This paper is concerned with the study of a parametric anisotropic double phase free boundary problem (DPFBP, for short) involving $ (p(\cdot),q(\cdot)) $-Laplacian, convection term (a reaction depending on gradient), and two parameters (\theta,\lambda) appearing in q(\cdot) $-Laplacian term, respectively. The $-Laplace operator (DPFBP) considered to be controlled by highly nonlinear nonlocal f...

We prove two identities that connect some natural tensor products in the category $\sf{LCS}$ of locally convex spaces with $\sf{Ste}$ stereotype spaces. In particular, we give sufficient conditions under which identity $$ X^\vartriangle\odot Y^\vartriangle\cong (X^\vartriangle\cdot Y^\vartriangle)^\vartriangle\cong (X\cdot Y)^\vartriangle holds, where $\odot$ is injective product $\sf{Ste}$, $\...

The current paper is concerned with the forced waves of Keller–Segel chemoattraction systems in shifting environments form, 0.1 $$\begin{aligned} {\left\{ \begin{array}{ll} u_t=u_{xx}-\chi (uv_x)_x +u(r(x-ct)-bu),\quad x\in \mathbb {R}\\ 0=v_{xx}- \nu v+\mu u,\quad {R}, \end{array}\right. } \end{aligned}$$ where $$\chi $$ , b, $$\nu and $$\mu are positive constants, $$c\in {R}$$ resource functi...

In the area of distributed graph algorithms a number of network's entities with local views solve some computational task by exchanging messages with their neighbors. Quite unfortunately, an inherent property of most existing distributed algorithms is that throughout the course of their execution, the nodes get to learn not only their own output but rather learn quite a lot on the inputs or out...

Electrical characteristics of self-aligned top-gate (SATG) amorphous InGaZnO (a-IGZO) thin-film transistors (TFTs) with 4 nm-thick atomic-layer-deposited (ALD) AlOx gate insulator (GI) are investigated. It is demonstrated that the SATG a-IGZO TFTs present high-performance metrics including a near-ideal subthreshold swing (SS) 60.9 mV/dec, low off-state current below 10&#x...

Cryptographic multilinear maps have many applications, such as multipartite key exchange and software obfuscation. However, the encodings of three current constructions are “noisy” and their multilinearity levels are fixed and bounded in advance. In this paper, we describe a candidate construction of ideal multilinear maps by using ideal lattices, which supports arbitrary multilinearity levels....

Cryptographic multilinear maps have many applications, such as multipartite key exchange and software obfuscation. However, the encodings of three current constructions are “noisy” and their multilinearity levels are fixed and bounded in advance. In this paper, we describe a candidate construction of ideal multilinear maps by using ideal lattices, which supports arbitrary multilinearity levels....

Let $L$ be a completely regular frame and $mathcal{R}L$ be the ‎ring of continuous real-valued functions on $L$‎. ‎We show that the‎ ‎lattice $Zid(mathcal{R}L)$ of $z$-ideals of $mathcal{R}L$ is a‎ ‎normal coherent Yosida frame‎, ‎which extends the corresponding $C(X)$‎ ‎result of Mart'{i}nez and Zenk‎. ‎This we do by exhibiting‎ ‎$Zid(mathcal{R}L)$ as a quotient of $Rad(mathcal{R}L)$‎, ‎the‎ ‎...

In the setting of non-type $\ty{II_1}$ representations, we propose a definition {\it deformed Fredholm module} $\big[D_\ct|D_\ct|^{-1}\,,\,{\bf\cdot}\,\big]_\ct$ for modular spectral triple $\ct$, where $D_\ct$ is Dirac operator. assumed to be invertible sake simplicity, and its domain an "essential" operator system $\ce_\ct$. According such definition, obtain $\big[D_\ct|D_\ct|^{-1}\,,\,{\bf\c...

Abstract In this paper we provide non-smooth atomic decompositions of 2-microlocal Besov-type and Triebel–Lizorkin-type spaces with variable exponents $$B^{\varvec{w}, \phi }_{p(\cdot ),q(\cdot )}({\mathbb {R}}^n)$$ B p ( · ) <mm...