We prove the following theorem: Let F be an algebraic closure of a finite field of characteristic p > 3. Let ρ be a continuous homomorphism from the absolute Galois group of Q to GL(3,F) which is isomorphic to a direct sum of a character and a two-dimensional odd irreducible representation. We assume that the image of ρ is contained in the intersection of the stabilizers of the line spanned by ...

The paper has a threefold purpose. The first purpose is to present an explicit description of expanded cyclic codes defined in GF(qm). The proposed explicit construction of expanded generator matrix and expanded parity check matrix maintains the symbol-wise algebraic structure and thus keeps many important original characteristics. The second purpose of this paper is to identify a class of cons...

Currently, it has been claimed that certain Hermitian Hamiltonians have parity (P) and they are PT-invariant. We propose generalized definitions of time-reversal operator (T) and orthonormality such that all Hermitian Hamil-tonians are P, T, PT, and CPT invariant. The PT-norm and CPT-norm are indefinite and definite respectively. The energy-eigenstates are either E-type (e.g., even) or O-type (...

‎An  oriented perfect path double cover (OPPDC) of a‎ ‎graph $G$ is a collection of directed paths in the symmetric‎ ‎orientation $G_s$ of‎ ‎$G$ such that‎ ‎each arc‎ ‎of $G_s$ lies in exactly one of the paths and each‎ ‎vertex of $G$ appears just once as a beginning and just once as an‎ ‎end of a path‎. ‎Maxov{'a} and Ne{v{s}}et{v{r}}il (Discrete‎ ‎Math‎. ‎276 (2004) 287-294) conjectured that ...

RAID storage systems protect data from storage errors, such as data corruption, using a set of one or more integrity techniques, such as checksums. The exact protection offered by certain techniques or a combination of techniques is sometimes unclear. We introduce and apply a formal method of analyzing the design of data protection strategies. Specifically, we use model checking to evaluate whe...

objective: to determine the status of serum zinc in pregnant women in different gestational ages and correlation with socio-demographic and anthropometric factors in iranian women referring to prenatal care public health clinics . materials and methods: we analyzed the zinc concentrations in plasma samples obtained at different gestational ages from 961 women and recorded bmi at the first trime...

The Erdős–Faber–Lovász conjecture states that if a graph G is the union of n cliques of size n no two of which share more than one vertex, then χ(G) = n. We provide a formulation of this conjecture in terms of maximal partial clones of partial operations on a set.

In this article we define a minor relation, which is stronger than the classical one, but too strong to become a well-quasi-order on the class of finite graphs. Nevertheless, with this terminology we are able to introduce a conjecture, which would imply the Lovasz conjecture and give an interesting insight on the symmetry of vertex-transitive graphs, if true. Though it could become an approach ...

let $g$ be a finite group and let $text{cd}(g)$ be the set of all‎ ‎complex irreducible character degrees of $g$‎. ‎b‎. ‎huppert conjectured‎ ‎that if $h$ is a finite nonabelian simple group such that‎ ‎$text{cd}(g) =text{cd}(h)$‎, ‎then $gcong h times a$‎, ‎where $a$ is‎ ‎an abelian group‎. ‎in this paper‎, ‎we verify the conjecture for‎ ‎${f_4(2)}.$‎

Locke’s conjecture (L) states that the binary hypercube Qn with k deleted vertices of each parity is Hamiltonian if n ≥ k + 2. In 2003, S. C. Locke and R. Stong published in The American Mathematical Monthly a proof of (L) for the case k = 1. In 2007, in the paper Path coverings with prescribed ends in faulty hypercubes the authors proved (L) for every k ≤ 4 and formulated the following conject...