In this paper we determine an upper bound for the covering radius of a q-ary MacDonald codeCk;u(q). Values of nq(4; d), the minimal length of a 4-dimensional q-ary code with minimum distance d is obtained for d = q 1 and q 2. These are used to determine the covering radius of C3;1(q),C3;2(q) and C4;2(q).

We consider the XPath evaluation problem: Evaluate an XPath query Q on a streaming XML document D. We consider two versions of the problem: 1). Filtering Problem: Determine if there is a match for Q in D. 2). Node Selection Problem: Determine the set Q(D) of document nodes selected by Q. We consider Conjunctive XPath (CXPath) queries that involve only the child and descendant axes. Let d denote...

As a continuation of Maruta [Finite Fields Appl. 10 (2004), 674–685], we investigate the extendability of [n, k, d]q codes with d ≡ −2 (mod q) whose weights are congruent to 0, −1 or −2 (mod q) for even q ≥ 4. We show that such codes are extendable for all even q ≥ 8, giving a new extension theorem for [n, k, d]q codes with gcd(d, q) = 2. We also consider the extendability of such codes for q = 4.

For d≥3, we prove that time-inhomogeneous stochastic differential equations driven by additive noises with drifts in critical Lebesgue space Lq([0,T];Lp(Rd)), where (p,q)∈(d,∞]×[2,∞) and d∕p+2∕q=1, or (p,q)=(d,∞) divb∈L∞([0,T];Ld∕2+ε(Rd)), are well-posed. The weak uniqueness is obtained solving corresponding Kolmogorov backward some second-order Sobolev spaces, which analytically interesting it...

For $q>2, \gamma > 1$, we prove that maximal regularity of $L^q$ type holds for periodic solutions to $-\Delta u + |Du|^\gamma = f$ in $\mathbb{R}^d$, under the (sharp) assumption $q d \frac{\gamma-1}\gamma$.

We obtain a complete characterization for doubly commuting mixed invariant subspaces of the Hardy space over unit polydisc. say closed subspace Q H2(Dn) is if Mzj(Q)⊆Q 1≤j≤k and Mzj⁎(Q)⊆Q, k+1≤j≤n some integer k∈{1,2,…,n−1}. prove that only ifQ=ΘH2(Dk)⊗Qθ1⊗⋯⊗Qθn−k, where Θ∈H∞(Dk) inner function Qθj either Jordan block H2(D)⊖θjH2(D) θj or H2(D). Furthermore, an explicit representation commutant ...

in this article, we prove the existence of extremal positive solution for the distributed order fractional hybrid differential equation$$int_{0}^{1}b(q)d^{q}[frac{x(t)}{f(t,x(t))}]dq=g(t,x(t)),$$using a fixed point theorem in the banach algebras. this proof is given in two cases of the continuous and discontinuous function $g$, under the generalized lipschitz and caratheodory conditions.

The categorical concept of Kan extensions form a more general notion of both limits and adjoints. The general definition of Kan extensions is given and motivated by several concrete examples. After providing the necessary background on some basic categorical objects and theorems, the relationship between Kan extensions, limits, and adjoints is expressed through two theorems from [3]. 1. Some Pr...