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...

cyclic groups, torsion-free extensions, Betti numbers We describe algorithms to determine extensions of infinite polycyclic groups having certain properties. In particular, we are interested in torsion-free extensions and extensions whose Fitting subgroup has a minimal centre. Then we apply these methods in topological applications. We discuss the calculation of Betti numbers for compact manifo...

OBJECTIVE With the emergence of semi- and nonparametric regression the generalized linear mixed model has been extended to account for additive predictors. However, available fitting methods fail in high dimensional settings where many explanatory variables are present. We extend the concept of boosting to generalized additive mixed models and present an appropriate algorithm that uses two diff...

Let g(G,λ) denote the deformed generalized Heisenberg-Virasoro algebra related to a complex parameter λ≠−1 and an additive subgroup G of C. For total order on that is compatible with addition, Verma module over defined. In this paper, we completely determine irreducibility these modules.

This article is concerned with frame constructions on domains and manifolds. The starting point is a unitary group representation which is square integrable modulo a suitable subgroup and therefore gives rise to a generalized continuous wavelet transform. Then generalized coorbit spaces can be defined by collecting all functions for which this wavelet transform is contained in a weighted Lp-spa...

For a positive integer m and a subgroup Λ of the unit group (Z/mZ)×, the corresponding generalized Kloosterman sum is the function K(a, b,m,Λ) = ∑ u∈Λ e( au+bu−1 m ). Unlike classical Kloosterman sums, which are real valued, generalized Kloosterman sums display a surprising array of visual features when their values are plotted in the complex plane. In a variety of instances, we identify the pr...

Background Globally, chronic kidney disease (CKD) is a growing public health concern. Serum uric acid (SUA) an easily detectable and readily available biochemical indicator that has long been recognized as independent risk factor for CKD. In addition, studies have indicated potential relationship between SUA body mass index (BMI). However, on the effect of levels estimated glomerular filtration...