scholarly journals Construction of Biholomorphic Convex Mappings of OrderαonBpn

2014 ◽  
Vol 2014 ◽  
pp. 1-15
Author(s):  
Ming-Sheng Liu ◽  
Fengying Yang ◽  
Kit Ian Kou ◽  
Changqin Huang
Keyword(s):  
Sufficient Conditions ◽  
Reinhardt Domain ◽  
Convex Mappings

Some sufficient conditions for biholomorphic convex mappings of orderαon the Reinhardt domainBpninCnare given; from that, criteria for biholomorphic convex mappings of orderαwith particular form become direct. As applications of these sufficient conditions, some concrete biholomorphic convex mappings of orderα  onBpnare provided.

scholarly journals Optimality and Duality with Respect to b-(E,m)-Convex Programming

Symmetry ◽  
2018 ◽  
Vol 10 (12) ◽  
pp. 774
Author(s):  
Bo Yu ◽  
Jiagen Liao ◽  
Tingsong Du
Keyword(s):  
Convex Programming ◽  
Convex Sets ◽  
Sufficient Conditions ◽  
Optimality Criteria ◽  
Sufficient Optimality Conditions ◽  
Duality Theorems ◽  
Symmetric Duality ◽  
Convex Mappings ◽  
Uniqueness Of The Solution ◽  
Optimality And Duality

Noticing that E -convexity, m-convexity and b-invexity have similar structures in their definitions, there are some possibilities to treat these three class of mappings uniformly. For this purpose, the definitions of the ( E , m ) -convex sets and the b- ( E , m ) -convex mappings are introduced. The properties concerning operations that preserve the ( E , m ) -convexity of the proposed mappings are derived. The unconstrained and inequality constrained b- ( E , m ) -convex programming are considered, where the sufficient conditions of optimality are developed and the uniqueness of the solution to the b- ( E , m ) -convex programming are investigated. Furthermore, the sufficient optimality conditions and the Fritz–John necessary optimality criteria for nonlinear multi-objective b- ( E , m ) -convex programming are established. The Wolfe-type symmetric duality theorems under the b- ( E , m ) -convexity, including weak and strong symmetric duality theorems, are also presented. Finally, we construct two examples in detail to show how the obtained results can be used in b- ( E , m ) -convex programming.

scholarly journals On a New Subclass of p-Valent Close-to-Convex Mappings Defined by Two-Sided Inequality

2018 ◽  
Vol 2018 ◽  
pp. 1-6
Author(s):  
Yi-Hui Xu ◽  
Jin-Lin Liu
Keyword(s):  
Sufficient Conditions ◽  
Convex Mappings

A new subclass Kp(α1,α2,β) of p-valent close-to-convex mappings defined by two-sided inequality is introduced. Some sufficient conditions for functions to be in Kp(α1,α2,β) are given.

Some Contributions to the Theory of Near-Critical Bisexual Branching Processes

2007 ◽  
Vol 44 (02) ◽  
pp. 492-505
Author(s):  
M. Molina ◽  
M. Mota ◽  
A. Ramos
Keyword(s):  
Branching Process ◽  
Branching Processes ◽  
Sufficient Conditions ◽  
Positive Probability ◽  
Limit Laws ◽  
Bisexual Branching Processes ◽  
Probabilistic Evolution

We investigate the probabilistic evolution of a near-critical bisexual branching process with mating depending on the number of couples in the population. We determine sufficient conditions which guarantee either the almost sure extinction of such a process or its survival with positive probability. We also establish some limiting results concerning the sequences of couples, females, and males, suitably normalized. In particular, gamma, normal, and degenerate distributions are proved to be limit laws. The results also hold for bisexual Bienaymé–Galton–Watson processes, and can be adapted to other classes of near-critical bisexual branching processes.

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj> 0 for eachj> 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

Normal approximations to discrete unimodal distributions

1986 ◽  
Vol 23 (04) ◽  
pp. 1013-1018
Author(s):  
B. G. Quinn ◽  
H. L. MacGillivray
Keyword(s):  
Stationary Distribution ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Hypergeometric Distribution ◽  
Death Process ◽  
Normal Approximations ◽  
Discrete Random Variables ◽  
Birth Death

Sufficient conditions are presented for the limiting normality of sequences of discrete random variables possessing unimodal distributions. The conditions are applied to obtain normal approximations directly for the hypergeometric distribution and the stationary distribution of a special birth-death process.

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