Abstract Let $p$ be a prime number and $k$ an algebraically closed field with characteristic $\ell \neq p$. We show that the supercuspidal support of irreducible smooth $k$-representations Levi subgroups $\textrm {M}^{\prime}$ {SL}_n(F)$ is unique up to {M}^{\prime}$-conjugation, where $F$ either finite or non-Archimedean locally compact residual $p$.

A Dedekind cut of an ordered abelian group G is a pair (X, Y) of nonempty subsets of G where Y=G−X and every member of X precedes every member of Y. A Dedekind cut (X, Y) is said to be continuous if X has a greatest member or Y has a least member, but not both; if every Dedekind cut of G is a continuous cut, G is said to be (Dedekind) continuous. The ordered abelian group R of real numbers is, ...

We construct a p-adic version of Elliptic Cohomology whose coefficient ring agrees with Serre’s ring of p-adic modular forms. We then construct a stable operation Ûp in this theory agreeing with Atkin’s operator Up on p-adic modular forms. Throughout the paper we assume given a fixed prime p ≥ 5. We begin as in [2] by considering the universal Weierstrass cubic (for Z(p) algebras) Ell/R∗: Ell:Y...

We study existence and absence of $\ell^2$-eigenfunctions the combinatorial Laplacian on 11 Archimedean tilings Euclidean plane by regular convex polygons. show that exactly two these (namely $(3.6)^2$ Kagome tiling $(3.12^2)$ tiling) have $\ell^2$-eigenfunctions. These eigenfunctions are infinitely degenerate constituted explicitly described which supported a finite number vertices underlying ...

The Archimedean property is one of the most beautiful axioms of the classical arithmetic and some of the methods of constructing the field of real numbers are based on this property. It is well-known that every Archimedean `-group is abelian and every pseudo-MV algebra is commutative. The aim of this paper is to introduce the Archimedean property for pseudo-MTL algebras and FLw-algebras. The ma...

For vectors $X, Yin mathbb{R}^{n}$, we say $X$ is left matrix majorized by $Y$ and write $X prec_{ell} Y$ if for some row stochastic matrix $R, ~X=RY.$ Also, we write $Xsim_{ell}Y,$ when $Xprec_{ell}Yprec_{ell}X.$ A linear operator $Tcolon mathbb{R}^{p}to mathbb{R}^{n}$ is said to be a linear preserver of a given relation $prec$ if $Xprec Y$ on $mathbb{R}^{p}$ implies that $TXprec TY$ on $mathb...

 The category of the title is called $mathcal{W}$. This has all free objects $F(I)$ ($I$ a set). For an object class $mathcal{A}$, $Hmathcal{A}$ consists of all homomorphic images of $mathcal{A}$-objects. This note continues the study of the $H$-closed monoreflections $(mathcal{R}, r)$ (meaning $Hmathcal{R} = mathcal{R}$), about which we show ({em inter alia}): $A in mathcal{A}$ if and  only if...