A significantly reduced stress concentration effect and a stable deformation behavior are exhibited by the arc-like S-shaped auxetic structure. Analytical works beyond the bar and hinge method to capture structural effects, such as bending, shearing, etc., in the S-structure are scarce in the literature. The deformation pattern of the S-structure is dominated by bending and shearing within the linear elastic region. In this work, Timoshenko beam theory is used to derive closed-form expressions for overall elastic modulus and Poisson’s ratio. This agrees well with the results of finite element simulations. An adjusted R-square value of over 0.99 and almost 0.82 is obtained for elastic modulus and Poisson’s ratio, respectively. From parametric studies, it’s established that under quasi-static transverse load, strut thickness and the angle `α’ are the most important parameters for controlling elastic modulus, specific energy absorption, negative Poisson’s ratio (NPR) effect, and relative density of the entire auxetic structure. Also, it’s found that energy absorption and elastic modulus increase together. Interestingly, the elastic modulus of the structure under transverse load lies in the range from 3 MPa to 250 MPa, which means this structure is compliant enough and can be used in cushioning, packaging, soft robotics applications, etc.

It has been more than a century since Erlang published his paper in 1909. The classical queueing system for the M/D/c queue has been investigated by many authors. The key is to find the roots of an equation using explicit or numerical methods. We present an alternate form of explicit solution(s) of this/these root(s) using the Lambert-W function in this paper. In addition, the unsaturated probabilities of the number of customers in the system is derived explicitly in terms of this/these root(s). Finally, the mean number of customers in the system and the mean queueing delay are obtained from these probabilities. The exact queueing delay formula for the M/D/c queue is expressed in closed-form in terms of the root(s). Numerical results show that they are in excellent agreement with the numerical results published by Seelen, Tijms and Van Hoorn.

We discuss three key points: defining mathematically the notions of phase, symmetry breaking, topological defects and their stability in a formal language of homotopy theory and fiber bundle formalism; postulating and proving two theorems for successive symmetry breaking scenarios in condensed matter physics and cosmology, and demonstrating application of theorems to superfluid Helium 3 and Kibble-Lazarides-Shafi (KLS) walls, supporting and mathematically justifying the results of [Volovik, 2020].

Real and complex analytic functions are largely studied in the field of complex analysis and are seen as very useful tools in solving problems in mathematics, physics and engineering. Real and complex numbers are a subset of semi-structured complex numbers (a new number set created to algebraically solve division by zero). Nevertheless, the properties of analytic functions made up of semi-structured complex variables (called semi-structured complex analytic functions) is yet to be explored. This limits the range of possible problems that can be resolved using analytic functions). In this regard, the aim of this paper was to expound upon the properties of semi-structured complex analytic functions and show their application in solving engineering problems. The results of this paper included (1) developing a full set of Cauchy–Riemann Equations for the semi-structured complex -space; (2) define sufficient and necessary conditions for a semi-structured complex function to be analytic; (3) determine the relationship between semi-structured complex analytic functions, Laplace’s Equations and Poisson’s Equations; and (5) provide an example of the use of these functions.

Let $m$ and $n$ be the fixed positive integers. Suppose $\mathcal{A}$ is a von Neuman algebra with no central summands of type $I_{1}$ and $L_{m}$ be a Lie type higher derivation i.e., an additive (linear) map $L_{m} :\mathcal{A}\to \mathcal{A}$ such that \begin{equation}\label{def2} \[L_{m}(p_{n}(\mathfrak{S}_{1},\mathfrak{S}_{2},\cdots,\mathfrak{S}_{n}))=\sum_{l_1+l_2+\cdots+l_n=m}p_{n}\big(L_{l_1}(\mathfrak{S}_{1}),L_{l_2}(\mathfrak{S}_{2}),\cdots,L_{l_n}(\mathfrak{S}_{n})\big)\] %L_{m}(p_{n}(\mathfrak{S}_{1},\mathfrak{S}_{2},\cdots,\mathfrak{S}_{n}))=\sum_{l_1+l_2+\cdots+l_n=m}p_{n}\big(L_{l_1}(\mathfrak{S}_{1}),L_{l_2}(\mathfrak{S}_{2}),\cdots,L_{l_n}(\mathfrak{S}_{n})\big)\nonumber \end{equation} for all $\mathfrak{S}_{1},\mathfrak{S}_{2},\cdots,\mathfrak{S}_{n}\in \mathcal{A}$. In the present paper, we study Lie type higher derivations on von Neuman algebras and prove that every additive Lie type higher derivation on $\mathcal{A}$ has a standard form at zero product as well as at projection product. Further, we discuss some more related results.

The main object of this work is to establish the existence and uniqueness of a solution to the 3D Navier-Stokes (NS) system for an incompressible fluid with viscosity. The nonlinearity of the NS system, as well as the need to estimate velocity and pressure for every value of the viscosity parameter [1] make them challenging to solve. In this regard, in the present work, we study the Navier-Stokes system, which describe the flow of a viscous incompressible fluid and the solution was obtained for velocity and pressure in an analytical form. In addition, the found pressure distribution law, which is described by a Poisson type equation and plays a fundamental role in the theory of Navier-Stokes systems in constructing analytic smooth (conditionally smooth) solutions.

Lie algebra plays an important role in the study of singularity theory and other field of sciences. Finding numerous invariants linked with isolated singularities is always a main interest in the classification theory of isolated singularities. Any Lie algebra that characterizes simple singularity produces a natural question. The study of properties such as to find the dimensions of newly defined algebra is a remarkable work. Hussain, Yau and Zuo \cite{HYZ10} have been found a new class of Lie algebra \texorpdfstring{ $ \mathcal{L}_ k (V)$}{LG}, \texorpdfstring{$k\geq 1$}{LG} i.e., Der ($M_{k}(V), M_{k}(V)$) and purposed a conjecture over its dimension $\delta_{k}(V)$ for $k\geq0$. Later they proved it true for $k$ up to $k=1,2,3,4,5$. In this work, the main concern is whether it's true for a higher value of $k$. According to this, we calculate first, the dimension of Lie algebra \texorpdfstring{$\mathcal{L}_ k (V)$}{LG} for $k=6$ and then compute the upper estimate conjecture of fewnomial isolated singularities. Along with, we also justify the inequality conjecture: \texorpdfstring{$\delta_{k+1}(V) < \delta_{k}(V)$}{LG} for $k=6$. Our calculated results are innovative and a new addition to the study of singularity theory.

This paper presents an in-depth study of the stress wave behavior propagating in a Rayleigh–Love rod with a sudden cross-sectional area change. The analytical solutions of stress waves are derived for the reflection and transmission propagation behavior at the interface of the cross-sectional area change in the rod, considering inertia and Poisson’s effects. Examples solved by the finite element method are provided to verify the correctness of the analytical results. In addition to the forward analysis of Rayleigh–Love wave propagation in rods impacted by a striker rod, a nondestructive testing method is proposed to conduct the defect assessment in the rod type of the structure component with a sudden cross-sectional area change within a cover medium by using the measured signals at the measurable zone of the rod to be inspected.

Among all the active confinement techniques, the use of pre-tensioned stainless steel straps has recently gained much attention. The flexibility of the stainless steel straps allows us to bend and pass them through the thickness of the masonry, thus creating a three-dimensional strengthening system between the two opposite facings. The use of the same perforation for the passage of several straps closed in a loop generates a continuous strengthening system that prevents parts of the structure from falling and injuring the occupants during seismic events. However, the perforations can nullify the in-plane strengthening, as they act as cylindrical hinges and make the reinforcement system labile for certain strap arrangements. Diagonal compression tests on square masonry panels performed in the present study show that the straps improve neither strength nor ductility when running along the mortar head and bed joints, arranged in square meshes. Conversely, they improve both strength and ductility when the straps make angles of 45° with the mortar joints. Furthermore, the experimental results show that the straps exert an anisotropic effect that decreases the apparent in-plane Poisson ratio. They also provide new insights into the diagonal compression test and allow formulating a new proposal for the pseudo-ductility factor.

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

This paper is the continuation of a previous study, which highlighted some inconsistencies in the RILEM guidelines for the interpretation of the diagonal compression test. Although improved compared to the ASTM guidelines, in fact, the RILEM guidelines underestimate the state of hydrostatic stress induced by the diagonal compression test at the center of the wallette. The new interpretation of the diagonal compression test proposed in this article shows that the RILEM guidelines actually underestimate both the hydrostatic and the deviatoric stress states at the center of the wallette. The new formulation complies with the linear elastic theory and allows us to use the the diagonal compression test to identify the three elastic coefficients of masonry. In particular, it allows the identification of the Poisson ratio, which instead takes on a conventional value in the RILEM and ASTM guidelines. The difference of one order of magnitude between the conventional and proposed Poisson’s ratio is in agreement with the experimental results on another brittle material, namely concrete. Finally, the new proposal fills the gap between the results provided by the two tests usually performed to identify the shear behavior of masonry: the diagonal compression test and the shear-compression test.

This study aims to spatially analyze the distribution characteristics of vacant homes in Asan-si, Chungcheongnam-do, and understand the differences in factors causing vacant homes by type. We use a variety of statistical methods to examine these factors and identify key influencing factors such as the number of vacant stores, changes in overall population, land use complexity, and physical characteristics of land and buildings. The findings reveal that the factors contributing to the occurrence of vacant homes vary significantly by region and property type, highlighting the need for region-specific policies. For instance, in old town areas, small lot ratios and land use complexity are significant, while in rural village, the average number of floors and land use complexity play a major role. This study underscores the diversity of factors influencing vacant homes, suggesting that policies should be tailored to the unique characteristics of different regions to effectively address this issue.

Euler-Poisson equations of a charged symmetrical body in external constant and homogeneous electric and magnetic fields are deduced starting from the variational problem, where the body is considered as a system of charged point particles subject to holonomic constraints. The final equations are written for the center-of mass-coordinate, rotation matrix and angular velocity. General solution to the equations of motion is obtained for the case of a charged ball. For the case of a symmetrical charged body (solenoid), the task of obtaining the general solution is reduced to the problem of a one-dimensional cubic pseudo-oscillator. Besides, we present a one-parametric family of solutions to the problem in elementary functions.

A one-dimensional model for fluid and solute transport in poroelastic materials (PEM) is studied. Although the model was recently derived and some exact solutions, in particular steady-state solutions and their applications, were studied, special cases occurring when some parameters vanish were not analysed earlier. Since the governing equations are nonintegrable in nonstationary case, the Lie symmetry method and modern tools for solving ODE systems are applied in order to construct time-dependent exact solutions. Depending on parameters arising in the governing equations, several special cases with new Lie symmetries are identified. Some of them have a highly nontrivial structure that cannot be predicted from a physical point of view or using Lie symmetries of other real-world models. Applying the symmetries obtained, multiparameter families of exact solutions are constructed, including those in terms of elementary and special functions (hypergeometric, Whittaker, Bessel and modified Bessel functions). A possible application of the solutions obtained is demonstrated and it is shown that some exact solutions can describe (at least qualitatively) the solute transport in PEM. The obtained exact solutions can also be used as test problems for estimating the accuracy of approximate analytical and numerical methods for solving relevant boundary value problems.

Semenov-Tian-Shansky has introduced the modified classical Yang-Baxter equation, which is called the modified $r$-matrix. Relevant studies have been extensive in recent times. This paper is devoted to study cohomology theory of modified Rota-Baxter pre-Lie algebras and its applications. First we introduce the concept and representations of modified Rota-Baxter pre-Lie algebras. We then develop the cohomology of modified Rota-Baxter pre-Lie algebras with coefficients in a suitable representation. As applications, we consider the infinitesimal deformations, abelian extensions and skeletal modified Rota-Baxter pre-Lie 2-algebra in terms of lower degree cohomology groups.

The paper provides a methodological framework based on Multiple Criteria Decision Aid methods for determining relative regional vulnerabilities associated with forest fires that occurred during a given period. Different notions of ex-post vulnerability are defined based on the forest area burned and the frequency of forest fires, and their relation to the regions’ area and several socioeconomic characteristics. The methodology is applied to Greece and its administrative regions for the period 2000–2022. Linking the forest fire events with summer and spring temperatures and precipitation and using econometric count data analysis, the paper explores the climatic drivers of forest fire occurrence and provides projections of the expected change in the frequency of fires of specific size classes conditional on the evolution of mean seasonal regional temperature and precipitation according to IPCC scenarios. The results regarding relative regional vulnerabilities and expected forest fires could be useful in designing policies for preserving forests as natural capital and promoting sustainability.

ct (Do not insert blank lines, i.e. \\) \abstract{We propose an $E_8 \otimes E_8$ unification of the standard model with pre-gravitation, on an exceptional Lie algebra-valued space . Each of the $E_8$ has in its branching an $SU(3)$ for space-time and an $SU(3)$ for three fermion generations. The first $E_8$ further branches to the standard model $SU(3)_c \otimes SU(2)_L \otimes U(1)_Y$ and describes the gauge bosons, Higgs and the left chiral fermions of the standard model. The second $E_8$ further branches into a right-handed counterpart (pre-gravitation) $SU(3)_{grav}\otimes SU(2)_R \otimes U(1)_g$ of the standard model, and describes right chiral fermions, a Higgs, and twelve gauge bosons associated with pre-gravitation, from which general relativity is emergent. We account for 208 out of the 496 degrees of freedom of $E_8 \otimes E_8$ and propose an interpretation for the remaining 288, motivated by the trace dynamics Lagrangian of our theory. We explain how the two copies of $SU(3)_{spacetime}$ together give rise to a 6D spacetime with signature $(3,3)$ which upon symmetry breaking gives rise to our 4D spacetime and to a second 4D anti-spacetime with flipped signature.