An r-perfect code of a graph G = (V, E) is a set C ⊆ V such that the r-balls centered at vertices of C form a partition of V . It is proved that the direct product of Cm and Cn (r ≥ 1, m,n ≥ 2r+1) contains an r-perfect code if and only if m and n are each a multiple of (r + 1)2 + r2 and that the direct product of Cm, Cn, and C` (r ≥ 1, m,n, ` ≥ 2r +1) contains an r-perfect code if and only if m...

The paper considers the interrelation between i-components of an arbitrary Preparata-like code P and i-components of a perfect code C containing P . It is shown that each i-component of P can uniquely be completed to an i-component of C by adding a certain number of special codewords of C. It is shown that the set of vertices of P in a characteristic graph of an arbitrary i-component of C forms...

The acid-base status and arterial blood gas change with temperature variation. To determine the changes in arterial pH and pC02, arterial blood samples of 50 neonates with different clinical conditions were examined at temperatures of 35 to 42°C with an increment of 0.5° C, which resulted in two nonlinear equations with perfect fit on data. The temperature correction factors of these equati...

In last ten years many mathematicians have studied properties of BL-algebras endowed with a topology. For example A. Di Nola and L. Leustean cite{dn} studied compact representations of BL-algebras, L. C. Ciungu cite{ciu} investigated some concepts of convergence in the class of perfect BL-algebras, J. Mi Ko and Y. C. Kim cite{jun} studied relationships between closure operators and BL-algebras,...

TWO theorems nre proved on perfect codes. The first cne states tk.at Lloyd's theorem is true without tne assumption that the number of symbols in the alphabet is a prime power. The second thevrem asser?s the impossibility of perfect group codes over non-prime-pcwer-alphabets. IA V be a finite set, I VI = q > 2, and let 1 <_ e 2 ye be Ia:ional integers. We pu?iV= (1, 2,. .. . n). Forv=(Vi)~=l E ...

water quality in each area, indicates the impact of geology, climate and anthropogenic pollutants. monitoring of water quality in most cases result in complex data which shows the perfect act of water resources, so they need appropriate method for analyzing. in this study hydro-chemical evaluation of hiv basin which located in west of hashtgerd have been done. to measure the concentration of ma...

A perfect number is any positive integer that is equal to the sum of its proper divisors. Several years ago, F. Luca showed that the Fibonacci and Lucas numbers contain no perfect numbers. In this paper, we alter the argument given by Luca for the nonexistence of both odd perfect Fibonacci and Lucas numbers, by making use of an 1888 result of C. Servais. We also provide a brief historical accou...