Unitariness in Ordered Semigroups

We introduce the concepts of unitary, almost unitary and strongly almost unitary subset of an ordered semigroup. For the notions of almost unitary and strongly almost unitary subset of an ordered semigroup, we use the notion of translational hull of an ordered semigroup. If (S,⋅,≤) is an ordered semigroup having an element e such that e ≤ e2 and U is a nonempty subset of S such that u ≤ eu, u ≤ ue for all u ∈ U, we show that U is almost unitary in S if and only if U is unitary in . Also if (S,⋅,≤) is an ordered semigroup, e ∉ S, U is a nonempty subset of S, Se:= S ∪ {e} and Ue:= U ∪ {e}, we give conditions that an (“extension” of S) ordered semigroup and the subset Ue of Se must satisfy in order for U to be almost unitary or strongly almost unitary in S (in case U is strongly almost unitary in S, then the given conditions are equivalent).

基于Ordered Probit模型的人车冲突安全影响因素研究

为探究和定量分析人车冲突严重程度的影响因素,通过采集3个信号交叉口的人车冲突视频数据,利用T-Analyst标定人车轨迹并计算冲突指标(PET),采用85%位累计频率曲线法划分人车冲突等级;从人、车、路及环境特征中选取10个因素作为变量,构建Ordered Probit模型,以确立人车冲突严重程度的显著影响因素,并通过边际效应定量分析不同显著因素的影响程度。研究结果表明:行人闯红灯情况、年龄、行人交通量、人行道占用情况、人行道起点终点、车辆速度变化及车流量是人车冲突严重程度的显著因素,相较于各自参考量,行人闯红灯、车辆加速通过冲突点、人行道起点及老年人造成严重冲突的概率分别增加8.2%,5.9%,5.1%,4.4%;相较于低流量的交通流,较高流量的车流和行人交通流使得严重冲突的概率分别增加3.7%,2.5%,但人行道占用使得严重冲突的概率下降6.8%。研究结果可为信号交叉口行人过街交通安全设施的设计和实施提供理论依据。

基于Ordered Logit模型的民办高校科研成果转化影响因素研究

为研究民办高校科研成果转化影响因素,在专家访谈和实地调研的基础上,对K高校、C高校、B高校、Z高校等民办高校教师发放调查问卷收集数据,应用Ordered Logit模型对其影响因素进行了实证分析。分析发现,科研经费支持力度与科研成果数量之间呈正相关关系,高校科研平台设置与服务地方经济建设之间呈正相关关系,高校科研管理制度与科研成果转化成效之间呈正相关关系。由此得出结论:我国民办高校科研成果转化与服务地方经济能力有待提升,民办高校科研成果转化的金融支持不够灵活、公共服务平台不够健全,完善民办高校科研管理制度是提高科研成果转化效率的重要保障。

Numerical Treatments for Crossover Cancer Model of Hybrid Variable-Order Fractional Derivatives

In this paper,two crossover hybrid variable-order derivatives of the cancer model are developed.Grünwald-Letnikov approximation is used to approximate the hybrid fractional and variable-order fractional operators.The existence,uniqueness,and stability of the proposed model are discussed.Adams Bashfourth’s fifth-step method with a hybrid variable-order fractional operator is developed to study the proposed models.Comparative studies with generalized fifth-order Runge-Kutta method are given.Numerical examples and comparative studies to verify the applicability of the used methods and to demonstrate the simplicity of these approximations are presented.We have showcased the efficiency of the proposed method and garnered robust empirical support for our theoretical findings.

Dynamic Uncertainty:Exploring the Spatial Order of Future Digital Architecture

The spatial order of architecture has been significantly impacted by digital architectural design and production,creating a dynamic uncertainty.This study aims to explore digital architecture from the perspective of spatial order,discussing the antidote/poison effect caused by digital technologies in architectural practice and the cultural digital changes in digital architectures.The study selected four digital architecture cases,including the(W)rapper at Los Angeles by Eric Owen Moss,Beijing Daxing International Airport by Zaha Hadid,3D Print Niaokan Bridge by Xu Weiguo,and World Internet Conference Center by Yuan Feng.This study is hypothesising that the future special order of digital architectures will be a dynamic and balanced new spatial order.This new order includes the symbiosis of a human-machine and virtual-real hierarchy;the interactive co-existence between nature,humanity and technology;and the creative multi-immersive sharing of parametric information,built-environment resources and cultural artistic information.The evolution of spatial order of future digital architecture will be discussed in connection with the idea of the metaverse.The value of this work is its ability to inspire a broader examination of the new order of digital architectural space.

Galerkin-Bernstein Approximations for the System of Third-Order Nonlinear Boundary Value Problems

This paper is devoted to find the numerical solutions of one dimensional general nonlinear system of third-order boundary value problems (BVPs) for the pair of functions using Galerkin weighted residual method. We derive mathematical formulations in matrix form, in detail, by exploiting Bernstein polynomials as basis functions. A reasonable accuracy is found when the proposed method is used on few examples. At the end of the study, a comparison is made between the approximate and exact solutions, and also with the solutions of the existing methods. Our results converge monotonically to the exact solutions. In addition, we show that the derived formulations may be applicable by reducing higher order complicated BVP into a lower order system of BVPs, and the performance of the numerical solutions is satisfactory. .

High-Order Soliton Solutions and Hybrid Behavior for the (2 + 1)-Dimensional Konopelchenko-Dubrovsky Equations

In this paper, the evolutionary behavior of N-solitons for a (2 + 1)-dimensional Konopelchenko-Dubrovsky equations is studied by using the Hirota bilinear method and the long wave limit method. Based on the N-soliton solution, we first study the evolution from N-soliton to T-order (T=1,2) breather wave solutions via the paired-complexification of parameters, and then we get the N-order rational solutions, M-order (M=1,2) lump solutions, and the hybrid behavior between a variety of different types of solitons combined with the parameter limit technique and the paired-complexification of parameters. Meanwhile, we also provide a large number of three-dimensional figures in order to better show the degeneration of the N-soliton and the interaction behavior between different N-solitons.

Transformation of long-period stacking ordered structures in Mg-Gd-Y-Zn alloys upon synergistic characterization of first-principles calculation and experiment and its effects on mechanical properties

Based on experiments and first-principles calculations,the microstructures and mechanical properties of as-cast and solution treated Mg-10Gd-4Y-xZn-0.6Zr(x=0,1,2,wt.%)alloys are investigated.The transformation process of long-period stacking ordered(LPSO)structure during solidification and heat treatment and its effect on the mechanical properties of experimental alloys are discussed.Results reveal that the stacking faults and 18R LPSO phases appear in the as-cast Mg-10Gd-4Y-1Zn-0.6Zr and Mg-10Gd-4Y-2Zn-0.6Zr alloys,respectively.After solution treatment,the stacking faults and 18R LPSO phase transform into 14H LPSO phase.The Enthalpies of formation and reaction energy of 14H and 18R LPSO are calculated based on first-principles.Results show that the alloying ability of 18R is stronger than that of 14H.The reaction energies show that the 14H LPSO phase is more stable than the 18R LPSO.The elastic properties of the 14H and 18R LPSO phases are also evaluated by first-principles calculations,and the results are in good agreement with the experimental results.The precipitation of LPSO phase improves the tensile strength,yield strength and elongation of the alloy.After solution treatment,the Mg-10Gd-4Y-2Zn-0.6Zr alloy has the best mechanical properties,and its ultimate tensile strength and yield strength are 278.7 MPa and 196.4 MPa,respectively.The elongation of Mg-10Gd-4Y-2Zn-0.6Zr reaches 15.1,which is higher than that of Mg-10Gd-4Y0.6Zr alloy.The improving mechanism of elastic modulus by the LPSO phases and the influence on the alloy mechanical properties are also analyzed.

Enhanced activation of peroxymonosulfate by Fe/N co-doped ordered mesoporous carbon with dual active sites for efficient removal of m-cresol

The novel Fe-N co-doped ordered mesoporous carbon with high catalytic activity in m-cresol removal was prepared by urea-assisted impregnation and simple pyrolysis method.During the preparation of the Fe-NC catalyst,the complexation of N elements in urea could anchor Fe,and the formation of C3N4during urea pyrolysis could also prevent migration and aggregation of Fe species,which jointly improve the dispersion and stability of Fe.The FeN4sites and highly dispersed Fe nanoparticles synergistically trigger the dual-site peroxymonosulfate (PMS) activation for highly efficient m-cresol degradation,while the ordered mesoporous structure of the catalyst could improve the mass transfer rate of the catalytic process,which together promote catalytic degradation of m-cresol by PMS activation.Reactive oxygen species (ROS) analytic experiments demonstrate that the system degrades m-cresol by free radical pathway mainly based on SO_(4)^(-)·and·OH,and partially based on·OH as the active components,and a possible PMS activation mechanism by 5Fe-50 for m-cresol degradation was proposed.This study can provide theoretical guidance for the preparation of efficient and stable catalysts for the degradation of organic pollutants by activated PMS.

A novel variable-order fractional chaotic map and its dynamics

In recent years,fractional-order chaotic maps have been paid more attention in publications because of the memory effect.This paper presents a novel variable-order fractional sine map(VFSM)based on the discrete fractional calculus.Specially,the order is defined as an iterative function that incorporates the current state of the system.By analyzing phase diagrams,time sequences,bifurcations,Lyapunov exponents and fuzzy entropy complexity,the dynamics of the proposed map are investigated comparing with the constant-order fractional sine map.The results reveal that the variable order has a good effect on improving the chaotic performance,and it enlarges the range of available parameter values as well as reduces non-chaotic windows.Multiple coexisting attractors also enrich the dynamics of VFSM and prove its sensitivity to initial values.Moreover,the sequence generated by the proposed map passes the statistical test for pseudorandom number and shows strong robustness to parameter estimation,which proves the potential applications in the field of information security.

Effect of distribution shape on the melting transition, local ordering,and dynamics in a model size-polydisperse two-dimensional fluid

We study the effect of particle size polydispersity(δ) on the melting transition(T*), local ordering, solid–liquid coexistence phase and dynamics of two-dimensional Lennard–Jones fluids up to moderate polydispersity by means of computer simulations. The particle sizes are drawn at random from the Gaussian(G) and uniform(U) distribution functions.For these systems, we further consider two different kinds of particles, viz., particles having the same mass irrespective of size, and in the other case the mass of the particle scales with its size. It is observed that with increasing polydispersity,the value of T*initially increases due to improved packing efficiency(φ) followed by a decrease and terminates at δ ≈8%(U-system) and 14%(G-system) with no significant difference for both mass types. The interesting observation is that the particular value at which φ drops suddenly coincides with the peak of the heat capacity(CP) curve, indicating a transition. The quantification of local particle ordering through the hexatic order parameter(Q_6), Voronoi construction and pair correlation function reveals that the ordering decreases with increasing δ and T. Furthermore, the solid–liquid coexistence region for the G-system is shown to be comparatively wider in the T –δ plane phase diagram than that for the U system. Finally, the study of dynamics reveals that polydisperse systems relax faster compared to monodisperse systems;however, no significant qualitative differences, depending on the distribution type and mass polydispersity, are observed.

Acid-rock reaction kinetics in a two-scale model based on reaction order correction

The reaction order plays a crucial role in evaluating the response rate of acid-rock.However,the conventional two-scale model typically assumes that the reaction order is constant as one,which can lead to significant deviations from reality.To address this issue,this study proposes a novel multi-order dynamic model for acid-rock reaction by combining rotating disk experimental data with theoretical derivation.Through numerical simulations,this model allows for the investigation of the impact of acidification conditions on different orders of reaction,thereby providing valuable insights for on-site construction.The analysis reveals that higher response orders require higher optimal acid liquid flow rates,and lower optimal H+diffusion coefficients,and demonstrate no significant correlation with acid concentration.Consequently,it is recommended to increase the displacement and use high-viscosity acid for reservoirs with high calcite content,while reducing the displacement and using low-viscosity acid for reservoirs with high dolomite content.

RKKY interaction in helical higher-order topological insulators

We theoretically investigate the Ruderman–Kittel–Kasuya–Yosida(RKKY) interaction in helical higher-order topological insulators(HOTIs), revealing distinct behaviors mediated by hinge and Dirac-type bulk carriers. Our findings show that hinge-mediated interactions consist of Heisenberg, Ising, and Dzyaloshinskii–Moriya(DM) terms, exhibiting a decay with impurity spacing z and oscillations with Fermi energy εF. These interactions demonstrate ferromagnetic behaviors for the Heisenberg and Ising terms and alternating behavior for the DM term. In contrast, bulk-mediated interactions include Heisenberg, twisted Ising, and DM terms, with a conventional cubic oscillating decay. This study highlights the nuanced interplay between hinge and bulk RKKY interactions in HOTIs, offering insights into designs of next-generation quantum devices based on HOTIs.

Fractional-order heterogeneous memristive Rulkov neuronal network and its medical image watermarking application

This article proposes a novel fractional heterogeneous neural network by coupling a Rulkov neuron with a Hopfield neural network(FRHNN),utilizing memristors for emulating neural synapses.The study firstly demonstrates the coexistence of multiple firing patterns through phase diagrams,Lyapunov exponents(LEs),and bifurcation diagrams.Secondly,the parameter related firing behaviors are described through two-parameter bifurcation diagrams.Subsequently,local attraction basins reveal multi-stability phenomena related to initial values.Moreover,the proposed model is implemented on a microcomputer-based ARM platform,and the experimental results correspond to the numerical simulations.Finally,the article explores the application of digital watermarking for medical images,illustrating its features of excellent imperceptibility,extensive key space,and robustness against attacks including noise and cropping.

Pedestrian lane formation with following–overtaking model and measurement of system order

Pedestrian self-organizing movement plays a significant role in evacuation studies and architectural design.Lane formation,a typical self-organizing phenomenon,helps pedestrian system to become more orderly,the majority of following behavior model and overtaking behavior model are imprecise and unrealistic compared with pedestrian movement in the real world.In this study,a pedestrian dynamic model considering detailed modelling of the following behavior and overtaking behavior is constructed,and a method of measuring the lane formation and pedestrian system order based on information entropy is proposed.Simulation and analysis demonstrate that the following and avoidance behaviors are important factors of lane formation.A high tendency of following results in good lane formation.Both non-selective following behavior and aggressive overtaking behavior cause the system order to decrease.The most orderly following strategy for a pedestrian is to overtake the former pedestrian whose speed is lower than approximately 70%of his own.The influence of the obstacle layout on pedestrian lane and egress efficiency is also studied with this model.The presence of a small obstacle does not obstruct the walking of pedestrians;in contrast,it may help to improve the egress efficiency by guiding the pedestrian flow and mitigating the reduction of pedestrian system orderliness.

Stable immobilization of lithium polysulfides using three-dimensional ordered mesoporous Mn_(2)O_(3) as the host material in lithium-sulfur batteries

Lithium-sulfur batteries(LSBs)have drawn significant attention owing to their high theoretical discharge capacity and energy density.However,the dissolution of long-chain polysulfides into the electrolyte during the charge and discharge process(“shuttle effect”)results in fast capacity fading and inferior electrochemical performance.In this study,Mn_(2)O_(3)with an ordered mesoporous structure(OM-Mn_(2)O_(3))was designed as a cathode host for LSBs via KIT-6 hard templating,to effectively inhibit the polysulfide shuttle effect.OM-Mn_(2)O_(3)offers numerous pores to confine sulfur and tightly anchor the dissolved polysulfides through the combined effects of strong polar-polar interactions,polysulfides,and sulfur chain catenation.The OM-Mn_(2)O_(3)/S composite electrode delivered a discharge capacity of 561 mAh g^(-1) after 250 cycles at 0.5 C owing to the excellent performance of OM-Mn_(2)O_(3).Furthermore,it retained a discharge capacity of 628mA h g^(-1) even at a rate of 2 C,which was significantly higher than that of a pristine sulfur electrode(206mA h g^(-1)).These findings provide a prospective strategy for designing cathode materials for high-performance LSBs.

Ordered mesoporous materials for water pollution treatment:Adsorption and catalysis

To meet the growing emission of water contaminants,the development of new materials that enhance the efficiency of the water treatment system is urgent.Ordered mesoporous materials provide opportunities in environmental processing applications due to their exceptionally high surface areas,large pore sizes,and enough pore volumes.These properties might enhance the performance of materials concerning adsorption/catalysis capability,durability,and stability.In this review,we enumerate the ordered mesoporous materials as adsorbents/catalysts and their modifications in water pollution treatment from the past decade,including heavy metals(Hg^(2+),Pb^(2+),Cd^(2+),Cr^(6+),etc.),toxic anions(nitrate,phosphate,fluoride,etc.),and organic contaminants(organic dyes,antibiotics,etc.).These contributions demonstrate a deep understanding of the synergistic effect between the incorporated framework and homogeneous active centers.Besides,the challenges and perspectives of the future developments of ordered mesoporous materials in wastewater treatment are proposed.This work provides a theoretical basis and complete summary for the application of ordered mesoporous materials in the removal of contaminants from aqueous solutions.

Cationic ordering transition in oxygen-redox layered oxide cathodes

Understanding the structural origin of the competition between oxygen 2p and transition-metal 3d orbitals in oxygen-redox(OR)layered oxides is eminently desirable for exploring reversible and high-energy-density Li/Na-ion cathodes.Here,we reveal the correlation between cationic ordering transition and OR degradation in ribbon-ordered P3-Na_(0.6)Li_(0.2)Mn_(0.8)O_(2) via in situ structural analysis.Comparing two different voltage windows,the OR capacity can be improved approximately twofold when suppressing the in-plane cationic ordering transition.We find that the intralayer cationic migration is promoted by electrochemical reduction from Mn^(4+)to Jahn–Teller Mn^(3+)and the concomitant NaO_(6) stacking transformation from triangular prisms to octahedra,resulting in the loss of ribbon ordering and electrochemical decay.First-principles calculations reveal that Mn^(4+)/Mn^(3+)charge ordering and alignment of the degenerate eg orbital induce lattice-level collective Jahn–Teller distortion,which favors intralayer Mn-ion migration and thereby accelerates OR degradation.These findings unravel the relationship between in-plane cationic ordering and OR reversibility and highlight the importance of superstructure protection for the rational design of reversible OR-active layered oxide cathodes.

The chemical environment and structural ordering in liquid Mg-Y-Zn system:An ab-initio molecular dynamics investigation of melt for the formation mechanism of LPSO structure

In an effort to clarify the formation mechanism of LPSO structure in Mg-Y-Zn alloy,the chemical environment and structural ordering in liquid Mg-rich Mg-Y-Zn system are investigated with the aid of ab-initio molecular dynamics simulation.In liquid Mg-rich Mg-Y alloys,the strong Mg-Y interaction is determined,which promotes the formation of fivefold symmetric local structure.For Mg-Zn alloys,the weak Mg-Zn interaction results in the fivefold symmetry weakening in the liquid structure.Due to the coexistence of Y and Zn,the strong attractive interaction is introduced in liquid Mg-Y-Zn ternary alloy,and contributes to the clustering of Mg,Y,Zn launched from Zn.What is more,the distribution of local structures becomes closer to that in pure Mg compared with that in binary Mg-Y and Mg-Zn alloys.These results should relate to the origins of the Y/Zn segregation zone and close-packed stacking mode in LPSO structure,which provides a new insight into the formation mechanism of LPSO structure at atomic level.

SHARP MORREY REGULARITY THEORY FOR A FOURTH ORDER GEOMETRICAL EQUATION

This paper is a continuation of recent work by Guo-Xiang-Zheng[10].We deduce the sharp Morrey regularity theory for weak solutions to the fourth order nonhomogeneous Lamm-Rivière equation △^{2}u=△(V▽u)+div(w▽u)+(▽ω+F)·▽u+f in B^(4),under the smallest regularity assumptions of V,ω,ω,F,where f belongs to some Morrey spaces.This work was motivated by many geometrical problems such as the flow of biharmonic mappings.Our results deepens the Lp type regularity theory of[10],and generalizes the work of Du,Kang and Wang[4]on a second order problem to our fourth order problems.