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61.
Lihong Huang 《数学学报(英文版)》1995,11(3):307-315
We first give an example to illustrate that the results in [12] concerning the boundedness of solutions of nonlinear oscillatory equations are not true. And then we obtain sufficient or necessary conditions for the boundedness of solutions of the nonlinear system of differential equations
相似文献
62.
Holger Dette 《Transactions of the American Mathematical Society》1996,348(2):691-711
A new characterization of the generalized Hermite polyno-
mials and of the orthogonal polynomials with respect to the measure is derived which is based on a ``reversing property" of the coefficients in the corresponding recurrence formulas and does not use the representation in terms of Laguerre and Jacobi polynomials. A similar characterization can be obtained for a generalization of the sieved ultraspherical polynomials of the first and second kind. These results are applied in order to determine the asymptotic limit distribution for the zeros when the degree and the parameters tend to infinity with the same order. 63.
For any -complexes and , we show that . We use this fact to compute generalized evaluation subgroups of generalized tori relative to a sphere.
64.
Carleson measure characterization of Bloch functions 总被引:1,自引:0,他引:1
Lou Zengjian 《数学学报(英文版)》1996,12(2):175-184
We give several equivalences of Bloch functions and little Bloch functions. Using these results we obtain the generalized Carleson measure characterization of Bloch functions and the generalized vanishing Carleson measure characterization of little Bloch functions, that is,f B if and only if |D
f(z)|
p
(1-|z|2)p-1
dm(z) is a generalized Carleson measure;f B
0 if and only if |D
f(z)|
p
(1-|z|2)p-1
dm(z) is a generalized vanishing Carleson measure, whereD
f( > 0) is the fractional derivative of analytic functionf of order, m denotes the normalised Lebesgue measure.Supported partly by the Young Teacher Natural Science Foundation of Shandong Province. 相似文献
65.
Helicenes form a subclass of polyhexes and correspond to hydrocarbons of considerable chemical interest. This paper is the first part of a general graph-theoretical treatment of helicenes. The invariants are studied: the relations between them, their possible values, and their upper and lower bounds in helicenes. Extremal helicenes and circular helicenes are useful definitions of subclasses of the systems under consideration. Finally an account of symmetry of helicenes is given.On leave from: Department of Mathematics, Xinjiang University, Wulumuqi Xinjiang 830046, People's Republic of China. 相似文献
66.
Mohamed Habibullah S. K. Katti 《Annals of the Institute of Statistical Mathematics》1991,43(2):391-404
In maximizing a non-linear function G(), it is well known that the steepest descent method has a slow convergence rate. Here we propose a systematic procedure to obtain a 1–1 transformation on the variables , so that in the space of the transformed variables, the steepest descent method produces the solution faster. The final solution in the original space is obtained by taking the inverse transformation. We apply the procedure in maximizing the likelihood functions of some generalized distributions which are widely used in modeling count data. It was shown that for these distributions, the steepest descent method via transformations produced the solutions very fast. It is also observed that the proposed procedure can be used to expedite the convergence rate of the first derivative based algorithms, such as Polak-Ribiere, Fletcher and Reeves conjugate gradient methods as well. 相似文献
67.
《Optimization》2012,61(1):77-94
In this article we study a recently introduced notion of non-smooth analysis, namely convexifactors. We study some properties of the convexifactors and introduce two new chain rules. A new notion of non-smooth pseudoconvex function is introduced and its properties are studied in terms of convexifactors. We also present some optimality conditions for vector minimization in terms of convexifactors. 相似文献
68.
Kang Qun Zhang 《数学学报(英文版)》2012,28(6):1135-1154
In this paper, we study the existence and regularity of a solution to the initial datum problem of a semilinear generalized Tricomi equation in mixed-type domain. We suppose that an initial datum on the degenerate plane is smooth away from the origin, and has a conormal singularity at this point, then we show that in some mixed-type domain, the solution exists and is conormal with respect to the characteristic conic surface which is issued from the origin and has a cusp singularity. 相似文献
69.
This Letter investigates generalized function synchronization of continuous and discrete complex networks by impulsive control. By constructing the reasonable corresponding impulsively controlled response networks, some criteria and corollaries are derived for the generalized function synchronization between the impulsively controlled complex networks, continuous and discrete networks are both included. Furthermore, the generalized linear synchronization and nonlinear synchronization are respectively illustrated by several examples. All the numerical simulations demonstrate the correctness of the theoretical results. 相似文献
70.
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