On some composition formulas

On Some Interesting Ternary Formulas

We show that, up to renaming of the letters, the only infinite ternary words avoiding the formulaABCAB.ABCBA.ACB.BAC (resp. ABCA.BCAB.BCB.CBA) have the same set of recurrent factors as the fixed point of 0 7→ 012, 1 7→ 02, 2 7→ 1. Also, we show that the formula ABAC.BACA.ABCA is 2-avoidable. Finally, we show that the pattern ABACADABCA is unavoidable for the class of C4-minor-free graphs with m...

On some cubature formulas on the sphere

We construct interpolatory cubature rules on the two-dimensional sphere, using the fundamental system of points obtained by Láın Fernández in [2,3]. The weights of the cubature rules are calculated explicitly. We also discuss the cases when this cubature leads to positive weights. Finally, we study the possibility to construct spherical designs and the degree of exactness.

Some Asymptotic Formulas on Generalized Divisor Functions

1 . Throughout this paper, we use the following notation : c•1 , c2 , . . ., X0 , X1 , . . . denote positive absolute constants. We denote the number of elements of the finite set S by BSI . We write ex =exp (x) . We denote the least prime factor of n by p(n) . We write pall n if pain but pa+1 f n . v(n) denotes the number of the distinct prime factors of n, while the number of all the prime fa...

On Some SAT-Variants over Linear Formulas

Composition formulas of binary eutectics.

The present paper addresses the long-standing composition puzzle of eutectic points by introducing a new structural tool for the description of short-range-order structural unit, the cluster-plus-glue-atom model. In this model, any structure is dissociated into a 1(st)-neighbor cluster and a few glue atoms between the clusters, expressed by a cluster formula [cluster]gluex. This model is applie...