Matiyasevich's theorem states that there is no algorithm to decide whether or not a given Diophantine equation has a solution in non-negative integers. Smorynski's theorem states that the set of all Diophantine equations which have at most finitely many solutions in non-negative integers is not recursively enumerable. We prove: (1) Smorynski's theorem easily follows from Matiyasevich's theorem, (2 ) Hilbert's Tenth Problem for Q has a negative solution if and only if the set of all Diophantine equations with a finite number of rational solutions is not recursively enumerable.

We prove: (1) the set of all Diophantine equations which have at most finitely many solutions in non-negative integers is not recursively enumerable, (2) the set of all Diophantine equations which have at most finitely many solutions in positive integers is not recursively enumerable, (3) the set of all Diophantine equations which have at most finitely many integer solutions is not recursively enumerable, (4) analogous theorems hold for Diophantine equations D(x₁, …, x_p) = 0, where p ∈ N\{0} and for every i ∈ {1, …, p} the polynomial D(x₁, …, x_p) involves a monomial M with a non-zero coefficient such that x_i divides M, (5) the set of all Diophantine equations which have at most k variables (where k ≥ 9) and at most finitely many solutions in non-negative integers is not recursively enumerable.

The Diophantine equation for which p is prime 2^n = p^2 + 7 and n is integers with p > 0, is examined in this work. It is demonstrated by examining the characteristics of the equation that the only solutions meeting these requirements are p = 3 with n = 5 and p = 5 with n = 7. In order to analyze the above equation, it is necessary to look at the properties of primes and how they relate to powers of two. These results advance our knowledge of prime numbers and how they behave in certain mathematical problems.

Strategic intelligence covers the examination of what impacts and influences the business and the related SWOT analysis, (strengths, weaknesses, opportunities, and threats mapping). Through this research, leaders will be able to properly allocate and re-route resources, identify areas of improvement, and ensure that strategic initiatives are aligned with the organization's mission. Strategic intelligence is, therefore, effective through the use of critical thought and data-driven decisions and seeing the outcomes of different positioned alternatives. It must also form and support a culture of cooperation and open communication within the organizations, stimulating employees' inputs and learning curves. The article's subject is the necessity for strategic intelligence, a crucial competence for leaders, managers, and companies striving to remain competitive, to be utilized and best leveraged in today's volatile and dynamic business contexts. It helps the leadership turn proactive, foresee trends, and make correct, agile decisions that enforce companies' long-term growth and success. This study follows a research design that includes a thorough literature review and bibliometric research, executed via VoSViewer, illustrating the concept of strategic intelligence from a leadership point of view as a driver of competitive advantage. Further, the article points out that the limitations are acknowledged because the literature on the matter is limited, as strategic intelligence is relatively new to the business sector; moreover, more research is required to fully understand and use the potential of strategic intelligence in business growth. By overcoming these limitations and continuing to study this concept, businesses can gain a competitive edge and make informed decisions that fuel their success in an ever-evolving market. As a result, this study contributes to developing strategic intelligence in leadership and business and paves the road for further research and applications of strategic intelligence theories in organizational contexts.

This study delves into a unique binary pattern found within the wellknown 3n+1 problem, or Collatz conjecture. Through careful analysis of the steps in the 3n+1 sequence, we have discovered a special binary representation that captures the behavior of all positive integers undergoing this transformation. With this new understanding, we have provided a solid proof confirming the validity of the 3n+1 problem for all positive integers. Our method goes beyond the need for extensive computational confirmation, providing a simple and elegant resolution to a long-standing mathematical mystery.

For a set of closed curved surfaces that resemble a Langmuir monolayer an energy is defined that depends only on the curvature of the surfaces interacting with the dimensions normal to the surfaces, that is, the thickness of these surfaces. The thickness, or depth, of the surfaces originates because of surface-particles with chains, that move freely on the inside of the surfaces at a certain depth. This is a purely geometrical description that does not depend on the introduction of ad hoc constants like the elastic constant. With a statistical mechanical model the equations of state are calculated for a gas of non-connected sphere-like surfaces in a volume. There are two states of which the lower temperature state is depending mostly on the interaction energy and surface properties, and the higher temperature state is depending mostly on sphere kinetic and volume properties. This results in aggregation of the sphere-like surfaces from many small ones to few large ones when lowering temperature and vice versa. The model allows for the calculation of the partition function and, when the emergence of the curvature - depth interaction is described as a phase-transformation, for the application of Noether’s theorem. Because of these properties the model is interesting in its own right apart from being an addition to existing elastic descriptions of surfaces.

We investigate a singularly perturbed q-difference differential Cauchy problem with polynomial coefficients in complex time and space with quadratic nonlinearity. We construct local holomorphic solutions on sectors in the complex plane with respect to the perturbation parameter with values in some Banach space of formal power series in space with analytic coefficients on shrinking domains in time. Two aspects of these solutions are addressed. One feature concerns asymptotic expansions in the parameter for which a Gevrey type structure is unveiled. The other fact deals with confluence properties as q tends to 1. In particular the built up Banach valued solutions are shown to merge in norm to a fully bounded holomorphic map in all its arguments that solves a nonlinear partial differential Cauchy problem.

A linear Cauchy problem with polynomial coefficients wich combines q-difference operators for q>1 and differential operators of irregular type is examined. A finite set of sectorial holomorphic solutions w.r.t the complex time is constructed by means of classical Laplace transforms. These functions share a common asymptotic expansion in the time variable which turns out to carry a double layers structure which couples q-Gevrey and Gevrey bounds. In the last part of the work, the problem of confluence of these solutions as q tends to 1 is investigated.

The asymptotic behavior of the analytic solutions of a family of singularly perturbed q-difference-differential equations in the complex domain is studied. Different asymptotic expansions with respect to the perturbation parameter and to the time variable are provided: one of Gevrey nature, and another of mixed type Gevrey and q-Gevrey. This asymptotic phenomena is observed due to the modification of the norm established on the space of coefficients of the formal solution. The techniques used are based on the adequate path deformation of the difference of two analytic solutions, and the application of several versions of Ramis-Sibuya theorem.

In this paper we exploit concepts from Information Theory to improve the classical Chvatal’s greedy algorithm for the Set Covering Problem. In particular, we develop a new greedy procedure, called Surprisal-Based Greedy Heuristic (SBH), incorporating the computation of a “surprisal” measure when selecting the solution columns. Computational experiments, performed on instances from the OR-Library, show that SBH yields a 2.5% improvement in terms of the objective function value over the Chvatal’s algorithm while retaining similar execution times, making it suitable for real-time applications. The new heuristic was also compared with Kordalewski’s greedy algorithm, obtaining similar solutions with much lower times on large instances, and Grossmann and Wool’s algorithm for unicost instances, where SBH obtained better solutions.

We examine a family of nonlinear q-difference-differential Cauchy problems obtained as a coupling of linear Cauchy problems containing dilation q-difference operators, recently investigated by the author, and quasi-linear Kowalevski type problems that involve contraction q-difference operators. We build up local holomorphic solutions to these problems. Two aspects of these solutions are explored. One facet deals with asymptotic expansions in the complex time variable for which a mixed type Gevrey and q-Gevrey structure is exhibited. The other feature concerns the problem of confluence of these solutions as q tends to 1.

The previous two parts of the paper (correspondingly, https://philpapers.org/rec/PENFLT-2 and https://philpapers.org/rec/PENFLT-3) demonstrate that the interpretation of Fermat’s last theorem (FLT) in Hilbert arithmetic meant both in a narrow sense and in a wide sense can suggest a proof by induction in Part I and by means of the Kochen - Specker theorem in Part II. The same interpretation can serve also for a proof FLT based on Gleason’s theorem and partly similar to that in Part II. The concept of (probabilistic) measure of a subspace of Hilbert space and especially its uniqueness can be unambiguously linked to that of partial algebra or incommensurability, or interpreted as a relation of the two dual branches of Hilbert arithmetic in a wide sense. The investigation of the last relation allows for FLT and Gleason’s theorem to be equated in a sense, as two dual counterparts, and the former to be inferred from the latter, as well as vice versa under an additional condition relevant to the Gödel incompleteness of arithmetic to set theory. The qubit Hilbert space itself in turn can be interpreted by the unity of FLT and Gleason’s theorem. The proof of such a fundamental result in number theory as FLT by means of Hilbert arithmetic in a wide sense can be generalized to an idea about “quantum number theory”. It is able to research mathematically the origin of Peano arithmetic from Hilbert arithmetic by mediation of the “nonstandard bijection” and its two dual branches inherently linking it to information theory. Then, infinitesimal analysis and its revolutionary application to physics can be also re-realized in that wider context, for example, as an exploration of the way for physical quantity of time (respectively, for time derivative in any temporal process considered in physics) to appear at all. Finally, the result admits a philosophical reflection of how any hierarchy arises or changes itself only thanks to its dual and idempotent counterpart.

An evolutionary game is introduced which considers game-theoretic strategies in the context of non-linear population matrix models. This game considers the states and actions of the organisms of the evolving population, and a notion of dynamic equilibrium between strategies is described. The game’s formalism is expounded and a proof about equilibrium is given; specifically that any stable equilibrium can be described by proportions of pure strategies; particularly when population matrices are not defective.

When an edge is removed, a cycle graph Cn becomes a n-1 tree graph. This observation from extremal set theory leads us to the realm of set theory, in which a topological manifold of genus-1 turns out to be of genus-0. Starting from these premises, we prove a theorem suggesting that a manifold with disjoint points must be of genus-0, while a manifold of genus-1 cannot encompass disjoint points.

The general theory of relativity (GR) is symmetric under smooth coordinate transformations also known as diffeomorphisms. The general coordinate transformation group has a linear subgroup denoted the Lorentz group of symmetry which is maintained also in the weak field approximation to GR. The dominant operator in the weak field equation of GR is thus the d'Alembert (wave) operator which has a retarded potential solution. Galaxy Clusters are huge physical systems having dimensions of many hundreds of millions of light years. Thus any change at the cluster center will be noticed at the rim only hundreds of millions of years later. Those retardation effects are neglected in present day cluster modelling and in particular are neglected in virial calculations used to relate mass and velocities on the cluster. The significant differences between the predictions of Newtonian instantaneous action at a distance and observed velocities are usually explained by either assuming dark matter or by modifying the laws of gravity (MOND). In this paper we will show that taking general relativity seriously without neglecting retardation effects one can explain the velocities in a galactic cluster without postulating dark matter. It should be stressed that the current approach does not require that velocities, $v$ are high, in fact the vast majority of cluster bodies are substantially subluminal. In other words, the ratio of $\frac{v}{c} \ll 1$. Typical velocities in galaxies are less than ~1000 km/s, which makes this ratio $0.01$ or smaller. However, one should consider the fact that every gravitational system even if it is made of subluminal bodies has a retardation distance, beyond which the retardation effect cannot be neglected. Every natural system such as stars and galaxies and even galactic clusters exchange mass with its environment. For example, the sun losses mass through the solar wind and galaxies accrete gas from the intergalactic medium. This means that all natural gravitational systems have a finite retardation distance. The question is thus quantitative, how large is the retardation distance? The change of mass of the sun is quite small and thus the retardation distance of the solar system is quite large allowing us to neglect retardation effects within the solar system. However, for galaxies and galaxy clusters the retardation distance is within the system itself and cannot be neglected.

The purpose of the research is to investigate the unique solvability of a nonlocal boundary value problem for a loaded equation of parabolic-hyperbolic type in a special domain. Methods: Using representations of a general regular solution, the existence and uniqueness of the problem posed is proved. Results: A new method for proving the unique solvability of nonlocal boundary value problems for one loaded equation of mixed type in a special domain has been formed and developed. Conclusions: The obtained results make it possible to solve some problems of genetics, immunology, transonic gas dynamics and thermal physics, which are associated with displacement.

Let $f\left(1\right)=1$ , and let $f(n+1)=2^{2^{f\left(n\right)}}$ for every positive integer n. We consider the following hypothesis: if a system S ⊆ {x_i · x_j = x_k : i, j, k ∈ {1, . . . , n}} ∪ {x_i + 1 = x_k : i, k ∈{1, . . . , n}} has only finitely many solutions in non-negative integers x₁, . . . , x_n, then each such solution (x₁, . . . , x_n) satisfies x₁, . . . , x_n ≤ f (2n). We prove: (1) the hypothesisimplies that there exists an algorithm which takes as input a Diophantine equation, returns an integer, and this integer is greater than the heights of integer (non-negative integer, positive integer, rational) solutions, if the solution set is finite; (2) the hypothesis implies that there exists an algorithm for listing the Diophantine equations with infinitely many solutions in non-negative integers; (3) the hypothesis implies that the question whether or not a given Diophantine equation has only finitely many rational solutions is decidable by a single query to an oracle that decides whether or not a given Diophantine equation has a rational solution; (4) the hypothesis implies that the question whether or not a given Diophantine equation has only finitely many integer solutions is decidable by a single query to an oracle that decides whether or not a given Diophantine equation has an integer solution; (5) the hypothesis implies that if a set $\mathfrak{M}$ ⊆ has a finite-fold Diophantine representation, then $\mathfrak{M}$ is computable.

The temporary immersion system bioreactor named GreenTray®[2], [3]presents advantages over the existing ones. Firstly, there is no need to use forceps to move the shoots or plantlets in or out of the recipient, neither the use of scalpel to divide them. Secondly, the basis of the shoot can remain in the GreenTray® and can sprout again in several cycles of growth. These two characteristics reduce the costs in the process of micropropagation. Besides, shoots or plantlets development is enhanced by the aeration of the recipient, thus enriching with CO2 the recipient atmosphere. The chapter describes and provides images and values of interest in (1) the micropropagation process of some commercial Prunus or Pyrus rootstocks; (2) the plantlet growth under autotrophic conditions; and (2) the inoculation of plants with pathogens that reproduce in vitro the symptoms observed in vivo, using the GreenTray® bioreactor.

In Functional Analysis as well as Topology, we frequently encounter sets, say $X$, that contain elements close to each other. These sets display a defining "finite-ness" property: for all open cover $\mathcal{O}$ of $X$, there exists a finite subcollection $\mathcal{U}\subseteq\mathcal{O}$ such that $\mathcal{U}$ covers $X$. Such spaces $X$ are called $\textbf{compact}$, and the above "finite-ness" property afford us great convenience, because we can always investigate $X$ by investigating its finite open cover $\mathcal{U}$Arzela-

This paper presents a theory on graph topological structure and graph coloring, proving that for any N-order graph structure (with a topological structure similar to ), the maximum number of colors required for coloring is less than or equal to . The Four Color Theorem is just one special case of this theory, with the maximum structure size for a four-color graph being a 4-order structure graph, hence requiring only a maximum of 4 colors for coloring.

There are many problems based on solving non-autonomous differential equations of the form x¨(t)+ω2(t)x(t)=0, where x(t) represents the coordinate of a material point and ω is the angular frequency. The inverse problem involves finding the bounded coefficient ω. Continuity of the function ω(t) is not required. The trajectory x(t) is unknown, but the initial and final values of the phase variables are given. The variation principle of minimum time for the entire dynamic process allows for the determination of the optimal solution {x(t),ω(t)}. Thus, the inverse problem is an optimal control problem. No simplifying assumptions were made.

We introduce a class of logarithmic wave equation. We study the global existence of week solution for this class of equation. We deal with the initial boundary value problem of this class. Using the Galerkin method and the Gross logarithmic Sobolev inequality we establish the main theorem of existence of week solution for this class of equation arising from Q-Ball Dynamic in particular.

Fingerprints are essential for human identification and are valuable tools in criminal investigations. The pursuit of new materials for digital printing is expanding, with increasing interest in natural compounds such as bixin, sourced from annatto seeds. Despite its traditional use as a natural dye with medicinal properties, the potential of bixin in papilloscopy remains largely untapped. In this study, we meticulously extracted bixin from annatto seeds and meticulously developed composites incorporating zinc carbonate (bixin/ZnCO3) and kaolinite (bixin/kaolinite). UV-visible spectroscopy was used for characterization, and the extracted bixin showed absorption peaks at 429, 453, and 481 nm, which were very similar to standard peaks at 429, 457, and 487 nm. The two samples also had the same retention times (7.07 min) according to further liquid chromatography analysis. Sweat pores were easier to detect thanks to the effectiveness of the bixin/ZnCO3 and bixin/kaolinite composites in creating high contrast sebaceous and natural latent fingerprints. These results highlight the composites’ potential as novel and fascinating instruments for papilloscopy applications, which might also improve forensic investigations.

A new method in which completely eliminated the negative value of the scattering power is proposed in this paper. Primarily, here are presented the Freeman-Durden decomposition of the scattering powers, which are computed by using the coherency matrix elements with rotation and without rotation. Secondly, this paper investigates the reasons of the occurrence of negative values of the scattering powers. Then using the modification like in algorithm proposed by Yamaguchi for G4U, it was applied for the algorithm of Freeman-Durden decomposition to eliminate negative values. In this research, Radarsat-2 radar remote sensing data were used, which are acquired for study area Yushu County, Qinghai province, China. At the end, the comparison results of Yamaguchi G4U and a modified Freeman-Durden decompositions were presented.

We have revised the problem of the motion of a heavy symmetric top. When formulating equations of motion of the Lagrange top with the diagonal inertia tensor, the potential energy has more complicated form as compared with that assumed in the literature on dynamics of a rigid body. Using the Liouville's theorem, we solve the improved equations in quadratures and present the explicit expressions for the resulting elliptic integrals.

Sustainable continuous cover forestry is defined and analyzed in several ways. The differential equation representing growth of the basal areas of individual trees, motivated by fundamental biological production theory by Lohmander (2017a), is analyzed and extended in different directions. From the solution of the differential equation, the basal area and the tree diameter are obtained as explicit functions of time. The diameter is a strictly increasing function of time. In the absence of competitors, the diameter increment is shown to be a strictly decreasing function of time. Hence, the diameter increment can also be interpreted as a strictly decreasing function of the diameter. Alternative forms of adjustment of the differential equation, with consideration of competition, are defined. If the competition is strong, with large trees in the vicinity of a particular tree, then the basal area increment, and the diameter increment, are reduced. The growth of a large tree is less sensitive than the growth of a small tree, to competition from other trees. Under strong competition, the basal area increment, and the diameter increment, are strictly concave functions of the size of the tree. The unique maximum of the diameter increment occurs at a higher diameter, if the competition increases. In dynamic equilibrium, the tree size frequency distribution is stationary. If natural tree mortality can be avoided via the harvest strategy, the tree size frequency distribution is a function of the size and competition dependent growth function, and the harvest strategy. Empirical tree size frequency data are used to simultaneously estimate parameters of a size and competition dependent growth function and the applied harvest strategy, via nonlinear optimization. The properties of the estimated growth function are consistent with the corresponding properties of the production theoretically motivated hypothetical function, and the properties of the estimated harvest strategy confirm the corresponding hypotheses. The R2 of the nonlinear regression exceeds 0.97. With access to an empirically estimated equilibrium tree size distribution, it is possible to: 1. Estimate size frequency relevant parameters of tree size and competition dependent growth functions for individual trees. 2. Estimate the applied harvest strategy. 3. Explain and reproduce the empirically estimated tree size equilibrium distribution.

Epithelial ovarian cancer (EOC) has not significantly benefited from advances in immunotherapy, mainly because of the lack of well-defined actionable antigen targets. Using proteogenomic analyses of primary EOC tumors, we previously identified 91 aberrantly expressed tumor-specific antigens (TSAs) originating from unmutated genomic sequences. Most of these TSAs derive from non-exonic regions, and their expression results from cancer-specific epigenetic changes. The present study aimed to evaluate the immunogenicity of 48 TSAs selected according to two criteria: presentation by highly prevalent HLA allotypes and expression in a significant fraction of EOC tumors. Using targeted mass spectrometry analyses, we found that pulsing with synthetic TSA peptides leads to a high-level presentation on dendritic cells. TSA abundance correlated with the predicted binding affinity to the HLA allotype. We stimulated naïve CD8 T cells from healthy blood donors with TSA-pulsed dendritic cells and assessed their expansion with two assays: MHC-peptide tetramer staining and TCR Vβ CDR3 sequencing. We report that these TSAs can expand sizeable populations of CD8 T cells and, therefore, represent attractive targets for EOC immunotherapy.

I demonstrate that Bell's theorem is based on circular reasoning and thus a fundamentally flawed argument. It unjustifiably assumes the additivity of expectation values for dispersion-free states of contextual hidden variable theories for non-commuting observables involved in Bell-test experiments, which is tautologous to assuming the bounds of ±2 on the Bell-CHSH sum of expectation values. Its premises thus assume in a different guise the bounds of ±2 it sets out to prove. Once this oversight is ameliorated from Bell's argument, the bounds on the Bell-CHSH sum of expectation values work out to be ±2√2 instead of ±2, thereby mitigating the conclusion of Bell's theorem. Consequently, what is ruled out by the Bell-test experiments is not local realism but the additivity of expectation values, which does not hold for non-commuting observables in any hidden variable theories to begin with.

In Brazil, Brazilian borreliosis (BB), characterized molecularly, exhibits symptoms akin to Lyme disease (LD) but presents unique epidemiological, clinical, and morphological features. This study explores the incidence, diagnostic challenges, and awareness initiatives regarding this disease in Brazil. Employing a narrative review methodology, data were sourced from Pubmed, Ebsco, Google Scholar, and Web of Science without temporal constraints. Results reveal diagnostic complexities in Brazil due to the low sensitivity of conventional tests and the use of North American B. burgdorferi antigens. Despite challenges, epidemiological studies indicate an upswing in cases in humans and animals. Therefore, there is an urgent need to define new biomarkers, molecular strategies, or new antigenic targets to advance the development of vaccines and diagnostics. Early and accurate pathogen identification is crucial for active surveillance to comprehend and manage this zoonosis.

In Germany, the phloem sucking planthopper Pentastiridius leporinus (Hemiptera: Cixiidae) currently represents the epidemiological driver for the spread of the syndrome “Basses Richesses” in sugar beet, which results in a reduced sugar content and an economic loss for the farmers. This disease is associated with the γ-proteobacterium ‘Candidatus Arsenophonus phytopathogenicus’ and the Stolbur phytoplasma ‘Candidatus Phytoplasma solani’. Recently, P. leporinus was found in potato fields in Germany associated with Stolbur-like symptoms in this crop. In this study, we confirmed that the vector completes its lifecycle on sugar beet as well as on potato when reared under controlled conditions. Transmission experiments with adults of this vector combined with molecular analyses showed for the first time that both pathogens are transmitted by this vector to potato. For an accurate assessment of the Ca. P. solani and Ca. A. phytopathogenicus titers in the vector and host plants, gBlocks derived from the hsp20- and 16S rRNA gene were employed, respectively. For Ca. P. solani the limit of detection was determined in potato and sugar beet material. The results of this study will further research on the epidemiology of the syndrome “Basses Richesses” and “Stolbur” diseases and the response of host plants and vector insects to both pathogens.

This study focuses on the optimal deployment problem, and determines the optimal size of a military force to send to the battle field. The decision is optimized, based on an objective function, that considers the cost of deployment, the cost of the time it takes to win the battle, and the costs of killed and wounded soldiers with equipment. The cost of deployment is modeled as an explicit function of the number of deployed troops and the value of a victory with access to a free territory, is modeled as a function of the length of the time it takes to win the battle. The cost of lost troops and equipment, is a function of the size of the reduction of these lives and resources. An objective function, based on these values and costs, is optimized, under different parameter assumptions. The battle dynamics is modeled via the Lanchester differential equation system based on the principles of directed fire. First, the deterministic problem is solved analytically, via derivations and comparative statics analysis. General mathematical results are reported, including the directions of changes of the optimal deployment decisions, under the influence of alternative types of parameter changes. Then, the first order optimum condition from the analytical model, in combination with numerically specified parameter values, is used to determine optimal values of the levels of deployment in different situations. A concrete numerical case, based on documented facts from the Battle of Iwo Jima, during WW II, is analyzed, and the optimal US deployment decisions are determined under different assumptions. The known attrition coefficients of both armies, from USA and Japan, and the initial size of the Japanese force, are parameters. The analysis is also based on some parameters without empirical documentation, that are necessary to include to make optimization possible. These parameter values are motivated in the text. The optimal solutions are found via Newton- Raphson iteration. Finally, a stochastic version of the optimal deployment problem is defined. The attrition parameters are considered as stochastic, before the deployment decisions have been made. The attrition parameters of the two armies have the same expected values as in the deterministic analysis, are independent of each other, have correlation zero, and have relative standard deviations of 20%. All possible deployment decisions, with 5000 units intervals, from 0 to 150000 troops, are investigated, and the optimal decisions are selected. The analytical, and the two numerical, methods, all show that the optimal deployment level is a decreasing function of the marginal deployment cost, an increasing function of the marginal cost of the time to win the battle, an increasing function of the marginal cost of killed and wounded soldiers and lost equipment, an increasing function of the initial size of the opposing army, an increasing function of the efficiency of the soldiers in the opposing army and a decreasing function of the efficiency of the soldiers in the deployed army. With stochastic attrition parameters, the stochastic model also shows that the probability to win the battle is an increasing function of the size of the deployed army. When the optimal deployment level is selected, the probability of a victory is usually less than 100%, since it would be too expensive to guarantee a victory with 100% probability. Some of many results of relevance to the Battle of Iwo Jima, are the following: In the deterministic Case 0 analysis, the optimal US deployment level is 66200, the time to win the battle is 30 days and 14000 US soldiers are killed or wounded. If the marginal cost of the time it takes to win a victory doubles, the optimal deployment increases to 75400, the time to win a victory is reduced to 26 days, and less than 12000 soldiers are killed or wounded. In the stochastic Case 0 analysis, the optimal US deployment level is 65000, the expected time to win the battle is 46 days and almost 25000 US soldiers are expected to be killed or wounded. If the cost per killed or wounded soldier increases from 0 to 5 M $US, the optimal deployment level increases to 75000. Then, the victory is expected to appear after 35 days and 19900 US soldiers are expected to be killed or wounded.

In this paper, we propose a method to find all efficient solutions of an interval multiple objective linear programming (IMOLP) problem with interval coefficients in the objective functions, the constraint matrix and the right-hand side vector. The set of all efficient solutions of an IMOLP problem can completely supply information to the decision makers in finding their most preferred solutions but, up to now, not all solutions of an IMOLP problem can be found by known methods. A numerical example is given to illustrate the working of the proposed method.

The unsteady Ekman problem involves finding the response of the near-surface currents to wind stress forcing under linearized dynamics. Its solution can be conveniently framed in the frequency domain in terms of a quantity that is known as the transfer function, the Fourier transform of the impulse response function. In this paper, a theoretical investigation of a fairly general transfer function form is undertaken with the goal of paving the way for future observational studies. Building on earlier work, we consider in detail the transfer function arising from a linearly-varying profile of the vertical eddy viscosity, subject to a no-slip lower boundary condition at a finite depth. The linearized horizontal momentum equations are shown to transform to a modified Bessel’s equation for the transfer function. Two self-similarities, or rescalings that each effectively eliminate one independent variable, are identified, enabling the dependence of the transfer function on its parameters to be more readily assessed. A systematic investigation of asymptotic behaviors of the transfer function is then undertaken, yielding expressions appropriate for eighteen different regimes, and unifying the results from numerous earlier studies. A solution to a numerical overflow problem that arises in the computation of the transfer function is also found. All numerical code associated with this paper is distributed freely for use by the community.

Two new dimacrolide sesquiterpene pyridine alkaloids (DMSPAs), dimacroregelines A (1) and B (2), were isolated from the stems of Tripterygium regelii. The structures of both compounds were characterized by extensive 1D and 2D NMR spectroscopic analyses, as well as HRESIMS data. Compounds 1 and 2 are two rare DMSPAs possessing unique 2-(3′-carboxybutyl)-3-furanoic acid units forming the second macrocyclic ring, representing the first example of DMSPAs bearing an extra furan ring in their second macrocyclic ring system. Compound 2 showed inhibitory effects on the proliferation of human rheumatoid arthritis synovial fibroblast cell (MH7A) at a concentration of 20 μM.

We examine a linear q-difference differential equation which is singular in complex time t at the origin. Its coefficients are polynomial in time and bounded holomorphic on horizontal strips in one complex space variable. The equation under study represents a q-analog of a singular partial differential equation, recently investigated by the author, which comprises Fuchsian operators and entails a forcing term that combines polynomial and logarithmic type functions in time. A sectorial holomorphic solution to the equation is constructed as a double complete Laplace transform in both time t and its complex logarithm log t and Fourier inverse integral in space. For a particular choice of the forcing term, this solution turns out to solve some specific nonlinear q-difference differential equation with polynomial coefficients in some positive rational power of t. Asymptotic expansions of the solution relatively to time t are investigated. A Gevrey type expansion is exhibited in a logarithmic scale. Furthermore, a formal asymptotic expansion in power scale is displayed, revealing a new fine structure involving remainders with both Gevrey and q-Gevrey type growth.

Preventive Maintenance (PM) is a periodic maintenance strategy, which has great results for devices in extending their life, increasing productivity, and most importantly, help avoid unexpected breakdowns and their costly consequence. A preventive maintenance scheduling (PMS) is determining the time for carrying out PM, and it represents a sensitive issue in terms of impact on production if the time for the PM process is not optimally distributed. In this study, hybrid heuristic methods were used to solve the PMS problem, as genetic algorithm and Tabu research were adopted. The optimal solution was reached in a short time compared to previous studies in which optimal methods were used, integer programming and nonlinear integer programming. Also, sensitivity analysis was applied to measure the robustness and strength of the method used, where an optimal solution was obtained for all experiments and in record time. This method can be used for power plants in privet or public sectors, to generate an optimal PMS, to save money, and to avoid water or electricity cuts.

Fluctuation theorems are a class of equalities each of which links a thermodynamic path functional such as heat and work to a state function such as entropy and free energy. Jinwoo and Tanaka [L. Jinwoo and H. Tanaka, Sci. Rep. 5, 7832 (2015)] have shown that each microstate of a fluctuating system can be regarded as an ensemble (or a 'macrostate') if we consider trajectories that reach each microstate. They have revealed that local forms of entropy and free energy are true thermodynamic potentials of each microstate, encoding heat, and work, respectively, within an ensemble of paths that reach each state. Here we show that information that is characterized by the local form of mutual information between two subsystems in a heat bath is also a true thermodynamic potential of each coupled state and encodes the entropy production of the subsystems and heat bath during a coupling process. To this end, we extend the fluctuation theorem of information exchange [T. Sagawa and M. Ueda, Phys. Rev. Lett. 109, 180602 (2012)] by showing that the fluctuation theorem holds even within an ensemble of paths that reach a coupled state during dynamic co-evolution of two subsystems.

The paper is a continuation of another paper (https://philpapers.org/rec/PENFLT-2) published as Part I. Now, the case of “n=3” is inferred as a corollary from the Kochen and Specker theorem (1967): the eventual solutions of Fermat’s equation for “n=3” would correspond to an admissible disjunctive division of qubit into two absolutely independent parts therefore versus the contextuality of any qubit, implied by the Kochen – Specker theorem. Incommensurability (implied by the absence of hidden variables) is considered as dual to quantum contextuality. The relevant mathematical structure is Hilbert arithmetic in a wide sense (https://dx.doi.org/10.2139/ssrn.3656179), in the framework of which Hilbert arithmetic in a narrow sense and the qubit Hilbert space are dual to each other. A few cases involving set theory are possible: (1) only within the case “n=3” and implicitly, within any next level of “n” in Fermat’s equation; (2) the identification of the case “n=3” and the general case utilizing the axiom of choice rather than the axiom of induction. If the former is the case, the application of set theory and arithmetic can remain disjunctively divided: set theory, “locally”, within any level; and arithmetic, “globally”, to all levels. If the latter is the case, the proof is thoroughly within set theory. Thus, the relevance of Yablo’s paradox to the statement of Fermat’s last theorem is avoided in both cases. The idea of “arithmetic mechanics” is sketched: it might deduce the basic physical dimensions of mechanics (mass, time, distance) from the axioms of arithmetic after a relevant generalization, Furthermore, a future Part III of the paper is suggested: FLT by mediation of Hilbert arithmetic in a wide sense can be considered as another expression of Gleason’s theorem in quantum mechanics: the exclusions about (n = 1, 2) in both theorems as well as the validity for all the rest values of “n” can be unified after the theory of quantum information. The availability (respectively, non-availability) of solutions of Fermat’s equation can be proved as equivalent to the non-availability (respectively, availability) of a single probabilistic measure as to Gleason’s theorem.

In this paper, we study the global existence and exponential decay for a dynamic contact problem between a Timoshenko beam with second sound and two rigid obstacles, of which the heat flux is given by Cattaneo's law instead of the usual Fourier's law. The main difficulties arise from the irregular boundary terms, from the low regularity of the weak solution and from the weaker dissipative effects of heat conduction induced by Cattaneo's law. By considering related penalized problems, proving some a priori estimates and passing to the limit, we prove the global existence of the solutions. By considering the approximate framework, constructing some new functionals and applying the perturbed energy method, we obtain the exponential decay result for the approximate solution, and then prove the exponential decay rate to the original problem by utilizing the weak lower semicontinuity arguments.

This paper presents a new approach to a different proof of "Fermat's Last Theorem.” For the proof of the theorem, it is proposed to use a more straightforward geometrical approach. A special family of curves, the Elba curves, is introduced to facilitate the proof. This approach makes the proof easier to comprehend by mathematicians and those interested in the subject.

Bell's theorem can be refuted by presenting a counterexample which predicts correctly the expectation values of QM. As Bell has only ruled out noncontextual models a contextual model with hidden variables would refute his theorem. Such a model is presented able to explain the spin measurement results with entangled photons or electrons. It is not ruled out by the Kochen-Specker Theorem. Consequences for the feasibility of quantum computers are discussed.

In this short paper we study some properties of the lines associated with van Aubel’s theorem in the special case when squares are replaced with equilateral triangles constructed on the sides of an arbitrary quadrilateral.

This paper offers a novel geometric and visual approach to the renowned Four Color Map Theorem and K5 non-planarity problem while unveiling their profound connection to the "kissing number" problem in 2D. We represent planar graphs through circles and tangents, simplifying complex structures and shedding light on these classic problems. Our proofs by contradiction, rooted in the kissing number concept, reveal that both the Four Color Map Theorem and K5 non-planarity are fundamentally linked, as they pivot around the concept of coloring. This study bridges the realms of geometry and graph theory, providing fresh insights and emphasizing the significance of the kissing number problem in various fields.

In (Semigroup Forum 77: 325-338, 2008) Mahmoudi M. and Renshaw J. solved a study that covers of cyclic $S$-acts over monoids. This article is an attempt to initiate the covers of finitely generated $S$-acts. We give a necessary and sufficient condition for a monoid to have the properties that $n$-generated $S$-acts have strongly flat covers, Condition $(P)$ covers and projective covers. The main conclusions extend some known results. We show also that Condition $(P)$ covers of finitely generated $S$-acts are not unique, unlike the situation for strongly flat covers. Additionally, we demonstrate that the property of Enochs' $\mathcal{X}$-precover of $S$-act $A$, where $\mathcal{X}$ denotes a class of $S$-acts that are closed under isomorphisms.

Congenital cytomegalovirus (cCMV) infection resulting from non-primary maternal infection or reactivation during pregnancy can cause serious fetal-neonatal sequelae. We describe a male newborn born at term, with signs of perinatal asphyxia, and intractable acute provoked seizures, in the context of severe cCMV infection. The newborn was delivered in a referral hospital by emergency caesarean section due to fetal distress. Due to signs of asphyxia at birth and clinical moderate encephalopathy (Sarnat 2), he was transferred to our center for therapeutic hypothermia. Continuous full video-electroencephalography monitoring showed no seizures during the first 72 hours, however, soon after rewarming, he presented refractory status epilepticus. Cranial ultrasonography revealed bilateral ventricular and intraparenchymal hemorrhage. Routine infectious screen-ing on urine, blood, cerebrospinal fluid, and nasopharyngeal secretions revealed positive CMV DNA Polymer-ase Chain Reaction (PCR) on all samples. The CMV DNA performed on the bloodspot (Guthrie) card taken at birth yielded a positive result, confirming the intrauterine transmission and congenital origin of the infection. Maternal non-primary CMV infection in pregnancy is transmitted to the fetus in 0.5-2% of cases. When transmitted, it may cause serious fetal abnormalities, complications in the immediate neonatal period, and se-vere sequelae later in childhood. During pregnancy, it is useful to monitor maternal serology for CMV, even in previously immunized mothers, to identify signs of new infection or viral reactivation and implement measures to prevent neonatal sequelae. The possible advantages of standardized CMV screening of all newborns are a pertinent discussion point, as this may enable us to identify affected neonates timeously and prevent long term disabilities.

Generative artificial intelligence tools are flourishing across various sciences, particularly in the educational domain. ChatGPT, with its versions 3.5 and 4.0, stands out for its multilingual capabilities, catering to both students and educators. This research aimed to evaluate the performance differences between these versions, and importantly, to compare the accuracy of ChatGPT's responses in English versus Arabic. In our study, we presented ChatGPT with 39 chemistry problems related to 6th-7th grade curriculum, including twenty-five open questions and fourteen multiple-choice questions. Each response was categorized as accurate, partially accurate, or inaccurate. Our analysis, focused on trends across versions and languages, revealed significant enhancements in version 4.0, particularly in its ability to process Arabic. However, despite these improvements, our findings indicate that responses in English consistently outperformed those in Arabic in terms of accuracy. In light of this discrepancy, we suggest that ChatGPT either incorporates additional Arabic databases into its training regimen or develops a code that adopts the following strategy to ensure more accurate responses in science education: questions should first be translated from Arabic to English, addressed, and then retranslated into Arabic before being presented to the user. This approach takes advantage of the greater accuracy of responses in English to benefit Arabic-speaking users, and it may also improve outcomes for speakers of other languages who experience less precise answers in the fields of chemistry or science education.

We provide a detailed analysis of the electronic properties of graphene-like materials with charge carriers living on a curved substrate, focusing in particular on constant negative-curvature spacetime. An explicit parametrization is also worked out in the remarkable case of Beltrami geometry, with an analytic solution for the pseudoparticles modes living on the curved bidimensional surface. We will then exploit the correspondent massless Dirac description, to determine how it affects the sample local density of states.

A careful examination of the fundamentals of electromagnetic theory shows that due to the underlying mathematical assumptions required for Stokes' Theorem, global charge conservation cannot be guaranteed in topologically non-trivial spacetimes. However, in order to break the charge conservation mechanism we must also allow the electromagnetic excitation fields D, H to possess a gauge freedom, just as the electromagnetic scalar and vector potentials $\varphi$ and A do. This has implications for the treatment of electromagnetism in spacetimes where black holes both form and then evaporate, as well as extending the possibilities for treating vacuum polarisation. Using this gauge freedom of D, H we also propose an alternative to the accepted notion that a charge passing through a wormhole necessarily leads to an additional (effective) charge on the wormhole's mouth.

In this paper, we derive and prove, by means of Binomial theorem and Faulhaber's formula, the following identity between $m$-order polynomials in $T$ $$\sum_{k=1}^{\ell}\sum_{j=0}^m A_{m,j}k^j(T-k)^j=\sum_{k=0}^{m}(-1)^{m-k}U_m(\ell,k)\cdot T^k=T^{2m+1}, \ \ell=T\in\mathbb{N}.$$

In this study, I examined the Beals conjecture on the basis of formulas that produce composite numbers, and I developed some other conjectures that, if answered, would be an answer to the Beals conjecture. Apart from this, I have examined the Beals conjecture from another perspective and posed The Germany Problem.

In 2023, the Bureau of Land Management (BLM) estimated that there were 68,928 mustangs living on United States public lands in 10 western states. The agency uses Appropriate Management Levels to determine the number of mustangs who need to be removed from the land. Once removed and processed, mustangs are sent to adoptions or sales events or retained in short-or long-term holding facilities. Adoptions and sales are the leading avenues for rehoming mustangs; however, the number of horses the BLM can place fluctuates annually and never approaches the greater number removed from the range. To explore opportunities for increasing the number of mustang adoptions, we conducted in-depth interviews with 23 horse trainers located on the U.S. East Coast, asking about participants’ training programs, relationships with horses, perceptions of mustangs, and challenges that mustangs face in the dressage and eventing industries. Participants had varying experiences with mustangs; however, all were willing to work with a mustang in some capacity. Participants voiced the need for more satellite adoption locations on the East Coast to decrease barriers to acquiring a mustang, notably cost and time, and for expanding existing training programs to include eventing and dressage.

In this paper, we study the gravitational lensing by some black hole classes within the non-linear electrodynamics in weak field limits. First, we calculate an optical geometry of the non-linear electrodynamics black hole then we use the Gauss-Bonnet theorem for finding deflection angle in weak field limits. The effect of non-linear electrodynamics on the deflection angle in leading order terms is studied. Furthermore, we discuss the effects of the plasma medium on the weak deflection angle.

A family of singularly perturbed q-difference-differential equations under the action of a small complex perturbation parameter is studied. The action of the formal monodromy around the origin is present in the equation, which suggests the construction of holomorphic solutions holding logarithmic terms in both, the formal and the analytic level. We provide both solutions and describe the asymptotic behavior relating them by means of q-gevrey asymptotic expansions of some positive order, with respect to the perturbation parameter. On the way, the development of a space product of Banach spaces in the Borel plane is needed to provide a fixed point for a coupled system of equations.

The optimal structural design is imperative to minimize material consumption and reduce the environmental impact of construction. Given the complexity in the formulation of structural design problems, the process of optimization is commonly performed using artificial intelligence (AI) global optimization, such as Genetic Algorithm (GA). However, the integration of AI-based optimization together with visual programming (VP) in building information modeling (BIM) projects warrants further investigation. This study proposes a workflow by combining structure analysis, VP, BIM, and GA to optimize trusses. The methodology encompasses several steps including: (i) generation of parametric trusses in Dynamo VP; (ii) performing the finite element modeling (FEM) using Robot Structural Analysis (RSA); (iii) retrieving and evaluating the FEM results interchangeably between Dynamo and RSA; (iv) finding the best solution using GA; and (v) importing the optimized model into Revit, enabling the user to perform simulations and engineering analysis, such as life cycle assessment (LCA) and quantity surveying. The feasibility of the proposed workflow was tested on benchmark problems and compared with open literature. The outcomes of this study offer insight into the opportunities and limitations of combining VP, GA, FEA, and BIM for structural optimization applications, particularly to enhance structural efficiency and sustainability in construction.

In this paper we address the understanding of the problem, of why a deep learning model decides that an individual is eligible for a loan or not. Here we propose a novel approach for inferring, which attributes matter the most, for making a decision in each specific individual case. Specifically we leverage concepts from neural attention to devise a novel feature wise attention mechanism. As we show, using real world datasets, our approach offers unique insights into the importance of various features, by producing a decision explanation for each specific loan case. At the same time, we observe that our novel mechanism, generates decisions which are much closer to the decisions generated by human experts, compared to the existent competitors.

In this paper we use Toeplitz quantization to extend in a very natural way Kostant's theorem for the group $SU(m)$ to the group of symplectomorphisms of the unit sphere and we also give another proof of the infinite dimensional version of Schur and Horn theorem for the sphere based on Schur and Horn theorem for Hermitian matrices.

Problem solving is one of the most important components of the human cognition that affects for ages the progress of the human society. Mathematical modelling is a special type of problem solving concerning problems related to science or everyday life situations. The present study is a review of the author’s earlier works on problem solving and mathematical modelling from the scope of Education. Its real goal is that it presents in a systematic way and in a few pages only the results of many years research on the subject. This helps the reader to get a comprehensive idea about a very important topic belonging to the core of Mathematics Education, which is very useful to those wanting to study deeper the subject and get directions for further research in the area.

Jacobian theta function identities are related to the Addition formula for the Weierstrass 1 Sigma function. In this paper, from the Addition formula for Weierstrass Sigma function, new and 2 simple proofs of four square sums theorem are given. Using the addition formula of the theta func- 3 tions, we also give simple proofs of two square sums and eight square sums theorem.

A well-known result of Posner’s second theorem states that if the commutator of each element in a prime ring and its image under a nonzero derivation is central, then the ring is commutative. In the present paper, we extend this bluestocking theorem to an arbitrary ring with involution involving prime ideals. Further, apart from proving several other interesting and exciting results, we establish *-version of Vukman’s theorem [48, Theorem 1]. Precisely, we describe the structure of quotient ring A/L, where A is an arbitrary ring and L is a prime ideal of A. Further, by taking advantage of the *-version of Vukman’s theorem, we show that if a 2-trosion free semiprime ring A with involution admits a nonzero *-centralizing derivation, then A contains a nonzero central ideal. This result is in a spirit of the classical result due to Bell and Martindale [19, Theorem 3]. As the applications, we extends and unify several classical theorems proved in [6],[25,[42], and [48] . Finally, we conclude our paper with a direction for further research.

Based on our recent thermodynamic formulation of the Friedmann equation, we demon- strate how the age of the universe must be approximately 14.6 billion years. This is about 800 million years older than predicted by the Λ-CDM model and therefore greatly alleviates the early galaxy formation problem.

In this paper we address the approximation of the coupling problem for the wave equation and Maxwell's equations of electromagnetism in the time domain in terms of the electric field, by means of a nodal linear finite-element discretization in space, combined with a classical'explicit finite-difference scheme for the time discretization. Our study applies to the particular case where the dielectric permittivity has a constant value outside a sub-domain, whose closure does not intersect the boundary of the domain where the problem is defined. Inside this sub-domain Maxwell's equations hold. Outside this sub-domain the wave equation holds, which may correspond to the Maxwell's equations with a constant permittivity under certain conditions. We consider as a model the case of first order absorbing boundary conditions. Optimal error estimates that hold in natural norms under reasonable assumptions are given, among which lies a typical CFL condition for hyperbolic equations.

In this work, we report the magnetocaloric effect (MCE) in two systems of non-interactive particles, the first corresponds to the Landau problem case and the second, the case of an electron in a quantum dot subjected to a parabolic confinement potential. In the first scenario, we realize that the effect is totally different from what happens when the degeneration of a single electron confined in a magnetic field is not taken into account. In particular, when the degeneracy of the system is negligible, the magnetocaloric effect cools the system, while in the other case, when the degeneracy is strong, the system heats up. For the second case, we study the competition between the characteristic frequency of the potential trap and the cyclotron frequency to find the optimal region that maximizes the ΔT of the magnetocaloric effect, and due to the strong degeneration of this problem, the results are in coherence with those obtained for the Landau problem. Finally, we consider the case of a transition from a normal MCE to an inverse one and back to normal as a function of temperature. This is due to the competition between the diamagnetic and paramagnetic response when the electron spin in the formulation is included.

P versus NP is considered as one of the most fundamental open problems in computer science. This consists in knowing the answer of the following question: Is P equal to NP? It was essentially mentioned in 1955 from a letter written by John Nash to the United States National Security Agency. However, a precise statement of the P versus NP problem was introduced independently by Stephen Cook and Leonid Levin. Since that date, all efforts to find a proof for this problem have failed. Another major complexity class is NP-complete. It is well-known that P is equal to NP under the assumption of the existence of a polynomial time algorithm for some NP-complete. We show that the Monotone Weighted Xor 2-satisfiability problem (MWX2SAT) is NP-complete and P at the same time. Certainly, we make a polynomial time reduction from every directed graph and positive integer k in the K-CLOSURE problem to an instance of MWX2SAT. In this way, we show that MWX2SAT is also an NP-complete problem. Moreover, we create and implement a polynomial time algorithm which decides the instances of MWX2SAT. Consequently, we prove that P = NP.

In this paper, a geometric model is introduced for Neutrosophic data problem for the first time. This model is based on neutrosophic sets and neutrosophic relations. Neutrosophic control points are defined according to these points, resulting in neutrosophic Bézier curves.

China planned to promote the large-scale adoption of Electric Vehicles (EVs) in the thirteenth five-year plan, however, this target faces many obstacles. This paper was trying to analyze the main barriers to widespread adoption of EVs through a survey in Shenzhen, which has the biggest EVs market share in China major cities. Based on previous scholarly findings, this paper conducted a new study which collected 406 approved questionnaires among 500 participants. The study proposed five hypotheses to examine the main barriers to widespread adoption of EVs. The analysis conducted by statistical methods: two-way frequency tables, chi-square test, and factor analysis. The results noted that perception of EVs advantages and recharging access remained the main barriers to EVs large-scale penetration. Besides, financial incentives drop would not cause a significant decline of EVs adoption in future. The study proposed suggestions to carmaker and government policy administrator on the analysis and discussion.

Companies are increasingly focusing on sustainable business practices. Internal and external stakeholders’ expectations manifest in legal requirements, national and international standards, and market and customer expectations, among other things, must be considered. In addition to profit maximization as the usual target for corporate management, management must consider environmental sustainability aspects such as resource efficiency, greenhouse gas intensity, and a company's emissions behavior. In addition, social aspects relating to the company's employees, the immediate urban environment, the situation in the supply chain, and effects on the market environment must increasingly be considered. Specifically, companies are faced with the chal-lenge of dealing with conflicting objectives regarding the various aspects of sustainability and, if necessary, weighing them up against each other. These trade-offs must be made against the company's socio-economic and ecological environment, corporate strategy, and sustainability goals. This paper provides an overview of current approaches and research gaps on this topic through a literature review. It shows a lack of methods and frameworks to specifically deal with trade-offs and conflicts of goals.

The authors argue that despite significant numbers of foreign workers present in the Russian labor market Russia remains unattractive for highly skilled foreign workers. The economic crisis the country has faced since 2014 has resulted in a further outflow of foreign nationals from OECD countries. So Russia has to look for employees among newcomers from the former Soviet states, the majority of whom come from Central Asia. Russian politics with regard to immigration is characterized by the collision between “geopolitical” and domestic policy rationales. On one hand, seeking to maximize its influence in the post-Soviet space Russia provides preferential conditions of employment for citizens of partner countries in the framework of the Eurasian Economic Union. On the other hand, the Kremlin is afraid to liberalize its approach to immigration and the integration of immigrants through fear of losing popularity among the electorate. The second substantial feature of Russian immigration politics is an extreme level of securitization of migration issues. The government considers these issues primarily through a policing lens. One cannot claim that the Russian state does not take any steps to liberalize “migratory regulation”; however, the effect of these measures is being vastly reduced by new restrictions. In addition, liberally designed laws do not bring the expected results due to the corrupt practices that pervade the whole of migration regulation.

In this paper, we consider a fourth-order suspension bridge equation with nonlinear damping term |u_t|^m-2u_t and source term |u|^p-2u. We give necessary and sufficient condition for global existence and energy decay results without considering the relation between m and p. Moreover, when p>m, we give sufficient condition for finite time blow-up of solutions. The lower bound of the blow-up time T_max is also established. It worth to mention that our obtained results extend the recent results of Wang (J. Math. Anal. Appl., 2014) to the nonlinear damping case.

We present a very computationally light and fast approximation algorithm and then verify it with genetic algorithm and simulated annealing. We show that our algorithm is on par with GA and SA in terms of output produced while having a tightly bounded time complexity. Our algorithm works best when there is a strong positive correlation between the reliability of a component and its cost. We present two algorithms with the same essence. One of them is system cost bounded and the other is target reliability bounded. Our proposed algorithm works on a subsystem level redundancy instead of component level redundancy.

It was the aim of this study to examine whether the usage of the vaccine COXEVAC® (Ceva Santé Animale) could reduce the consumption of antibiotics in Q-fever-positive dairy farms. Additionally, the effects of other herd-level factors on the consumption of antibiotics were investigated. In this longitudinal cohort study, 36 farms with vaccination and 13 farms without vaccination participated. In all herds, Coxiella burnetii had been directly or indirectly diagnosed. To compare the treatment frequency of antibiotics between the vaccinated group and the non-vaccinated group, the consumption of antibiotics for each farm was collected using the veterinary documents about the application and delivery of antibiotics. To gather detailed information about herd data, nutrition, milking management, housing, and animal health, the farmers were interviewed with the help of a questionnaire. The results suggest that there might be an association between the vaccination against Q fever and a reduced consumption of antibiotics. Neither herd size nor milk yield level influenced the consumption of antibiotics in the study herds. Type of flooring and udder cluster disinfection while milking were associated with a lower and higher therapy frequency, respectively. Further studies are necessary to elucidate the cause-effect relationship between vaccination and the consumption of antibiotics.

Recycling waste products is an environmental-friendly activity that can bring benefits to accompany, saving manufacturing costs and improving economic efficiency. For the beer industry, recycling bottles can reduce manufacturing costs and reduce the industry's carbon footprint. This paper presents a model for a multi-objective collection-distribution center location and allocation problem in a closed loop supply chain for the beer industry, in which the objective is to minimize total costs and transportation pollution. Uncertainties in the form of randomness and fuzziness are jointly handled in this paper to ensure a more practical problem solution, for which returned bottle sand unusable bottles are considered fuzzy random variables. A heuristic algorithm based on priority-based global-local-neighbor particle swarm optimization (pb-glnPSO) is applied to ensure reliable solutions for this NP-hard problem. A case study on a beer operation company is conducted to illustrate the application of the proposed model and demonstrate the priority-based global-local-neighbor particle swarm optimization.

The theoretical limit of link prediction is a fundamental problem in this field. Taking the network structure as object to research this problem is the mainstream method. This paper proposes a new viewpoint that link prediction methods can be divided into single or combination methods, based on the way they derive the similarity matrix, and investigates whether there a theoretical limit exists for combination methods. We propose and prove necessary and sufficient conditions for the combination method to reach the theoretical limit. The limit theorem reveals the essence of combination method that is to estimate probability density functions of existing links and nonexistent links. Based on limit theorem, a new combination method, theoretical limit fusion (TLF) method, is proposed. Simulations and experiments on real networks demonstrated that TLF method can achieve higher prediction accuracy.

Considering the current needs of industry 4.0, especially in the condition of systems linked to artificial intelligence, this multidisciplinary concept work and difficult to execute, proposes the main idea of recognizing patterns using mathematical concepts of simple access and logical resolution of great potential. The objective of this work is to demonstrate a process for pattern recognition by applying the Fibonacci concept to vibration signals of hybrid dynamical systems. For this to be possible, it was necessary to use the concepts of preprocessing in a vector for pattern recognition, together with the concepts of the golden rule of Fibonacci, finally, all applied in the theorem of Jeffcott Rotors. The general result, from a technical point of view, demonstrates positivity and relationship of patterns, because, considering the aspect of the location between the values of the experimental and numerical result, both signs have similarities.

Cancers are complex, adaptive ecosystems. They remain the leading cause of disease-related death among children in North America. As we approach computational oncology and Deep Learning Healthcare, our mathematical models of cancer dynamics must be revised. Recent findings support the perspective that cancer-microenvironment interactions consist of turbulent flows. As such, cancer pattern formation, protein-folding and metastatic invasion are discussed herein as processes driven by chemical turbulence within the framework of complex systems theory. Current state-of-the-art quantitative approaches used in reconstructing cancer stem cell networks are reviewed. To conclude, cancer stem cells are presented as strange attractors of the Waddington landscape.

This paper aims to investigate the Landau problem within a two-dimensional dynamical noncommutative (DNC) space. We address the deformed Landau problem using time-independent perturbation theory, where the eigenenergies are successfully determined. Notably, the energy shift depends on the DNC parameter $\tau$. Using the accuracy of energy measurement, we put an upper bound on the parameter $\tau$. Moreover, we study magnetoconductivity by employing the Kubo formula. This approach has allowed us to test the effects of noncommutative and DNC spaces on the behavior of magnetoconductivity. We show that dynamical noncommutativity of space has no effects on the x-component of the conductivity.

Discussing quantum theory foundations, von Neumann noted that the measurement process should not be regarded in terms of a temporal evolution. A reason for his claim is insurmountability of the gap between reversible and irreversible processes. The time operator formalism that goes beyond such a gap is adequate framework for elaboration of the measurement problem. It considers signals to be stochastic processes, whether they correspond to variables or distribution densities. Signal processing like that utilizes statistical properties to perform its tasks, which is the definition of statistical signal processing. A hierarchy of the measurement process is indicated by crossing between states and devices, which implies an evolution in the temporal domain. The concept has generalized to an open system by the use of duality in frame theory.

As one of the typical deposits in Sichuan-Yunnan-Guizhou Pb-Zn metallogenic province, the Daliangzi Pb-Zn deposit has a close genetic relation with the structural system of “black/fracture zone” formed under the action of NWW-approx. EW strike-slip structures in the metallogenic province, but the mechanism of rock and ore-controlling action of the structural system remains unclear. Based on detailed analysis of tectonite-mineralized alteration lithofacies of R1 “black/fracture zone”, the tectonite-mineralized alteration lithofacies zones can be divided into 4 types in succession outward from the Pb-Zn mineralization center, i.e., ① brecciated and stockwork-like Pb-Zn mineralization-complex breccia facies zone, ② stockwork-like Pb-Zn mineralization-simple breccia and cataclasite facies zone, ③ veined pyrite-sulfide-dolomitic cataclasite facies zone, and ④ fine-veined calcite-black carbonized dolomite facies zone; Cl- and SO42--rich high-temperature oxidizing ore-bearing fluid mixes with reducing fluid in Zone ① while migration and precipitation occur in Zone ④. With the evolution of ore-forming fluid, the homogenization temperature decreases from Zone ① to Zone ④, the salinity increases from Zone ① to Zone ② and then decreases to Zones ③ and ④, and the fluid density has little change on the whole; the contents of Zn, Pb, Cu, Ga, Ge, Cd, Ag, and other metallogenic elements, the Zn/Pb ratio, and the CaO/MgO mole ratio decrease gradually from Zone ① to Zone ④; and REE fractionation, calcilization, silicification, and pyritization enhance gradually from Zone ① to Zone ④. This series of changes are the product of diapirism (cryptoexplosion) of strike-slip structures and “black/fracture zone”, among which the second-order structures (F5, F100, and other faults) derived from NWW-approx. EW striking dextral shear-tension faults F1 and F15 control the brecciated and stockwork-like Pb-Zn mineralized complex breccia facies zones and the stockwork-like Pb-Zn mineralized simple breccia and cataclasite facies zones. Therefore, this paper establishes the zoning mode of tectonite-mineralized alteration lithofacies of “black/fracture zone” and proposes that Zones ① and ② are important prospecting criteria. conclusions.

Sialylated milk oligosaccharides (SMOs) is the most important oligosaccharides in human milk oligosaccharides (HMOs), and have a multifunctional health benefit, and the most abundant SMOs are sialyllactose (SLs). The previous studies indicate that the growth of tumor cells, and angiogenesis on tumor tissues with Lewis lung carcinoma, melanoma, and colon carcinoma cells could be prevented by SL. Thus, it has been proposed that SL might be an ideal candidate for the development of anti-angiogenic drugs without any side effects. It has been proposed that the Sialic acid (Sia) can be produced through SL’s hydrolysis, and the dietary Sia is further transported to the brain and other tissues though blood for formation of CMP-Sia, the activated precursor of Sia, and then is catalyzed by polysialyltransferases (polySTs) for synthesis of polysialic acid (polySia) or polysialylation of neural cell adhesion molecule (NCAM). Thus, it’s necessary to study and develop new inhibitors, which not only modulate a proper balance between the gut health and neuros system development, but also inhibit the overexpression of polySia, and thus block the tumor cell migration. In this study, we proposed that 3’-SL and 6’-SL may be more ideal inhibitors comparing with two previous inhibitors, the low molecular weight heparin (LMWH) and cytidine monophosphate (CMP) in the previous studies.

In this study, we adopt a unique approach by utilizing the responses of human autonomic systems to gauge the abundance of pollutants in inhaled air. Air pollution has numerous impacts on human health on a variety of time scales. This study uses biometric observations of the human autonomic response on the second timescale to investigate how the human body autonomically responds to inhaled pollutants in microenvironments, including particulate matter. PM1 and PM2.5, carbon dioxide (CO2), nitrogen dioxide (NO2), and nitric oxide (NO) on small temporal and spatial scales. These pollutants are exemplars of the wider human exposome. We compare two experimental approaches that use a similar methodology, employing a biometric suite to capture the physiological responses of cyclists and sensors to monitor the pollutants in the air surrounding them. We employ machine learning algorithms to estimate the levels of these pollutants and decipher the body’s automatic reactions to them. We observed high precision in predicting PM1, PM2.5 and CO2 using a limited set of biometrics from participants. Although the predictions for NO2 and NO were reliable at lower concentrations, the precision varied throughout the data range. This discrepancy suggests the potential to improve our models with more comprehensive data collection or advanced machine learning techniques.

Complex problem-solving (CPS) tasks have become an increasingly popular tool for understand-ing and assessing cognitive ability. These tasks have been repeatedly shown to be predictors of academic and workplace success above and beyond traditional measures of general intelligence and fluid intelligence. To date, there has been little exploration of the underlying mechanisms that drive this additional predictive utility. In this study, we examined the role of a variety of non-cognitive personality and investment traits that could drive performance on CPS tasks. Adult participants (n = 152) were recruited via M-Turk and completed a battery of personality and in-vestment trait measures, a measure of general mental ability, and a 61-trial microworlds-style CPS task. Generalised linear mixed-effects models revealed a wide variety of personality and in-vestment traits influenced task performance above and beyond general mental ability. Specifical-ly, two clusters of traits emerged as important determinants of performance: one cluster that in-fluenced the capacity to deal with the introduction of system randomness (Conscientiousness and Extraversion) and one cluster that influenced the capacity to deal with the introduction of system delays (NFC, Learning Goal Orientation, and Intellect). These findings suggest that CPS tasks do capture more than just general mental ability and may be good predictors of academic and workplace success because they tap into both cognitive ability and the motivation and willingness to engage in cognitive exploration and mental effort.

Saliva, as a diagnostic medium, offers a promising alternative to blood by virtue of its non-invasive collection, which enhances patient compliance, especially in paediatric and geriatric populations. In this study, we assessed the utility of saliva as a non-invasive medium for measuring V. cholerae-specific serum antibodies in naturally infected individuals. We tested paired serum and saliva samples obtained from a total of 63 cholera patients enrolled in a cohort study. Vibriocidal antibodies assay (IgM/IgG) as markers for accurate determination was used to determine cholera specific antibody levels. Using receiver operating characteristics (ROC) curve, we found that the best cut-off that maximizes (sensitivity + specificity) is 10 titers. At this saliva titer, the sensitivity is 76.9% (95%CI: 60.9%, 87.7%) and specificity is 80.0% (95%CI: 56.6%, 92.5%). Using Spearman’s correlation coefficient, we also found evidence of a positive correlation between Vibrio Cholerae saliva and serum antibodies (rho=0.66, p<0.001). In conclusion, saliva-based diagnostic cholera tests has high diagnostic accuracy, and would be advantageous, cheaper, and quicker for early diagnosis of severe cholera outcomes.

The massive amount of human biological, imaging and clinical data produced by multiple and diverse sources, necessitates integrative modeling approaches able to summarize all this information into answers to specific clinical questions. In this paper, we present a hypermodeling scheme able to combine models of diverse cancer aspects regardless of their underlying method or scale. Describing tissue-scale cancer cell proliferation, biomechanical tumor growth, nutrient transport, genomic-scale aberrant cancer cell metabolism, and cell signaling pathways that regulate the cellular response to therapy, the hypermodel integrates mutation, miRNA expression, imaging, and clinical data. The constituting hypomodels as well as their orchestration and links are described. Two specific cancer types, Wilms tumor (nephroblastoma) and non-small cell lung cancer, are addressed as proof of concept study cases. Personalized simulations over the actual anatomy of a patient have been carried out. The hypermodel has also applied to predict tumor control after radiotherapy and the relationship between tumor proliferative activity and response to neoadjuvant chemotherapy. Our innovative hypermodel holds promise as a digital twin based clinical decision support system and the core of future in silico trial platforms, although additional retrospective adaptation and validation is necessary.

Private Set Intersection (PSI) is a cryptographic method in secure multi-party computation that allows entities to identify common elements in their datasets without revealing their private data. Traditional approaches assume similar-sized datasets and equal computational power, overlooking practical imbalances. In real-world applications, dataset sizes and computational capacities often vary, particularly in the Internet of Things and mobile scenarios where device limitations restrict computational types. Traditional PSI protocols are inefficient here, as computational and communication complexities correlate with the size of larger datasets. Thus, adapting PSI protocols to these imbalances is crucial. This paper explores unbalanced PSI scenarios where one party (the receiver) has a relatively small dataset and limited computational power, while the other party (the sender) has a large amount of data and strong computational capabilities. It introduces three innovative solutions for unbalanced PSI: unbalanced PSI protocol based on Cuckoo filters, unbalanced PSI protocol based on single cloud assistance, and unbalanced PSI protocol based on dual cloud assistance, each addressing the shortcomings of the previous solution. These protocols primarily optimize database computational load, storage capacity, protocol execution time, and security. Depending on performance and security needs, different protocols can be employed for applications such as private contact discovery.

Despite the successful introduction of oral cholera vaccines, Zambia continues to experience multiple, sporadic, and protracted cholera outbreaks in various parts of the country. While vaccines have been useful in staying the cholera outbreaks, the ideal window for re-vaccinating individual’s resident in cholera hotspot areas remains unclear. Using a prospective cohort study design, 225 individuals were enrolled, re-vaccinated with two doses of Shanchol™ regardless of previous vaccination and followed-up for 90 days. Bloods collected at baseline before re-vaccination, at day 14 prior to second dosing and subsequently on days 28, 60, and 90. Vibriocidal assay was performed on samples collected at all five time points. Our results showed that anti-LPS and vibriocidal antibody titers increased at day 14 after re-vaccination and decreased gradually at 28, 60 and 90 across all the groups. Seroconversion rates were generally comparable in all treatment arms. We therefore conclude that vibriocidal antibody titers generated in response to re-vaccination still wane quickly irrespective of previous vaccination status. However, despite the observed decline, the levels of vibriocidal antibodies remained elevated over baseline values across all groups, an important aspect for Zambia where there is no empirical evidence as to the ideal time for re-vaccination.

Proposed article deals with analyses on trends of problem-solving robotic applications in manu-facturing, especially in transportations and manipulations. Intelligent agent-based manufacturing systems with robotic agents are observed. Intelligent core of such units must be able to propose the plan of problem-solving in form of strategy. The logical model of adaptive strategies planning for intelligent robotic system is described in form of predicates with presentation of data processing on base of set theory descriptions. Dynamic structure of workspace and possible change of goals are considered as reasons for functional strategies adaptation. Proposed formal descriptions are sup-ported by model of mobile robotic platform, acting in warehouse.

The problem of scheduling is an area that has attracted a lot of attention from researchers for many years. Its goal is to optimize resources in the system. The assigning task to the lecturer is an example of the timetabling problem, a class of scheduling. This study introduces a mathematical model to assign fixed tasks (the time and required skills to be fixed) to university lecturers. Our model is capable of generating a calendar that maximizes faculty expectations. The formulated problem is in the form of a multi-objective problem that optimal makes decisions require the trade-off presence of trade-offs between two or more conflicting objectives. To solve this, we use the Compromise Programming approach to multi-objective programming. We then proposed the new version of the Genetic Algorithm to solve the introduced model. Finally, the model and algorithm tested with real scheduling data collected at the Computing Fundamental Department, FPT University, Hanoi, Vietnam.

We study the effect of the degeneracy factor in the energy levels of the well-known Landau problem for a magnetic engine. The scheme of the cycle is composed of two adiabatic processes and two isomagnetic processes driven by a quasi-static modulation of external magnetic field intensity. We derive the analytical expression of the relation between the magnetic field and temperature along the adiabatic process and, in particular, reproduce the expression for the efficiency as a function of the compression ratio.

Although there is a common physiological notion that the origin of the membrane potential is attributed to transmembrane ion transport, it is theoretically possible to explain its generation by the mechanism of ion adsorption. It was previously suggested that the ion adsorption mechanism led even to the potential formulas which are even identical to either the famous Nernst equation or Goldman-Hodgkin-Katz equation. Our further analysis shown in this paper indicates that the potential formula based on the ion adsorption mechanism leads to one equation which is the function of material surface charge density and the material surface potential. Furthermore, we confirmed that the equation holds in all the different experimental systems we studied. Although we have not succeeded in elucidating why such an equation is established, the equation appears to be the key equation governing the characteristics of the membrane potential regardless of the systems in question.

The paper primarily demonstrates that the three internal triangles formed by connecting any point on a midsegment with the vertices of a generic triangle satisfy the geometric Proof of the Pythagorean theorem in Euclidean geometry. Moreover, this study elucidates the Pythagorean relationships inherent within three-dimensional geometric constructs resulting from the arrangement of three-dimensional spatial triangles. This geometric relationship, akin to a generalized extension of the Pythagorean theorem, unveils a unique spatial region characterized by this harmonious area interrelation among triangles.

Climate change is a global issue that draws widespread attention from the international society. As an important component of the climate system, the water cycle is directly affected by climate change. Thus, it is very important to study the influences of climate change on the basin water cycle with respect to maintenance of healthy rivers, sustainable use of water resources, and sustainable socioeconomic development in the basin. In this study, by assessing the suitability of multiple General Circulation Models (GCMs) recommended by the Intergovernmental Panel on Climate Change, Statistical Downscaling Model (SDSM) and Automated Statistical Downscaling model (ASD) were used to generate future climate change scenarios. These were then used to drive distributed hydrologic models (Variable Infiltration Capacity, Soil and Water Assessment Tool) for hydrological simulation of the Yangtze River and Yellow River basins, thereby quantifying the effects of climate change on the basin water cycle. The results showed that suitability assessment adopted in this study could effectively reduce the uncertainty of GCMs, and that statistical downscaling was able to greatly improve precipitation and temperature outputs in global climate mode. Compared to a baseline period (1961–1990), projected future periods (2046–2065 and 2081–2100) had a slightly decreasing tendency of runoff in the lower reaches of the Yangtze River basin. In particular, a significant increase in runoff was observed during flood seasons in the southeast part. However, runoff of the upper Yellow River basin decreased continuously. The results provide a reference for studying climate change in major river basins of China.

Grazing incidence X-Ray Diffraction spectroscopy was employed to characterize crystallinity of Iron, Nickel, Copper and Tungsten, prepared by sparking discharge process in presence of 0.4 T magnetic field at ambient temperature 25 °C. Iron thin film preserved crystallinity even after one year of ageing. Nickel exhibit higher crystallinity when sparked in nitrogen gas flow from the one sparked in oxygen. Tungsten was successfully crystalized after just 40 minutes of sparking inside of magnetic field.

The typically qualitative treatment of evidence underlying different causal hypotheses that attempt to explain singular historic events is criticized. Instead of using ad hoc qualitative arguments, it is here advocated to use Bayes theorem to assess how well evidence either support or weaken a specific causal hypothesis. It is argued that such a practice will enable scientists who study singular historic events to discuss, compare and aggregate different beliefs in a meaningful way.

By using Modified simple equation method, we study the Cahn Allen equation which arises in many scientific applications such as mathematical biology, quantum mechanics and plasma physics. As a result, the existence of solitary wave solutions of the Cahn Allen equation is obtained. Exact explicit solutions interms of hyperbolic solutions of the associated Cahn Allen equation are characterized with some free parameters. Finally, the variety of structure and graphical representation make the dynamics of the equations visible and provides the mathematical foundation in mathematical biology, quantum mechanics and plasma physics.

Background: MR image classification in datasets collected from multiple sources is complicated by inconsistent and missing DICOM metadata. Therefore, we aimed to establish a method for the efficient automatic classification of MR brain sequences. Methods: Deep convolutional neural networks (DCNN) were trained as one-vs-all classifiers to differentiate between six classes, T1 weighted (w), contrast-enhanced T1w, T2w, T2w-FLAIR, ADC, and SWI. Each classifier yields a probability, allowing threshold-based and relative probability assignment while excluding images with low probability (label: unknown, open-set recognition problem). Data from three high-grade glioma (HGG) cohorts was assessed; C1 (320 patients, 20101 MRI images) was used for training, while C2 (197, 11333) and C3 (256, 3522) were for testing. Two raters manually checked images through an interactive labeling tool. Finally, MR-Class' added value was evaluated via radiomics models' performance for progression-free survival (PFS) prediction in C2, utilizing the concordance index (C-I). Results: Approximately 10% of annotation errors were observed in each cohort between the DICOM series descriptions and the derived labels. MR-Class accuracy was 96.7% [95%-Cl: 95.8, 97.3] for C2 and 94.4% [93.6, 96.1] for C3. 620 images were misclassified; Manual assessment of those frequently showed motion artifacts or alterations of anatomy by large tumors. Implementation of MR-Class increased on average the PFS model C-I by 14.6% compared to a model trained without MR-Class. Conclusions: We provide a DCNN-based method for sequence classification of brain MR images and demonstrate its usability in two independent HGG datasets.

The separability problem is one of the basic and emergent problems in present and future quantum information processing. The latter focuses on information and computing based on quantum mechanics and uses quantum bits as its basic information units. In this paper we present an overview of the progress in the separability problem in bipartite systems, more specifically in two quantum bits (qubits) system, from the criterion based on the Bell’s inequalities in 1964 to the Li-Qiao Criterion and the enhanced entanglement criterion based on the symmetric informationally complete positive operator valued measures (SIC POVMs) in 2018.

The generation and maintenance of membrane potential is considered a fundamental element of the cellular machinery. They are based on elements of physics and chemistry. Mathematics is used to validate the equations and evaluate the results. However, this computation process can lead to a misunderstanding of the phenomena involved or to the masking of crucial events. It is even possible that the calculation no longer corresponds to the hypothesis considered. Membrane theory is no exception to these trivial considerations, which are essential for normal theory validation.

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

The Gol'denveizer problem of a torus can be described as follows: a toroidal shell is loaded under axial forces and the outer and inner equators are loaded with opposite balanced forces. Gol'denveizer pointed out that the membrane theory of shells is unable to predict deformation in this problem, as it yields diverging stress near the crowns. Although the problem has been studied by Audoly and Pomeau (2002) with the membrane theory of shells, the problem is still far from resolved within the framework of bending theory of shells. In this paper, the bending theory of shells is applied to formulate the Gol'denveizer problem of a torus. To overcome the computational difficulties of the governing complex-form ordinary differential equation (ODE), the complex-form ODE is converted into a real-form ODE system. Several numerical studies are carried out and verified by finite-element analysis. Investigations reveal that the deformation and stress of an elastic torus are sensitive to the radius ratio, and the Gol'denveizer problem of a torus can only be fully understood based on the bending theory of shells.

A given problem in physics can be solved if it is well formulated. Well formulated means that it has a bijective correspondence to physical reality. Mass Gap Problem has no bijective correspondence with the physical reality and is that’s why not solvable mathematically. It can be solved in the frame of quantum mechanics by the formulation of the photon’s mass accordingly to the Planck-Einstein relation.

We consider the thermodynamic and stability problem of Kerr black holes arising from the nonextensive/nonadditive nature of the Bekenstein-Hawking entropy formula. Nonadditive thermodynamics is often criticized by asserting that the zeroth law cannot be compatible with nonadditive composition rules, so in this work we follow the so-called formal logarithm method to derive an additive entropy function for Kerr black holes satisfying also the zeroth law's requirement. Starting from the most general, equilibrium compatible, nonadditive entropy composition rule of Abe, we consider the simplest, non-parametric approach that is generated by the explicit nonadditive form of the Bekenstein-Hawking formula. This analysis extends our previous results on the Schwarzschild case and shows that the zeroth law compatible temperature function in the model is independent of the mass-energy parameter of the black hole. By applying the Poincaré turning point method we also study the thermodynamic stability problem in the system.