In network code setting, a constant dimension code is a set of k-dimensional subspaces of F nq . If F_q n is a nondegenerated symlectic vector space with bilinear form f, an isotropic subspace U of F n q is a subspace that for all x, y ∈ U, f(x, y) = 0. We introduce isotropic subspace codes simply as a set of isotropic subspaces and show how the isotropic property use in decoding process, then...

Let and B̄ be a subset of = PG(2n − 1, q) and a subset of PG(2n, q) respectively, with ⊂ PG(2n, q) and B̄ ⊂ . Denote by K the cone of vertex and base B̄ and consider the point set B defined by B = (K\ ) ∪ {X ∈ S : X ∩ K = ∅}, in the André, Bruck-Bose representation of PG(2, qn) in PG(2n, q) associated to a regular spread S of PG(2n − 1, q). We are interested in finding conditions on B̄ and in order...

We study a class of interacting particle systems with asymmetric interaction showing self-duality property. The includes the ASEP(q,θ), exclusion process, repulsive interaction, allowing up to θ∈N particles in each site, and ASIP(q,θ), θ∈R+, inclusion that is its attractive counterpart. extend setting investigation orthogonal duality properties done [8] for symmetric processes. analysis leads m...

We prove that a wide class of strongly proper forcing posets have quotients with strong properties. Specifically, we prove that quotients of forcing posets which have universal strongly generic conditions on a stationary set of models by certain nice regular suborders satisfy the ω1-approximation property. We prove that the existence of stationarily many ω1-guessing models in Pω2 (H(θ)), for su...

The Q-property of a multiplicative transformation AXAT in semidefinite linear complementarity problems is characterized when A is normal.

The Q-property of a multiplicative transformation AXAT in semidefinite linear complementarity problems is characterized when A is normal.

Let F be any field of prime characteristic p and let q a power p. We assume that contains the finite order q. A q-polynomial L over is an element polynomial ring F[x] with property all exponents are coefficient x term nonzero. investigate Galois group G F, under assumption L(x)/x irreducible in F[x]. It well known if has q-degree n, its roots n-dimensional vector space acts linearly on this spa...

For positive integers n and q and a monotone graph property A, we consider the two player, perfect information game WC(n, q,A), which is defined as follows. The game proceeds in rounds. In each round, the first player, called Waiter, offers the second player, called Client, q + 1 edges of the complete graph Kn which have not been offered previously. Client then chooses one of these edges which ...

A set S is convex if for every pair of points P, Q~S, the line segment PQ is contained in S, This definition can be generalized in various ways. One class of generalizations makes use of k-tuples, rather than pairs, of points-for example, Valentine's property P3: For every triple of points P, Q, R of S, at least one of the line segments PQ, QR, or RP is contained in S. It can be shown that if a...

In the case of a continuous integrand L : R n m —> RU {00} and a probability measure v supported in R n m we indicate conditions both necessary and sufficient for this measure to be generated as a homogeneous Young measure by gradients of piece-wise affine functions Uk € I A + Wo'°°(Q) with the property L(Duk) -* (L;v) in L(Q). Here A is the center of mass of v and I A is a linear function with...