scholarly journals Entwined Hom-modules and frobenius properties

Filomat ◽  
2019 ◽  
Vol 33 (11) ◽  
pp. 3307-3322
Author(s):  
Shuangjian Guo ◽  
Xiaohui Zhang ◽  
Yuanyuan Ke
Keyword(s):  
Necessary Conditions ◽  
Type Theorem ◽  
Forgetful Functor ◽  
Frobenius Pair ◽  
Hopf Modules ◽  
Sufficient And Necessary Conditions ◽  
Maschke Type Theorem ◽  
Generalized Type

Entwined Hom-modules were introduced by Karacuha in [13], which can be viewed as a generalization of Doi-Hom Hopf modules and entwined modules. In this paper, the sufficient and necessary conditions for the forgetful functor F : ?H(Mk)(?)CA ? ?H(Mk)A and its adjoint G : ?H(Mk)A ? ?H (Mk)(?)CA form a Frobenius pair are obtained, one is that A?C and the C*?A are isomorphic as (A;C*op#A)-bimodules, where (A,C,?) is a Hom-entwining structure. Then we can describe the isomorphism by using a generalized type of integral. As an application, a Maschke type theorem for entwined Hom-modules is given.

A Maschke-type theorem for weak (A, B)-Doi-Hopf modules

2011 ◽  
Vol 89 (1-2) ◽  
pp. 98-105 ◽  
Author(s):  
Q. X. Pan ◽  
L. Y. Zhang
Keyword(s):  
Type Theorem ◽  
Hopf Modules ◽  
Maschke Type Theorem

scholarly journals A Maschke Type Theorem for Doi–Hopf Modules and Applications

1997 ◽  
Vol 187 (2) ◽  
pp. 388-412 ◽  
Author(s):  
S. Caenepeel ◽  
G. Militaru ◽  
Zhu Shenglin
Keyword(s):  
Type Theorem ◽  
Hopf Modules ◽  
Maschke Type Theorem

scholarly journals A Maschke type theorem for relative Hom-Hopf modules

2014 ◽  
Vol 64 (3) ◽  
pp. 783-799 ◽  
Author(s):  
Shuangjian Guo ◽  
Xiu-Li Chen
Keyword(s):  
Type Theorem ◽  
Hopf Modules ◽  
Maschke Type Theorem

scholarly journals Oscillation of Second-Order Differential Equations with Multiple and Mixed Delays under a Canonical Operator

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1323
Author(s):  
Shyam Sundar Santra ◽  
Rami Ahmad El-Nabulsi ◽  
Khaled Mohamed Khedher
Keyword(s):  
Differential Equations ◽  
Necessary Conditions ◽  
Second Order ◽  
Multiple Delays ◽  
Mixed Delays ◽  
Neutral Differential Equations ◽  
Canonical Operator ◽  
Second Order Differential Equations ◽  
The Future ◽  
Sufficient And Necessary Conditions

In this work, we obtained new sufficient and necessary conditions for the oscillation of second-order differential equations with mixed and multiple delays under a canonical operator. Our methods could be applicable to find the sufficient and necessary conditions for any neutral differential equations. Furthermore, we proved the validity of the obtained results via particular examples. At the end of the paper, we provide the future scope of this study.

scholarly journals Properties of Certain Subclass of Meromorphic Multivalent Functions Associated with q-Difference Operator

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1035
Author(s):  
Cai-Mei Yan ◽  
Rekha Srivastava ◽  
Jin-Lin Liu
Keyword(s):  
Difference Operator ◽  
Necessary Conditions ◽  
Partial Sums ◽  
Coefficient Estimates ◽  
Radius Of Starlikeness ◽  
Closure Theorems ◽  
Sufficient And Necessary Conditions ◽  
Distortion Theorems ◽  
Growth And Distortion Theorems

A new subclass Σp,q(α,A,B) of meromorphic multivalent functions is defined by means of a q-difference operator. Some properties of the functions in this new subclass, such as sufficient and necessary conditions, coefficient estimates, growth and distortion theorems, radius of starlikeness and convexity, partial sums and closure theorems, are investigated.

Perfect colorings of patterns with multiple orbits

2019 ◽  
Vol 75 (6) ◽  
pp. 814-826
Author(s):  
Allan Junio ◽  
Ma. Lailani Walo
Keyword(s):  
Necessary Conditions ◽  
Sufficient And Necessary Conditions

This paper studies colorings of patterns with multiple orbits, particularly those colorings where the orbits share colors. The main problem is determining when such colorings become perfect. This problem is attacked by characterizing all perfect colorings of patterns through the construction of sufficient and necessary conditions for a coloring to be perfect. These results are then applied on symmetrical objects to construct both perfect and non-perfect colorings.

scholarly journals On a Periodic Predator-Prey System with Holling III Functional Response and Stage Structure for Prey

2010 ◽  
Vol 2010 ◽  
pp. 1-12
Author(s):  
Xiangzeng Kong ◽  
Zhiqin Chen ◽  
Li Xu ◽  
Wensheng Yang
Keyword(s):  
Functional Response ◽  
Prey Species ◽  
Necessary Conditions ◽  
Stage Structure ◽  
Predator Prey ◽  
Prey System ◽  
Sufficient And Necessary Conditions ◽  
Holling Iii Functional Response

We propose and study the permanence of the following periodic Holling III predator-prey system with stage structure for prey and both two predators which consume immature prey. Sufficient and necessary conditions which guarantee the predator and the prey species to be permanent are obtained.

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