in this paper, we deal with the subdierential concept onhadamard spaces. flat hadamard spaces are characterized, and nec-essary and sucient conditions are presented to prove that the subdif-ferential set in hadamard spaces is nonempty. proximal subdierentialin hadamard spaces is addressed and some basic properties are high-lighted. finally, a density theorem for subdierential set is establi...

Let $\mathcal U_\hbar(\hat{\mathfrak g})$ be the untwisted quantum affinization of a symmetrizable Kac-Moody algebra U_\hbar({\mathfrak g})$. For $\ell\in\mathbb C$, we construct an $\hbar$-adic vertex $V_{\hat{\mathfrak g},\hbar}(\ell,0)$, and establish one-to-one correspondence between $\phi$-coordinated g},\hbar}(\ell,0)$-modules restricted g})$-modules level $\ell$. Suppose that $\ell$ is p...

introduction of modern architecture in iran and its popularization in 1950s and after, brought some new concepts in everyday life of iranian women, among which was “kitchen as heart of home-life”. younger members of current generation are grown in these modernized spaces while a bit older ones have experienced houses of traditional style. this study is designed to explore what previous concept ...

In this paper we consider some algebraic structures associated to a class of outer automorphisms of generalized Kac-Moody (GKM) algebras. These structures have recently been introduced in [2] for a smaller class of outer automorphisms in the case of ordinary Kac-Moody algebras with symmetrizable Cartan matrices. A GKM algebra G = G(A) is essentially described by its Cartan matrix, A = (aij)i,j∈...

Reversible logic is of growing importance to many future computer technologies. We introduce a regular structure to realize symmetric functions in binary reversible logic. This structure, called a 2 * 2 Net Structure, allows for more efficient realization of symmetric functions than the methods shown by previous authors. Our synthesis method allows to realize arbitrary symmetric function in a c...

We introduce the quasi-Hopf superalgebras which are Z2 graded versions of Drinfeld’s quasi-Hopf algebras. We describe the realization of elliptic quantum supergroups as quasi-triangular quasi-Hopf superalgebras obtained from twisting the normal quantum supergroups by twistors which satisfy the graded shifted cocycle condition, thus generalizing the quasi-Hopf twisting procedure to the supersymm...

In a series of works [18, 21, 19, 20, 23, 22], Geiß-Leclerc-Schröer defined the cluster algebra structure on the coordinate ring C[N(w)] of the unipotent subgroup, associated with a Weyl group element w. And they proved cluster monomials are contained in Lusztig’s dual semicanonical basis S∗. We give a set up for the quantization of their results and propose a conjecture which relates the quant...

This paper is concerned with the derivation and analysis of hydrodynamic models for systems of self-propelled particles subject to alignment interaction and attractionrepulsion. The starting point is the kinetic model considered in [10] with the addition of an attraction-repulsion interaction potential. Introducing different scalings than in [10], the non-local effects of the alignment and attr...

A class of upwind flux splitting methods in the Euler equations of compressible flow is considered in this paper. Using the property that Euler flux F (U) is a homogeneous function of degree one in U , we reformulate the splitting fluxes with F+ = A+U , F− = A−U , and the corresponding matrices are either symmetric or symmetrizable and keep only non-negative and non-positive eigenvalues. That l...