On the Residual Finiteness of a Class of Infinite Soluble Groups

Let A be a completely decomposable homogeneous torsion-free abelian group of rank n(n≥2).Let m(n)=A×(a)be the split extension of A by an automorphismαwhich is a cyclic permutation of the direct components twisted by a rational integer m.Then Om(n)is an infinite soluble group.In this paper,the residual finiteness of Om(n)is investigated.

Rapid rupture characterization for the 2023 M_(S)6.2 Jishishan earthquake

On December 18, 2023, the M_(S)6.2 Jishishan earthquake occurred in the northeastern region of the QinghaiXizang Plateau, causing heavy casualties and property damage in Gansu and Qinghai Provinces. In this study,we integrate space imaging geodesy, finite fault inversion, and back-projection methods to decipher its rupture property, including fault geometry, coseismic slip distribution, rupture direction, and propagation speed. The results reveal that the seismogenic fault dips to the southwest at an angle of 29°. The major slip asperity is dominated by reverse slip and is concentrated within a depth range of 7–16 km, which explains the significant uplift near the epicenter observed by both the Sentinel-1 ascending and descending In SAR data. Moreover, the teleseismic array waveforms indicate a northwest propagating rupture with an overall slow rupture velocity of~1.91 km/s(AK array) or 1.01 km/s(AU array).

Numerical analysis of moving train induced vibrations on tunnel,surrounding ground and structure

This study is focused on the effect of vibration induced by moving trains in tunnels on the surrounding ground and structures.A three-dimensional finite element model is established for a one-track railway tunnel and an adjacent twelve-storey building frame by using commercial software Midas GTS-NX(2019)and Midas Gen.This study considered the moving load effect of a complete train,which varies with space as well as with time.The effect of factors such as train speed,overburden pressure on the tunnel and variation in soil properties are studied in the time domain.As a result,the variations in horizontal and vertical acceleration for two different sites,i.e.,the free ground surface(without structure)and the area containing the structure,are compared.Also,the displacement pattern of the raft foundation is plotted for different train velocities.At lower speeds,the heaving phenomenon is negligible,but as the speed increases,both the heaving and differential settlement increase in the foundation.This study demonstrates that the effect of moving train vibrations should be considered in the design of new nearby structures and proper ground improvement should be considered for existing structures.

A stable implicit nodal integration-based particle finite element method(N-PFEM)for modelling saturated soil dynamics

In this study,we present a novel nodal integration-based particle finite element method(N-PFEM)designed for the dynamic analysis of saturated soils.Our approach incorporates the nodal integration technique into a generalised Hellinger-Reissner(HR)variational principle,creating an implicit PFEM formulation.To mitigate the volumetric locking issue in low-order elements,we employ a node-based strain smoothing technique.By discretising field variables at the centre of smoothing cells,we achieve nodal integration over cells,eliminating the need for sophisticated mapping operations after re-meshing in the PFEM.We express the discretised governing equations as a min-max optimisation problem,which is further reformulated as a standard second-order cone programming(SOCP)problem.Stresses,pore water pressure,and displacements are simultaneously determined using the advanced primal-dual interior point method.Consequently,our numerical model offers improved accuracy for stresses and pore water pressure compared to the displacement-based PFEM formulation.Numerical experiments demonstrate that the N-PFEM efficiently captures both transient and long-term hydro-mechanical behaviour of saturated soils with high accuracy,obviating the need for stabilisation or regularisation techniques commonly employed in other nodal integration-based PFEM approaches.This work holds significant implications for the development of robust and accurate numerical tools for studying saturated soil dynamics.

ON A FINITENESS THEOREM ABOUT PROBLEMS INVOLVING INEQUALITIES

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Mathematical modeling and simulations of stress mitigation by coating polycrystalline particles in lithium-ion batteries

A chemo-mechanical model is developed to investigate the effects on the stress development of the coating of polycrystalline Ni-rich LiNixMnyCo_(z)O_(2)(x≥0.8)(NMC)particles with poly(3,4-ethylenedioxythiophene)(PEDOT).The simulation results show that the coating of primary NMC particles significantly reduces the stress generation by efficiently accommodating the volume change associated with the lithium diffusion,and the coating layer plays roles both as a cushion against the volume change and a channel for the lithium transport,promoting the lithium distribution across the secondary particles more homogeneously.Besides,the lower stiffness,higher ionic conductivity,and larger thickness of the coating layer improve the stress mitigation.This paper provides a mathematical framework for calculating the chemo-mechanical responses of anisotropic electrode materials and fundamental insights into how the coating of NMC active particles mitigates stress levels.

Finiteness results for equifocal hypersurfaces in compact symmetric spaces

We prove that there are only finitely many diffeomorphism types of curvature-adapted equifocal hypersurfaces in a simply connected compact symmetric space.Moreover,if the symmetric space is of rank one,the result can be strengthened by dropping the condition curvature-adapted.

Finiteness of Mapping Degree Sets for 3-Manifolds

By constructing certain maps, this note completes the answer of the question： For which closed orientable 3-manifold N, is the set of mapping degrees D（M, N） finite for any closed orientable 3-manifold M？

On the Finiteness Dimension of Local Cohomology Modules

Let R be a commutative Noetherian ring, α an ideal of R, and M a non-zero finitely generated R-module. Let t be a non-negative integer. In this paper, it is shown that dim Supp Hi a（M） ≤ 1 for all i 〈 t if and only if there exists an ideal b of R such that dimR/b ≤ 1 and Hia（M） ≌ Hi b（M） for all i 〈 t. Moreover, we prove that dimSuppHia（M） 〈≤dim M - i for all i.

A generalized π2-diffeomorphism finiteness theorem

Theπ2-diffeomorphism finiteness result of F.Fang-X.Rong and A.Petrunin-W.Tuschmann(independently)asserts that the diffeomorphic types of compact n-manifolds M with vanishing first and second homotopy groups can be bounded above in terms of n,and upper bounds on the absolute value of sectional curvature and diameter of M.In this paper,we will generalize thisπ2-diffeomorphism finiteness by removing the condition thatπ1(M)-0 and asserting the diffeomorphism finiteness on the Riemannian universal cover of M.

Finite Size Effect on Gluon Dissociation of J/ψin Relativistic Heavy Ion Collisions

Thermal quantities,including the the entropy density and gluon spectrum,of quark matter within a box that is finite in the longitudinal direction are calculated using a bag model.Under the assumption of entropy conservation,the corresponding gluon dissociation rate of J/ψis studied.It reaches a maximum at a certain longitudinal size𝐿m,below which the suppression is weak even if the temperature becomes higher than that without the finite size effect,and above which the dissociation rate approaches to the thermodynamic limit gradually with increasing longitudinal size of the fireball.

Profiling Electronic and Phononic Band Structures of Semiconductors at Finite Temperatures: Methods and Applications

Semiconductor devices are often operated at elevated temperatures that are well above zero Kelvin,which is the temperature in most first-principles density functional calculations.Computational approaches to com-puting and understanding the properties of semiconductors at finite temperatures are thus in critical demand.In this review,we discuss the recent progress in computationally assessing the electronic and phononic band structures of semiconductors at finite temperatures.As an emerging semiconductor with particularly strong temperature-induced renormalization of the electronic and phononic band structures,halide perovskites are used as a representative example to demonstrate how computational advances may help to understand the band struc-tures at elevated temperatures.Finally,we briefly illustrate the remaining computational challenges and outlook promising research directions that may help to guide future research in this field.

Recurrent Neural Network Inspired Finite-Time Control Design

Dear Editor,This letter is concerned with the role of recurrent neural networks(RNNs)on the controller design for a class of nonlinear systems.Inspired by the architectures of RNNs,the system states are stacked according to the dynamic along with time while the controller is represented as the neural network output.To build the bridge between RNNs and finite-time controller,a novel activation function is imposed on RNNs to drive the convergence of states at finite-time and propel the overall control process smoother.Rigorous stability proof is briefly provided for the convergence of the proposed finite-time controller.At last,a numerical simulation example is presented to illustrate the efficiency of the proposed strategy.Neural networks can be classified as static(feedforward)and dynamic(recurrent)nets[1].The former nets do not perform well in dealing with training data and using any information of the local data structure[2].In contrast to the feedforward neural networks,RNNs are constituted by high dimensional hidden states with dynamics.

THE SUPERCLOSENESS OF THE FINITE ELEMENT METHOD FOR A SINGULARLY PERTURBED CONVECTION-DIFFUSION PROBLEM ON A BAKHVALOV-TYPE MESH IN 2D

For singularly perturbed convection-diffusion problems,supercloseness analysis of the finite element method is still open on Bakhvalov-type meshes,especially in the case of 2D.The difficulties arise from the width of the mesh in the layer adjacent to the transition point,resulting in a suboptimal estimate for convergence.Existing analysis techniques cannot handle these difficulties well.To fill this gap,here a novel interpolation is designed delicately for the smooth part of the solution,bringing about the optimal supercloseness result of almost order 2 under an energy norm for the finite element method.Our theoretical result is uniform in the singular perturbation parameterεand is supported by the numerical experiments.

Natural Convection and Irreversibility of Nanofluid Due to Inclined Magnetohydrodynamics(MHD)Filled in a Cavity with Y-Shape Heated Fin:FEM Computational

This study explains the entropy process of natural convective heating in the nanofluid-saturated cavity in a heated fin andmagnetic field.The temperature is constant on the Y-shaped fin,insulating the topwall while the remaining walls remain cold.All walls are subject to impermeability and non-slip conditions.The mathematical modeling of the problem is demonstrated by the continuity,momentum,and energy equations incorporating the inclined magnetic field.For elucidating the flow characteristics Finite ElementMethod(FEM)is implemented using stable FE pair.A hybrid fine mesh is used for discretizing the domain.Velocity and thermal plots concerning parameters are drawn.In addition,a detailed discussion regarding generation energy by monitoring changes in magnetic,viscous,total,and thermal irreversibility is provided.In addition,line graphs are created for the u and v components of the velocity profile to predict the flow behavior.Current simulations assume the dimensionless representative of magnetic field Hartmann number Ha between 0 and 100 and a magnetic field inclination between 0 and 90 degrees.A constant 4% volume proportion of nanoparticles is employed throughout all scenarios.

On entire solutions of some Fermat type differential-difference equations

On one hand,we study the existence of transcendental entire solutions with finite order of the Fermat type difference equations.On the other hand,we also investigate the existence and growth of solutions of nonlinear differential-difference equations.These results extend and improve some previous in[5,14].

Effect of Size Change on Mechanical Properties of Monolayer Arsenene

The Young's modulus, shear modulus and Poisson's ratio of monolayer arsenene with different sizes were calculated by finite element method, so as to explore the influence of dimension and orientation on the mechanical properties of monolayer arsenene. The calculation results show that the small size has a significant effect on the mechanical properties of the monolayer arsenene. The smaller the size, the larger the Young's modulus and Poisson's ratio of the monolayer arsenene. The size change has a great influence on the Young's modulus of the arsenene handrail direction, and the Young's modulus of the zigzag direction is not sensitive to the size change. Similarly, the size change has a significant effect on the shear modulus of arsenene in the handrail direction, while the shear modulus in the zigzag direction has no significant effect on its size change. For the Poisson's ratio, the situation is just the opposite, and the effect of the size change on the Poisson's ratio of the arsenene zigzag direction is greater than that of the handrail direction.

Tuning microstructures of TC4 ELI to improve explosion resistance

A reasonable heat treatment process for TC4 ELI titanium alloy is crucial to tune microstructures to improve its explosion resistance.However,there is limited investigation on tuning microstructures of TC4 ELI to improve explosion resistance.Moreover,the current challenge is quantifying microstructural changes'effects on explosion resistance and incorporating microstructural changes into finite element models.This work aims to tune microstructures to improve explosion resistance and elucidate their anti-explosion mechanism,and find a suitable method to incorporate microstructural changes into finite element models.In this work,we systematically study the deformation and failure characteristics of TC4 ELI plates with varying microstructures using an air explosion test and LS-DYNA finite element modeling.The Johnson-Cook(JC)constitutive parameters are used to quantify the effects of microstructural changes on explosion resistance and incorporate microstructural changes into finite element models.Because of the heat treatment,one plate has equiaxed microstructure and the other has bimodal microstructure.The convex of the plate after the explosion has a quadratic relationship with the charge mass,and the simulation results demonstrate high reliability,with the error less than 17.5%.Therefore,it is feasible to obtain corresponding JC constitutive parameters based on the differences in microstructures and mechanical properties and characterize the effects of microstructural changes on explosion resistance.The bimodal target exhibits excellent deformation resistance.The response of bimodal microstructure to the shock wave may be more intense under explosive loading.The well-coordinated structure of the bimodal target enhances its resistance to deformation.

Study on Dynamic Mechanical Behavior of Al-Mg-Si Alloy

The dynamic mechanical behavior of Al-Mg-Si alloy was investigated under different strain rates by mechanical property and microstructure characterization,constitutive behavior analysis and numerical simulation in the present study.As the strain rate increases,the yield strength,ultimate tensile strength and elongation increase first,then remain almost constant,and finally increase.The alloy always exhibits a typical ductile fracture mode,not depending on the strain rate.However,as the strain rate increases,the number of dimples gradually increases.Tensile deformation can refine grains,however,the grain structure is slightly affected by the strain rate.An optimized Johnson-Cook constitutive equation was used to describe the mechanical behavior and obtained by fitting the true stress-strain curves.The parameter C was described by a function related to the strain rate.The fitting true stress-strain curves by the JC model agree very well with the experimental true stress-strain curves.The true stress-strain curves calculated by the finite element numerical simulation agree well with the experimental true stress-strain curves.

Structural Analysis for Qazzaz Metamorphic Core Complex,Northwestern Arabian Shield,Saudi Arabia

Identifying deformational mechanisms and associated structures at various scales,ranging from regional-scale structures to microscopic fabric,is crucial for the assessment of tectonic development.Thirty-three samples were taken from the Qazzaz metamorphic core complex to estimate the finite strain for felsic and mafic minerals.These samples included gneisses rocks,monzogranite,and metavolcano-sedimentary rocks for both the Thalbah and Bayda groups.Using the Rf/j and Fry methods,the axial ratios(XZ)range about 2.20 to 7.10 and 1.90 to 9.10,respectively.For various rock units,the strain measurements show moderate to highly deformation.Most of the observed samples show shallow WNW dipping along a N to WNW trend of finite strain(X).The short axes(Z)based to be subvertical foliation related with a subhorizontal foliation.The results demonstrate that contacts generated at semi-brittle to ductile deformation and that the strain of magnitude has the same value for different lithologic units.It concluded that nappe generation in orogens results from pure shear deformation.