We introduce a new cluster character with coefficients for category $\mathcal{C}$ and rather than using Frobenius $2$-Calabi-Yau realization to incorporate into the representation-theoretic model algebra, as done by Fu Keller, we exploit intrinsic properties of $\mathcal{C}$. For this purpose, define an ice quiver associated each tilting object in In Dynkin case $\mathbb{A}_n$, also prove that ...

This paper is an attempt to prove the following result:Let $n>1$ be an integer and let $mathcal{R}$ be a $n!$-torsion-free ring with the identity element. Suppose that $d, delta, varepsilon$ are additive mappings satisfyingbegin{equation}d(x^n) = sum^{n}_{j=1}x^{n-j}d(x)x^{j-1}+sum^{n-1}_{j=1}sum^{j}_{i=1}x^{n-1-j}Big(delta(x)x^{j-i}varepsilon(x)+varepsilon(x)x^{j-i}delta(x)Big)x^{i-1}quadend{e...

We consider the quasilinear Kirchhoff's problem$$ u_{tt}-phi (x)||nabla u(t)||^{2}Delta u+f(u)=0 ,;; x in {mathcal{R}}^{N}, ;; t geq 0,$$with the initial conditions  $ u(x,0) = u_0 (x)$  and $u_t(x,0) = u_1 (x)$, in the case where $N geq 3, ;  f(u)=|u|^{a}u$ and $(phi (x))^{-1} in L^{N/2}({mathcal{R}}^{N})cap L^{infty}({mathcal{R}}^{N} )$ is a positive function. The purpose of our work is to ...

Generalizing work of Smith and Hara, we give a new characterization of logterminal singularities for finitely generated algebras over C, in terms of purity properties of ultraproducts of characteristic p Frobenii. As a first application we obtain a Boutot-type theorem for log-terminal singularities: given a pure morphism Y → X between affine Q-Gorenstein varieties of finite type over C, if Y ha...

Let $k$ be a field, let ${\sf C}$ $k$-linear abelian category, $\underline{\mathcal{L}}:=\{\mathcal{L}_{i}\}_{i \in \mathbb{Z}}$ sequence of objects in C}$, and $B_{\underline{\mathcal{L}}}$ the associated orbit algebra. We describe sufficient conditions on $\underline{\mathcal{L}}$ such that there is canonical morphism from noncommutative space Proj }B_{\underline{\mathcal{L}}}$ to projective ...

This paper generalize the idea of the authors in J. Pure Appl. Algebra 210 (2007) 437–445. Namely, we define and study a particular case of Gorenstein projective modules. We investigate some change of rings results for this new kind of modules. Examples over not necessarily Noetherian rings are given.

We prove that in an abelian category with enough projective objects, the extension subcategory of two covariantly finite subcategories is still covariantly finite. This extends a result by Sikko and Smalø. We also prove a triangulated version of the result. As applications, we obtain short proofs to a classical result by Ringel and a recent result by Krause and Solberg. 1. Main Theorems Let C b...

The problem of minimax detection of Gaussian random signal vector in White Gaussian additive noise is considered. It is supposed that an unknown vector $\boldsymbol{\sigma}$ of the signal vector intensities belong to the given set ${\mathcal E}$. It is investigated when it is possible to replace the set ${\mathcal E}$ by a smaller set ${\mathcal E}_{0}$ without loss of quality (and, in particul...

The so-called ’change-of-ring’ results are well-known expressions which present several connections between projective, injective and flat dimensions over the various base rings. In this note we extend these results to the Gorenstein dimensions over Cohen-Macaulay local rings.

Abstract We introduce the cohomological blowup of a graded Artinian Gorenstein algebra along surjective map, which we term BUG (blowup Gorenstein) for short. This is intended to translate an algebraic context cohomology ring projective manifold submanifold. show, among other things, that connected sum, it general fiber in flat family algebras, and preserves strong Lefschetz property. also show ...