In this paper, we prove the unique existence of global strong solutions and decay estimates for simplified Ericksen–Leslie system describing compressible nematic liquid crystal flows in RN, 3≤N≤7. Firstly, rewrite Lagrange coordinates, secondly, well-posedness transformed system, which is main task paper. The proof based on maximal Lp-Lq regularity to linearized problem.

Recently, there has been a lot of interest around multi-task learning (MTL) problem with the constraints that tasks should share a common sparsity profile. Such a problem can be addressed through a regularization framework where the regularizer induces a joint-sparsity pattern between task decision functions. We follow this principled framework and focus on lp−lq (with 0 ≤ p ≤ 1 and 1 ≤ q ≤ 2) ...

LP can be seen as a logic of knowledge with justifications. Artemov’s Realization Theorem says justifications can be extracted from validities in the more conventional Hintikka-style logic of knowledge S4, in which they are not explicitly present. Justifications, however, are far from unique. There are many ways of realizing each theorem of S4 in the logic LP. If the machinery of justifications...

in this paper, a vector version of the intermediate value theorem is established. the main theorem of this article can be considered as an improvement of the main results have been appeared in [textit{on fixed point theorems for monotone increasing vector valued mappings via scalarizing}, positivity, 19 (2) (2015) 333-340] with containing the uniqueness, convergent of each iteration to the fixe...

This paper presents a new Lp-primal–dual weak Galerkin (PDWG) finite element method for the div–curl system with normal boundary condition p>1. Two crucial features proposed Lp-PDWG scheme are as follows: (1) it offers an accurate and reliable numerical solution to under low W?,p-regularity (?>0) assumption exact solution; (2) effective approximation of harmonic vector fields on domains complex...

in this paper, a fuzzy version of the analytic form of hahn-banachextension theorem is given. as application, the hahn-banach theorem for$r$-fuzzy bounded linear functionals on $r$-fuzzy normedlinear spaces is obtained.

‎The concept of self-similarity on subsets of algebraic varieties‎ ‎is defined by considering algebraic endomorphisms of the variety‎ ‎as `similarity' maps‎. ‎Self-similar fractals are subsets of algebraic varieties‎ ‎which can be written as a finite and disjoint union of‎ ‎`similar' copies‎. ‎Fractals provide a framework in which‎, ‎one can‎ ‎unite some results and conjectures in Diophantine g...

In this paper, a fuzzy version of the analytic form of Hahn-Banachextension theorem is given. As application, the Hahn-Banach theorem for$r$-fuzzy bounded linear functionals on $r$-fuzzy normedlinear spaces is obtained.

The main result of this paper is an intersection representation for a class anisotropic vector-valued function spaces in axiomatic setting à la Hedberg and Netrusov (2007), which includes weighted mixed-norm Besov Lizorkin–Triebel spaces. In the special case classical spaces, gives improvement well-known Fubini property. has applications Lq-Lp-maximal regularity problem parabolic boundary value...