Computing lattice ideals of unions of monomial curves

AbstractIn this paper we present a combinatorial study of binomial ideals of dimension 1 of k[X1,…,Xn], using monomial parametrizations of the irreducible affine curves defined by their associated primes. We find an algorithm that checks whether or not the ideal of a union of monomial curves is binomial and another one that calculates curves such that their associated ideal is a prescribed lattice ideal

New Extrapolation Estimates

AbstractGiven a sublinear operator T satisfying that ‖TχA‖Lp(ν)⩽Cp−1‖χA‖Lp(μ), for every measurable set A and every 1<p⩽p0, with C independent of A and p, we show that supr>0∫∞1/rλνTf(y)dy1+log+r≲∫M|f(x)|(1+log+|f(x)|)dμ(x). This estimate allows us to improve Yano's extrapolation theorem and also to obtain that for every f∈LlogL(μ), r→∞∫∞1/rλνTf(y)dylogr≲‖f‖1. Other types of extrapolation results are also given

A multiplier theorem using the Schechter's method of interpolation

AbstractLet m be a measurable bounded function and let us assume that there exists a bounded functions S so that m(ξ)S(ξ)it−1 is a Fourier multiplier on Lp uniformly in t∈R. Then, using the analytic interpolation theorem of Stein, one can show that necessarily m is a Lp multiplier. The purpose of this work is to show that under the above conditions, it holds that, for every k∈N, m(logS)k∈Mp. The technique is based on the Schechter's interpolation method

The Finite Upper Half Space and Related Hypergraphs

AbstractA space generalizing the finite upper half plane is presented along with a projective action by the finite general linear group. A volume generalizing the pseudo-distance on the finite upper half plane is also given. Then this volume is used to create hypergraphs which are analyzed with respect to the Ramanujan property

Hochschild Cohomology of Triangular Matrix Algebras

AbstractWe study the Hochschild cohomology of triangular matrix rings B=R0AMRA , where A and R are finite dimensional algebras over an algebraically closed field K and M is an A-R-bimodule. We prove the existence of two long exact sequences of K-vector spaces relating the Hochschild cohomology of A, R, and B

The C-type lectin homologue gene (EP153R) of African swine fever virus inhibits apoptosis both in virus infection and in heterologous expression

AbstractThe open reading frame EP153R of African swine fever virus (ASFV) encodes a nonessential protein that has been involved in the hemadsorption process induced in virus-infected cells. By the use of a virus deletion mutant lacking the EP153R gene, we have detected, in several virus-sensitive cells, increased levels of caspase-3 and cell death as compared with those obtained after infection with the parental BA71V strain. Both transient and stable expression of the EP153R gene in Vero or COS cells resulted in a partial protection of the transfected lines from the apoptosis induced in response to virus infection or external stimuli. The presence of gene EP153R resulted in a reduction of the transactivating activity of the cellular protein p53 in Vero cell cultures in which apoptosis was induced by virus infection or staurosporine treatment. This is to our knowledge the first description of a viral C-type lectin with anti-apoptotic properties

Presentations of Trivial Extensions of Finite Dimensional Algebras and a Theorem of Sheila Brenner

AbstractLet Λ be a finite dimensional algebra over an algebraically closed field such that any oriented cycle in the ordinary quiver of Λ is zero in Λ. We describe the ordinary quiver and relations for T(Λ)=Λ⋉D(Λ), the trivial extension of Λ by its minimal injective cogenerator D(Λ), and also for the repetitive algebra [formula] of Λ. Associated with this description we give an application of a theorem of Sheila Brenner

On Internal Characterizations of CompletelyL-Regular Spaces

AbstractCompleteL-regularity is internally characterized in terms of separating chains of openL-sets. A possible characterization in terms of normal and separating families of closedL-sets is discussed and it is shown that spaces admitting such families are completelyL-regular. The question of whether the converse holds true remains open. Some partial solutions are however given, e.g. in the class of countably compact spaces

Pseudocomplemented Semilattices, Boolean Algebras, and Compatible Products

AbstractPseudocomplemented semilattices are studied here from an algebraic point of view, stressing the pivotal role played by the pseudocomplements and the relationship between pseudocomplemented semilattices and Boolean algebras. Following the pattern of semiprime ring theory, a notion of Goldie dimension is introduced for complete pseudocomplemented lattices and calculated in terms of maximal uniform elements if they exist in abundance. Products in lattices with 0-element are studied and questions about the existence and uniqueness of compatible products in pseudocomplemented lattices, as well as about the abundance of prime elements in lattices with a compatible product, are discussed. Finally, a Yood decomposition theorem for topological rings is extended to complete pseudocomplemented lattices

Spin wave mediated non-reciprocal effects in antiferromagnets

By using an effective field theory for the electromagnetic interaction of spin waves, we show that, in certain antiferromagnets, the latter induce non-reciprocal effects in the microwave region, which should be observable in the second harmonic generation and produce gyrotropic birefringency. We calculate the various (non-linear) susceptibilities in terms of a few parameters the order of magnitude of which is under control.Comment: Latex file, 22p . Published versio