In this paper, some theorems of the classical power series are generalized for the fractional power series. Some of these theorems are constructed by using Caputo fractional derivatives. Under some constraints, we proved that the Caputo fractional derivative can be expressed in terms of the ordinary derivative. A new construction of the generalized Taylor’s power series is obtained. Some applic...

Let $R$ be a commutative Noetherian ring with non-zero identity and $fa$ an ideal of $R$. Let $M$ be a finite $R$--module of finite projective dimension and $N$ an arbitrary finite $R$--module. We characterize the membership of the generalized local cohomology modules $lc^{i}_{fa}(M,N)$ in certain Serre subcategories of the category of modules from upper bounds. We define and study the properti...

the generalized principal ideal theorem is one of the cornerstones of dimension theory for noetherian rings. for an r-module m, we identify certain submodules of m that play a role analogous to that of prime ideals in the ring r. using this definition, we extend the generalized principal ideal theorem to modules.

An important instance of Rota-Baxter algebras from their quantum field theory application is the ring of Laurent series with a suitable projection. We view the ring of Laurent series as a special case of generalized power series rings with exponents in an ordered monoid. We study when a generalized power series ring has a Rota-Baxter operator and how this is related to the ordered monoid.

a new intelligent photovoltaic (PV) panel structure to extract the maximum power in mismatch irradiance is proposed. In conventional structures, difference of irradiance between series panels can cause the deviation of maximum power point. In this condition tracking MPP becomes difficult and reduces efficiency. Improvements in power electronics and its effects in PV industrial technology, devel...

We show that  higher derivations on a Hilbert$C^{*}-$module associated with the Cauchy functional equation satisfying generalized Hyers--Ulam stability.  

In this paper, applying the concept of generalized A-valued norm on a right $H^*$-module and also the notion of ϕ-homomorphism of Finsler modules over $C^*$-algebras we first improve the definition of the Finsler module over $H^*$-algebra and then define ϕ-morphism of Finsler modules over $H^*$-algebras. Finally we present some results concerning these new ones.

A vibration isolation module with zero-power magnetic suspension is developed to retrofit a passive vibration isolation system to improve the performance against direct disturbance. In the module, the zero-power magnetic suspension mechanism is connected in series with a normal spring through a middle mass. This structure can generate zero compliance to direct disturbance while the transmitted ...

A novel power series representation of the generalized Marcum Q-function of positive order involving generalized Laguerre polynomials is presented. The absolute convergence of the proposed power series expansion is showed, together with a convergence speed analysis by means of truncation error. A brief review of related studies and some numerical results are also provided.