In this article, we apply common fixed point results in incomplete metric spaces to examine the existence of a unique common solution for the following systems of Urysohn integral equations and Volterra-Hammerstein integral equations, respectively: [Formula: see text] where [Formula: see text]; [Formula: see text] and [Formula: see text], [Formula: see text] and [Formula: see text] where [Formu...

A set S of vertices in graph [Formula: see text] is a [Formula: see text], abbreviated TRDS, of G if every vertex of G is adjacent to a vertex in S and every vertex of [Formula: see text] is adjacent to a vertex in [Formula: see text]. The [Formula: see text] of G, denoted by [Formula: see text], is the minimum cardinality of a TRDS of G. Jiang and Kang (J Comb Optim. 19:60-68, 2010) characteri...

A Boolean formula in a conjunctive normal form is called a (k, s)-formula if every clause contains exactly k variables and every variable occurs in at most s clauses. We show that there are unsatisfiable (k, 4 · 2 k

In the present paper a generalization of the Erlang's B formula is proposée, for a loss System in which arriving calls follow a Poisson process. The holding time of each call follows a négative exponential distribution. The application of the results obtained can be used for the improvement of the grade of service, the efficient use o f the existing equipment and the appropriate tariff policy a...

Using Bochner-Martinelli type residual currents we prove some generalizations of Jacobi’s Residue Formula, which allow proper polynomial maps to have ’common zeroes at infinity ’, in projective or toric situations.

We develop the theory of Hopf bimodules for a finite rigid tensor category C. Then we use this theory to define a distinguished invertible object D of C and an isomorphism of tensor functors δ : V ∗∗ → D⊗∗∗V ⊗D. This provides a categorical generalization of Radford’s S formula for finite dimensional Hopf algebras [R1], which was proved in [N] for weak Hopf algebras, in [HN] for quasi-Hopf algeb...

The notion of binomial coefficients (T S ) of finite planar, reduced rooted trees T, S is defined and a recursive formula for its computation is shown. The nonassociative binomial formula (1 + x) = ∑

In this paper, we present some extensions of interpolation between the arithmetic-geometric means inequality. Among other inequalities, it is shown that if A, B, X are [Formula: see text] matrices, then [Formula: see text] where [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] are non-negative continuous functions such that [Formula: see text] and [Formula: see...