A version of the second main theorem of Nevanlinna theory is proved, where the ramification term is replaced by a term depending on a certain composition operator of a meromorphic function of small hyper-order. As a corollary of this result it is shown that if n ∈ N and three distinct values of a meromorphic function f of hyper-order less than 1/n have forward invariant pre-images with respect ...

In this paper, the transmutation of TRUs of the DUPIC (Direct Use of Spent PWR Fuel in CANDU) spent fuel has been studied with the HYPER system, which is an LBE-cooled ADS. The DUPIC concept is a synergistic combination of PWRs and CANDUs, in which PWR spent fuels are directly reutilized in CANDU reactors after a very simple re-fabrication process. In the DUPICHYPER fuel cycle, TRUs are recover...

The recent theory of plausible and paradoxical reasoning (DSmT) developed by the authors appears to be a nice promising theoretical tools to solve many information fusion problems where the Shafer’s model cannot be used due to the intrinsic paradoxical nature of the elements of the frame of discernment and where a strong internal conflict between sources arises. The main idea of DSmT is to work...

In this paper, due to the Borel lemma and Clunie lemma, we will deduce relationship between an entire function f of hyper-order less than 1 its n-th difference operator ?nc (z) if they share a finite set has exceptional value 0, where consists two functions smaller orders. Moreover, exact form is given example provided show sharpness condition.

Hypermedia authors are now acquiring experience to build good hypermedia systems and assess their quality, and this experience should be compiled and organized in order to be shared with other authors. We propose three hypermedia design patterns for hypermedia publishing: hyper-book, hyper-map and virtual product.

In this note first we define the notion of dual positive implicative hyper Kideal of type 4, where for simplicity is written by DPIHKI − T4. Then we give some related results. Finally we determine all of hyper K-algebras of order 3, which have D1 = {1}, D2 = {1, 2} or D3 = {0, 1} as a DPIHKI − T4.

In this paper, we investigate the growth of solutions of the differential equation f (k) +Ak−1 (z) f (k−1) + · · ·+A1 (z) f ′ +A0 (z) f = F, where A0 (z) , . . . , Ak−1 (z) , F (z) / ≡ 0 are entire functions, and we obtain general estimates of the hyper-exponent of convergence of distinct zeros and the hyper-order of solutions for the above equation.

*Correspondence: [email protected] 2Department of Applied Mathematics, Huainan Normal University, Huainan, 232038, China Full list of author information is available at the end of the article Abstract By constructing two scaling matrices, i.e., a function matrix (t) and a constant matrix W which is not equal to the identity matrix, a kind ofW – (t) synchronization between fractional-order an...

In this paper, we investigate the growth of solutions of the linear differential equation 0 = Bf f A f      , where ) (z A and 0) )( (  z B are meromorphic functions. More specifically, we estimate the lower bounded of hyperorder of solutions of the equation with respect to the conditions of ) (z A and 0) )( (  z B if solutions 0 ( f ) of the equation is of infinite order. keywords: ...