The concept of a four-dimensional generalized difference matrix and its domain on some double sequence spaces was recently introduced and studied by Tuğ and Başar (AIP Conference Proceedings, vol. 1759, 2016) and Tuğ (J. Inequal. Appl. 2017(1):149, 2017). In this present paper, as a natural continuation of (J. Inequal. Appl. 2017(1):149, 2017), we introduce new almost null and almost convergent...

Y. Palu has generalized the cluster multiplication formulas to 2Calabi-Yau categories with cluster tilting objects ([Pa2]). The aim of this note is to construct a variant of Y. Palu’s formula and deduce a new version of the cluster multiplication formula ([XX]) for acyclic quivers in the context of cluster categories. Introduction Cluster algebras were introduced by S. Fomin and A. Zelevinsky [...

A short proof of the generalized Faà di Bruno formula is given and an explicit parametrization of the set of indices involved in the coefficient of a specific term of the formula, is provided. An application is also included.

In this note, we give some estimate of the generalized quadrature formula of Gauss-Jacobi$$underset{a}{overset{a+eta left( b,aright) }{int }}left( x-aright)^{p}left( a+eta left( b,aright) -xright) ^{q}fleft( xright) dx$$in the cases where $f$ and $left| fright| ^{lambda }$ for $lambda >1$, are $s$-preinvex functions in the second sense.

We give an immersion formula, the Sym-Bobenko formula, for minimal surfaces in the 3-dimensional Heisenberg space. Such a formula can be used to give a generalized Weierstrass type representation and construct explicit examples of minimal surfaces. Mathematics Subject Classification: Primary 53A10, Secondary 53C42.

Let R be a ring and U be a Lie ideal of R. Suppose that σ, τ are endomorphisms of R. A family D = {d n } n ∈ N of additive mappings d n :R → R is said to be a (σ,τ)- higher derivation of U into R if d 0 = I R , the identity map on R and [Formula: see text] holds for all a, b ∈ U and for each n ∈ N. A family F = {f n } n ∈ N of additive mappings f n :R → R is said to be a generalized (σ,τ)- high...

We establish a generalized version of the classical Poisson summation formula. This formula incorporates a special feature called "compression", whereby, at the same time that the formula equates a series to its Fourier dual, the compressive feature serves to enable both sides of the equation to converge.

Fractional calculus is a mathematical approach dealing with derivatives and integrals of arbitrary and complex orders. Therefore, it adds a new dimension to understand and describe basic nature and behavior of complex systems in an improved way. Here we use the fractional calculus for modeling electrical properties of biological systems. We derived a new class of generalized models for electric...

We construct the path integral formula in terms of “multi-periodic” coherent state as an extension of the Nielsen-Rohrlich formula for spin. We make an exact calculation of the formula and show that, when a parameter corresponding to the magnitude of spin becomes large, the leading order term of the expansion coincides with the exact result. We also give an explicit correspondence between the t...

We argue that the thermodynamics of conformal field theories with AdS duals exhibits a remarkable universality. At strong coupling, a Cardy-Verlinde entropy formula holds even when R-charges or bulk supergravity scalars are turned on. In such a setting, the Casimir entropy can be identified with a generalized C-function that changes monotonically with temperature as well as when non-trivial bul...