Some criteria for meromorphic multivalent starlike functions

The main purpose of the present paper is to derive some new criteria for meromorphic multivalent starlike functions.     

亚纯函数族的几个正规定则

研究了亚纯函数族的正规族问题.利用Zalcman引理的方法,获得了亚纯函数族的几个正规定则.并改进了相关文献的结论.     

Some improved criteria for global robust exponential stability of neural networks with time-varying delays

In this paper, some sufficient conditions for global robust exponential stability of interval neural networks with time-varying delays are presented. It is shown that our results include some counterparts of the previous literatures. On basis of the obtained results, some linear matrix inequality (LMI) criteria are derived. Moreover, three numerical examples and a simulation are given to show the effectiveness of the obtained results.     

New differentiability criteria for complex-valued functions

We prove a theorem which states that the existence of an asymptotic limit off _¯z aszz ₀ implies -differentiability of a complex-valued functionf(z) atz ₀.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 4, pp. 329–337, April, 1994.     

Optimal boundedness criteria for extended-real-valued functions

The notion of genuinely bounded below function is introduced and characterized by means of the concept of co-equilibrated function. As an application, we state two boundedness criteria for extended-real-valued functions, both optimal in a clearly defined sense. The first one says that an extended-real-valued function minorized by an affine map and coinciding from some value up with a co-equilibrated function is bounded below. The second criterion states that an extended-real-valued function minorized by an affine map is bounded below provided that one of its sub-level sets is co-equilibrated.     

Some criteria for Buchsbaum modules

The paper gives a criterion for Buchsbaum modules over a local ringR which depends only on a finite system of elements ofR.     

On some criteria for the univalence of analytic functions

Criteria for the univalence of functions f(z) which are regular in the domain ¦z¦ < 1 are obtained in the form of restrictions on the modulus of the quotient f (z) [f '(z)]^–1. Analogous results are obtained also for functions which are analytic in the interior of the unit disk except for a simple pole at infinity.Translated from Matematicheskie Zametki, Vol. 13, No. 3, pp. 359–366, March, 1973.In conclusion the author wishes to thank L. A. Aksent'ev and F. G. Avkhadiev for discussion of the results and valuable remarks.     

Normal criteria for families of meromorphic functions

By using the Nevanlinna theory, we prove some normality criteria for a family of meromorphic functions under a condition on differential polynomials generated by the members of the family.     

Some criteria for the decomposability of finite groups

In this paper we prove the following fundamental results.Theorem 1: A finite unsolvable group, every involution of which is contained in a proper isolated subgroup, is decomposable.Theorem 2: Suppose the finite unsolvable group G contains a strongly isolated subgroup M of odd order with isolated normalizer N(M) of even order. If ¦N(M) (M) ¦ > 2, the group G is isomorphic with one of the groups: 1) PSL(2, q), q odd; 2) PGL (2, q), qodd.Translated from Matematicheski Zametki, Vol. 12, No. 6, pp. 717–725, December, 1972.     

Frequency-domain criteria for the global stability of phase synchronization systems

New criteria for the global stability of phase synchronization systems are formulated and proved. The efficiency of the criteria for phase-locked loops is demonstrated.     

Filled functions for unconstrained global optimization

This paper is concerned with filled function techniques for unconstrained global minimization of a continuous function of several variables. More general forms of filled functions are presented for smooth and non-smooth optimization problems. These functions have either one or two adjustable parameters. Conditions on functions and on the values of parameters are given so that the constructed functions have the desired properties of filled functions.     

Filled functions for unconstrained global optimization

The paper is concerned with the filled functions for global optimization of a continuous function of several variables. More general forms of filled functions are presented for smooth and nonsmooth optimizations. These functions have either two adjustable parameters or one adjustable parameter. Conditions on functions and on the values of parameters are given so that the constructed functions are desired filled functions.     

Matrix-theoretic criteria for the quasiconvexity of twice continuously differentiable functions

The author examines matrices and bordered matrices having exactly one or at most one negative eigenvalue. These results are then used to state matrix-theoretic criteria for the quasiconvexity of twice continuously differentiable functions. For quadratic functions, a new criterion for quasiconvexity is established, and its equivalence to the already known criterion [11,23] is also shown.     

Some criteria for maximal abstract monotonicity

In this paper, we develop a theory of monotone operators in the framework of abstract convexity. First, we provide a surjectivity result for a broad class of abstract monotone operators. Then, by using an additivity constraint qualification, we prove a generalization of Fenchel??s duality theorem in the framework of abstract convexity and give some criteria for maximal abstract monotonicity. Finally, we present necessary and sufficient conditions for maximality of abstract monotone operators.