formulas of these polynomials by summation techniques series. Furthermore, we consider some relationships for $(p,q)$-Fubini polynomials associated with $(p,q)$-Bernoulli polynomials, $(p,q)$-Euler polynomials and $(p,q)$-Genocchi polynomials and $(p,q)$-Stirling numbers of the second kind.

In this paper, we investigate the new degenerate Daehee polynomials and numbers which are called the degenerate Daehee polynomials of the second kind, and derive some new and interesting identities and properties of those polynomials.

The main goal of the present paper is to construct some families of the Carlitz’s q-Bernoulli polynomials and numbers. We firstly introduce the modified Carlitz’s q-Bernoulli polynomials and numbers with weight (α, β) and investigate their some explicit properties and identities arising from the bosonic q-Volkenborn integral on ℤ_p. We then define the modified degenerate Carlitz’s q-Bernoulli polynomials and numbers with weight (α, β) and obtain some recurrence relations and other identities. Moreover, we derive some correlations with the modified Carlitz’s q-Bernoulli polynomials with weight (α, β), the modified degenerate Carlitz’s q-Bernoulli polynomials with weight (α, β), the Stirling numbers of the first kind and second kind.

In the paper, by the Faά di Bruno formula, several identities for the Bell polynomials of the second kind, and an inversion theorem, the authors simplify coefficients of two families of nonlinear ordinary differential equations for the generating function of the Catalan numbers and discover inverses of fifteen closely related lower triangular integer matrices.

In fuzzy decision problems, the ordering of fuzzy numbers is the basic problem. Among which, the fuzzy preference relation is the reasonable one to represent preference relation by a fuzzy membership function. This paper studies the Nakamura’s and Kołodziejczyk’s preference relations. Eight cases of representing different level of overlapping between two triangular fuzzy numbers are considered. We analyze the ranking behaviors of all possible combinations of decomposition and intersection of two fuzzy numbers for the Nakamura’s and Kołodziejczyk’s preference relations of these test cases. The results indicate that the decomposition and intersection can affect the fuzzy preference relations, thereby the final total order relation of fuzzy numbers.

In this article, the usual factorials and binomial coefficients have been generalized and extended to the negative integers. Basing on this generalization and extension, a new kind of polynomials has been proposed, which led directly to the non-classical hypergeometric orthogonal polynomials and the non-classical second-order hypergeometric linear DEs. The resulting polynomials can be used in non-relativistic and relativistic QM, particularly, in the case of the Schrödinger equation, and Dirac equations for an electron in a Coulomb potential field.

Biodegradable poly(ɛ-caprolactone) (PCL) and its composites or blends have gotten a lot of attention in the last decade because of their potential applications in human life and environmental remediation. As a result, there is a growing interest in the synthesis of PCL-composites/blends and their applications. Greater efforts have been made to develop biodegradable chemical materials as adsorbents that do not pollute the environment in order to replace traditional materials. Among the numerous types of degradable materials, PCL is currently the most promising, the most popular, and the best material to be developed, and it is referred to as the "green" eco-friendly material. Membranes and adsorbents for water treatment, packaging and compost bags, controlled drug carriers, biomaterials for tissues such as bone, cartilage, ligament, skeletal muscle, skin, cardiovascular and nerve tissues are just some of the applications of this biodegradable polymer (PCL). The goal of this review is to present a brief overview of PCL, its properties, syntheses of PCL, PCL composites, and PCL blends, but to provide a detailed investigation into the utility of PCL/PCL-based adsorbing agents in the removal of dyes/heavy metal ions.

Hybrid fiber reinforced composites can be controlled by price, weight and various mechanical properties depending on fiber ratio and lamination method. Despite these excellent hybrid properties, there is a disadvantage that inter-laminar fracture due to external impact, which is the biggest weakness of fiber reinforced composite materials, is weak. The test specimens were prepared by using a vacuum bag method, which is manufactured by using an autoclave device. The pre-preg is manufactured in the form of a B-stage. In the process of fabricating the nanoparticle pre-preg, the homogeneizer using an ultrasonic wave was used to disperse the epoxy subject without the curing agent into nanoparticles. The dispersion of the nanoparticles was dispersed by the weight of the epoxy resin. This is to take into account the cohesion of HNT and to understand the range of cohesion of HNT in a matrix with viscosity and its phenomenon. According to the Comparison of the interlayer interfacial properties and mechanical properties of Aramid / Basalt fiber hybrid composites by HNT addition, the fracture toughness, ILSS and bending strength of specimens with HNT content of more than a certain level were decreased because of the aggregation of HNT.

Epoxy matrix composites reinforced with high-performance fibers such as carbon, Kevlar, and glass, exhibit excellent specific stiffness and strength in many mechanical applications. However, these composites are disappointingly non-recyclable and are usually disposed of in landfill sites, with no realistic prospect for biodegradation in reasonable time. In contrast, moldable composites with carbonized elastomeric matrices developed in the last decades possess attractive mechanical properties in final net-shape products and can also be incinerated or recycled. Many carbon and inorganic fillers have recently been evaluated to adjust the properties of carbonized elastomeric composites. Renewable organic fillers such as human or animal hair offer an attractive fibrous material with substantial potential for reinforcing composites with elastomeric matrices. Samples of unidirectional fiber composites (with hair volume fraction up to 7 %) and quasi-isotropic short fiber composites (with hair volume fraction up to 20 %) of human hair-reinforced nitrile butadiene rubbers (HH-NBR) were produced in the peroxide-cured and carbonized states. The samples were characterized using SEM, Raman spectroscopy and photoacoustic microscopy. Mechanical tests were performed in tension using a miniature universal testing machine. The expected effect of fiber reinforcement on the overall mechanical performance has been demonstrated for both cured and carbonized composites. Considerable enhancement of the elastic modulus (up to 10 times), ultimate tensile strength (up to 3 times) and damage tolerance was achieved. The evidence of satisfactory interfacial bonding between hair and rubber was confirmed by SEM imaging of fracture surfaces. The suitability of photoacoustic microscopy was assessed for 3D reconstruction of the fiber sub-system spatial distribution and non-destructive testing.

Acoustic energy dissipates in multi-phase or multi-boundary materials. Hybrid composites are described as multi-phase with many interfaces between their materials. The current research proposes studying the acoustic behavior of polymeric hybrid composites by estimating the time, velocity, and hybrid composite acoustic impedance. Two groups of hybrid composites were prepared, including unsaturated polyester with PMMA, except one with HDPE and the other with PS. Each group has 28, 35, and 40% weight fractions. An ultrasonic test measured time to determine velocity and acoustic impedance later. The results show that increasing the weight fraction will increase density with respect to the density of the reinforcing material. Different ultrasonic times were obtained with increasing weight fractions. As the weight fraction of PS increased, the time increased; unlike the velocity, it decreased but increased with density. In contrast, this behavior was changed if the hybrid had PE. The highest acoustic impedance was at 28% UP/PMMA+PS. In conclusion, UP/PMMA+PS can dissipate ultrasonic waves more than UP/PMMA+PE.

In the present study, piecewise integrated composite (PIC) bumper beam for passenger cars was proposed and design optimisation process for composite bumper beam against IIHS test was carried out with the help of machine learning. Several elements in IIHS bumper FE model have been assigned to be references, in order to collect training data which, allow the machine learning model to study the method of predicting loading types of each finite element. 2-D and 3-D implementations were provided by machine learning models, which determined stacking sequences of each finite element in PIC bumper beam. It was found that the PIC bumper beam, which was designed by machine learning model has direct impact on reducing the possibility of failure as well as increasing bending strength effectively than conventional composite bumper beam. Moreover, 3-D implementation produced better results compared with 2-D implementation since it was preferable to choose loading type information which was achieved from surroundings when the target elements were located either at corner or junction of planes instead of using information came from the same plane of target.

We construct a repeated quantum game with public goods by the quantum entanglement and strong reciprocity. By using the paradigm of quantum game analysis, we obtain that both the quantum entanglement and strong reciprocity are helpful to intensify cooperation and achieving Pareto optimality. In addition, under an example which is greenhouse green viable planting industry, we verify that the quantum entanglement and strong reciprocity have a positive role in cooperation.

Controllable, quantum-strong correlations of polarization states can be implemented with multi-photon independent states. Polarization-based photonic quantum correlations can be traced back to the overlap of the polarization Stokes vectors on the Poincaré sphere between two polarization filters. The quantum Rayleigh scattering prevents a single photon from propagating in a straight line inside a dielectric medium, and it also provides a mechanism for the projective measurement of polarization. Complexities associated with single-photon sources and detectors can be eliminated because the quantum Rayleigh scattering in a dielectric medium destroys entangled photons. Entanglement-free, identical sources and processing devices give rise to correlations rather than these being caused by “quantum nonlocality”. These analytic developments were prompted by the vanishing expectation values of the Pauli spin vector for a single photon of maximally entangled photonic Bell states.

Chess is an interesting game for artificial intelligence research and an entertaining hobby and sport for a growing number of people. However, humans differ greatly in their ability to play. Typically, the Elo rating is used to determine a player's skill and to predict who will win. When differences in Elo are too great the weaker player is almost guaranteed to lose. While on one hand, the Elo rating allows players to be matched to equally well-playing opponents, it also to some degree restricts the games to be played between equally strong opponents since otherwise the result is known beforehand. Here a handicap system where stronger players remove pieces at the start of the game is evaluated. Specifically, the effect each removed piece or combination of pieces have on a player. Interestingly, pieces do not always reduce the Elo of a player by a predefined amount, but their effect depends strongly on the player's current Elo. The results presented here are from playing the computer engine Stockfish because data about humans playing this scheme is limited. However, the results make direct predictions about the effect of piece removal on Elo.

The purpose of this paper is to bring to light a method through which the global in time existence for arbitrary large in H¹ initial data of a strong solution to 3D periodic Navier-Stokes equations follows. The method consists of subdividing the time interval of existence into smaller sub-intervals carefully chosen. These sub-intervals are chosen based on the hypothesis that for any wavenumber m, one can find an interval of time on which the energy quantized in low-frequency components (up to m) of the solution u is lesser than the energy quantized in high-frequency components (down to m) or otherwise the opposite. We associate then a suitable number m to each one of the intervals and we prove that the norm ||u(t)||_H1 is bounded in both mentioned cases. The process can be continued until reaching the maximal time of existence T_max which yields the global in time existence of strong solution.

The new hybrid composite materials for PEM fuel cell were synthesized by UV-polymerization of acrylic monomers (acrylonitrile (AN), acrylic acid (AA), ethylene glycol dimethacrylate (EGDMA)) and sulfo aromatic monomer – sodium styrene sulfonate (SSS), and tetraethoxysilane/3-methacryloxypropyltrimethoxysilane (TEOS/MAPTMS)-based sol-gel system. By means of X-ray spectroscopy fractal structure of the obtained materials was characterized. Proton conductivity and viscoelastic properties of the materials were investigated depending on the content of inorganic component in nanocomposites. On the basis of impedance studies, an equivalent scheme is proposed that successfully describes the proton conductivity in the synthesized composite electrolyte membranes.

In this article, we discuss the concept of infinity (∞), infinitesimals □ , and a new mathematical operation that expands calculations into the realm of the infinite. This breakthrough allows for the computation of infinite numbers, leading to new possibilities for mathematical research and practical applications. By introducing infinite numbers, numerous advantages arise, such as accurately representing limits, divergences in integrals and infinite series, and extending calculations to infinity. This mathematical advancement opens doors to exploring uncharted territories, offering valuable insights and breakthroughs.

We developed some questions regarding twin prime conjecture by examining the bounded gaps between composite numbers and explained the relations between the formulas regarding composite numbers. Then we proved the twin prime conjecture to answer the new questions raised by proving the expression: \[ \liminf_{n\to\infty} (c_n_+_1 - c_n) \ge 10. \] In addition, we prove many different approaches have been and it has been proved that there must be a twin prime in the range $(p_k_2\cdot p_k_1, p^2_k_1)$, where $p \neq 2$.

This short technical note proves some observed novel corollaries of the Collatz Conjecture. For this, a unique ‘Collatz Representation’ of Hailstone numbers has been employed. After that, an extension of this corollary is explained using the fact that only certain differences in the last digit of the ‘Collatz Representation’ gives a whole number difference between numbers. A more general result is obtained. The final proof is for a corollary that some numbers the same number of steps to reach 1 if the Collatz Conjecture is true and all variables are whole numbers.

Starting with a positive odd integer $n$, apply a function $f(n)$ repetitively such that $f(n) = 3n + 1$ if $n \not\equiv 0 (\text{mod}\:2)$ or $f(n) = n/2$ if $n \equiv 0 (\text{mod}\:2)$. Let the sequence of all the odd integers obtained form an orbit $n, f^1(n) , f^2(n), \ldots, f^k(n), f^{k + 1}(n)$. The $k^{th}$ odd integer is written as $f^k(n) = (3^k + \mathbf{B(k)})/2^{\mathbf{z(k)}}$ where $\mathbf{B(k)}$ is the collection of terms without the coefficient $n$. We show that when $1 - \mathbf{B(k)}/(2^{\mathbf{z(k)}} n) \approx 1$, the condition for unbounded orbit is given by OEIS A022921. Further, if there exists at least one orbit for which $f^{k + 1}(n) = n$ when $(k + 1) < 3$, we show that there exists no orbit with $k + 1 > 3$ for which $f^{k + 1}(n) = n$. The final result is that the odd integers that can violate the Collatz conjecture are smaller than 5.

For each non-prime odd number as F=pq , if we consider m/n as an approximation for q/p and choose k=mn , then by proving some lemmas and theorems, we can compute the values of m and n. Finally, by using Fermat’s factorization method for F and 4kF as difference of two non-consecutive natural numbers, we should be able to find the values of p and q. Then we introduce two new and powerful sieves for separating composite numbers from prime numbers.

In standard construction of hyperrational numbers using ultra-power we assume that the ultralter is selective. It makes possible toassign real value to any nite hyperrational number. So, we can consider hyperrational numbers with selective ultralter as extension of traditional real numbers. Also proved the existence of strictly monotonic or stationary representing sequence for any hyperrational number.

In fuzzy group decision making problems and fuzzy shortest path problems, the addition and subtraction are the basic problems. For the mixed normal fuzzy numbers and trapezoidal fuzzy numbers, the addition and subtraction operations are approximated by the normal fuzzy numbers in this paper. The behaviors of approximated normal fuzzy numbers are the same as those of the normal distributions from the viewpoint of probability. An application of the addition and subtraction operations of mixed fuzzy numbers to the fuzzy sample mean is also proposed.

Upholstery nonwoven fabric is a waste product mainly generated during upholstered furniture production. The polyester composition makes it problematic to recycle and reuse this product. This study examined the manufacturing process of nonwoven fabric-reinforced plywood composites and their selected mechanical and physical properties. Nonwoven fabric was integrated between veneers bound with urea-formaldehyde resin to improve standard layered composites' mechanical and physical properties. Several board variants were produced, differing in the position of the nonwoven layers in the composite structure. The composites were evaluated for modulus of rupture (MOR), modulus of elasticity (MOE), and screw withdrawal resistance, among others. The results showed that the addition of nonwoven fabric significantly improved some properties. Variants with strategically placed nonwoven layers showed the highest performance increases. The results underscore the potential of nonwoven fabric as an effective reinforcing material, offering a path to developing high-performance plywood composites suitable for demanding applications. Another, environmental profit is that the nonwoven fabric waste, that was used in tested plywood production, has not been subjected burning nor landfilling, but, by incorporation to plywood structure, have positively contributed to Carbon Capture and Storage (CCS) policy. The findings advocate for a circular economy approach, where industrial waste is effectively repurposed, contributing to the development of green materials in the wood-based composite industry.

Weather radar plays a crucial role in the monitoring of severe convective weather. However, due to its limited detection range, it cannot conduct effective monitoring in remote offshore areas. Therefore, this paper utilized the Unet++ to establish a model for retrieving radar composite reflectivity based on Himawari-9 satellite datasets. In the process of comparative analysis, we found that both satellite and radar data exhibit significant diurnal cycles, but there are notable differences in their variation characteristics. To address this, we established 4 comparative models to test the influence of latitude and diurnal cycles on the inversion results. The results show that adding the distribution map of the minimum cloud-top brightness temperature at the corresponding time in the model can effectively reduce the root mean square error (RMSE) of the model and enhance the accuracy of severe convective weather monitoring. This conclusion can be applied in the future to enhance and improve satellite quantitative precipitation estimation.

The main aim of this work is to report an alternative energy efficient technique of fabricating flexible thermoelectric generators (TEGs) using printable ink. In this process, we have fabricated thermoelectric (TE) composite thick film and we are experimenting several ways to overcome the challenges of conventional and additive manufacturing methods. Two different mesh sizes of n-type bismuth particle, various binder to thermoelectric (TE) material weight ratio, and two different pressure (200 MPa and 300 MPa) were employed for optimizing the thermoelectric properties of TE composite films. We are also exploring naturally occurring chitosan as a binder. Dimethyl sulfoxide (DMSO) dissolved chitosan was used for the binder and less than 0.2 wt% of chitosan was sufficient for the fabrication of TE inks and composite films. Low energy intensive curing process was employed to evaporate the solvent from the drop casted inks. External uniaxial pressure not only eliminated high energy intensive curing processes but also increased the packing density of the film by removing pores and voids in the chitosan-bismuth composite film. The microstructure analysis reveals that bulk-like structure, which rarely has voids, pores and grain boundaries, was observed in the composite films pressed at sufficiently high pressures. The highest performing composite film was obtained with the conditions of 1:2000 binder to bismuth weight ratio, 100 mesh of particle size, and 300 MPa of pressure. The best performing bismuth chitosan composite film pressed at 300 MPa had the power factor as 4009 ± 391 μW/m·K² with high electrical conductivity value of 7337 ± 522 S/cm. The measured thermal conductivity of the best performing chitosan-bismuth composite film was 4.4 ± 0.7 W/m·K and the figure of merit calculated from the thermal conductivity was 0.27 at room temperature.

In this paper a robust version of the Wald test statistic for composite likelihood is considered by using the composite minimum density power divergence estimator instead of the composite maximum likelihood estimator. This new family of test statistics will be called Wald-type test statistics. The problem of testing a simple and a composite null hypothesis is considered and the robustness is studied on the basis of a simulation study. Previously, the composite minimum density power divergence estimator is introduced and its asymptotic properties are studied.

Inspired by the process of bone formation in living organisms, many studies have been conducted to develop organic-inorganic composite materials by generating calcium phosphate crystals within solutions or dispersions of polymers with appropriate functional groups. Bones are composite materials consisting of organic polymers (mainly Type I collagen), carbonated apatite, and water, with volume fractions 35-45%, 35-45%, 15-25%, respectively. Carbonated apatite in bone contributes to rigidity, while organic polymers and water contribute to toughness. The inorganic crystal, carbonated apatite, is a plate-shaped crystal with dimensions of 50 nm × 25 nm × 1-4 nm, generating a significant organic-inorganic interface due to its nanoscale size. This interface is believed to absorb externally applied forces to dissipate mechanical energy to thermal energy. Creating such nanometer-scale structures using top-down approaches is challenging, making bottom-up methods like co-precipitation of polymer and inorganic crystals more suitable. In this account, efforts to develop eco-friendly mechanical materials using biomass such as cellulose and starch based on the bottom-up approach to bone-like composites are described.

The strong coupling between individual quantum emitters and resonant optical micro/nanocavities is beneficial to understand light and matter interactions. Here we propose a plasmonic nanoantenna placed on a metal film to achieve an ultra-high electric field enhancement in the nanogap and ultra-small optical mode volume. The strong coupling between a single quantum dot and the designed structure is investigated in detail by both numerical simulations and theoretical calculations. When a single QD is inserted into the nanogap of the silver nanoantenna, scattering spectra show remarkably large spectral splitting and typical anti-crossing behavior of the vacuum Rabi splitting, which can be realized in the scattering spectra by varying the nanoantenna thickness. Our work shows a possible way to enhance light-matter interaction at a single quantum emitter limit, which can be useful for future quantum and nanophotonic applications.

The evidence is presented for the long-range previtreous changes of two static properties: dielectric constant ( ) and its strong electric field related counterpart - the nonlinear dielectric effect (NDE). Notable is the evidence for the functional characterizations of (T) temperature changes by the ‘Mossotti Catastrophe’ formula, and NDE vs. T evolution by the relations resembling one developed for critical liquids. The analysis of dynamic properties based on the activation energy index excluded the Vogel-Fulcher-Tammann (VFT) relation as a validated tool for portraying the evolution of the primary relaxation time. Such a result questions the commonly applied ‘Stickel operator’ routine as the reliable tool for determining the dynamic crossover temperature. It is worth stressing that the strong electric field radically affects the distribution of relaxation times, the form of the evolution of the primary relaxation time as well as the fragility. Obtained results support the concept of a possible semi-continuous phase transition hidden below Tg. Studies were carried out in supercooled squalene, the material with extremely low electric conductivity, strongly elongated molecule, and vitally important for biology and medicine related issues.

An attempt is made to model the atomic nucleus as a combination of bound and free or unbound nucleons. Due to strong interaction, bound nucleons help in increasing nuclear binding energy and due to electroweak interaction, free or unbound nucleons help in decreasing nuclear binding energy. In this context, with reference to proposed 4G model of final unification and strong interaction, recently we have developed a unified nuclear binding energy scheme with four simple terms, one energy coefficient of 10.1 MeV and two small numbers 0.0016 and 0.0019. In this paper, by eliminating the number 0.0019, we try to fine tune the estimation procedure of number of free or unbound nucleons pertaining to the second term with an energy coefficient of 11.9 MeV. It seems that, some kind of electroweak interaction is playing a strange role in maintaining free or unbound nucleons within the nucleus. It is possible to say that, strong interaction plays a vital role in increasing nuclear binding energy and electroweak interaction plays a vital role in reducing nuclear binding energy. Interesting observation is that, Z can be considered as a characteristic representation of range of number of bound isotopes of Z. For medium, heavy and super heavy atoms, beginning and ending mass numbers pertaining to bound states can be understood with 2Z+0.004Z^2 and 3Z+0.004Z^2 respectively. With further study, neutron drip lines can be understood. Based on this kind of data fitting procedure and by considering the mass ratio of pions and electroweak bosons, existence of our 4G model of electroweak fermion of rest energy 584.725 GeV can be confirmed confidently.

Scattering of elastic waves in heterogeneous media has become one of the most important problems in the field of wave propagation due to its broad applications in seismology, natural resource exploration, ultrasonic nondestructive evaluation and biomedical ultrasound. Nevertheless, it is one of the most challenging problems because of the complicated medium inhomogeneity and the complexity of the elastodynamic equations. A widely accepted model for the propagation and scattering of elastic waves, which properly incorporates the multiple scattering phenomenon and the statistical information of the inhomogeneities is still missing. In this work, the author developed a multiple scattering model for heterogeneous elastic continua with strong property fluctuation and obtained the exact solution to the dispersion equation under the first-order smoothing approximation. The model establishes an accurate quantitative relation between the microstructural properties and the coherent wave propagation parameters and can be used for characterization or inversion of microstructures. Starting from the elastodynamic differential equations, a system of integral equation for the Green functions of the heterogeneous medium was developed by using Green’s functions of a homogeneous reference medium. After properly eliminating the singularity of the Green tensor and introducing a new set of renormalized field variables, the original integral equation is reformulated into a system of renormalized integral equations. Dyson’s equation and its first-order smoothing approximation, describing the ensemble averaged response of the heterogeneous system, are then derived with the aid of Feynman’s diagram technique. The dispersion equations for the longitudinal and transverse coherent waves are then obtained by applying Fourier transform to the Dyson equation. The exact solution to the dispersion equations are obtained numerically. To validate the new model, the results for weak-property-fluctuation materials are compared to the predictions given by an improved weak-fluctuation multiple scattering theory. It is shown that the new model is capable of giving a more robust and accurate prediction of the dispersion behavior of weak-property-fluctuation materials. Numerical results further show that the new model is still able to provide accurate results for strong-property-fluctuation materials while the weak-fluctuation model is completely failed. As applications of the new model, dispersion and attenuation curves for coherent waves in the Earth’s lithosphere, the porous and two-phase alloys, and human cortical bone are calculated. Detailed analysis shows the model can capture the major dispersion and attenuation characteristics, such as the longitudinal and transverse wave Q-factors and their ratios, existence of two propagation modes, anomalous negative dispersion, nonlinear attenuation-frequency relation, and even the disappearance of coherent waves. Additionally, it helps gain new insights into a series of longstanding problems, such as the dominant mechanism of seismic attenuation and the existence of the Mohorovičić discontinuity. This work provides a general and accurate theoretical framework for quantitative characterization of microstructures in a broad spectrum of heterogeneous materials and it is anticipated to have vital applications in seismology, ultrasonic nondestructive evaluation and biomedical ultrasound.

Timber-concrete composite (TCC) systems join the positive aspects of engineered wood products (good seismic behaviour, low thermal conductivity, environmental sustainability, good behaviour under fire if appropriately designed) with those of concrete (high thermal inertia, durability, excellent fire resistance). TCC facades are typically composed by an internal insulated timber-frame wall and an external concrete slab, separated by a ventilated air cavity. However, there is very limited knowledge concerning the performance of TCC facades, especially for what concerns their thermal behaviour. The present paper deals with the development and optimisation of a 2D CFD model for the analysis of TCC ventilated façades thermal behaviour. The model is calibrated and validated against the experimental data collected during the annual monitoring of a real TCC ventilated envelope in the north of Italy. Also, a new solver algorithm is developed to significantly speed up the simulation. The final model can be used for the time-efficient analysis and optimisation of the thermal performance of TCC ventilated facades, as well as other ventilated facades with external massive cladding, avoiding the expensive and time-consuming construction of mock-ups, or the use of comparably slow (conventional) CFD solvers that are less suitable for optimization studies.

Monitoring the integrity of aeronautical structures is fundamental for safety. Structural Health Monitoring Systems (SHMS) perform real-time monitoring functions, but their performances must be carefully assessed. In this work the damage detection performances of a strain-based SHMS, were evaluated on a composite helicopter rotor blade root. The SHMS monitored the bonding between the central core and the surrounding antitorsional layer. A damage detection algorithm was trained through Finite Element analyses performed on the component. The effects of the loads variability and of damages were decoupled by including a load recognition step in the algorithm. Load recognition was accomplished in different ways: version#1 adopted an Artificial Neural Network (ANN) trained on blades in pristine condition; version#2 was trained also on damaged blades; version#3 adopted a calibration matrix method. Anomaly detection, damage assessment, and localization were performed by using an ANN. Results showed a higher load identification and anomaly detection accuracy for version#1 and version#2 compared to version#3. Gaussian noise reduced anomaly detection and damage assessment performances, and reduced damage localization accuracy for bigger damages. The damage detection performance were obtained for a fibre optic based-SHMS, including the trade-off between probability of detection and false alarm rate for different damage sizes.

Phage therapeutics offer a potentially powerful approach to combat multidrug-resistant bacterial infections. However, to be effective, phage therapy must overcome existing and developing phage resistance. While phage cocktails can reduce this risk by targeting multiple receptors in a single therapeutic, bacteria have mechanisms of resistance beyond receptor modification. A rapidly growing body of knowledge describes a broad and varied arsenal of antiphage systems encoded by bacteria to counter phage infection. We sought to understand the types and frequencies of antiphage systems present in a highly diverse panel of Pseudomonas aeruginosa clinical isolates utilized to characterize novel antibacterials. Using web-server tool PADLOC (Prokaryotic Antiviral Defense Locator), putative antiphage systems were identified in these P. aeruginosa clinical isolates based on sequence homology to a validated and curated catalog of known defense systems. Coupling this host bacterium sequence analysis with host range data for 70 phages, we observed a correlation between existing phage resistance and the presence of higher numbers of antiphage systems in bacterial genomes. We were also able to identify antiphage systems that were more prevalent in highly phage-resistant P. aeruginosa strains, suggesting their importance in conferring the resistance.

The 3x+1 problem asks the following: Suppose we start with a positive integer, and if it is odd then multiply it by 3 and add 1, and if it is even, divide it by 2. Then repeat this process as long as you can. Do you eventually reach the integer 1, no matter what you started with? Collatz conjecture (or 3n+1 problem) has been explored for about 85 years. In this paper, we convert an integer number from decimal to binary number, and convert the Collatz function to binary function, which is multiplication and division of two binary numbers. Finally the iternation of the Collatz function, eventually reach the integer 1, thus we solve the 3x+1 problem completely.

Kim-Kim [12] introduced the new type of degenerate Bernoulli numbers and polynomials arising from the degenerate logarithm function. In this paper, we introduce a new type of degenerate poly-Euler polynomials and numbers, are called degenerate poly-Euler polynomials and numbers, by using the degenerate polylogarithm function and derive several properties on the degenerate poly-Euler polynomials and numbers. In the last section, we also consider the degenerate unipoly-Euler polynomials attached to an arithmetic function, by using the degenerate polylogarithm function and investigate some identities of those polynomials. In particular, we give some new explicit expressions and identities of degenerate unipoly polynomials related to special numbers and polynomials.

In this study, the elastic properties of composite materials are investigated, considering the effects of separation of fiber-matrix joint boundary and matrix failure. In this method, by assuming periodic microstructure and using a linear approximation of the displacement field by applying continuity and equilibrium conditions, the composite fiber composite relation is determined. The effect of separation is assumed by introducing tangential and normal scalar parameters in the equations by assuming the displacement field jump at the common boundary. In order to express the effect of matrix micro-cracks, the fracture mechanics framework of continuous environments was used and the micro-cracks parallel to the fibers, perpendicular to the fibers and in the thickness direction with scalar parameters were expressed. At the end of the effect of these parameters the results are presented in graphs. The results show that the presence of defective joint at the joint boundary and the matrix micro-components reduce the hardness of the composite and thus it’s bearing load, which is more significant at the defective joint state.

The first paper of this two-part series paper discussed the development of a novel lightweight 3D wood dowel-reinforced glass epoxy hybrid composite material (3DdrFRP) and its manufacturing procedures. It also experimentally compared the performance of scaled utility poles made from conventional 2D E-glass epoxy and 3DdrFRP materials. In the second part, we developed robust finite element (FE) models in LS-DYNA, calibrated them based on experimental results, and used them to simulate the performance of equivalent 2D and 3D poles, proving the integrity of the numerical model. Additionally, we developed a simplified analytical calculation method for engi-neers to determine the stiffness of 3D-DrFRP poles accurately and quickly.

In this paper, various Ni-P composite coatings containing toner, MoS2, and nano-SiO2 particles were deposited on steel substrates by the electroless method. Then, the electrochemical properties of these coatings after a heat treatment process were compared. The microstructural evaluations were also done by using the optical and electron microscopy methods. Both Tafel polarization and electrochemical impedance spectroscopy techniques were utilized to survey the electrochemical behavior of such coatings. The surface morphology of all coatings contained cauliflower-like nodules. The X-ray diffraction patterns showed the crystalline phases of Ni and Ni3P for all coatings after the heat-treatment step. Obtained results showed that all composite coatings exhibited lower corrosion rates with respect to Ni-P coatings. Such a reduction was about 21.6-92.2%. This behavior was attributed to the presence of reinforcement as barriers for corrosive ion diffusion through the coating plus the changes in detected phases and thickness. Electrochemical impedance spectroscopy test results also demonstrated that the increase in the polarization resistance for composites coatings was about 18.4-85.3% after 1 h immersion in a 0.6M NaCl solution; however, when the immersion time increased to 24 h, such increased resistance changed to 18.1 to 73.1%. Totally, despite the lower deposition rate, the presence of MoS2 and nano-SiO2 particles were more effective than toner particles to raise the corrosion rate of the Ni-P coating.

The idea of strong and weak adjacencies between vertices has been generalized into fuzzy graphs and intuitionistic fuzzy graphs (IFGs) and it is an important part of making decisions. However, one or two membership degrees are not always sufficient for making decisions on real-world problems that need an answer of types “yes, neutral, and no". Consequently, in previous work, we generalized the concept into picture fuzzy graphs (PFGs) where each element in the PFG has membership, neutral, and non-membership degrees. Moreover, we constructed the notion of the coloring of PFGs based on strong and weak adjacencies between vertices. In this paper, we investigate some properties of the chromatic number of PFGs based on the concept of strong and weak adjacencies between vertices. According to the properties, we construct an algorithm to find the chromatic number of PFGs. The algorithm is usefull when we work with large PFGs. Further, we improve the method to implement the PFG’s coloring for determining traffic signal phasing at an intersection. A case study has also been done to evaluate the method.

In the present study, hypereutectic Al-Si alloy compacts and Al-Si/B4C composites were produced by conventional, microwave and spark plasma sintering techniques. The effects of sintering techniques and B4C particle addition on microstructural properties, density, hardness and electrical conductivity were investigated. The microstructures were examined with an optical microscope. Densities were measured using the Archimedes technique. Electrical resistance measurements were made with the four-point probe measurement technique. Elemental Al grains, master alloy grains and primary Si particles were determined in the microstructures of all samples. The addition of 15 wt% B4C caused the porosity rate to increase in the samples. Samples produced with SPS technique gave ≈80% higher hardness values than samples produced with CS and MWS. Compared to the samples produced with CS and MWS, the samples produced with SPS gave higher electrical conductivity values. Electrical conductivities were decreased as the weight percentage of B4C increased in all samples.

The article presents a method for obtaining new composites using a well-known mineral, expanded perlite (EP), and an industrial polymer, butadiene rubber (BR). For the design of composites, a joint oxidative chlorophosphorylation reaction of BR and EP (as well as BR and modified EP) was carried out, and the modifications obtained from this reaction were further hydrolyzed. The structure and morphology of the obtained samples were characterized in detail using Fourier transform infrared spectroscopy, ultraviolet-visible spectroscopy, X-ray powder diffraction, as well as scanning electron microscopy, and energy-dispersive X-ray analysis. EP and BR were separately modified with a similar reaction and characterized for data interpretation.

Nano/micron-sized bioactive glass (BG) particles are attractive candidates for both soft and hard tissue engineering. They can chemically bond to the host tissues, enhance new tissue formation, activate cell proliferation, stimulate the genetic expression of proteins, and trigger unique an-ti-bacterial, anti-inflammatory, and anti-cancer functionalities. Recently, composites based on bi-opolymers and BG particles have been developed with various state-of-the-art techniques for tis-sue engineering. Gelatin, a semi-synthetic biopolymer, has attracted the attention of researchers because it is derived from the most abundant protein in the body, viz., collagen. It is a polymer that can be dissolved in water and processed to acquire different configurations, such as hydro-gels, fibers, films, scaffolds, etc. Searching "bioactive glass gelatin" in the tile on Scopus renders 80 highly relevant articles published in the last ~10 years, which signifies the importance of such composites. First, this review addresses the basic concepts of soft and hard tissue engineering, in-cluding the healing mechanisms and limitations ahead. Then, current knowledge on gelatin/BG composites including composition, processing and properties is summarized and discussed both for soft and hard tissue applications. This review explores physical, chemical and mechanical features and ion-release effects of such composites concerning osteogenic and angiogenic respons-es in vivo and in vitro. Additionally, recent developments of BG/gelatin composites using 3D/4D printing for tissue engineering are presented. Finally, the perspectives and current challenges in developing desirable composites for the regeneration of different tissues are outlined.

Some time ago, Kobayashi et al. experimentally studied the so-called Lee-Naughton-Lebed's (LNL) angular effect in strong electric fields [K. Kobayashi, M. Saito, E. Omichi, and T. Osada, Phys. Rev. Lett. \textbf{96}, 126601 (2006)]. They found that strong electric fields split the LNL conductivity maxima in $\alpha$-(ET)$_2$-based organic conductor and hypothetically introduced the corresponding equation for conductivity. In this Letter, for the first time we suggest quantum mechanical theory of the LNL angular oscillations in moderately strong electric fields. In particular, we demonstrate that the obtained by us approximate theoretical formula coincides with the hypothetical one and well describes the above mentioned experiments.