Using a result of Salberger [9] we show that the number of non-trivial positive integer solutions x0, . . . , x5 6 B to the simultaneous equations x0 + x c 1 + x c 2 = x c 3 + x c 4 + x c 5, x d 0 + x d 1 + x d 2 = x d 3 + x d 4 + x d 5, is o(B) whenever d > max{2, c}. Mathematics Subject Classification (2000): 11D45 (11D41, 11P05)

Abstract Zarrabi proved in 1993 that if the spectrum of a contraction T on Banach space is countable subset unit circle

The radio k-chromatic number $$rc_k(G)$$ of a graph G is the minimum integer $$\lambda $$ such that there exists function $$\phi : V(G) \rightarrow \{0,1,\cdots , \lambda \}$$ satisfying $$|\phi (u)-\phi (v)| \ge k+1 - d(u,v)$$ where d(u, v) denotes distance between u and v. To date, several upper lower bounds $$rc_k(\cdot )$$ established for different families. One most notable works in this d...

It is shown that there are no non-trivial fifth-, seventh-, eleventh-, thirteenthor seventeenth powers in the Fibonacci sequence. For eleventh, thirteenthand seventeenth powers an alternative (to the usual exhaustive check of products of powers of fundamental units) method is used to overcome the problem of having a large number of independent units and relatively high bounds on their exponents...

Introdouction: Dentinal hypersensitivity (DH) is one of the most painful chronic problems reported in dental offices. Various methods have been applied for the treatment of DH. However, majority of them are either ineffective or last for a short period of time. It has been reported that lasers, particularly Neodymium- doped: Yttrium Aluminum Garnet laser (Nd: YAG), can be helpful in the treatme...

sometimes, disharmony among the three powers of sovereignty emerges as an important crisis in political system and reduces its efficiency. in this article, analyzing the disharmony crisis, a theoretical description regarding the main indicators of this crisis has been offered. in the framework of the above mentioned theoretical description the main indicators of the disharmony crisis are 1) the...