Admissible perturbations of α‐ψ‐pseudocontractive operators: convergence theorems

We prove some convergence theorems for α‐ψ‐pseudocontractive operators in real Hilbert spaces, by using the concept of admissible perturbation. Our results extend and complement some theorems in the existing literature. Copyright © 2016 John Wiley & Sons, Ltd.     

Riemann–Stieltjes operators between α ‐Bloch spaces and Besov spaces

We study the following two integral operators where g is an analytic function on the open unit disk in the complex plane. The boundedness and compactness of these two operators between the α ‐Bloch space B^α and the Besov space are discussed in this paper (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Bloch spaces on bounded symmetric domains in complex Banach spaces Dedicated to Professor Sheng GONG on the occasion of his 75th birthday

We give a definition of Bloch space on bounded symmetric domains in arbitrary complex Banach space and prove such function space is a Banach space. The properties such as boundedness, compactness and closed range of composition operators on such Bloch space are studied.     

Ricci η‐recurrent real hypersurfaces in 2‐dimensional nonflat complex space forms

Let M be a Hopf hypersurface in a nonflat complex space form $M^2(c)$, $c\ne 0$, of complex dimension two. In this paper, we prove that M has η‐recurrent Ricci operator if and only if it is locally congruent to a homogeneous real hypersurface of type (A) or (B) or a non‐homogeneous real hypersurface with vanishing Hopf principal curvature. This is an extension of main results in [17, 21] for real hypersurfaces of dimension three. By means of this result, we give some new characterizations of Hopf hypersurfaces of type (A) and (B) which generalize those in [14, 18, 26].     

Time decay rate for two 3D magnetohydrodynamics‐ α models

We consider the long time behavior of solutions to the magnetohydrodynamics‐ α model in three spatial dimensions. Time decay rate in L²‐norm of the solution is obtained. Similar results for a generalized Leray‐ α‐magnetohydrodynamics model are also established. As a by‐product, an optimal time decay rate for the Navier–Stokes‐ α model is achieved. Copyright © 2013 John Wiley & Sons, Ltd.     

Local well‐posedness and zero‐α limit for the Euler‐α equations

In this paper, we prove the local‐in‐time existence and a blow‐up criterion of solutions in the Besov spaces for the Euler‐α equations of inviscid incompressible fluid flows in . We also establish the convergence rate of the solutions of the Euler‐α equations to the corresponding solutions of the Euler equations as the regularization parameter α approaches 0 in . Copyright © 2016 John Wiley & Sons, Ltd.     

从Hardy空间到加权Bloch型空间的加权复合算子

研究了单位圆上从Hardy空间到α-Bloch空间的加权复合算子uC_φ的有界性和紧性.分别给出从H~p空间到β~α空间和β_0~α空间的算子uC_φ的有界性和紧性的充分和必要条件.     

Weighted Composition Operators from the Bloch Spaces to Weighted Hardy Spaces on Bounded Symmetric Domains*

Let B_E be a bounded symmetric domain realized as the unit open ball of JB*-triples.The authors will characterize the bounded weighted composition operator from the Bloch space B(BE) to weighted Hardy space H_v^∞ in terms of Kobayashi distance.The authors also give a sufficient condition for the compactness,and also give the upper bound of its essential norm.As a corollary,they show that the boundedness and compactness are equivalent for composition operator fromB(B...     

Global well‐posedness for two modified‐Leray‐α‐MHD models with partial viscous terms

In this paper, we will prove global well‐posedness for the Cauchy problems of two modified‐Leray‐α‐MHD models with partial viscous terms. Copyright © 2009 John Wiley & Sons, Ltd.     

Exceptions and characterization results for type‐1 λ‐designs

Let $X$ be a finite set with $v$ elements, called points and $\beta$ be a family of subsets of $X$, called blocks. A pair $\left(X,\beta \right)$ is called $\lambda$‐design whenever $\mid \beta \mid =\mid X\mid$ and

• 1. for all $B_i,B_j\in \beta ,i\ne j,\mid B_i\cap B_j\mid =\lambda$;
• 2. for all $B_j\in \beta ,\mid B_j\mid =k_j>\lambda$, and not all $k_j$ are equal.

The only known examples of $\lambda$‐designs are so‐called type‐1 designs, which are obtained from symmetric designs by a certain complementation procedure. Ryser and Woodall had independently conjectured that all $\lambda$‐designs are type‐1. Let $r,r^{*}?(r>r^{*})$ be replication numbers of a $\lambda$‐design $D=\left(X,\beta \right)$ and $g=\text{gcd}\left(r?1,r^{*}?1\right),m=\text{gcd}\left(\left(r?r^{*}\right)∕g,\lambda \right)$, and $m\prime =m$, if $m$ is odd and $m\prime =m∕2$, otherwise. For distinct points $x$ and $y$ of $D$, let $\lambda \left(x,y\right)$ denote the number of blocks of $X$ containing $x$ and $y$. We strengthen a lemma of S.S. Shrikhande and N.M. Singhi and use it to prove that if $\frac{r\left(r?1\right)}{\left(v?1\right)}?\frac{k\left(r?r^{*}\right)}{m\prime \left(v?1\right)}$ are not integers for $k=1,2,\text{…},m\prime ?1$, then $D$ is type‐1. As an application of these results, we show that for fixed positive integer $\theta$ there are finitely many nontype‐1 $\lambda$‐designs with $r=r^{*}+\theta$. If $r?r^{*}=27$ or $r?r^{*}=4p$ and $r^{*}\ne {\left(p?1\right)}^2$, or $v=7p+1$ such that $p?1,13\left(\mathrm{mod}21\right)$ and $p?4,9,19,24\left(\mathrm{mod}35\right)$, where $p$ is a positive prime, then $D$ is type‐1. We further obtain several inequalities involving $\lambda (x,y)$, where equality holds if and only if D is type‐1.     

Well‐posedness of time‐space fractional stochastic evolution equations driven by α‐stable noise

This paper is devoted to the well‐posedness for time‐space fractional Ginzburg‐Landau equation and time‐space fractional Navier‐Stokes equations by α‐stable noise. The spatial regularity and the temporal regularity of the nonlocal stochastic convolution are firstly established, and then the existence and uniqueness of the global mild solution are obtained by the Banach fixed point theorem and Mittag‐Leffler functions, respectively. Numerical simulations for time‐space fractional Ginzburg‐Landau equation are provided to verify the analysis results.     

On admissible topologies in JB*‐triples

Given a complex JB*‐triple X, we define and study admissible topologies on X, i.e., locally convex topologies τ on X coarser than the norm topology, invariant under the group of surjective linear isometries of X, and such that the triple product is jointly ‐continuous on bounded subsets of X. As a consequence of the joint ‐continuity of the triple product, all holomorphic automorphisms of the open unit ball are homeomorphisms of and the natural action is jointly ‐continuous on .     

On effective σ‐boundedness and σ‐compactness

We prove several dichotomy theorems which extend some known results on σ‐bounded and σ‐compact pointsets. In particular we show that, given a finite number of $\Delta ^{1}_{1}$ equivalence relations $\mathrel {\mathsf {F}}_1,\dots ,\mathrel {\mathsf {F}}_n$, any $\Sigma ^{1}_{1}$ set A of the Baire space either is covered by compact $\Delta ^{1}_{1}$ sets and lightface $\Delta ^{1}_{1}$ equivalence classes of the relations $\mathrel {\mathsf {F}}_i$, or A contains a superperfect subset which is pairwise $\mathrel {\mathsf {F}}_i$‐inequivalent for all i = 1, …, n. Further generalizations to $\Sigma ^{1}_{2}$ sets A are obtained.     

Asymptotic normality in conditional wavelet density with left‐truncated α‐mixing observations

In this paper we define a new nonlinear wavelet‐based estimator of conditional density function for a left truncation model. Asymptotic normality of the estimator is established. It is assumed that the lifetime observations form a stationary α‐mixing sequence. Copyright © 2010 John Wiley & Sons, Ltd.     

Backward uniqueness of 3D MHD‐α model driven by linear multiplicative Gaussian noise

In this paper, we devote to proving the backward uniqueness property of the solution to three‐dimensional stochastic magnetohydrodynamic‐α model (3D stochastic MHD‐α model) driven by linear multiplicative Gaussian noise, which involves not only the study of multiplicative noise but also the challenging nonlinear drift terms.     

Fixed points of (α,ψ)‐contractions in Hausdorff partial metric spaces

The concept of (α,ψ)‐contractions was introduced by Samet et al. in this paper, we introduce (α,ψ)‐generalized contractions in a Hausdorff partial metric space. We discuss its significance and obtain some common fixed point theorems for a pair of self‐mappings. Some examples are given to support the theory.     

Procrustes problems and inverse eigenproblems for multilevel block α‐circulants

Let n = (n₁,n₂,…,n_k) and α = (α₁,α₂,…,α_k) be integer k‐tuples with α_i∈{1,2,…,n_i?1} and for all i = 1,2,…,k. Multilevel block α ‐circulants are (k + 1)‐level block matrices, where the first k levels have the block α_i‐circulant structure with orders and the entries in the (k + 1)‐st level are unstructured rectangular matrices with the same size . When k = 1, Trench discussed on his paper "Inverse problems for unilevel block α‐circulants" the Procrustes problems and inverse problems of unilevel block α‐circulants and their approximations. But the results are not perfect for the case gcd( α , n ) > 1 (i.e., gcd(α₁,n₁) > 1). In this paper, we also discuss Procrustes problems for multilevel block α ‐circulants. Our results can further make up for the deficiency when k = 1. When , inverse eigenproblems for this kind of matrices are also solved. By using the related results, we can design an artificial Hopfield neural network system that possesses the prescribed equilibria, where the Jacobian matrix of this system has the constrained multilevel α ‐circulative structure. Finally, some examples are employed to illustrate the effectiveness of the proposed results. Copyright © 2016 John Wiley & Sons, Ltd.