On the structure of the automorphism group of certain automorphic loop

Automorphic loops, or A-loops, are loops in which all inner mappings are automorphisms. We investigated A-loops arising from a Lie algebra and describe their automorphism group. Also, we identify and describe their inner mapping group.     

On Existence of Common Fixed Points Under Lipschitz-Type Mapping Pairs with Applications

In this paper, we propose some su?cient conditions to obtain the existence of common fixed points for a pair of self-mappings satisfying Lipschitz-type conditions in noncomplete metric space. Our results improve and extend the results of Pant [Common fixed points of Lipschitz-type mapping pairs, J. Math. Anal. Appl. 240, (1999), 280–283] and Khan et al. [Coincidences of Lipschitz-type hybrid maps and invariant approximation, Numer. Funct. Anal. Optim. 28(9–10), (2007), 1165–1177]. As an application of our results we solve an eigenvalue problem for operators defined on a normed space.     

Strong Convergence Theorems for a Countable Family of Multi-Valued Bregman Quasi-Nonexpansive Mappings in Reflexive Banach Spaces

This article uses the shrinking projection method introduced by Takahashi, Kubota and Takeuchi to propose an iteration algorithm for a countable family of Bregman multi-valued quasi-nonexpansive mappings in order to have the strong convergence under a limit condition in the framework of reflexive Banach spaces. We apply our results to a zero point problem of maximal monotone mappings and equilibrium problems in reflexive Banach spaces. The results presented in the article improve and extend the corresponding results of that found in the literature.     

Contraction of the proximal mapping and applications to the equilibrium problem

In this paper, we introduce a new definition of Lipschitz-type continuity of a bifunction. Using this definition, we prove the contraction of the proximal mapping and apply it to the equilibrium problem over the fixed-point set of a nonexpansive mapping. We present a new algorithm for this problem. Under classical conditions, the convergence of the algorithm is proved. Finally, we present some numerical results for the proposed algorithm.     

Quantitative asymptotic regularity results for the composition of two mappings

In this paper, we use techniques which originate from proof mining to give rates of asymptotic regularity and metastability for a sequence associated to the composition of two firmly nonexpansive mappings.     

一维六方准晶压电材料中幂函数型曲线裂纹的反平面问题

依据一维六方准晶压电材料反平面问题的基本方程,利用复变函数方法,通过引入适当的保角映射,研究了一维六方准晶压电材料中幂函数型曲线裂纹的反平面问题,并利用Cauchy积分理论,得到电不可通和电可通边界条件下的应力场和位移场的复表示以及裂纹尖端场强度因子的解析表达式.     

2-距离空间中平方型压缩映象的一个新的耦合公共不动点定理

在2-距离空间的框架下, 利用映象对的ω-相容性条件, 建立了一类新的平方型压缩条件, 讨论了此类映象耦合公共不动点的存在性和唯一性.证明了一个新的耦合公共不动点定理, 也提供了一个有效的例子来支持该文的新结果.该文的结果改善了之前文献中的相关结果.     

A characterization of generalized derivations of JSL algebras

Let AlgL be a J-subspace lattice algebra on a Banach space X and M be an operator in AlgL. We prove that if δ : AlgL → B(X) is a linear mapping satisfying δ(AB) = δ(A)B + Aδ(B)for all A, B ∈ AlgL with AMB = 0, then δ is a generalized derivation. This result can be applied to atomic Boolean subspace lattice algebras and pentagon subspace lattice algebras.     

Isometries and additive mapping on the unit spheres of normed spaces

In this paper, we investigate isometric extension problem in general normed space. We prove that an isometry between spheres can be extended to a linear isometry between the spaces if and only if the natural positive homogeneous extension is additive on spheres. Moreover, this conclusion still holds provided that the additivity holds on a restricted domain of spheres.     

Activation-induced layered structure in NiCoAl by atomic modulation for energy storage application

The surface activation of alloys favors their electrochemical interactions, ion diffusivity, and the rapid kinetics of ions and electrons, leading to the formation of self-supported layered double hydroxides (LDHs) in them. However, the formation of LDHs at different depths in the alloy upon activation, their electronic/atomic structures, and their electrochemical charge storage mechanism, have not been thoroughly explored. Herein, Ni ion-substituted CoAl alloys are prepared by arc melting and activated by KOH electrolyte, which is responsible for the modulation of the atomic configuration as confirmed by XRD. Raman depth mapping demonstrates how the LDHs vary with depth upon activation and that the octahedral and tetrahedral symmetry sites of CoO and Co₃O₄ are responsible for the formation of the layered structures of CoOOH and Co(OH)₂, respectively. The activated Ni₁₀Co₈₅Al₅ has a superior volumetric capacitance of 4.15 F/cm³ at 0.5 mA/g, which is 38.6 times that of an unactivated one, and excellent cyclic stability up to 5000 cycles, and a voltage of 0.54 V generated from a fabricated supercapacitor cell. X-ray Absorption Spectroscopy (XAS) analysis indicates greater charge transfer by Co than by Ni and the modulation of the local atomic structures facilitates electrochemical charge storage in Ni₁₀Co₈₅Al₅. This work presents an easy route for the development of advanced LDHs, and the mechanism of electrochemical charge storage in them.