Relationship between the unique microstructures and behaviors of high-entropy alloys

High-entropy alloys(HEAs),which were introduced as a pioneering concept in 2004,have captured the keen interest of nu-merous researchers.Entropy,in this context,can be perceived as representing disorder and randomness.By contrast,elemental composi-tions within alloy systems occupy specific structural sites in space,a concept referred to as structure.In accordance with Shannon entropy,structure is analogous to information.Generally,the arrangement of atoms within a material,termed its structure,plays a pivotal role in dictating its properties.In addition to expanding the array of options for alloy composites,HEAs afford ample opportunities for diverse structural designs.The profound influence of distinct structural features on the exceptional behaviors of alloys is underscored by numer-ous examples.These features include remarkably high fracture strength with excellent ductility,antiballistic capability,exceptional radi-ation resistance,and corrosion resistance.In this paper,we delve into various unique material structures and properties while elucidating the intricate relationship between structure and performance.

GLOBAL UNIQUE SOLUTIONS FOR THE INCOMPRESSIBLE MHD EQUATIONS WITH VARIABLE DENSITY AND ELECTRICAL CONDUCTIVITY

We study the global unique solutions to the 2-D inhomogeneous incompressible MHD equations,with the initial data(u0,B0)being located in the critical Besov space■and the initial densityρ0 being close to a positive constant.By using weighted global estimates,maximal regularity estimates in the Lorentz space for the Stokes system,and the Lagrangian approach,we show that the 2-D MHD equations have a unique global solution.

WEAK-STRONG UNIQUENESS FOR THREE DIMENSIONAL INCOMPRESSIBLE ACTIVE LIQUID CRYSTALS

The hydrodynamics of active liquid crystal models has attracted much attention in recent years due to many applications of these models.In this paper,we study the weak-strong uniqueness for the Leray-Hopf type weak solutions to the incompressible active liquid crystals in R^(3).Our results yield that if there exists a strong solution,then it is unique among the Leray-Hopf type weak solutions associated with the same initial data.

Local existence and uniqueness of solutions to the evolutionary model for magnetoviscoelasticity

In this paper,we prove the local existence and uniqueness of solutions to the evolutionary model for magnetoviscoelasticity in R^(2),R^(3).This model consists of an incompressible Navier-Stokes,a regularized system for the evolution of the deformation gradient and the Landau-Lifshitz-Gilbert system for the dynamics of the mag-netization.Our approach depends on approximating the system with a sequence of perturbed systems.

Understanding the superior mechanical properties of Mg-3Al-Zn alloy sheets:Role of multi-type unique textures

Mg-3Al-1Zn(AZ31)sheets were produced by transverse gradient extrusion(TGE)process.The flow behavior and dynamic recrystallization during extrusion were systematically analyzed.The microstructures,textures,and mechanical behavior of extruded AZ31 sheet were also analyzed and compared with conventional extruded(CE)sheet.The results showed that fine grain structure and multi-type unique textures were formed in TGE sheet because of the generation of extra flow velocity along transverse direction(TD)and flow velocity gradient along extrusion direction(ED)during extrusion.The basal poles gradually deviated away normal direction(ND)from edge to center of the TGE sheet along TD,and the largest inclination angle at center region reached around 65°.Furthermore,the basal poles inclined from ED to TD 40°-63°,except for the center region of TGE sheet.The TGE sheet presented higher ductility and strain hardening exponent(n-value),but lower yield strength and Lankford value(r-value)in comparison with the CE sheet.Both the basal<a>slip and tensile twins were easy to be activated during deformation,and the largest elongation of 41%and the lowest yield strength of 86.5 MPa were obtained for the ED-center sample in the TGE sheet.

THE REGULARITY AND UNIQUENESS OF A GLOBAL SOLUTION TO THE ISENTROPIC NAVIER-STOKES EQUATION WITH ROUGH INITIAL DATA

A global weak solution to the isentropic Navier-Stokes equation with initial data around a constant state in the L^(1)∩BV class was constructed in[1].In the current paper,we will continue to study the uniqueness and regularity of the constructed solution.The key ingredients are the Holder continuity estimates of the heat kernel in both spatial and time variables.With these finer estimates,we obtain higher order regularity of the constructed solution to Navier-Stokes equation,so that all of the derivatives in the equation of conservative form are in the strong sense.Moreover,this regularity also allows us to identify a function space such that the stability of the solutions can be established there,which eventually implies the uniqueness.

UNIQUENESS OF INVERSE TRANSMISSION SCATTERING WITH A CONDUCTIVE BOUNDARY CONDITION BY PHASELESS FAR FIELD PATTERN

In this paper,we establish the unique determination result for inverse acoustic scattering of a penetrable obstacle with a general conductive boundary condition by using phaseless far field data at a fixed frequency.It is well-known that the modulus of the far field pattern is invariant under translations of the scattering obstacle if only one plane wave is used as the incident field,so it is impossible to reconstruct the location of the underlying scatterers.Based on some new research results on the impenetrable obstacle and inhomogeneous isotropic medium,we consider different types of superpositions of incident waves to break the translation invariance property.

Uniquely Decomposable Constellation Group-Based Sparse Vector Coding for Short Packet Communications

Sparse vector coding(SVC)is emerging as a potential technology for short packet communications.To further improve the block error rate(BLER)performance,a uniquely decomposable constellation group-based SVC(UDCG-SVC)is proposed in this article.Additionally,in order to achieve an optimal BLER performance of UDCG-SVC,a problem to optimize the coding gain of UDCG-based superimposed constellation is formulated.Given the energy of rotation constellations in UDCG,this problem is solved by converting it into finding the maximized minimum Euclidean distance of the superimposed constellation.Simulation results demonstrate the validness of our derivation.We also find that the proposed UDCGSVC has better BLER performance compared to other SVC schemes,especially under the high order modulation scenarios.

THE EXISTENCE AND LOCAL UNIQUENESS OF MULTI-PEAK SOLUTIONS TO A CLASS OF KIRCHHOFF TYPE EQUATIONS

In this paper,we study the existence and local uniqueness of multi-peak solutions to the Kirchhoff type equations-(ε^(2)a+εb∫_(R^(3))|■u|^(2))△u+V(x)u=u^(p),u>0 in R^(3),which concentrate at non-degenerate critical points of the potential function V(x),where a,b>0,1<p<5 are constants,andε>0 is a parameter.Applying the Lyapunov-Schmidt reduction method and a local Pohozaev type identity,we establish the existence and local uniqueness results of multi-peak solutions,which concentrate at{a_(i)}1≤i≤k,where{a_(i)}1≤i≤k are non-degenerate critical points of V(x)asε→0.

Uniqueness of Viscosity Solutions to the Dirichlet Problem Involving Infinity Laplacian

In this paper, we study the Dirichlet boundary value problem involving the highly degenerate and h-homogeneous quasilinear operator associated with the infinity Laplacian, where the right hand side term is and the boundary value is . First, we establish the comparison principle by the double variables method based on the viscosity solutions theory for the general equation in. We propose two different conditions for the right hand side and get the comparison principle results under different conditions by making different perturbations. Then, we obtain the uniqueness of the viscosity solution to the Dirichlet boundary value problem by the comparison principle. Moreover, we establish the local Lipschitz continuity of the viscosity solution.

Existence and Uniqueness Results for a Fully Third-Order Boundary Value Problem

The boundary value problems of the third-order ordinary differential equation have many practical application backgrounds and their some special cases have been studied by many authors. However, few scholars have studied the boundary value problems of the complete third-order differential equations u′′′(t) = f (t,u(t),u′(t),u′′(t)). In this paper, we discuss the existence and uniqueness of solutions and positive solutions of the fully third-order ordinary differential equation on [0,1] with the boundary condition u(0) = u′(1) = u′′(1) = 0. Under some inequality conditions on nonlinearity f some new existence and uniqueness results of solutions and positive solutions are obtained.

2023:A year of accomplishments for the 13 Science Citation Index Expanded-and Emerging Sources Citation Index-indexed Baishideng journals

In 2023,Baishideng Publishing Group(Baishideng)routinely published 47 openaccess journals,including 46 English-language journals and 1 Chinese-language journal.Our successes were accomplished through the collective dedicated efforts of Baishideng staffs,Editorial Board Members,and Peer Reviewers.Among these 47 Baishideng journals,7 are included in the Science Citation Index Expanded(SCIE)and 6 in the Emerging Sources Citation Index(ESCI).With the support of Baishideng authors,company staffs,Editorial Board Members,and Peer Reviewers,the publication work of 2023 is about to be successfully completed.This editorial summarizes the 2023 activities and accomplishments of the 13 SCIEand ESCI-indexed Baishideng journals,outlines the Baishideng publishing policy changes and additions made this year,and highlights the unique advantages of Baishideng journals.

Fractal Fractional Order Operators in Computational Techniques for Mathematical Models in Epidemiology

New fractional operators, the COVID-19 model has been studied in this paper. By using different numericaltechniques and the time fractional parameters, the mechanical characteristics of the fractional order model areidentified. The uniqueness and existence have been established. Themodel’sUlam-Hyers stability analysis has beenfound. In order to justify the theoretical results, numerical simulations are carried out for the presented methodin the range of fractional order to show the implications of fractional and fractal orders.We applied very effectivenumerical techniques to obtain the solutions of themodel and simulations. Also, we present conditions of existencefor a solution to the proposed epidemicmodel and to calculate the reproduction number in certain state conditionsof the analyzed dynamic system. COVID-19 fractional order model for the case of Wuhan, China, is offered foranalysis with simulations in order to determine the possible efficacy of Coronavirus disease transmission in theCommunity. For this reason, we employed the COVID-19 fractal fractional derivative model in the example ofWuhan, China, with the given beginning conditions. In conclusion, again the mathematical models with fractionaloperators can facilitate the improvement of decision-making for measures to be taken in the management of anepidemic situation.

Novel Investigation of Stochastic Fractional Differential Equations Measles Model via the White Noise and Global Derivative Operator Depending on Mittag-Leffler Kernel

Because of the features involved with their varied kernels,differential operators relying on convolution formulations have been acknowledged as effective mathematical resources for modeling real-world issues.In this paper,we constructed a stochastic fractional framework of measles spreading mechanisms with dual medication immunization considering the exponential decay and Mittag-Leffler kernels.In this approach,the overall population was separated into five cohorts.Furthermore,the descriptive behavior of the system was investigated,including prerequisites for the positivity of solutions,invariant domain of the solution,presence and stability of equilibrium points,and sensitivity analysis.We included a stochastic element in every cohort and employed linear growth and Lipschitz criteria to show the existence and uniqueness of solutions.Several numerical simulations for various fractional orders and randomization intensities are illustrated.

Strong Uniqueness of Best Approximations from RS-sets in Banach Spaces

The problem of strong uniqueness of best approximation from an RS set in a Banach space is considered. For a fixed RS set G and an element x∈X , we proved that the best approximation g * to x from G is strongly unique.

The Global Uniqueness of Solutions for a Class of Inverse Problem in 1-D Wave Equations of Hyperbolic Type

This paper has given the global uniquene ss theory of solutions for a class of inverse problem in 1_D Wave equation of hype rbolic type.

Application of Unique Resources in Recreational Agriculture of Hainan Island,China

The development status and significance of recreational agriculture in Hainan were analyzed.By introducing advantages of Hainan Island in political institution,natural resources and humanistic resources,it was proposed that special topographical scenery,Qiong Opera(Hainan Opera),tropical plants,rare animal species,customs of Li and Miao nationalities,and agricultural product resources could be applied in the development of recreational agriculture,and many activities of recreational agriculture could be organized.

Tackling application limitations of high-safetyγ-butyrolactone electrolytes:Exploring mechanisms and proposing solutions

Developing wide-temperature and high-safety lithium-ion batteries(LIBs)presents significant challenges attributed to the absence of suitable solvents possessing broad liquid range and non-flammability properties.γ-Butyrolactone(GBL)has emerged as a promising solvent;however,its incompatibility with graphite anode has hindered its application.This limitation necessitates a comprehensive investigation into the underlying mechanisms and potential solutions.In this study,we achieve a molecular-level understanding of the perplexing interphase formation process by employing in-situ spectroelectrochemical techniques and density function calculations.Our findings reveal that,even at high salt concentrations,GBL consistently occupies the primary Li^(+)solvation sheath,leading to extensive GBL decomposition and the formation of a high-impedance and inorganic-poor solid-electrolyte interphase(SEI)layer.Contrary to manipulating solvation structures,our research demonstrates that the utilization of filmforming additives with higher reduction potential facilitates the pre-establishment of a robust SEI film on the graphite anode.This approach effectively inhibits GBL decomposition and significantly enhances the battery's lifespan.This study provides the first reported intrinsic understanding of the unique GBLgraphite incompatibility and offers valuable insights for the development of wide-temperature and high-safety LIBs.

Two Results on Uniquely r-Pancyclic Graphs

In this paper,we prove that there does not exist an r-UPC[2]-graph for each r≥5 and there does not exist an r-UPC[C_t^2]-graph for each r≥3,where t is the number of bridges in a graph and C_t^2 is the number of combinations of t bridges taken 2 at a time.

A SINGULAR DIRICHLET PROBLEM FOR THE MONGE-AMPÈRE TYPE EQUATION

We consider the singular Dirichlet problem for the Monge-Ampère type equation{\rm det}\D^2 u=b(x)g(-u)(1+|\nabla u|^2)^{q/2},\u<0,\x\in\Omega,\u|_{\partial\Omega}=0,whereΩis a strictly convex and bounded smooth domain inℝn,q∈[0,n+1),g∈C∞(0,∞)is positive and strictly decreasing in(0,∞)with\lim\limits_{s\rightarrow 0^+}g(s)=\infty,and b∈C∞(Ω)is positive inΩ.We obtain the existence,nonexistence and global asymptotic behavior of the convex solution to such a problem for more general b and g.Our approach is based on the Karamata regular variation theory and the construction of suitable sub-and super-solutions.