Functions meromorphic in the whole space 𝐶ⁿ. Entire functions

It can divide the atomization effect in the direction of the nozzle axial injection into the jet area and the non-jet area by using the second crushing theory. On this basis, according to the feed liquid atomization particles discrete degree index of characteristics particle size of feed liquid atomization, it divides the injection zone into the atomization area and the diffusion area, so as to realize the axial direction of jet nozzle injection zone, atomization zone and the diffusion zone accurately. Simulation and experiment are used to verify the three zones of atomization nozzle. The division of three zones drives the study from the whole space of liquid distribution in the roller to atomization zone, clears the key zone of the roller in tobacco primary processing, and provides a basis for further work.

Download Full-text

On $$\psi _{{\mathcal{H}}}( . )$$-operator in weak structure spaces with hereditary classes

Journal of the Egyptian Mathematical Society ◽

10.1186/s42787-020-00107-2 ◽

2020 ◽

Vol 28 (1) ◽

Author(s):

H. M. Abu-Donia ◽

Rodyna A. Hosny

Keyword(s):

Topological Spaces ◽

Structure Space ◽

Hereditary Class ◽

The Family ◽

Main Target ◽

Whole Space ◽

Weak Structure

Abstract Weak structure space (briefly, wss) has master looks, when the whole space is not open, and these classes of subsets are not closed under arbitrary unions and finite intersections, which classify it from typical topology. Our main target of this article is to introduce $$\psi _{{\mathcal {H}}}(.)$$ ψ H ( . ) -operator in hereditary class weak structure space (briefly, $${\mathcal {H}}wss$$ H w s s ) $$(X, w, {\mathcal {H}})$$ ( X , w , H ) and examine a number of its characteristics. Additionally, we clarify some relations that are credible in topological spaces but cannot be realized in generalized ones. As a generalization of w-open sets and w-semiopen sets, certain new kind of sets in a weak structure space via $$\psi _{{\mathcal {H}}}(.)$$ ψ H ( . ) -operator called $$\psi _{{\mathcal {H}}}$$ ψ H -semiopen sets are introduced. We prove that the family of $$\psi _{{\mathcal {H}}}$$ ψ H -semiopen sets composes a supra-topology on X. In view of hereditary class $${\mathcal {H}}_{0}$$ H 0 , $$w T_{1}$$ w T 1 -axiom is formulated and also some of their features are investigated.

Download Full-text

Uniqueness on entire functions and their nth order exact differences with two shared values

Open Mathematics ◽

10.1515/math-2020-0022 ◽

2020 ◽

Vol 18 (1) ◽

pp. 211-215

Author(s):

Shengjiang Chen ◽

Aizhu Xu

Keyword(s):

Entire Function ◽

Entire Functions ◽

Shared Values ◽

Simple Method ◽

Exact Difference ◽

Hyper Order

Abstract Let f(z) be an entire function of hyper order strictly less than 1. We prove that if f(z) and its nth exact difference {\Delta }_{c}^{n}f(z) share 0 CM and 1 IM, then {\Delta }_{c}^{n}f(z)\equiv f(z) . Our result improves the related results of Zhang and Liao [Sci. China A, 2014] and Gao et al. [Anal. Math., 2019] by using a simple method.

Download Full-text