On order-preserving and order-reversing mappings defined on cones of convex functions

In this paper,we first show that for a Banach space X,there is a fully order-reversing mapping T from conv(X)(the cone of all the extended real-valued lower semicontinuous proper convex functions defined on X) onto itself if and only if X is reflexive and linearly isomorphic to its dual X~*.Then we further prove the following generalized Artstein-Avidan-Milman representation theorem:For every fully order-reversing mapping T:conv(X)→conv(X),there exist a linear isomorphism U:X→X~*,x_0~*,φ_0∈X~*,α0 and r_0∈R so that(Tf)(x)=α(Ff)(Ux+x_0~*)+φ_0,x+r_0,■x∈X where T:conv(X)→conv(X~*) is the Fenchel transform.Hence,these resolve two open questions.We also show several representation theorems of fully order-preserving mappings defined on certain cones of convex functions.For example,for every fully order-preserving mapping S:semn(X)→ semn(X),there is a linear isomorphism U:X→ X so that(Sf)(x)=f(Ux),■f∈semn(X),x∈X where semn(X) is the cone of all the lower semicontinuous seminorms on X.     

Quantum Watermark Algorithm Based on Maximum Pixel Difference and Tent Map

International Journal of Theoretical Physics - A new quantum watermark algorithm is presented by combining maximum pixel difference partitioning with the least significant bit substitution...     

In situ confinement of iron-based active sites within high porosity carbon frameworks with enhanced activity for rechargeable Zn–air battery

Non-noble bifunctional electrocatalysts with robust activity and stability toward oxygen evolution reaction (OER) and oxygen reduction reaction (ORR) are greatly significant but challenging for Zn-air batteries. Here, in situ confinement of FeN_x active sites in high porosity carbon framework (FeN_x/CMCC) derived from chelate of carboxymethylcellulose (CMC) and iron ions were synthesized. Particularly, construction of FeN_x within porous carbon framework accelerates the electron transfer and the sufficient utilization of active centers, and then expedites the reaction kinetics of ORR and OER. As expected, the optimized FeN_x/CMCC exhibits superior ORR activity with a larger half-wave potential of 0.869 V. The rechargeable Zn-air battery delivers a higher power density of 99.6 mW/cm² and a special capacity of 781.9 mA h/g_Zn at 10 mA/cm², together with excellent durability of over 335 h. Remarkably, the as-assembled solid-state battery exhibits a higher open circuit voltage (OCV) of 1.5 V, a special capacity of 709.7 mA h/g_Zn, as well as prolonged cycling stability (90 h). Moreover, the flexible solid-state battery displays negligible loss of electrochemical performance under various bending angles, illustrating its potential application in flexible electronic devices.     

Pure tetrahedral quadruple systems with index two

An oriented tetrahedron defined on four vertices is a set of four cyclic triples with the property that any ordered pair of vertices is contained in exactly one of the cyclic triples. A tetrahedral quadruple system of order $n$ with index $\lambda$, denoted by ${\text{TQS}}_{\lambda }\left(n\right)$, is a pair $\left(X,\mathrm{?}\right)$, where $X$ is an $n$‐set and $\mathrm{?}$ is a set of oriented tetrahedra (blocks) such that every cyclic triple on $X$ is contained in exactly $\lambda$ members of $\mathrm{?}$. A ${\text{TQS}}_{\lambda }\left(n\right)$ is pure if there do not exist two blocks with the same vertex set. When $\lambda =1$, the spectrum of a pure TQS $\left(n\right)$ has been completely determined by Ji. In this paper, we show that there exists a pure ${\text{TQS}}_2\left(n\right)$ if and only if $n\equiv 1,2\left(\mathrm{mod}3\right)$ and $n\ge 7$. A corollary is that a simple ${\text{QS}}_4\left(n\right)$ also exists if and only if $n\equiv 1,2\left(\mathrm{mod}3\right)$ and $n\ge 7$.     

Horizontal convection in a rectangular enclosure driven by a linear temperature profile

The horizontal convection in a square enclosure driven by a linear temperature profile along the bottom boundary is investigated numerically by using a finite difference method. The Prandtl number is fixed at 4.38, and the Rayleigh number Ra ranges from107 to 1011. The convective flow is steady at a relatively low Rayleigh number, and no thermal plume is observed, whereas it transits to be unsteady when the Rayleigh number increases beyond the critical value. The scaling law for the Nusselt number Nu changes from Rossby's scaling Nu ～ Ra~(1/5) in a steady regime to Nu ～ Ra~(1/4) in an unsteady regime, which agrees well with the theoretically predicted results. Accordingly,the Reynolds number Re scaling varies from Re ～ Ra~(3/11) to Re ～ Ra~(2/5). The investigation on the mean flows shows that the thermal and kinetic boundary layer thickness and the mean temperature in the bulk zone decrease with the increasing Ra. The intensity of fluctuating velocity increases with the increasing Ra.     

Adaptive finite-time prescribed performance control for stochastic nonlinear systems with unknown virtual control coefficients

Nonlinear Dynamics - This paper is devoted to the adaptive finite-time prescribed performance control (FTPPC) for stochastic nonlinear systems with unknown virtual control coefficients (UVCCs),...     

A Structural Entropy Measurement Principle of Propositional Formulas in Conjunctive Normal Form

The satisfiability (SAT) problem is a core problem in computer science. Existing studies have shown that most industrial SAT instances can be effectively solved by modern SAT solvers while random SAT instances cannot. It is believed that the structural characteristics of different SAT formula classes are the reasons behind this difference. In this paper, we study the structural properties of propositional formulas in conjunctive normal form (CNF) by the principle of structural entropy of formulas. First, we used structural entropy to measure the complex structure of a formula and found that the difficulty solving the formula is related to the structural entropy of the formula. The smaller the compressing information of a formula, the more difficult it is to solve the formula. Secondly, we proposed a λ-approximation strategy to approximate the structural entropy of large formulas. The experimental results showed that the proposed strategy can effectively approximate the structural entropy of the original formula and that the approximation ratio is more than 92%. Finally, we analyzed the structural properties of a formula in the solution process and found that a local search solver tends to select variables in different communities to perform the next round of searches during a search and that the structural entropy of a variable affects the probability of the variable being flipped. By using these conclusions, we also proposed an initial candidate solution generation strategy for a local search for SAT, and the experimental results showed that this strategy effectively improves the performance of the solvers CCAsat and Sparrow2011 when incorporated into these two solvers.     

Synthesis of yolk-shell Bi2O3@TiO2 submicrospheres with enhanced potassium storage

Science China Chemistry - Due to their enormous potential for large-scale energy storage, rechargeable potassium-ion batteries have been widely researched and developed. However, the drastic volume...     

加强型Bi-2212超导股线有限元拉伸性能分析

为探究加强型Bi-2212超导股线的力学性能以及不锈钢包带对超导股线力学性能的影响，运用Ansys软件建立加强型Bi-2212超导股线的三维模型，采用有限元分析方法，对其机械结构进行仿真，模拟高温高压热处理后轴向受拉形变量和应力应变分布情况。仿真结果显示，在同样施加100 N拉力的情况下，与超导原线（Bi-2212超导线）相比，密绕Ni₈₀Cr₂₀包带后的加强型Bi-2212超导股线轴向受拉形变程度减小，约10%;应力应变均降低，约30%。采用Ni₈₀Cr₂₀作为外包带制成的加强型Bi-2212超导股线力学性能显著，是未来超导线发展方向之一。     

Asymptotic Behavior of Least Energy Solutions for a Fractional Laplacian Eigenvalue Problem on ℝN

Acta Mathematica Sinica, English Series - We are interested in the existence and asymptotic behavior for the least energy solutions of the following fractional eigenvalue problem $$\left({\rm{P}}...