The aim of this paper is to construct generating functions, related to nonnegative real parameters, for q-Eulerian type polynomials and numbers (or q-Apostol type Frobenius–Euler polynomials and numbers). We derive some identities for these polynomials and numbers based on the generating functions and functional equations. We also give multiplication formula for the generalized Apostol type Fro...

The object of this paper is to introduce and study the properties unified Apostol-Bernoulli Apostol-Euler polynomials noted by $$\left\{ \mathfrak {V_{n}}(x;\lambda ;\mu )\right\} _{n \ge 0}$$ . We some arithmetic as their connection polynomials. Also, we give derivation integration representations Finally, use umbral calculus approach deduce symmetric identities.

In this research complexation of dioxovanadium(V) with nitrilotriacetic acid (NTA) at differentionic strengths (0.1 to 1.0 mol dm-3) of sodium perchlorate as supporting electrolyte and pH rangeof 1.00-2.50 at 25 °C has been investigated by a combination of potentiometric and UVspectrophotometric measurements. Stability constants of two species, V0211L- and VO2H2L havebeen calculated. Ionic stre...

In response to a letter from Goldbach, Euler considered sums of the form ∞ ∑ k=1 ( 1 + 1 2m + · · ·+ 1 km ) (k + 1)−n for positive integers m and n. Euler was able to give explicit values for certain of these sums in terms of the Riemann zeta function. In a recent companion paper, Euler’s results were extended to a significantly larger class of sums of this type, including sums with alternating...

Analytical relations between the critical buckling load of a functionally graded material (FGM) Timoshenko beam and that of the corresponding homogeneous Euler–Bernoulli beam subjected to axial compressive load have been derived for clamped–clamped (C–C), simply supported–simply supported (S–S) and clamped–free (C–F) edges. However, no such relation is found for clamped–simply supported (C–S) b...

One of the simplest and, at the same time, most important invariants of a topological space is the Euler characteristic. A generalization of the notion of the Euler characteristic to the equivariant setting, that is, to spaces with an action of a group (say, finite) is far from unique. An equivariant analogue of the Euler characteristic can be defined as an element of the ring of representation...

We establish an existence theorem for entropy solutions to the Euler equations modeling isentropic compressible fluids. We develop a new approach for constructing mathematical entropies for the Euler equations, which are singular near the vacuum. In particular, we identify the optimal assumption required on the singular behavior on the pressure law at the vacuum in order to validate the two-ter...

We have adapted a simple method of numerical integration to predict the equilibrium state of a population of components undergoing reversible association according to the Law of Mass Action. Its particular application is to populations of protein molecules in aqueous solution. The method is based on Euler integration but employs an adaptive step size: the time increment being reduced if it woul...