A counterexample to weighted estimates for multilinear Fourier multipliers with Sobolev regularity

The problem whether the weighted estimates for multilinear Fourier multipliers with Sobolev regularity hold under weak condition on weights is considered.     

Necessary and sufficient condition for uniqueness of solution to the first boundary value problem for the diffusion equation in unbounded domains

This paper introduces a notion of regularity of t=-∞$t=-\infty$ for the diffusion (or heat) equation and establishes a necessary and sufficient condition for the existence of a unique bounded solution to the first boundary value problem for the diffusion equation in a general domain Ω⊂R^N+1$\Omega \subset {\mathbb{R}}^{N+1}$ which extends up to t=-∞$t=-\infty$.     

Vector analysis for Dirichlet forms and quasilinear PDE and SPDE on metric measure spaces

Starting with a regular symmetric Dirichlet form on a locally compact separable metric space X$X$, our paper studies elements of vector analysis, _Lp$L_p$-spaces of vector fields and related Sobolev spaces. These tools are then employed to obtain existence and uniqueness results for some quasilinear elliptic PDE and SPDE in variational form on X$X$ by standard methods. For many of our results locality is not assumed, but most interesting applications involve local regular Dirichlet forms on fractal spaces such as nested fractals and Sierpinski carpets.     

Stable categories of higher preprojective algebras

We introduce (n+1)$(n+1)$-preprojective algebras of algebras of global dimension n$n$. We show that if an algebra is n$n$-representation-finite then its (n+1)$(n+1)$-preprojective algebra is self-injective. In this situation, we show that the stable module category of the (n+1)$(n+1)$-preprojective algebra is (n+1)$(n+1)$-Calabi–Yau, and, more precisely, it is the (n+1)$(n+1)$-Amiot cluster category of the stable n$n$-Auslander algebra of the original algebra. In particular this stable category contains an (n+1)$(n+1)$-cluster tilting object. We show that even if the (n+1)$(n+1)$-preprojective algebra is not self-injective, under certain assumptions (which are always satisfied for n∈{1,2}$n\in \{1,2\}$) the results above still hold for the stable category of Cohen–Macaulay modules.     

The approximation characteristic of diagonal matrix in probabilistic setting

In this paper, the approximation characteristic of a diagonal matrix in probabilistic and average case settings is investigated. And the asymptotic degree of the probabilistic linear (n,δ)$(n,\delta )$-width and p$p$-average linear n$n$-width of diagonal matrix M$M$ are determined.     

Gradient estimates in Orlicz spaces for quasilinear elliptic equation

In this paper we generalize classical L^q$L^q$, q≥p$q\ge p$, estimates of the gradient to the Orlicz space for weak solutions of quasilinear elliptic equations of p-Laplacian type.     

Second-order multiobjective symmetric duality with cone constraints

In this paper, we formulate Wolfe and Mond–Weir type second-order multiobjective symmetric dual problems over arbitrary cones. Weak, strong and converse duality theorems are established under η$\eta$-bonvexity/η$\eta$-pseudobonvexity assumptions. This work also removes several omissions in definitions, models and proofs for Wolfe type problems studied in Mishra [9]. Moreover, self-duality theorems for these pairs are obtained assuming the function involved to be skew symmetric.     

Periodic solutions for a Rayleigh system of p-Laplacian type

By using the generalized Borsuk theorem in coincidence degree theory, some criteria for guaranteeing the existence of ω$\omega$-periodic solutions for a Rayleigh system of p$p$-Laplacian type are derived.     

On symmetric and locally finite actions of groups on the quintic tree

In this paper, we determine all faithful, symmetric and locally finite actions of a group on the tree of valency five. As a corollary we complete the classification of the isomorphism types of vertex and edge stabilisers in a group acting symmetrically on a graph of valency five. This builds on work of Weiss and recent work of Feng, Zhou and Feng, Guo. Our approach is to classify the isomorphism types of finite, faithful amalgams of degree (5, 2).     

Labeling constructions using digraph products

In this paper we study the edge-magicness of graphs with equal size and order, and we use such graphs and digraph products in order to construct labelings of different classes and of different graphs. We also study super edge-magic labelings of 2$2$-regular graphs with exactly two components and their implications to other labelings.     

Multiple comparisons with a control in direction-mixed families of hypothesis under heteroscedasticity

For general inferential families with a mixture of one- and two-sided inferences two procedures are proposed to compare several treatments with a control under heteroscedasticity. Critical constants required for the proposed procedures are tabulated, and a numerical example is given.     

Poincaré type inequalities for group measure spaces and related transportation cost inequalities

Let G be a countable discrete group with an orthogonal representation α on a real Hilbert space H  . We prove _Lp$L_p$ Poincaré inequalities for the group measure space _L∞(_ΩH,γ)?G$L_{\infty }({\Omega }_H,\gamma )?G$, where both the group action and the Gaussian measure space (_ΩH,γ)$({\Omega }_H,\gamma )$ are associated with the representation α  . The idea of proof comes from Pisier?s method on the boundedness of Riesz transform and Lust-Piquard?s work on spin systems. Then we deduce a transportation type inequality from the _Lp$L_p$ Poincaré inequalities in the general noncommutative setting. This inequality is sharp up to a constant (in the Gaussian setting). Several applications are given, including Wiener/Rademacher chaos estimation and new examples of Rieffel?s compact quantum metric spaces.     

Generalized vector variational inequalities with star-pseudomonotone and discontinuous operators

It is well known that a vector variational inequality can be a very efficient model for use in studying vector optimization problems. By using the Ky Fan fixed point theorem and the scalarization method we will prove some existence theorems for strong solutions for generalized vector variational inequalities where discontinuous and star-pseudomonotone operators are involved. Our results can be applied to the study of the existence of solutions of vector optimal problems. Some examples are given and analyzed.