Let mod kG be the stable category of finitely generated modular representations of a finite group G over a field k. We prove a Krull-Remak-Schmidt theorem for thick subcategories of mod kG. It is shown that every thick tensor-ideal C of mod kG (i.e. a thick subcategory which is a tensor ideal) has a (usually infinite) unique decomposition C = ∐ i∈I Ci into indecomposable thick tensor-ideals. Th...

We characterize all pairs of graphs (G1, G2), for which the binomial edge ideal JG1,G2 has linear relations. We show that JG1,G2 has a linear resolution if and only if G1 and G2 are complete and one of them is just an edge. We also compute some of the graded Betti numbers of the binomial edge ideal of a pair of graphs with respect to some graphical terms. In particular, we show that for every p...

In this paper we introduce a function for multilinear operators that can be considered as an extension of the so-called outer measure associated to linear operator ideal. We prove it allows characterize belong closed surjective ideal those having equal zero. also obtain some interpolation formulas new measure. As consequence deduce results arbitrary ideals which recover, in particular, differen...

the main purpose of this paper is to introduce and study new classes of soft closed sets like soft regular generalized b-closed sets in soft topological spaces (brie y soft rgb-closed set) moreover, soft rg-closed, soft gpr-closed, soft gb-closed, soft gsp-closed, soft g-closed, soft gb-closed, and soft sgb-closed sets in soft topological spaces are introduced in this paper and we investigat...

let $r$ be a 2-torsion free ring and $u$ be a square closed lie ideal of $r$. suppose that $alpha, beta$ are automorphisms of $r$. an additive mapping $delta: r longrightarrow r$ is said to be a jordan left $(alpha,beta)$-derivation of $r$ if $delta(x^2)=alpha(x)delta(x)+beta(x)delta(x)$ holds for all $xin r$. in this paper it is established that if $r$ admits an additive mapping $g : rlongrigh...

Character groundtruth for real, scanned document images is crucial for evaluating the performance of OCR systems, training OCR algorithms, and validating document degradation models. Unfortunately, manual collection of accurate groundtruth for characters in a real (scanned) document image is not practical because (i) accuracy in delineating groundtruth character bounding boxes is not high enoug...

noroviruses (novs), an important pathogenic agent of foodborne illness, lead to acute and chronic gastroenteritis in humans of all ages and to travelers’ diarrhea. many genotypes exist in nature; gii.4 is widely known as the most predominant. outbreaks mostly occur in semi-closed settings. although the disease is self-limited to person, many cases have resulted in death, which has raised more c...

Let P := k [X,Y, Z] be a polynomial ring over an algebraic closed field k and (X, Y , Z, XY Z, XY Z ) · k [X,Y, Z] an (X,Y, Z)-primary ideal in P , (m, n, l, a, b, c, d, e, f are integers). The ideal Q=(X, Y , Z, XY Z, XY Z ) ·R is (X,Y, Z) · R-primary ideal in the local ring R = k [X,Y, Z](x,y,z). In this short note we give a formula for the calculation of Samuel multiplicity e0(Q,R) of the id...

A language L over an alphabet Σ is suffix-convex if, for any words x, y, z ∈ Σ∗, whenever z and xyz are in L, then so is yz. Suffixconvex languages include three special cases: left-ideal, suffix-closed, and suffix-free languages. We examine complexity properties of these three special classes of suffix-convex regular languages. In particular, we study the quotient/state complexity of boolean o...