The main purpose of this paper is to prove a group-theoretic generalization of a theorem of Katz on isocrystals. Along the way we reprove the group-theoretic generalization of Mazur’s inequality for isocrystals due to Rapoport-Richartz, and generalize from split groups to unramified groups a result from [KR] which determines when the affine Deligne-Lusztig subset X μ (b) of G(L)/G(oL) is non-em...

A class of discrete convex functions that can efficiently be minimized has been considered by Murota. Among them are L\-convex functions, which are natural extensions of submodular set functions. We first consider the problem of minimizing an L\-convex function with a linear inequality constraint having a positive normal vector. We propose a polynomial algorithm to solve it based on a binary se...

We show that the number of rational points a subgroup inside toric variety over finite field defined by homogeneous lattice ideal can be computed via Smith normal form matrix whose columns constitute basis lattice. This generalizes and yields concise geometric proof same fact proven purely algebraically Lopez Villarreal for case projective space standard dimension one. also prove Nullstellensat...

Abstract We are dealing with projective classes (in short $\textrm {PC}$) over first-order vocabularies no restrictions on the (possibly infinite) arities of relation or operation symbols. verify that {PC}(\mathbin {\mathscr {L}}_{\infty \lambda })=\textrm {RPC}(\mathbin })$ for any infinite cardinal $\lambda $, and if $ is singular, then ^+})$. If regular, a class structures $-ary vocabulary }...

The main focus in this work is to establish that L-group theory, which uses the language of functions instead formal set theoretic language, capable capturing most refined ideas and concepts classical group theory. We demonstrate by extending notion subnormality L-setting investigating its properties. develop a mechanism tackle join problem subnormal L-subgroups. conjugate L-subgroup as defined...

In this paper we prove new lower bounds for the minimum distance of a toric surface code CP defined by a convex lattice polygon P ⊂ R 2 . The bounds involve a geometric invariant L(P ) , called the full Minkowski length of P which can be easily computed for any given P .

We obtain new upper bounds on the minimal density $\Theta _{n, \mathcal {K}}$ of lattice coverings ${\mathbb {R}}^n$ by dilates a convex body $\mathcal {K}$. also probability (with respect to natural Haar-Siegel measure space lattices) that randomly chosen $L$ satisfies $L+\mathcal {K}= {\mathbb {R}}^n$. As step in proof, we utilize and strengthen results discrete Kakeya problem.

the aim of this paper is to extend results established by h. onoand t. kowalski regarding directly indecomposable commutative residuatedlattices to the non-commutative case. the main theorem states that a residuatedlattice a is directly indecomposable if and only if its boolean center b(a)is {0, 1}. we also prove that any linearly ordered residuated lattice and anylocal residuated lattice are d...

We show that maximal S-free convex sets are polyhedra when S is the set of integral points in some rational polyhedron of R. This result extends a theorem of Lovász characterizing maximal lattice-free convex sets. We then consider a model that arises in integer programming, and show that all irredundant inequalities are obtained from maximal S-free convex sets. 1 Maximal S-free convex sets Let ...