This article successfully synthesized a polymer adsorbent TOC containing S functional groups through thiophene and ethanedioyl chloride. The TOC was characterized by IR, molecular weight determination, EDS, SEM, and TG. For Pb(II), the maximum adsorption capacity of TOC can reach 122.7 mg/g (0.593 mmol/g) at pH=4, 250 minutes. After adsorption, it can be desorbed with 1.00 mol/L HCl, and the adsorbent can be reused 10 times; For Cu(II), the maximum adsorption capacity of TOC can reach 95.9mg/g (1.498mmol/g) at pH=6, 180min. After adsorption, it can be desorbed with 0.50 mol/L HNO3, and the adsorbent can be reused 11 times. The adsorption process of TOC on Pb(II) and Cu(II) conforms to the Freundlich model of multi-layer adsorption and the chemical adsorption process controlled by pseudo-second-order kinetic reactions.

The famous Toms effect (1948) consists of a substantial increase of the critical Reynolds number when a small amount of soluble polymer is introduced into water. The most noticeable influence of polymer additives is manifested in the boundary layer near solid surfaces. The goal of the present paper is a group analysis of the boundary layer equations in two mathematical models of the flow of aqueous polymer solutions: the second grade fluid (Rivlin and Ericksen, 1955) and the model derived by Pavlovskii (1971). The equations of the unsteady two-dimensional boundary layer in the Pavlovskii and Rivlin-Ericksen models are analyzed for the first time here. These equations have no definite type so that finding their exact solutions is very important in order to understand the mathematical nature of the above mentioned models. The problem of group classification with respect to the arbitrary function of the longitudinal coordinate and time present in the equations, which sets the pressure gradient of the external flow, arises. All functions for which an extension of the admitted Lie group occurs are found. The task includes the ratio of two characteristic length scales. One of them is the Prandtl scale, and another is defined as the square root of the normalized coefficient of relaxation viscosity (Frolovskaya and Pukhnachev, 2018) and does not depend on the characteristics of the motion. The paper contains a number of exact solutions in the Pavlovskii model including a solution describing the flow near a critical point. Among the solutions of the new model of the boundary layer, a special place is taken by the solution of the stationary problem of flow around a rectilinear plate. Within the framework of the Prandtl theory of the boundary layer, such a solution was constructed by Blasius (1908). As is well-known, this solution has a non-removable defect: the transverse velocity near the edge of the plate increases without bound. The introduction of a relaxation term into the model makes it possible to eliminate this singularity.

Parkinson’s Disease (PD) is a debilitating neurodegenerative disease, causing loss of motor function, and in some instances, cognitive decline and dementia, in those affected. The quality of life can be improved, and disease progression delayed through early interventions, however, current methods of confirming a PD diagnosis are extremely invasive. This prevents their use as a screening tool for the early onset stages of PD. We propose a surface imprinted polymer (SIP) electroimpedance spectroscopy (EIS) biosensor for detecting α-Synuclein (αSyn) and its aggregates, a biomarker that appears in saliva and blood during the early stages of PD as the blood brain barrier degrades. The surface imprinted polymer stamp is fabricated by low temperature melt stamping polycaprolactone (PCL) on interdigitated EIS electrodes. The result is a low-cost, small footprint biosensor that is highly suitable for non-invasive monitoring of the disease biomarker. The sensors were tested with αSyn dilutions in deionized water, and in constant ionic concentration matrix solutions with decreasing concentrations of αSyn to remove the background effects of concentration. The device response confirmed the specificity of these devices to the target protein of monomeric αSyn. The sensor limit of detection was measured to be 5 pg/L and its linear detection range was 5 pg/L – 5 µg/L. This covers the physiological range of αSyn in saliva and makes this a highly promising method of quantifying αSyn monomers for PD patients in the future. The SIP surface was regenerated, and the sensor reused to demonstrate its capability for repeat sensing as a potential continuous monitoring tool for the disease biomarker.

In this paper, we consider the problem that the maximal order consider the groups that consisting of transformations we called NG-Transformation on a nonempty set A has no bijection as its element. We find the order of these groups not greater that (n-1)!. In addition, we will prove our result by showing that any kind of NG-group in the theorem be isomorphic to a permutation group on a quotient set of A with respect to an equivalence relation on A.

Let R be a commutative ring with identity and S be a multiplicatively closed subset of R. The purpose of this paper is to introduce the concept of weakly S-primary ideals as a new generalization of weakly primary ideals. An ideal I of R disjoint with S is called a weakly S-primary ideal if there exists s∈S such that whenever 0≠ab∈I for a,b∈R, then sa∈√I or sb∈I. The relationships among S-prime, S-primary, weakly S-primary and S-n-ideals are investigated. For an element r in any general ZPI-ring, the (weakly) S_{r}-primary ideals are charctarized where S={1,r,r²,⋯}. Several properties, characterizations and examples concerning weakly S-primary ideals are presented. The stability of this new concept with respect to various ring-theoretic constructions such as the trivial ring extension and the amalgamation of rings along an ideal are studied. Furthermore, weakly S-decomposable ideals and S-weakly Laskerian rings which are generalizations of S-decomposable ideals and S-Laskerian rings are introduced.

In this paper, we present a new concept of the generalized core orthogonality (called the C-S orthogonality) for two generalized core invertible matrices $A$ and $B$. $A$ is said to be C-S orthogonal to $B$ if $A^{\tiny\textcircled{S}}B=0$ and $BA^{\tiny\textcircled{S}}=0$, where $A^{\tiny\textcircled{S}}$ is the generalized core inverse of $A$. The characterizations of C-S orthogonal matries and the C-S additivity are also provided. And the connection between the C-S orthogonality and C-S partial order has been given using their canonical form. Moreover, the concept of the strongly C-S orthogonality is defined and characterized.

Using different frequency group period phase synchronization, a precise frequency detecting technology is presented. On the basis of the phase comparison for different frequencies, a high-accuracy frequency measuring can be achieved by quantization of phase comparison results and analysis of quantization results. Using the phase coincidence points between comparison signals as the counter’s open and close signals, the time interval between the same phase coincidence points is a group period. Via the detection and analysis of the phase coincidence points, the ±1-word counting error can be eliminated, and measuring speed is also improved. By using FPGA technology, the measuring device can be simplified, and the development cost can be reduced. Testing results indicate that the frequency measuring accuracy with 10−13/s level can be achieved. The technology is greater than the common frequency measuring technology in more ways than one, such as power consumption, device volume, measuring rate, etc., so it plays an important role in Beidou satellite positioning, precise timing, high-precision time frequency transfer and comparison, scientific metrology and other fields.

AbstractBackground: the development of nursing, especially related to the nursing intervention approach, is running so fast. This can be seen from the use of peer group support in nursing interventions in individual humans. The purpose of this literature is to find the impact of implementing nursing interventions using a peer group support approach.Method: this literature review method uses JBI and Prisma on 120 articles taken from journal databases, namely Scopus, PubMed and Sciendirect.Result: From the articles analyzed, it was found that the application of peer groups can improve individual abilities both in psychological and behavioral aspects.Conclusion: the application of the peer group approach is able to be one of the approaches in the world of nursing in carrying out nursing actions today.

In the literature, frames generated by unitary representations of groups (known as group-frames) are studied only for Hilbert spaces. We make first study of frames for Banach spaces generated by isometric invertible representations of discrete groups on Banach spaces. These frames are characterized using left regular, right regular, Gram-matrices and group-matrices on classical sequence spaces. A sufficiently large collection of functional-vector pairs using the double commutant of the representation is identified which generate group-frames for Banach spaces. Subsequently, we study Schauder frames generated by time-frequency shift operators on finite dimensional Banach spaces. We derive Moyal formula, fundamental identity of Gabor analysis, Wexler-Raz criterion and Ron-Shen duality in functional form.

Topological indices have been used to modeling biological and chemical properties of molecules in quantitive structure property relationship studies and quantitive structure activity studies. All the degree based topological indices have been defined via classical degree concept. In this paper we define a novel degree concept for a vertex of a simple connected graph: S degree. And also we define S indices of a simple connected graph by using the S degree concept. We compute the S indices for well-known simple connected graphs such as paths, stars, complete graphs and cycles.

In this work, Further properties of bornological groups are studied to find the sufficient conditions to introduce a bornology on a group. In particular, we show that every left (right) translations in bornological groups are isomorphisms and therefore the bornological group's structures are homogeneous, and this property from the bornological group is not shared with bornological semigroups. Further, the boundedness of a bornological group can be deduced from its boundedness at the identity.

Using the orbit decomposition, a new enumerative polynomial P(x) is introduced for abstract (simplicial) complexes of a given type, e.g., trees with a fixed number of vertices or triangulations of the torus with a fixed graph. The polynomial has the following three useful properties. (I) The value P(1) is equal to the total number of unlabeled complexes (of a given type). (II) The value of the derivative P'(1) is equal to the total number of nontrivial automorphisms when counted across all unlabeled complexes. (III) The integral of P(x) from 0 to 1 is equal to the total number of vertex-labeled complexes, divided by the order of the acting group. The enumerative polynomial P(x) is demonstrated for trees and then is applied to the triangulations of the torus with the vertex-labeled complete four-partite graph G = K_{2,2,2,2}, in which specific case P(x) = x^{31}. The graph G embeds in the torus as a triangulation, T(G). The automorphism group of G naturally acts on the set of triangulations of the torus with the vertex-labeled graph G. For the first time, by a combination of algebraic and symmetry techniques, all vertex-labeled triangulations of the torus (twelve in number) with the graph G are classified intelligently without using computing technology, in a uniform and systematic way. It is helpful to notice that the graph G can be converted to the Cayley graph of the quaternion group Q_8 with the three imaginary quaternions i, j, k as generators.

Any quantization maps linearly functions on a phase space to symmetric operators in a Hilbert space. Covariant integral quantization combines operator-valued measure with symmetry group of the phase space. Covariant means that the quantization map intertwines classical (geometric operation) and quantum (unitary transformations) symmetries. Integral means that we use all ressources of integral calculus, in order to implement the method when we apply it to singular functions, or distributions, for which the integral calculus is an essential ingredient. In this paper we emphasize the deep connection between Fourier transform and covariant integral quantization when the Weyl-Heisenberg and affine groups are involved. We show with our generalisations of the Wigner-Weyl transform that many properties of the Weyl integral quantization, commonly viewed as optimal, are actually shared by a large family of integral quantizations.

The -blocker (S)-practolol ((S)-N-(4-(2-hydroxy (isopropylamino)propoxy)phenyl)acetamide) was synthesized with 96% enantiomeric excess (ee) from the chlorohydrin (R)-N-(4-(3-chloro-2 hydroxypropoxy)phenyl)acetamide, which was produced in 97% ee and with 27% yield. Racemic building block 1-((1H-indol-4-yl)oxy)-3-chloropropan-2-ol for the -blocker pindolol was produced in 53% yield and (R)-1-((1H-indol-4-yl)oxy)-3-chloropropan-2-ol was produced in 92% ee. The chlorohydrin 7-(3-chloro-2-hydroxypropoxy)-3,4-dihydroquinolin-2(1H)-one, a building block for a derivative of carteolol was produced in 77% yield. (R)-7-(3-chloro-2-hydroxypropoxy)-3,4-dihydroquinolin-2(1H)-one was obtained in 96% ee. The S-enantiomer of this carteolol derivative was produced in 97% ee in 87% yield. Racemic building block 5-(3-chloro-2-hydroxypropoxy)- 3,4-dihydroquinolin-2(1H)-one, building block for the drug carteolol was also produced in 53% yield, with 99% ee of the R-chlorohydrin (R)-5-(3-chloro-2-hydroxypropoxy)-3,4-dihydroquinolin-2(1H)-one. The yield of all four chlorohydrins increased by use of catalytic amounts of base. The reason for this was found to be less formation of the dimeric by-products compared to use of higher concentration of the base. An overall reduction of reagents and reaction time was also obtained compared to our previous reported data of similar compounds. The enantiomers of the chlorohydrin building blocks were obtained by kinetic resolution of the racemate in transesterification reactions catalyzed by Candida antarctica Lipase B (CALB) from SyncoZymes Co, Shanghai, China. Optical rotations confirmed the absolute configuration of the enantiopure drugs.

In this article, we first defined a stronger form of (r,s)-generalized fuzzy semi-closed sets (briefly, (r,s)-gfsc sets) called (r,s)-g*fsc sets and investigated some of its features. Moreover, we showed that (r,s)-fsc set → (r,s)-g*fsc set → (r,s)-gfsc set, but the converse may not be true. In addition, we explored novel types of fuzzy generalized mappings between double fuzzy topological spaces (U, τ, τ*) and (V, η, η*), and the relationships between these classes of mappings were examined with the help of some illustrative examples. Thereafter, we introduced novel types of higher separation axioms called (r,s)-GFS-regular and (r,s)-GFS-normal spaces with the help of (r,s)-gfsc sets and discussed some topological properties of them. Finally, some novel types of compactness via (r,s)-gfso sets were defined and the relationships between them were introduced.

Formulating a relativistic equation for particles with arbitrary spin remains an open challenge in theoretical physics. In this study, the main algebraic approaches used to generalize the Dirac and Kemmer–Duffin equations for particles of arbitrary spin are investigated. It is proved that an irreducible relativistic equation formulated using spin matrices satisfying the commutation relations of the de Sitter group leads to inconsistent results, mainly as a consequence of violation of unitarity and the appearance of a mass spectrum that does not reflect the physical reality of elementary particles. However, the introduction of subsidiary conditions resolves the problem of unitarity and restores the physical meaning of the mass spectrum. The equations obtained by these approaches are solved and the physical nature of the solutions is discussed.

This paper introduces $\mathbb{NS}_4$, a novel number system that extends traditional binary arithmetic by incorporating algorithmic mappings for addition, carry-over, and multiplication operations. We establish a mathematical framework demonstrating that $\mathbb{NS}_4$ forms a commutative ring, thereby extending beyond conventional number systems like complex numbers. The proposed system offers efficient representation and manipulation of numerical structures, with potential applications in computational mathematics and digital logic design.

Physical laws manifest themselves through the amalgamation of mathematical symbols, numbers, functions, geometries, and relationships. These intricate combinations unfold within a mathematical model devised to capture and represent the ``objective reality'' of the system under examination. In this symbiotic relationship between physics and mathematics, the language of mathematics becomes a powerful tool for describing and predicting the behavior of the physical world. The language used and the associated concepts are in a perpetual state of evolution, mirroring the ongoing expansion of the phenomena accessible to our scientific understanding. In this contribution, written in honor of Richard Kerner, we delve into fundamental, at times seemingly elementary, elements of the mathematical language inherent to the physical sciences, guided by the overarching principles of symmetry and group theory. Our focus turns to the captivating realm of spheres, those strikingly symmetric entities that manifest prominently within our geometric landscape. By exploring the interplay between mathematical abstraction and the tangible beauty of symmetry, we seek to deepen our understanding of the underlying structures that govern our interpretation of the physical world.

The calculation of the surface tension of ordinary organic and ionic liquids, based on a computer algorithm applying a refined group-additivity method, is presented. The refinement consists of a complete breakdown of the molecules into their constituting atoms, further distinguishing them by their immediate neighbour atoms and bond constitution. The evaluation of the atom-groups’ contributions was carried out by means of a fast Gauss-Seidel fitting method founded upon the experimental data of 1895 compounds from literature. The result has been tested for plausibility using a 10-fold cross-validation (cv) procedure. The direct calculation and the cv test proved the applicability of the present method by the close similarity and excellent goodness of fit R2 and Q2 of 0.9023 and 0.8821, respectively. The respective standard deviations are ±2.01 and ±2.16 dyn/cm. Some correlation peculiarities have been observed in a series of ordinary and ionic liquids with homologous alkyl chains which are illustrated and discussed in detail, exhibiting the limit of the present method.

In this paper, we introduce the notion of the generalized $w$-group inverse in a Banach algebra with proper involution. This is a natural generalization of generalized (weak) group inverse in Banach *-algebras. Many elementary properties of such new weighted generalized inverse are presented. We further establish the equivalent relations between generalized weighted group inverse and weighted generalized Drazin inverse. Related properties of generalized (weak) group inverse are extended to the wider cases.

In this paper, we focus on the influence of Riemann space-time curvature on the laws of electromagnetism, such as Gauss’s law, Maxwell-Amp´ere’s law, and Faraday’s law. Furthermore, we also introduce the work done on the unification of the gravitation and electromagnetic fields.

We present a modified version of the Szilard Engine, demonstrating that an explicit measurement procedure is entirely unnecessary for its operation. By considering our modified engine, we are able to provide a new interpretation of Landauer’s original argument for the cost of erasure. From this view, we demonstrate that a reset operation is strictly impossible in a dynamical system with only conservative forces. Then, we prove that to approach a reset yields an unavoidable instability at the reset point. Finally, we present an original proof of Landauer’s principle that is completely independent from the Second Law of Thermodynamics.

This study aimed to delineate the longitudinal antibody responses to the Pfizer- BioNTech COVID-19 vaccine (BNT162b2) within the Ugandan subset of the Sub-Saharan African (SSA) demographic, filling a significant gap in global datasets. We enrolled 48 participants, collecting 320 specimens over 12 months after vaccination. A validated enzyme-linked immunosorbent assay (ELISA) was used to quantify SARS-CoV-2-specific IgG, IgM, and IgA concentrations (ng/ml) and optical densities (ODs). Statistical analyses included box plots, diverging bar graphs, and the Wilcoxon test with Bonferroni correction. We showed a robust SIgG response within 14 days of the primary vaccine dose, consistent with global data. Remarkably, we observed no significant surge in S-IgG levels following the booster, contrasting trends other global populations. The S-IgM response was transient, and predominantly established thresholds, reflecting its typical early emergence and subsequent decline. S-IgA increased initially but declined six months post-vaccination, in line with the temporal dynamics of mucosal immunity. Eleven breakthrough infections occurred; however, all were asymptomatic, indicating a protective effect from the vaccination regardless of the participants' initial S-IgG serostatus. The Pfizer-BioNTech COVID-19 vaccine elicited strong S-IgG responses in the SSA demographic. However, antibody dynamics distinctly differed from global data highlight the significance of region-specific research and the necessity for customized vaccination strategies.

The group delay response of chirped fiber Bragg gratings (CFBG) written in polarization-maintaining fiber can be measured using the beat spectrum of the reflections from the two polarization axis, with a resolution and reproducibility better than 50 fs. The method is theoretically described, and we analyze the effect of group delay ripples (GDR) on the performance of a stretcher-compressor pair used in chirped pulse amplification systems. Ripples with a spectral period of the order of the pulse bandwidth are the most deleterious. Those are readily captured with our method, despite the limit on resolution due to the fiber polarization beat length. As a rule of thumb, the GDR should not exceed half the pulse duration. The reconstructed phase of the CFBG is also used to predict the pulse compression performance for a given device. Measurement of GDR as low as 161 fs is experimentally demonstrated.

Postpartum depression is a significant health issue during the postpartum period and not only affects the woman but also has important repercussions for the newborn. Group support interventions during the postpartum period have proven effective in helping women cope with depression and improving breastfeeding rates. The aim of this study was to assess the effectiveness of a midwife-led breastfeeding support group intervention on breastfeeding rates, postpartum depression and general self-efficacy. This was a multicentric cluster randomized controlled trial with control and intervention groups and was not blinded. It was conducted in Andalusia (southern Spain) from October 2021 to May 2023. A total of 382 women participated in the study. Results showed a significant difference in exclusive breastfeeding rates at 4 months postpartum between the groups (p < 0.001). Additionally, there was a lower mean score on the Edinburgh Postnatal Depression Scale in the intervention group (12.49 ± 3.6 vs 13.39 ± 4.0; p = 0.044). Similarly, higher scores of general self-efficacy were observed among breastfeeding women at 2 and 4 months postpartum (p = 0.002 and p < 0.001, respectively). In conclusion, midwife-led breastfeeding support groups enhanced self-efficacy, prolonged breastfeeding and reduced postpartum depression 4 months after giving birth.

Streptococcus mutans is a key bacterium in dental caries- one of the most prevalent chronic infectious diseases. Conventional treatment both fails to specifically target the pathogenic bacteria and at-tempts to eradicate commensal bacteria as well. Thus, caries remains one of most common and challenging diseases. The use of bacterial viruses as anti-bacterial agents, is gaining interest worldwide. Hardly any phages were described against S. mutans. The objective of this study was to isolate anti-S. mutans phages and to characterize their antimi-crobial properties. Human saliva samples were filtered and screened for potential phages. Standard double-layered agar method was used for isolation. Whole genome sequence analysis and morphology visualization by TEM, were used for anti-S. mutans phage identification. Antibacterial properties were evaluated using clinical strains and ATCC strains of S. mutans in various states. Antibacterial effect was also tested on human cariogenic dentin. One phage against S. mutans was isolated and termed SMHBZ8. This phage showed effective lytic activity in vitro against both planktonic and biofilm S. mutans cultures. Moreover, the phage showed antibacterial effect when used on cariogenic dentin. The isolation and characterization of SMHBZ8 may be the first step in developing a potential phage therapy for dental caries.

A time interval only description necessarily needs its own independent definitions, without one moment time coordinates to it. In this paper derived are time interval only set properties, including commutation relations, addition, multiplication and derivatives. Time interval only set commutation relations, consistent with one moment time set properties, are introduced by defining correspondence relations for these sets. Time development and equilibrium within the time interval description depend on the well-known ‘mean velocity theorem’ and the time interval version of the Legendre transform. In contrast, usually applied is only the traditional vector and one moment time coordinate kinematic approach from Newton’s laws. The main results of this paper are correspondences and time interval only set commutation relations. All other properties are derived from these results, while for the time interval only set, different from the one moment time set the canonical property is not valid. The time interval only description can be applied assuming spherical symmetric star-source radiation propagation, with finite time intervals for realistic measurement events. From time development with (a-)symmetry of time intervals, and from Curie’s principle, change can be described with a set theoretic approach. Time interval only set properties include the time interval only version of Noether charges and structure constants. A time interval only description for wave propagation, including group-velocity, for zero and non-zero mass wave particles, relates to the properties of the time interval only set. A second result in terms of the time interval only description is propagation wave energy equivalence with gravitation energy, derived from time interval only set commutation relations. A time interval approach, however including one moment time description dependence, was introduced in earlier publications of this author. In part 1 investigated are the time interval only set and its properties, a forthcoming part 2 to application of the time interval only description to specific groups of stars as emission sources.

Focus Group Discussions (FGDs) are widely employed in qualitative research to delve into complex social issues, yet their application in conservation studies lacks standardised guidelines and thorough evaluation. This review assesses the utilisation of FGDs in biodiversity and conservation research from 2000 to April 2022, identifying 170 pertinent articles, primarily published between 2015 and 2022. FGDs, often integrated with other methodologies, predominantly sought to understand community perspectives, evaluate conservation practices, explore challenges, and document indigenous knowledge. Despite their extensive use, methodological intricacies were frequently underreported. This paper underscores the necessity for enhanced reporting standards and comprehensive guidelines to optimise the effectiveness and reliability of FGDs in conservation research. By means of critically investigating existing literature, this study contributes critical important insights into the strengths and limitations of FGDs, ultimately advocating for greater methodological rigour and transparency in their application within the realm of conservation science.

In This paper we introduce the integration of Renormalization Group (RG) methods with Deep Q-Networks (DQNs) to improve reinforcement learning in high-dimensional state spaces. RG methods provide multi-scale analysis, enhancing state representation, learning stability, and exploration. The proposed RG-DQN algorithm uses hierarchical Q-value estimation and multi-scale representations, demonstrating superior performance on synthetic genomic data compared to traditional DQNs.}

The health status of Hungary's population is unfavorable, with significant differences in health indicators not only compared to the EU15 but also to the Visegrad countries. Unfavorable health indicators can be disproportionate and particularly affect vulnerable groups, such as people with disabilities. The aim of the present study is to compare the health behaviour and indicators of adolescents with disabilities in Hungary with those of the HBSC survey in the Visegrad countries, and to compare the results of the Hungarian special needs adolescent population with those of the Visegrad countries. Eating habits are unfavourable for both the Visegrad countries and the young people we studied. Children with disabilities have significantly higher rates of schoolwork stress compared to other countries. Significantly higher prevalence of somatic complaints and worse mental well-being parameters higher in Hungary than in the other Visegrad countries. The results suggest that further interventions are needed in Hungary and that differentiated, professionalised health promotion is needed for young people with disabilities. The researchers propose to extend the research to adolescents with disabilities living in the Visegrad countries, on the basis of which a methodology for injury-specific health promotion could be developed, including through interna-tional interprofessional cooperation.

Symmetry, as a key concept in geometry and the foundational principle of mathematical concepts, is a fundamental part of geometry and nature, creating patterns that help us conceptually organize our world. It is often linked with aesthetic beauty and can be observed in both natural phenomena and human-made objects, such as artworks and manufactured products, across the globe. The automorphism group of a graph is a mathematical structure that captures all the symmetries of the graph. symmetry refers to the property of a graph, indicating that it can be transformed without changing its structure, while the automorphism group is the collection of all permutations of the vertices that preserve the graph's adjacency relationships. In graph theory, the concepts of symmetry group and automorphism group play fundamental roles in understanding the symmetries and structural properties of graphs. This paper aims to explore the relationship between symmetry groups and automorphism groups, shedding light on their interconnected nature and their significance in graph theory. We delve into the definitions and properties of both symmetry groups and automorphism groups, highlighting their similarities and distinctions. Furthermore, we discuss their applications in various fields, including computer science, chemistry, and network analysis. Through this exploration, we aim to provide a comprehensive understanding of the relationship between symmetry groups and automorphism groups, deepening our comprehension of the symmetries and structures inherent in graphs.

Self-selecting the intensity of aerobic training is a perspective that allows practitioners to develop autonomy (choice of pace), improve physical fitness and achieve weight loss. To compare the effect of four aerobic training protocols on cardiometabolic and psycho-affective responses in physically inactive adult men and women. The sample consisted of 11 individuals aged 56 ± 10 years and BMI 29.2 ± 2.4 kg/m2 performed four different treadmill aerobic training protocols, including: 1-individual with self-selected intensity (ISS), 2-individual with prescribed intensity (IPI) (64-76% of HR max), 3-small group with self-select. selected intensity (SGS) and 4-small group prescribed intensity (SGP) (64-76% of HR max). Heart rate (HR), lactate (LACT), perceived exertion (RPE), affective response (FS), activation scale (FAS), enjoyment (PACES) and intention to repeat the session (INT) were analyzed. Statistical analysis used ANOVA with Tukey's post hoc test (p<0.05). HR, LACT and RPE analyzes did not show significant differences between protocols. The FS showed a smaller decline in the SI protocol (p<0.05), and the intention to repeat the training session was greater in the SI protocol (p<0.05). Conclusion: The data allow us to conclude that the SI training protocol produced superior results in affective response, pleasure and intention to repeat the session.

Abstract: Because of outstanding heat resistance and processing qualities, benzoxazine resins are widely employed in a variety of applications. However, traditional benzoxazine resins still confront hurdles in today's engineering applications, such as can’t long-term service in high-temperature settings and inadequate toughness. Four alkyne-functionalized benzoxazines with phthalide side group and cyano group of varying molecular weights were produced in this study. Fourier trans-form infrared spectroscopy (FT-IR) and hydrogen nuclear magnetic resonance spectroscopy ( 1H-NMR ) were used to characterize the resin structure, and differential scanning calorimetry (DSC) was used to investigate the thermal curing kinetics at different warming rates, the apparent activation energy was 116.9 kJ/mol. In-situ FTIR was used to investigate the cure mechanism. Dynamic mechanical analysis (DMA) was used to evaluate the gelationation time of BOZ series resins at various temperatures, and the curing process was designed by combined the results of DSC. The Tg of the composites made using BOZ-1N21 as the matrix was 336°C, which was much higher than the Tg of the BP-a resin made with aniline, phenolphthalein, and formaldehyde (Tg=251°C). As a result, the resin system is expected to be employed in applications requiring high-temperature resistance and toughness.

Various formulations of the exact renormalization group can be compared in the perturbative domain, in which we have reliable expressions for regularization-independent (universal) quantities. We consider the renormalization of the $\lambda\phi^4$ theory in three dimensions and make a comparison between the sharp-cutoff regularization method and other more recent methods. The former gives considerably better results, while the other methods are far from optimal in the perturbative domain. In addition, these methods present theoretical problems that are already manifest in the renormalization of mass.

A review on several classical, algebraic models in nuclear structure physics, which use symmetries as an important tool, are presented. After a conceptual introduction to group theory, a selection of models is chosen to illustrate the methods and the power of the usage of symmetries. It enables to describe very involved systems in a greatly simplified manner. Some problems are also discussed, when ignoring basic principles of nature, as the Pauli Exclusion principle. We also show that, nevertheless, occasionally one can rescue these omissions. In a couple of representative models, applications of symmetries are explicitly applied, in order to illustrate how extremely complicate systems can be treated. This contribution is meant bas a review on the use of algebraic models in nuclear physics, leading to a better understanding of the articles in the same special volume.

The goal of finding a commutative group of gates from the set of unitary matrices is to simplify the process of quantum computing. If a set of gates is commutative, then we can apply the gates in any order without affecting the final outcome. This is important because quantum systems are very sensitive to errors and decoherence, and any disruption to the system can cause errors in the computation.By having a commutative group of gates, we can simplify the process of designing quantum algorithms and reduce the risk of errors. This is particularly important for solving complex computational problems that cannot be solved by classical computers.

Starting from the SU(2) group of weak interactions in the presence of Electric Charge Swap (ECS) symmetry, we show that ordinary and non-regular (ECS) leptons are related by the ECS rotational group SO(3). We find that many Standard Model (SM) algebras depend on the sin of the angle θs of the ECS rotational group SO (3). We call these ECSM algebras. Furthermore, the break of the gauge symmetry of the SM groupoid gives the massive ECS particle. We find that the ECS particle masses are related with the SM particle masses by sinθs . We also investigate the finite subgroups of the ECS Möbius transformations. We find that sinθs could be derived from the ECS dihedral group DF, which refers to the symmetry of the fermionic polygon (F-gon). The average value of the anchor of the SM algebroid depends on the fermionic Catalan numbers (CF). Finally, we find that the ECS physics at loop level differs the SM physics. The ECSM mass is suppressed by the CF numbers. For 24 fermions, the calculated one-loop radiative correction to the bare Higgs mass µ is 125GeV—a value very close to the experimental one.

We show that if the quadratic twist family of a given elliptic curve over F_q[t] with char(F_q) > 5 has an element whose Neron model has a multiplicative reduction away from infinity, then the average p-Selmer rank is p+1 in large q-limit for almost all primes p.

In the advent of COVID-19 pandemic, testing is highly essential to be able to isolate, treat infected persons, and finally curb transmission of this infectious respiratory disease. Group testing has been used previously for various infectious diseases and recently reported for large-scale population testing of COVID-19. However, possible sample dilution as a result of large pool sizes has been reported, limiting testing methods’ detection sensitivity. Moreover, the need to sample all individuals prior to pooling overburden the limited resources such as test kits. An alternative proposed strategy where test is performed on pooled samples from individuals representing different households is presented here. This strategy intends to improve group testing method through the reduction in the number of samples collected and pooled during large-scale population testing. Moreover, it introduces database system which enables continuous monitoring of the population’s virus exposure for better decision making.

We review past and present results on the non-local form-factors of the effective action of semiclassical gravity in two and four dimensions computed by means of a covariant expansion of the heat kernel up to the second order in the curvatures. We discuss the importance of these form-factors in the construction of mass-dependent beta functions for the Newton's constant and the other gravitational couplings.

We show that, as in the case of the principle of minimum action in classical and quantum mechanics, there exists an even more general principle in the very fundamental structure of quantum space-time: This is the principle of minimal group that allows to consistently and simultaneously obtain a natural description of the spacetime dynamics and the physical states admissible in it. The theoretical construction is based on the physical states that are average values of the generators of the Metaplectic group Mp(n) , the double covering of SL(2C) in a vector representation, with respect to the coherent states carrying the spin weight. Our main results here are: (i) There exists a connection between the dynamics given by the Metaplectic group symmetry generators and the physical states (mappings of the generators through bilinear combinations of the basic states). (ii) The ground states are coherent states of the Perelomov-Klauder type defined by the action of the Metaplectic group which divide the Hilbert space into even and odd states mutually orthogonal. They carry a spin weight 1/4 and 3/4 respectively from which, two other basic states can be formed. (iii) The physical states, mapped bilinearly with the basic 1/4 and 3/4 spin weight states, plus their symmetric and antisymmetric combinations, have spin contents s = 0, 1/2, 1, 3/2 and 2. (iv) The generators realized with the bosonic variables of the harmonic oscillator introduce a natural supersymmetry and a superspace whose line element is the geometrical Lagrangian of our model. (v) From the line element as operator level, a coherent physical state of spin 2 can be obtained and naturally related to the metric tensor. (vi) The metric tensor is naturally discretized by taking the discrete series given by the basic states (coherent states) in the n number representation, reaching the classical (continuous) space-time for n going to infinity. (vii) There emerges a relation between the eigenvalue of our coherent state metric solution and the black hole area (entropy) as A_{bh}/4 l_{p}^{2} = I alpha I relating the phase space of the metric found g_{ab} and the black hole area A_{bh} through the Planck length l_{p}^{2} and the eigenvalue I alpha I of the coherent states. As a consequence of the lowest level of the quantum discrete space-time spectrum, eg the ground state associated to n = 0 and its characteristic length, there exists a minimum entropy related to the black hole history.

The biofilm is a conglomerate of cells surrounded by an extracellular matrix, which contributes to the persistence of infections. The difficulty in removing the biofilm drives the research for new therapeutic options. In this work, the effect of terpenes (-)-trans-Caryophyllene, (S)-cis-Verbenol, (S)-(-)-Limonene, (R)-(+)-Limonene, and linalool was evaluated, individually and in combinations on bacterial growth, by assay with resazurin; the formation of biofilm, by assay with violet crystal; and the expression of associated genes, by real-time PCR, in two clinical isolates of S. aureus, ST30-t019 and ST5-t311, responsible for more than 90% of pediatric infections by this pathogen in Paraguay. All combinations of terpenes can inhibit biofilm formation in more than 50% without affecting bacterial growth. The most effective combination was (-)-trans-Caryophyllene and linalool at a 500 μg/mL concentration for each, with an inhibition percentage of 88%. This combination decreased the expression levels of the sdrD, spa, agr, and hld genes associated with the initial cell adhesion stage and quorum sensing. At the same time, it increased the expression levels of the cap5B and cap5C genes related to the production of capsular polysaccharides. The combinations of compounds tested are promising alternatives to inhibit biofilm formation in S. aureus.

Background/Objectives: This study aimed to evaluate compliance and accuracy in comparison with traditional PD diaries for tracking motor symptoms using a new smartphone application (My Parkinson’s) and paper diary strategies. Parkinson's disease (PD) is a neurodegenerative disorder with progressive motor symptoms. Treatment becomes more challenging as PD progresses, motor complications in the form of wearing-off phenomenon and levodopa-induced dyskinesia develop. Traditional paper diaries and clinical scales used to evaluate patients may be inadequate in assessing whether the patient is “on” or “off,” resulting in less-than-ideal treatment changes. Methods: A randomized crossover design was utilized to examine 22 advanced PD patients who underwent symptomatic assessment with both diaries during two separate 24-hour periods seven days apart. The compliance and accuracy of data were assessed by comparing diary entries with the clinical examination notes and WhatsApp queries. Latterly, patients' diary preferences were also evaluated.; Results: The digital diary had significantly better compliance and accuracy than the paper diaries, with substantial/almost perfect levels of agreement (κ = 0·615 to 0·818) between logged symptoms and clinical examination notes. 65% of patients preferred the digital diary for follow-ups, and there was no significant difference in ease of use compared to paper diaries. Conclusions: Digital diaries are helpful in the clinical management of PD patients as they minimize recall bias and reduce data errors in appropriately selected patients. Our study suggests a broader adoption of digital health technologies in PD management. Still, additional research is necessary to improve the tools and assess long-term patient outcomes.

Staphylococcus aureus, found in the oral cavity as an opportunistic bacterium, has been reported as a cause of infective endocarditis and pneumonia. Salt is an essential mineral component for maintaining human body cells and has attracted attention as a promoter of S. aureus biofilms. This study was conducted to clarify how salt affects biofilm formation by S. aureus and S. mutans, which is a pathogen implicated in the dental caries. Bacteria were cultivated with various concentration of sodium chloride (NaCl) in Toryptic Soy Broth with 0.25% sucrose and 0.25% glucose (TSBs and TSBg) for 16 hours. Contribution of GTF on the membrane vesicles (MVs) from S. mutans and extracellular DNA (eDNA) was also analyzed in the biofilm formation. S. aureus biofilms were induced by the addition of 0.004–0.25 M NaCl but decreased by NaCl concentrations greater than 0.25 M, in TSBs. The biofilm formation of mixed bacteria (S. aureus and S. mutans) gradually increased in a NaCl concentration-dependent manner in TSBs and TSBg. Moreover, the biofilm was dependent on glucan formation by GTF in MVs at high salinity. The mixed-species biofilm of S. aureus and S. mutans was upregulated by the collaboration of eDNA and MVs. Therefore, eDNA and MVs are developmental factors for S. aureus biofilm formation under harsh conditions. The intake of sucrose and glucose may be a risk factor for infection by opportunistic pathogens such as S. aureus in persons who consume high concentrations of salt in foods and drinks in custom-type foods.

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.

Neurological disorders are the leading cause of cognitive and physical disability worldwide, affecting 15% of the global population. Due to the demographics of aging, the prevalence of neurological disorders, including neurodegenerative diseases, will double over the next two decades. Unfortunately, while available therapies provide symptomatic relief for cognitive and motor impairment, there is an urgent unmet need to develop disease-modifying therapies that slow the rate of pathological progression. In that context, biomarkers could identify at-risk and prodromal patients, monitor disease progression, track response to therapy, and parse causality of molecular events to identify novel targets for further clinical investigation. Thus, identifying biomarkers that discriminate between diseases and reflect specific stages of pathology would catalyze the discovery and development of therapeutic targets. This review will describe the prevalence, known mechanisms, ongoing or recently concluded therapeutic clinical trials, and biomarkers of three of the most prevalent neurodegenerative diseases, including Alzheimer’s disease (AD), amyotrophic lateral sclerosis (ALS), and Parkinson’s disease (PD).

In vitro circular RNA (circRNA) preparation methods have been gaining a lot of attention recently as several reports suggest that circRNAs are more stable with better performances in cells and in vivo than linear RNAs in various biomedical applications. Self-splicing ribozymes are considered a major in vitro circRNA generation method for biomedical applications due to their simplicity and efficiency in circularization of gene of interest. This review summarizes updates and discusses recently developed self-circularization methods based on the self-splicing ribozyme such as group I and II intron ribozymes and pros and cons of each method to prepare circRNA in vitro.

In this paper, we introduce the notion of weighted generalized group inverse in a Banach algebra with proper involution. This is a natural generalization of weighted weak group inverse for a complex matrix and Hilbert space operator. We present several characterizations and representations of this generalized inverse. In addition, a new partial order on elements in a Banach *-algebra is investigated by using the weighted generalized group inverse and some known results are thus generalized.

These counterexamples have shown the relationships between the power of a Pythagorean equation and Pythagorean’s triples. There are three positive integers that satisfy Fermat’s equation when the power n is equal to 2 in the case of the Pythagorean theorem and it’s applicable relationships in right triangles. On the other hand, as the power varies from positive to negative integers or any integers other than 2, such as in the case of Fermat’s last theorem, the hypotenuse z of a right triangle tends to be equal to one of the sides x or y of the triangle and the other side tends to be equal to zero. And the application of this idea describes the behavior of a mass object in motion. Since the total energy of the object is the sum of its energy in motion and its rest energy, at a particular power n, the total energy of the object tends to be equal to either the rest energy or the photon energy.

Formation of Fe- and Mg-rich smectite and zeolite under alkaline conditions is concerned as secondary minerals after alkaline alteration of bentonite in a repository of radioactive wastes. It might be crucial for safety assessment whether smectite will be formed or not as secondary minerals after alkaline alteration of bentonite. In present paper, Fe- and Mg-rich smectite which are currently interacting with hyperalkaline groundwater was found at Narra in Palawan, Philippines. Mineralogical and geochemical investigation was conducted to understand formation process of smectite and factors determined secondary mineral species. Our study revealed a certain amount of smectite may have been produced under hyperalkaline conditions, altered from amorphous or poorly crystalline material such as M-S-H and F-S-H. Key factor which decides smectite or zeolite as secondary minerals after alkaline alteration of bentonite might be whether nuclei of M-S-H and/or F-S-H will be formed or not. This might be decided by the presence of dissolved Mg2+ and Fe2+ in the system. Our suggested formation process of smectite under alkaline conditions is analogue with generally-accepted model of smectite formation that might have been occurred on early Mars.

Alzheimer's disease (AD) and Parkinson's disease (PD) are the most prevalent and irreversible neurological disorders that primarily affect the aged population. These conditions lead to disability and mortality as there is currently no medication for a complete cure. Existing drugs only provide symptomatic relief of the disease. Inhibition of Acetylcholinesterase (AChE) and Butyrylcholinesterase (BuChE) will reduce the hydroxylation of Acetylcholine, a molecule possessing a significant role in the neurotransmission pathways and is accounted as a remedial objective for the treatment of AD and PD. This study aimed to identify potent lead molecules from plants that could inhibit AChE and BuChE. We employed molecular docking, molecular dynamic simulation, and MMPBSA approaches to screen and evaluate potential compounds. The docking results were analysed based on binding affinity and hydrogen bond interactions at the active-site residues of the targets. From the analysis, four phytocompounds - Tricetin, Luteolin, Withasomniferol C, and Withanolide were identified as potential hits. These compounds demonstrated strong binding affinities of -8.49, -9.85, -25.26, and -24.1 kcal/mol, respectively. The significant binding affinity suggests that these compounds may effectively inhibit the activity of AChE and BuChE, potentially leading to therapeutic benefits for AD and PD. However, further in-vitro analysis is recommended to validate the activity of these compounds. In-vitro experiments will provide a better understanding of their efficacy, safety, and potential as drug candidates for treating AD and PD.

Around 1637, Pierre de Fermat famously wrote in the margin of a book that he had a proof for the equation $a^n + b^n = c^n$ having no positive integer solutions for exponents $n$ greater than 2. This statement, now known as Fermat's Last Theorem, remained unproven for centuries, despite the efforts of countless mathematicians. Andrew Wiles' work in 1994 finally provided a rigorous proof of Fermat's Last Theorem. However, Wiles' proof relied on advanced mathematical techniques that were far beyond the scope of Fermat's time, raising questions about whether Fermat could have truly possessed a proof using the methods available to him. Wiles's achievement was widely celebrated, and he was awarded the Abel Prize in 2016 in recognition of his groundbreaking work. The citation for the award described his proof as a "stunning advance" in mathematics. The present work offers a potential solution to Fermat's Last Theorem that may be more aligned with the original approach that Fermat claimed to have used.

HIGHLIGHTS Mach's principle is linked with inertia and the mass around. Nowadays, physicists believe its effect is infinitesimal, so Mach's principle is simply ignored. This paper looks at the consequence of applying Mach's principle. It could replace dark matter. ABSTRACT After seeing the history of Mach's principle, we will work out a new model of galaxies inspired by Mach’s principle, which is more satisfactory than current dark matter models. This new model is just maths and needs an explanation. One possible explanation is obviously that Mach's principle is at work in a galaxy.

Urban tourism has witnessed significant growth in recent years, driven by various factors that foster the transformation of urban areas into tourist hotspots. These factors include a rising interest in culture and heritage, ongoing urban redevelopment and conversion processes, and the introduction of new experiences and activities. Two particularly influential factors contributing to this growth are low-cost travel, which facilitates more accessible access to urban destinations, and the emergence of new types of accommodation, such as short-term rental (also known as local accommodation or Airbnb-type accommodation). This sudden and continuous growth of this type of tourist accommodation brings new challenges to cities and local communities. On the positive side, it contributes to job opportunities, the dynamism of the local economy, and urban revitalization. On the other hand, it also represents more difficulty in retaining the local population in city centers, as more and more buildings are converted into hostels and tourist apartments. In this context, it becomes essential to conduct studies evaluating the impacts of these dynamics in urban areas and how they influence residents' and visitors' perspectives. Therefore, this study aims to identify the main transformations resulting from short-term rental (STR) development, focusing on the impacts felt by tourists and residents in Porto. A questionnaire was distributed to tourists and residents in Porto's city center in June 2023. The results reveal differences in opinions between tourists and residents, particularly concerning historical heritage preservation, local population relocation, and reduced housing availability for residents. Nevertheless, there is a similarity in their opinions regarding the stimulus that local accommodation brings to the economy and the rehabilitation of buildings and urban areas. This study reinforces the need to pay more attention to the future development of tourist accommodation in city centers, especially regarding local policies and territorial planning, to balance better tourism development and local communities' quality of life.

Although the empirical Kepler’s laws can be proven by applying Newton’s laws to the dynamics of two particles attracted due to the gravitational interaction, there is no explicit formula for the motion as a function of time. In this paper, a quasi-analytical solution for this problem is proposed. It approximates the real behavior of celestial bodies with an acceptable degree of accuracy. All calculations involved require a low computational cost. This problem is closely related to Kepler’s equation, since, the solution for the equations of motion as a function of time gives us the solution to Kepler’s equation as well. The results are presented for each planet of the solar system (including Pluto), and the solution is compared against the real orbits.

The conformity assessment of products or a measured value with the given standards is carried out based on the global risk of producers and consumers calculation. A product may conform to specifications but be falsely rejected as non-conforming. This is about the producer's risk. If a product doesn't meet the requirements but is falsely accepted as conforming, that poses a risk to the consumer. The conventional approach to risk assessment, which yields only a single numerical value for the global risk of producers and consumers, is naturally extended, and utilized for assessing risk in measurement models with linear regression. The outcomes of the two-dimensional extension, along a moderate scale, are the parabolas with an opening upwards. Risk surfaces were obtained through three-dimensional extension over the area limited by the moderate scale and guard band axes. Four models with different ranges of tolerance intervals were used to test this innovative method of risk assessment in linear regression. The corresponding standard measurement uncertainties are determined by applying a simplified measurement model with the use of comprehensive data on the measurement performance and by determining measurement uncertainty derived from consideration of the functional relationship obtained by linear regression analysis. Models that utilize information from linear regression analysis to determine measurement uncertainty are biased towards risks at the edges of the moderate scale. Testing the model's performances with metrics related to the confusion matrix, such as the F1 score, further substantiated this assertion. The diagnostic odds ratio has been proven to be extremely effective in identifying the curve along the guard band axis, along which the global risks of producers and consumers are at their lowest.

Let R be a commutative graded ring with unity, S be a multiplicative subset of homogeneous elements of R and P be a graded ideal of R such that P\bigcap S=\emptyset In this article, we introduce several results concerning graded S-prime ideals. Then we introduce the concept of graded weakly S-prime ideals which is a generalization of graded weakly prime ideals. We say that P is a graded weakly S-prime ideal of R if there exists s\in S such that for all x, y\in h(R), if 0\neq xy\in P, then sx\in P or sy\in P. We show that graded weakly S-prime ideals have many acquaintance properties to these of graded weakly prime ideals.

We discuss two queueing-inventory systems with catastrophes in the warehouse. Catastrophes occur according to Poisson process and upon arrival of a catastrophe all inventory in the system is instantly destroyed. But consumer customers in the system (in the server or in the buffer) continue still waiting for the replenishment of the stock. The arrivals of the consumer customers follow a Markovian Arrival Process (MAP) and they can be queued in an infinite buffer. Service time of a consumer customer follows a phase-type distribution. The system receives negative customers whose have Poisson flows to service facility and upon arrival of a negative customer one consumer customer is pushed out from the system, if any. One of two replenishment policies can be used in the system: either (s,S) or (s,Q). If upon arrival of the consumer customer, the inventory level is zero, then according to the Bernoulli scheme, this customer is either lost (lost sale scheme) or join the queue (backorder sale scheme). The system is formulated by a four-dimensional continuous-time Markov chain. Steady state distribution is obtained using the matrix-geometric method. A comprehensive numerical study is performed on the performance measures under various replenishment policies. Finally, an optimization study is presented.

The de-oxygenation process in water used in well injection operations is an important matter to eliminate corrosion in petroleum industry. This study used molecular dynamics simulations to understand the behavior of siloxane surface through studding the surface properties with two functional groups attached to the end of siloxane and their effect on de-oxygenation process. The simulations were performed using LAMMPS to characterize of surface properties. Jmol software was used to generate siloxane chains with (8, 20, and 35) repeat units. Firstly, we evaluated properties such as total energy, surface tension and viscosity. Then, we used siloxane as a membrane to compare the efficiency of de-oxygenation for the both types of functional groups. The results indicated that longer chains length increased total energy, viscosity while decreased surface tension. Replacing methyl groups with trifluoromethyl (CF3) groups increased all the above mentioned properties in varying proportions. Trifluoromethyl (CF3) groups showed better removal efficiency than methyl (CH3) groups but allowed more water to pass. Furthermore, the simulations were run using the class II potential developed by Sun, Rigby, and others within an explicit-atom (EA) model.

This article presents a narrative review of neonatal and paediatric complications in post-dated pregnancy and covers scientific views on the aetiology, pathology, risk factors, symptoms and complications of post-dated pregnancy. A pregnancy extending beyond 42 weeks of gestation is termed as a post term pregnancy. There are multiple complications that can occur in the perinatal period, some of the most common ones are stillbirth, asphyxia, meconium aspiration syndrome, fetal distress syndrome, etc which are found to be greater in post-dated pregnancy and hence ultimately leads to increased mortality and morbidity of the new born. Studies have shown that post-term pregnancy also causes increased risk of developing behavioural and emotional problems in children of paediatric age group. It is surprising not much importance has been given to the maternal and neonatal consequences of post- term pregnancies. It is not well understood why some women experience post-dated pregnancies. It is found that factors such as hormones and genetic build up, are responsible for causing post-term pregnancy in an obese female. The treatment and management of a post-term pregnancy still poses a challenge to clinicians in determining the right choice and right time for a particular intervention so that both mother and fetus can be prevented from having complications.

Suppose G is a graph with vertex-orbits O1,1 O2, . . . ,Ot, and jOi j denotes the cardinallity of Oi. Then OG (x) = åt 2 i=1 xjOi j is called as orbit polynomial. It is well-known that this polynomial 3 has a unique positive zero d in the interval [0, 1]. The aim of this paper is to study the specific 4 properties of this polynomial and then we determine the location of this root for several classes of 5 complex networks to compare with other graphical measures. Besides, we compare the unique 6 positive zero measure with several well-known centrality graph measures.

Global research on the Covid-19 vaccine’s effectiveness is using methods that are misleading the scientific community and public opinion. There is a golden rule in medicine: to measure the effectiveness of an experimental medicine you need to have two groups. The group that will take medicine and the group that will not take medicine. You follow the health status of both groups for a few months and you will get objective results. This is the only proper methodology to verify the effectiveness of a new medicine. Articles cited from 1-5 did not use the gold rule. They develop different kinds of methodologies that all have no statistical significance. On the basis of their methodologies, they conclude that Covid-19 vaccines have a positive effect on public health. By comparing graphs of the intensity of vaccination and the rate of mortality we see that after the period of intense vaccination follows the period of higher excess mortality. Basic statistical data are confirming that Covid-19 vaccines increased the mortality rate.

The aim of the presents study is to further expand the model of translational cross-validation by investigating the brain circuits or networks which underpin the same tasks by means of group independent component analysis for FMRI toolbox (GIFT). We hypothesized that there will be neural network patterns of activation and deactivation, which correspond to real time performance on clinical self-evaluation scales. We recruited 42 subjects: 20 healthy controls and 22 patients with major depressive episode. All subjects underwent functional MRI scanning using paradigm comprised of diagnostic clinical self-assessment depression scale contrasted to neutral scale. The data were processed with group independent component analysis for functional MRI toolbox and statistical parametric mapping. The results have demonstrated that there exist positively or negatively modulated brain networks during processing of diagnostic specific task questions for major depressive disorder. There have also been confirmed differences in the networks processing diagnostic versus off blocks between patients and controls in anterior cingulate cortex and middle frontal gyrus. Diagnostic conditions (depression scale) when contrasted to neutral conditions demonstrate differential activity of right superior frontal gyrus and right middle cingulate cortex in the comparison of patients with healthy controls. It is for the first time when potential neuroimaging state dependent biomarker has been directly linked with clinical assessment self-evaluation scale, administered as stimuli simultaneously with the fMRI acquisition. It may be regarded as further evidence in support of the ability of both methods to concordantly distinguish groups by means of incremental translational cross-validation.

Introduction: Leprosy, caused by Mycobacterium leprae is one of the oldest infectious diseases in human history and its eradication is linked to poverty control, lack of basic sanitation, the fragility of health, and education services. Objective: To evaluate the frequency of blood groups (ABO/Rh) and the sociodemographic and clinical profile of Angolan patients with Leprosy treated at the Anti-Tuberculosis and Leprosy Dispensary in Luanda, the capital city of Angola. Methodology: A descriptive, introspective, cross-sectional study with a quantitative approach was carried out with 102 patients of Luanda, in the second half of 2021. Results: Of the 102 patients included in the study, the majority belonged to the ORh+ group (51.9%), followed by the BRh+ group (27.4%) and ARh+ (18.6%), most were under 51 years of age ( 87.3%), with low education (54.9%), coming from urban areas (44.1%). As for clinical conditions, most had a multibacillary infection (93.1%), diagnosed mainly by smear microscopy (75.5%) without other infection (79.4%), some of them with complications (28.4%) and individuals with non-O blood group showed changes in the blood count. Conclusion: Leprosy seems to be common in ORh+ individuals, it continues to affect especially those residing in areas of population agglomerations and with low education, presenting itself as a multibacillary infection, where changes in the blood count are greater in non-O individuals.

A novel hypothesis concerning language evolution is advanced. It posits that languages have evolved as a means of binding individuals to a group, as well as for defining those groups. This means that language evolution has to be considered on the level of groups and not only on the level of individuals. This hypothesis helps to explain the huge diversity of human languages, as well as their complexity. Perhaps more importantly, it explains why adults lose the ability to learn languages with the ease that children possess.

We study factorization properties of continuous homomorphisms defined on subgroups (or submonoids) of products of (para)topological groups (or monoids). A typical result is the following one: Let $D=\prod_{i\in I}D_i$ be a product of paratopological groups, $S$ be a dense subgroup of $D$, and $\chi$ a continuous character of $S$. Then one can find a finite set $E\subset I$ and continuous characters $\chi_i$ of $D_i$, for $i\in E$, such that $\chi=\big(\prod_{i\in E} \chi_i\circ p_i\big)\hs1\res\hs1 S$, where $p_i\colon D\to D_i$ is the projection.

Background and Aim: Multiple sclerosis (MS) is known as an autoimmune disease and a chronic inflammatory condition, inducing a wide variety of mood affective disorders, including depression and feelings of hopelessness in many aspects of patients’ quality of life (QoL). In view of the positive side effects of spirituality and spiritual care on finding appropriate strategies for further adaptation, this study aimed to determine the impact of group spiritual care (GSC) on levels of hope in patients suffering from MS. Materials and Methods: This clinical trial was conducted on a total number of 96 patients with MS, referring to the National Multiple Sclerosis Society (NMSS) in the city of Zahedan, Iran. Following sample selection via the convenience sampling technique, the patients meeting the inclusion criteria were randomized into two groups, i.e., intervention and control. The data collection tools for this purpose included a demographic information form and the Adult Hope Scale (AHS, Snyder et al. 1991), completed by the subjects at the pre- and post-intervention stages. As well, the intervention group received five sessions of GSC during three weeks but the control group members only talked over daily issues along with their mental health problems. The data were also analyzed using the SPSS Statistics software (ver. 14). Results: The Kruskal-Wallis test results revealed that the GSC intervention could have a significant positive effect on raising hope in the patients with MS (p<0.001). Moreover, a significant growth was observed in the scores of hope dimensions including agency and pathway (p<0.001). Conclusion: GSC can effectively boost levels of hope in patients suffering from MS in all dimensions. Therefore, it is recommended to utilize this type of care in order to nurture hope in such individuals.

The calculation of the isobaric heat capacities of the liquid and solid phase of molecules at 298.15 K is presented, applying a universal computer algorithm based on the atom-groups additivity method, using refined atom groups. The atom groups are defined as the molecules' constituting atoms and their immediate neighbourhood. In addition, the hydroxy group of alcohols are further subdivided to take account of the different intermolecular interactions of primary, secondary and tertiary alcohols. The evaluation of the groups' contributions has been carried out by means of a fast Gauss-Seidel fitting calculus using experimental data from literature. Plausibility has been tested immediately after each fitting calculation using a 10-fold cross-validation procedure. For the heat capacity of liquids, the respective goodness of fit of the direct (R2) and the cross-validation calculations (Q2) of 0.998 and 0.9975, and the respective standard deviations of 8.2 and 9.16 J/mol/K, together with a medium absolute percentage deviation (MAPD) of 2.69%, based on the experimental data of 1133 compounds, proves the excellent predictive applicability of the present method. The statistical values for the heat capacity of solids are only slightly inferior: for R2 and Q2, the respective values are 0.9915 and 0.9875, the respective standard deviations are 12.19 and 14.13 J/mol/K and the MAPD is 4.65%, based on 732 solids. The predicted heat capacities for a series of liquid and solid compounds has been directly compared to those received by a complementary method based on the "true" molecular volume [1] and their deviations elucidated.

The entropy of Boltzmann-Gibbs, as proved by Shannon and Khinchin, is based on four axioms, where the fourth one concerns additivity. The group theoretic entropies make use of formal group theory to replace this axiom with a more general composability axiom. As has been pointed out before, generalized entropies crucially depend on the number of allowed number degrees of freedom $N$. The functional form of group entropies is restricted (though not uniquely determined) by assuming extensivity on the equal probability ensemble, which leads to classes of functionals corresponding to sub-exponential, exponential or super-exponential dependence of the phase space volume $W$ on $N$. We review the ensuing entropies, discuss the composability axiom, relate to the Gibbs' paradox discussion and explain why group entropies may be particularly relevant from an information theoretic perspective.

Let G be a finite group. The prime graph Γ(G) of G is defined as follows: The set of vertices of Γ(G) is the set of prime divisors of |G| and two distinct vertices p and p' are connected in Γ(G), whenever G has an element of order pp'. A non-abelian simple group P is called recognizable by prime graph if for any finite group G with Γ(G)=Γ(P), G has a composition factor isomorphic to P. In [4] proved finite simple groups ²D_n(q), where n ≠ 4k are quasirecognizable by prime graph. Now in this paper we discuss the quasirecognizability by prime graph of the simple groups ²D_2k(q), where k ≥ 9 and q is a prime power less than 10⁵.

Single-Anastomosis Duodeno-Ileal bypass with Sleeve Gastrectomy (SADI-S) is a modification of the duodenal switch in which only one anastomosis is performed, with a longer common limb and an expected less malabsorptive effect. The present study analyzes presentation and treatment of malnutrition after SADI-S. 258 consecutive patients undergoing SADI-S between May 2007 and September 2017 were included. The common limb length was 200 cm in 50 cases, 250 cm in 156 and 300 in 52. 30 patients were admitted for severe hypoalbuminemia and 16 patients were submitted to revisional surgery and constitute the series of our study. Mean weight before reoperation was 57 kg and mean body mass index (BMI) was 21 kg/m2. Mean number of daily bowel movements was 5,6. Mean time to reoperation was 56 months. Revisional surgery consisted mainly in elongation of the common limb. Mean weight regain was 14 kg and mean final BMI was 26 kg/m2. Daily bowel movements were decreased to 1,3. Factors related to hypoalbuminemia were hypertension, poor controlled diabetes, age over 55 years and a shorter common limb. Although SADI-S is expected to be less malabsorptive than previous biliopancreatic diversions, caution has to be taken with selected patients to avoid postoperative malnutrition.

Brain capillary endothelial cell(s) (BECs) have numerous functions including their semipermeable interface-barrier (transfer and diffusion of solutes), trophic (metabolic homeostasis), tonic (vascular hemodynamics), and trafficking (vascular permeability, coagulation, and leukocyte extravasation) functions to provide brain homeostasis. BECs also serve as the brain’s sentinel cell of the innate immune system and are capable of antigen presentation. In metabolic syndrome (MetS) there are two regions resulting in proinflammatory signaling of BECs. Namely, visceral adipose tissue depots supplying excessive peripheral cytokines/chemokines (pCC) and gut microbiota dysbiotic regions supplying excessive soluble lipopolysaccharide (sLPS), small LPS-enriched extracellular vesicle exosomes (lpsEVexos), and pCC. This dual signaling of BECs at their receptor sites results in BEC activation and dysfunction (BECact/dys) and neuroinflammation. sLPS and lpsEVexos signal BECs toll-like receptor four, which then signals translocated nuclear factor kappa B (NFkB). Translocated NFkB promotes the synthesis and secretion of BEC proinflammatory cytokines and chemokines. Specifically, the chemokine CCL5 (RANTES) is capable of attracting microglia cells to BECs. BEC neuroinflammation activates perivascular space(s) (PVS) resident macrophages. Excessive phagocytosis by reactive resident PVS macrophages results in a stagnation-like obstruction, which along with increased capillary permeability due to BECact/dys could expand the fluid volume within the PVS to result in enlarged PVS (EPVS). Importantly, this remodeling may result in pre- and post-capillary EPVS that would contribute to their identification on T2-weighted MRI, which are considered to be biomarkers for cerebral small vessel disease.

This text deals with exploring random solutions for generalized nonlinear variational inequality problems. Using the Fan-KKM theorem and Aumann's measurable selection theorem, we are able to prove the existence and uniqueness of random solution sets under the conditions of monotonicity and convexity. Additionally, we use Minty's lemma to demonstrate the compactness and convexity of the random solution sets.

3D Zernike moments based on 3D Zernike polynomials have been successfully applied to the field of voxelized 3D shape retrieval and have attracted more attention in biomedical image processing. As the order of 3D Zernike moments increases, both computational efficiency and numerical accuracy decrease. Due to this phenomenon, a more efficient and stable method for computing high-order 3D Zernike moments was proposed in this study. The proposed recursive formula for computing 3D Zernike radial polynomials combines the recursive calculation of spherical harmonics to develop a voxel-based algorithm for the calculation of 3D Zernike moments. The algorithm was applied to the 3D shape Michelangelo's David with a size of 150×150×150 voxels. As compared to the method without additional acceleration, the proposed method uses a group action of order sixteen orthogonal group and saving unnecessary iterations, the factor of speed-up is 56.783±3.999 when the order of Zernike moments is between 10 and 450. The proposed method also obtained an accurate reconstructed shape with the error rate (normalized mean square error) of 0.00 (4.17×10^-3) when the reconstruction was computed for all moments up to order 450.

We report an unusual case of Terson's syndrome that resulted in the di-agnosis of a right posterior communicating artery aneurysm. Interest-ingly Terson's syndrome presented with Roth spot resembling features accompanied by third nerve palsy in a patient without any disturbance of consciousness. To our knowledge, the association of Terson's syndrome with third nerve palsy has not been described before in the absence of radiologically diagnosed subarachnoid haemorrhage. We present the case of a 48-year old woman who presented in the De-partment of Emergencies of the University Hospital of Patras with right-sided complete pupil-involving third nerve palsy combined with bilateral Terson's syndrome. More precisely, fundoscopy revealed multi-ple scattered intra- and pre-retinal haemorrhages in both eyes while some retinal haemorrhages had a white-centered pattern resembling Roth spots. Neurological examination revealed no nuchal rigidity or any other neurological signs. The Glasgow coma scale was 15/15. A cerebral computed tomography angiography revealed a 5mm aneurysm of the right posterior communicating artery and the patient underwent a mi-crovascular clipping operation after craniotomy. The significant contribution of the ophthalmological consultation to the appropriate and timely diagnosis and management of a life-threatening condition is highlighted.

Neurodegenerative diseases (NDs) are a set of progressive, chronic, and incurable diseases characterized by the gradual loss of neurons, culminating in the decline of cognitive and/or motor functions. Alzheimer’s disease (AD) and Parkinson’s disease (PD) are the most common NDs and represent an enormous burden both in terms of human suffering and economic cost. The available therapies for AD and PD only provide symptomatic and palliative relief for a limited period and are unable to modify the diseases’ progression. Over the last decades, research efforts have been focused on developing new pharmacological treatments for these NDs. However, to date, no breakthrough treatment has been discovered. Hence, the development of disease-modifying drugs able to halt or reverse the progression of NDs remains an unmet clinical need. This review summarizes the major hallmarks of AD and PD and the drugs available for pharmacological treatment. It also sheds light on potential directions that can be pursued to develop of new, disease-modifying drugs to treat AD and PD, thereby decreasing the social and economic burdens linked to these NDs.

In this article, we present two topics related to mathematical economics. We offer an intriguing proposal for securing cost and production functions in the face of uncertainty and risk. We discuss the relationship between individual and social preferences. This is important because traditional revealed preference theory does not account for such factors.

This paper will explore analogs of groups formed by the transformations of two ropes as presented by Minh-Tam Quang Trinh.1 The two operations acting on these ropes are T and S, defined as twists and clockwise turns, respectively. These actions intertwine the ropes, creating tangles. T and S also have the ability to untangle the rope when used in certain combinations. In the two-rope case, these actions expressed as a group presentation were shown to be isomorphic to SL₂(Z). We explored the analog of these opera- tions, T and S, and conjectured the corresponding group to which they are isomorphic. Partial proofs for this conjecture are included and future work would include proving our conjecture as well as generalizing results to k ropes.

The fall armyworm, Spodoptera frugiperda, arrived during the 2016/2017 cropping season in Limpopo, South Africa and it continues to cause devastating damage on maize in this region. The present study investigated knowledge, perception and management of S. frugiperda by smallholder farmers at Dzindi and Tshiombo irrigation schemes in this region. The study was conducted in 16 focus group discussion interviews, 12 at Dzindi and four at Tshiombo irrigation scheme. Although farmers failed to identify S. frugiperda eggs and pupal stages, they positively identified the pest by its larval stage and refer to it by several local names. All farmers relied extensively on insecticides for S. frugiperda control. With the exception of the Dzindi irrigation scheme farmers, who have adopted Bt maize, very few farmers have adopted alternative methods to chemical control such as mechanical control, physical control (crushing egg and handpicking of larvae), biological control, cultural practices (such as Push-Pull Technology), possible indigenous knowledge, or the use of monitoring tools, for the management of S. frugiperda. The study provided valuable information for designing sustainable management practices to control S. frugiperda on maize in smallholder farming communities.

Recently, polyetheretherketone (PEEK) has shown promising dental applications; although surface treatment is essential for dental applications owing to its poor surface energy and wettability, no consensus on an effective treatment method has been achieved. In this study, we attempt to carboxylate PEEK sample surfaces via Friedel–Crafts acylation using succinic anhydride and AlBr3. The possibility of further chemical modifications using carboxyl groups is examined. The samples are subjected to dehydration–condensation reactions with 1H,1H-pentadecafluorooctylamine and N,N'-dicyclohexylcarbodiimide. The sample surface properties at each reaction stage are evaluated. An absorption band in the 3300–3500 cm-1 wavenumber region is observed. Additionally, peak suggestive of COOH is observed in the sample spectra. Secondary modification diminished the absorption band in 3300–3500 cm-1 and a clear F1s signal is observed. Thus, Friedel–Crafts acylation with succinic anhydride produces carboxyl groups on the PEEK sample surfaces. Further chemical modification of the carboxyl groups by dehydration-condensation reactions is also possible. Thus, a series of reactions can be employed to impart desired chemical structures to PEEK surfaces.

Hessenberg differential algebraic equations (Hessenberg-DAEs) with high index play a critical role in the modeling of mechanical systems and multibody dynamics. Motivated by the widely used Lie Group Differential Algebraic Equation (LGDAE) method which only handles index 2 systems, we propose a Modified Extended Lie Group Differential Algebraic Equation (MELGDAE) method for solving index 3 Hessenberg-DAEs, and provide theoretical analysis to deepen the foundation of the MELGDAE method.The performance of the MELGDAE method is compared with the standard methods RADAU and MEBDF on index 2 and 3 DAE systems, and it is demonstrated that the MELGDAE integrator exhibits competitive performance in terms of high accuracy and the preservation of algebraic constraints. In particular, all differential variables in index 3 Hessenberg DAEs achieve second-order convergence using the MELGDAE method, which suggests potential for extension to Hessenberg-DAEs with an index of 4 or higher.

The super-weak interaction includes three simple extensions of the standard model: gauge extension, fermionic extension, and scalar extension. All of these extensions are strongly influenced by their complex phenomenology. They can explain a number of unresolved questions in particle physics and cosmology, including the genesis of dark matter, cosmic inflation, asymmetry of matter and antimatter, neutrino masses, and vacuum stability, if combined into a single structure. This is an extension of the gauge group of the standard model $G_{\rm SM}$ by $G_{\rm SM}\otimes U(1)_Z$ without any anomalies. We investigate the implications of the development of a general Majorana mass renormalization group for neutrinos with masses in the range of 0.03 $eV$ and 0.1 $eV$, which fall within the recently published range as well as the range to be explored in future planned experiments.

The Svenonius theorem establishes the correspondence between definability of relations in a countable structure and automorphism groups of these relations in the extension of the structure. This correspondence may help in finding the description of the definability lattice constituted by all definability spaces (reducts) of the original structure. However, the major difficulty here is the necessity to consider the extensions which generally are obscure and hardly amenable to classification. Because of that results on definability lattices were obtained only for $\omega$-categorical structures (i.\,e. those in which all elementary extensions are isomorphic to the structure itself). All known definability lattices for such structures proved to be finite. In this work we introduce the concept of upwards complete structure as such in which all its extensions are isomorphic. Further we define upwards completions structures. For such structures Galois correspondence between definability lattice and the lattice of closed supergroups of automorphism group of the structure is an anti-automorphism. These lattices could be infinite in general. We describe the natural class of structures which have upwards completion, that is discretely homogeneous graphs, present the explicit constrcution of their completion and automorphism groups of completions. We establish the general \emph{localness} property of discretely homogeneous graphs and present the examples of completable structures and their completions.

The Seljuks, who came from the Central Asian prairies, invaded Asia Minor towards the end of the 11th century. The land had been settled by then mainly by the Christian Eastern Romans and Armenian peoples. Seljuks were Moslems; they built monumental structures, some of which have survived the natural disasters of several centuries to the present day. Most of these architectural marvels contain extraordinary decorations in the form of ornaments, friezes and rosettes. I have studied periodic ornaments and classified them into 17 mathematical wallpaper groups according to their symmetry properties that reveal their global structure. On the other hand, the local details of the ornaments, the motifs, show a clear variation from simple geometric patterns to complicated and refined forms. Seljuk art was originally influenced by Persian styles, later influenced by the Christian population in Asia Minor, and finally represents the impact of Islamic culture.

The article is devoted to the assessment of the network community as a collective subject, as a group of interconnected and interdependent persons performing joint activities. According to the main research hypothesis, various forms of group subjectness, which determine its readiness for joint activities, are manifested in the discourse of the network community. Discourse constitutes a network community, mediates the interaction of its participants, represents ideas about the world, values, relationships, attitudes, sets patterns of behavior. A procedure is proposed for identifying discernible traces of the subjectness of a network community at various levels (lexical, semantic, content-analytical scales, etc.). The subjective structure of the network community is described based on experts’ implicit representations. The revealed components of the subjectness of network communities are compared with the characteristics of the subjectness of offline social groups. It is shown that the structure of the subjectness of network communities for some components is similar to the structure of the characteristics of the subjectness of offline social groups: the discourse of the network community represents a discussion of joint activities, group norms and values, problems of civic identity. The specificity of network communities’ subjectness is revealed, which is manifested in the positive support of communication within the community, the identification and support of distinction between “us” and “them”. Two models of the relationship between discursive features and the construct “subjectness” are compared: additive-cumulative and additive. The equivalence of models is established based on the discriminativeness and the level of consistency with expert evaluation by external criteria.

A fast algorithm is established to transform points of the unit sphere into fundamental region symmetrically. With the resulting algorithm, a flexible form of invariant mappings is achieved to generate aesthetic patterns with symmetries of the regular polyhedra. This method avoids the order restriction of symmetry groups, which can be similarly extended to treat regular polytopes in n-dimensional space for n>=4.

The aim of this paper is to investigate the amenability modulo an ideal of Banach algebras with emphasis on applications to homological algebras. In doing so, we show that amenability modulo an ideal of A^** implies amenability modulo an ideal of A. Finally, for a large class of semigroups, we prove that l¹(S)^** is amenable modulo Iσ^** if and only if an appropriate group homomorphic image of S is finite where Iσ is the closed ideal induced by the least group congruence σ.

Cytokinesis, the process by which the cytoplasm divides to generate two daughter cells after mitosis, is a crucial stage of the cell cycle. Successful cytokinesis must be coordinated with chromosome segregation and requires the fine orchestration of several processes, such as constriction of the actomyosin ring, membrane reorganisation, and, in fungi, cell wall deposition. In Saccharomyces cerevisiae, commonly known as budding yeast, septins play a pivotal role in the control of cytokinesis by assisting the assembly of the cytokinetic machinery at the division site and controlling its activity. Yeast septins form a collar at the division site that undergoes major dynamic transitions during the cell cycle. This review will discuss the functions of septins in yeast cytokinesis, their regulation and the implications of their dynamic remodelling for cell division.

Background and objective: Symptoms of most neurodegenerative diseases, including Parkinson’s disease (PD), usually do not occur until substantial neuronal loss occurs. This makes the process of early diagnosis very challenging. Hence, this research used variant call format (VCF) analysis to detect variants and novel genes that could be used as prognostic indicators in the early diagnosis of prodromal PD. Materials and Methods: Data were obtained from the Parkinson’s Progression Markers Initiative (PPMI), and we analyzed prodromal patients with gVCF data collected in the 2021 cohort. A total of 304 participants were included, including 100 healthy controls, 146 prodromal genetic individuals, 21 prodromal hyposmia individuals, and 37 prodromal RBDs. A pipeline was developed to process the samples from gVCF to reach variant annotation and pathway and disease association analysis. Results: Novel variant percentages were detected in the analyzed prodromal subgroups. The prodromal subgroup analysis revealed novel variations of 1.0%, 1.2%, 0.6%, 0.3%, 0.5%, and 0.4% for the genetic male, genetic female, hyposmia male, hyposmia female, RBD male, and RBD female, respectively. Interestingly, 12 potentially novel loci (MTF2, PIK3CA, ADD1, SYBU, IRS2, USP8, PIGL, FASN, MYLK2, USP25, EP300 and PPP6R2) that were recently detected in PD patients were detected in the prodromal stage of PD. Conclusion: Genetic biomarkers are crucial for the early detection of Parkinson’s disease and its prodromal stage. The novel PD genes detected in prodromal patients could aid in the use of gene biomarkers for early diagnosis of the prodromal stage without relying only on phenotypic traits.

Dynamic virtual testing by Hardware in the Loop (HIL) real time simulation systems is common to minimize physical tests to validate and verify control algorithms, logics and software, under normal and emergency conditions. The accurate but costly HIL models setup activities could have an extended use to simulate faulty conditions that are seldom observable in the real system, yet they must be detected in advance and recognized. Data driven diagnostic methods have reached a mature development, in various sectors, proving effective in early detecting slowly varying deviations from nominal patterns of signals, even without a priori knowledge of their nature and behavior. These methods rely on vast amount of data logged from real systems that are ever and ever richer of monitoring telemetries that are worth being exploited. However, due to the usually reliable and safe systems being managed, it is often difficult to collect enough data on anomalous situations to validate fault detection and isolation and limit false positives. HIL model-based simulations allow generating and observing operational domains or transients rarely observed in real operations. This allows identifying the signals that are most correlated to faults and that could be selected to setup data-based diagnostic models of parts or subsystems, which are more suitable than the whole HIL model for online diagnostics, as well as to identify the features and trends that are most symptomatic of anomalous conditions.

The article proposes asymptotic methods for calculating Sommerfeld integrals, which enable us to calculate the integral using the expansion of a function into an infinite power series at the saddle point, where the role of a rapidly oscillating function under the integral can be fulfilled either by an exponential or by its product by the Hankel function. The proposed types of Sommerfeld integrals are generalized on the basis of integral representations of the Hertz radiator fields in the form of the inverse Hankel transform with the subsequent replacement of the Bessel function by the Hankel function. It is shown that the numerical values of the saddle point are complex. During integration, auxiliary or so-called standard integrals, which contain the main features of the integrand function, were used. As a demonstration of the accuracy of the technique, a previously known asymptotic formula for the Hankel functions was obtained in the form of an infinite series. The proposed method for calculating Sommerfeld integrals can be useful in solving the half-space Sommerfeld problem. An example is the expression in the form of an infinite series for the magnetic field of reflected waves, obtained directly through the Sommerfeld integral (SI).

The variation of the cationic composition in I2-II-IV-VI4 semiconductor compounds is an effective tool for altering their properties in a controlled manner. In particular, a partial substitution of Cu for Ag in kesterite Cu2ZnSnS4 was proposed to suppress Cu-Zn antisite defects and the improve photovoltaic performance. However, the efficiency of this approach may substantially depend on the fabrication route. Here, we report on the synthesis of (Cu,Ag)-Zn-Sn-S (CAZTS) and Ag-Zn-Sn-S (AZTS) nanocrystals (NCs) by means of "green" chemistry in aqueous solution and their detailed characterization by Raman spectroscopy and by several complementary techniques. Through a systematic variation of the nominal composition and quantification of the constituent elements in CAZTS and AZTS NCs by XPS, we identified the vibrational Raman and IR fingerprints of both the main AZTS phase and secondary phases of Ag-Zn-S and Ag-Sn-S compounds (for the first time). The formation of the secondary phases of Ag-S and Ag-Zn-S cannot be avoided entirely for this type of synthesis. The Ag-Zn-S phase, having its bandgap in near infrared range, is the reason of the non-monotonous dependence of the absorption edge of CAZTS NCs on the Ag content, with a trend to redshift even below the bandgaps of bulk AZTS and CZTS.

Recently, the conformable derivative and its properties have been introduced. In this paper, we propose and prove some new results on conformable Boundary Value Problems. First, we introduce a conformable version of classical Sturm´s separation, and comparison theorems. For a conformable Sturm-Liouville problem, Green's function is constructed, and its properties are also studied. In addition, we propose the applicability of the Green´s Function in solving conformable inhomogeneous linear differential equations with homogeneous boundary conditions, whose associated homogeneous boundary value problem has only trivial solution. Finally, we prove the generalized Hyers-Ulam stability of the conformable inhomogeneous boundary value problem.

In this paper, I introduce a new concept of representing numbers in base ; in other words, I have found new series for any number similar to series that could be written according to the collatz sequence which is called zi(n) in this article. These series need to end with 1. Then, we use two sets of rules to make a diagram which then proves the existence of such series for any number.In this diagram, by branching numbers into different branches in accordance to the modularity of 4 and continuing branching to the point that their numbers have enough common terms in their collatz series, we could reduce zi(n) to zi(k) so that k<n in any branch by Rule Number One. This diagram shows that zi(n) exists for every number, in other words, this proves the theorem (A) or zi-existence theorem. The proof of zi-existence theorem leads to a proof of the collatz conjecture because the collatz series could be written as a linear combination of such series that all of them end with 1, so the collatz series for any number ends with 1.

Nursing, a profession known for its compassion and dedication to providing exceptional patient care, relies heavily on the cultivation of caring attributes to uphold the highest standards of practice. Despite the common use of small group work in nursing education, there is a gap in understanding how these caring attributes are developed through this approach. This qualitative study sought to explore the emergence of caring attributes in small group settings as perceived by nursing students and educators. Thirteen nursing students and ten educators participated in semi-structured group interviews at a professional educational institution. The study identified four key sets of caring attributes nurtured through small group work: interpersonal communication with respect, compassion, and empathy; competence and confidence; and accountability to commitment. These findings underscore the essential role of caring in nursing, emphasizing how collaborative group work can facilitate the development of crucial attributes through interpersonal interactions. The cultivation of respectful communication skills among students is highlighted as pivotal for enhancing interactions with healthcare professionals, patients, and families, ultimately improving the quality of care provided. By providing opportunities for interactive learning and ongoing practice, students can effectively embody these caring attributes, fostering their nursing professionalism throughout their careers.

Background: Nanotechnology has emerged as a promising field of study, aiming to revolutionize healthcare through the innovative development of drugs, diagnostic tools, and medical devices. As a result, healthcare professionals in training are constantly faced with the challenge of understanding and applying these emerging technologies. The objective of this study is to determine the factors to consider for including the teaching of nanotechnological tools in medical specialty postgraduate programs. Methods: A study based on the Nominal Group Technique (NGT) was conducted to identify the factors that promote and hinder the implementation of nanotechnology in certain postgraduate programs where nanotechnology is employed, such as Internal Medicine, Critical Care Medicine, Family Medicine, and Clinical Pharmacology at the School of Medicine of Universidad de La Sabana. A framework analysis was used to analyze the collected data. Results: Based on the two research questions, several aspects were identified for the inclusion of nanotechnology in the medical practice of specialties. Key challenges include lack of knowledge and resource availability, misinformation, and lack of knowledge, as well as paradigmatic analysis as the main obstacles to the use of nanotechnology. Conclusions: The findings provide a first-time study on nanotechnology curricula within medical specialty programs in Colombia, with potential extrapolation to similar situations in other medical schools.

The aim of this study is to investigate the impact of delegated monitoring by the group leader and peer monitoring by group members on loan defaults in a group-based lending program in Vietnam. Data used in the study were collected from a questionnaire survey of 675 participants involved in group-based lending program in the Mekong River Delta, Vietnam. The group-based lending program employs a unique monitoring system that involves hiring the group leader to supervise the group and encouraging group members to monitor each other. The empirical findings derived from the Probit model indicated that delegated monitoring significantly reduces loan defaults, but there was no evidence supporting the effectiveness of peer monitoring within the group. Additionally, under the delegated monitoring scheme, group size plays an important role in decreasing loan defaults.

This paper studies the Bondi-Metzner-Sachs group in homogeneous projective coordinates, because it is then possible to write all transformations of such a group in a manifestly linear way. The 2-sphere metric, Bondi-Metzner-Sachs metric, asymptotic Killing vectors, generators of supertranslations, as well as boosts and rotations of Minkowski spacetime, are all re-expressed in homogeneous projective coordinates. Last, the integral curves of vector fields which generate supertranslations are evaluated in detail. This work prepares the ground for more advanced applications of the differential geometry of asymptotically flat spacetimes in projective coordinates.

Wellbeing is a multifaceted concept that involves various facets of human condition and experience, including individual and communal spiritual, emotional, intellectual, physical, and social dimensions. To explore the complex facets of sustainable wellbeing, this study utilized an interpretive qualitative research approach, looking at round table (focus group) discussion data obtained from a diverse group of public and private sector representatives, including education, government, non-governmental organizations, and businesses in Qatar. The purpose of this study was to gain a contextualized understanding of how participants perceive and experience wellbeing. A purposive sampling technique was employed to recruit participants representing different sectors of society. To elicit participants’ perspectives on wellbeing, thematic analysis was used to identify recurring themes and patterns that emerged from the focus groups, viewed through the lens of Bronfenbrenner’ Ecological Systems Theory. Findings reveal that wellbeing is a very personal and subjective experience. Key themes extracted from the data include challenges to sustainable wellbeing in Qatar, including technological disruptions and socio-cultural influences. These challenges require proactive measures that reflect educational priorities, promote cultural preservation, and foster resilient communities while emphasizing individual and collective sustainable wellbeing. This research also identified opportunities for enhancing sustainable wellbeing in Qatar.

The electron of spin −1/2 is a Dirac fermion of a complex four-component spinor field. Though it is effectively addressed by relativistic quantum field theory, an intuitive form of the fermion still remains lacking and it is often described by the so-called Dirac belt trick. In this novel undertaking, the electron is examined within the boundary posed by a recently proposed MP model of a hydrogen atom into 4D space-time. Its transformation to Dirac fermion appears consistent with Dirac belt trick, quantum mechanics and Lie group with gravity considered to be a classical force for an irreducible spinor field. These outcomes are compatible with Dirac field theory and its associated features like wave function collapse, quantized Hamiltonian, non-relativistic wave function, Weyl spinor, Lorentz transformation and Feynman diagrams. The model though speculative, it could become important towards defining the fundamental state of matter subject to further examinations.