Robustness of Mann Type Algorithm with Perturbed Mapping for Nonexpansive Mappings in Banach Spaces

The purpose of this paper is to study the robustness of Mann type algorithm in the sense that approximately perturbed mapping does not alter the convergence of Mann type algorithm. It is proven that Mann type algorithm with perturbed mapping xn+1=λnxn+(1−λn)(Txn+en)−λnμnF(xn) remains convergent in a Banach space setting where λn,μn∈[0,1], T a nonexpansive mapping, en, n=0,1,…, errors and F a strongly accretive and strictly pseudocontractive mapping

Implicit Iterative Method for Hierarchical Variational Inequalities

We introduce a new implicit iterative scheme with perturbation for finding the approximate solutions of a hierarchical variational inequality, that is, a variational inequality over the common fixed point set of a finite family of nonexpansive mappings. We establish some convergence theorems for the sequence generated by the proposed implicit iterative scheme. In particular, necessary and sufficient conditions for the strong convergence of the sequence are obtained

Polar ferromagnet induced by fluorine positioning in isomeric layered copper halide perovskites

We acknowledge the University of St Andrews and the China Scholarship Council (studentship to CH) and the University of St Andrews (studentship to AJB).We present the influence of positional isomerism on the crystal structure of fluorobenzylammonium copper (II) chloride perovskites A2CuCl4, by incorporating ortho, meta and para- fluorine substitution in the benzylamine structure. Two-dimensional (2D) polar ferromagnet (3-FbaH)2CuCl4 (3-FbaH+ = 3-fluorobenzylammonium) is successfully obtained, which crystallizes in a polar orthorhombic space group Pca21 at room temperature. In contrast, both (2-FbaH)2CuCl4 (2-FbaH+ = 2-fluorobenzylammonium) and (4-FbaH)2CuCl4 (4-FbaH+ = 4-fluorobenzylammonium) crystallize in centrosymmetric space groups P21/c and Pnma at room temperature, respectively, displaying significant differences in crystal structures. These differences indicate that the position of the fluorine atom is a driver for the polar behaviour in (3-FbaH)2CuCl4. Preliminary magnetic measurements confirm that these three perovskites possess dominant ferromagnetic interactions within the inorganic [CuCl4]∞ layers. Therefore, (3-FbaH)2CuCl4 is a polar ferromagnet, with potential as a type I multiferroic. This work is expected to promote further development of high performance 2D copper (II) halide perovskite multiferroic materials.Publisher PDFPeer reviewe

Exclusive semileptonic rare decays B−>(B ->_ (K,K^*) \ell^+ \ell^- in supersymmetric theories

The invariant mass spectrum, forward-backward asymmetry, and lepton polarizations of the exclusive processes $B\to K(K^*)\ell^+ \ell^-, \ell=\mu, \tau$ are analyzed under supersymmetric context. Special attention is paid to the effects of neutral Higgs bosons (NHBs). Our analysis shows that the branching ratio of the process \bkm can be quite largely modified by the effects of neutral Higgs bosons and the forward-backward asymmetry would not vanish. For the process \bksm, the lepton transverse polarization is quite sensitive to the effects of NHBs, while the invariant mass spectrum, forward-backward asymmetry, and lepton longitudinal polarization are not. For both \bkt and \bkst, the effects of NHBs are quite significant. The partial decay widths of these processes are also analyzed, and our analysis manifest that even taking into account the theoretical uncertainties in calculating weak form factors, the effects of NHBs could make SUSY shown up.Comment: Several references are added, typo are correcte