Some Theorems on Meromorphic Univalent Functions

In this paper, we will show some deviation theorems and theorems of rotational angles in classes of Σ(p) and Σ(p,q) of meromorphic univalent functions.     

Commutator inequalities for Hilbert space operators

We prove singular value inequalities for positive operators. Some of these inequalities generalize recent results for commutators due to Bhatia-Kitttaneh, Kittaneh, and Wang-Du. Applications of our results are given.     

STATUS DIFFERENTIATION AND THE COHESION OF SOCIAL NETWORKS

This article examines the effects of status differentiation on the cohesion of a social structure. Using a formal model, we simulate the fates of a hypothetical cohort of newly hired employees, who are equals in the eyes of their boss and in the nascent stages of sorting into a status hierarchy. We cast these employees in a process in which they exert effort, receive public approval from the boss in exchange, and thus come to fill different places in a status order. We then consider the circumstances under which these workers cohere as a group and when, by contrast, differentiation makes cohesion among them unlikely. Our results show that the extent of the boss's autonomy in relationship to employees accounts for this difference in outcomes. Under an autonomous boss, as differentiation transpires, status-based social forces break the group of workers apart. Conversely, when the boss occupies a compromised position, group-level cohesion coexists with differentiation. Our main contribution is the intuition that the cohesion-related consequences of status differentiation can substantially depend on the tie between contestants and their external audience. We conclude by developing conjectures for empirical research consistent with our main findings.     

Inequalities for ranks of partitions and the first moment of ranks and cranks of partitions

We prove two monotonicity properties of N(m,n)$N(m,n)$, the number of partitions of n with rank m. They are (i) for any nonnegative integers m and n,

N(m,n)?N(m+2,n),$N(m,n)?N(m+2,n),$

and, (ii) for any nonnegative integers m and n   such that n?12$n?12$, n≠m+2$n\ne m+2$,

N(m,n)?N(m,n−1).$N(m,n)?N(m,n-1).$

G.E. Andrews, B. Kim, and the first author introduced ospt(n)$\mathrm{ospt}(n)$, a function counting the difference between the first positive rank and crank moments. They proved that ospt(n)>0$\mathrm{ospt}(n)>0$. In another article, K. Bringmann and K. Mahlburg gave an asymptotic estimate for ospt(n)$\mathrm{ospt}(n)$. The two monotonicity properties for N(m,n)$N(m,n)$ lead to stronger inequalities for ospt(n)$\mathrm{ospt}(n)$ that imply the asymptotic estimate.     

一类含Caffarem-Kohn-Nirenberg不等式的奇异椭圆型方程正解的存在性

本文研究一类带奇异项及临界指数的方程 利用纤维方法证明方程在满足一定条件下正解的存在性．     

一类具有时变时滞的中立型系统的稳定性分析

本文研究一类具有状态时滞和输入时滞的时变时滞线性中立型系统.首先,通过选取合适的Lya-punov-Krasovskii泛函,应用LMI方法和Lyapunov-Krasovskii稳定性定理对时滞相关的系统进行稳定性分析,并设计了相应的控制器.改进了时不变时滞线性系统方面的一些结果.最后用实例验证所得到结果.     

On the stability of time-varying differential equations *

This paper deals with stability of time-varying differential equations. New asymptotic stability conditions for time-varying continuous systems with more general assumptions are given. The Gronwall's inequality and its discrete-time versions play a crucial role in our investigation.     

The Method of Multipliers for Nonlinearly Constrained Variational Inequalities

The method of multipliers for variational inequalities with nonstrictly monotone cost mappings and convex differentiable constraints is considered. We prove the convergence of the method with an arbitrary value of the penalty parameter. We suggest to evaluate accuracy of solutions of auxiliary subproblems with the help of gap functions.     

模糊输入时滞系统的输出反馈控制及稳定性分析

针对一类状态不可测的模糊输入时滞系统,应用平行分布补偿算法(PDC),设计了模糊观测器,提出了基于模糊观测器的输出反馈控制方法,给出了保证模糊时滞系统渐近稳定的新的充分条件.应用广义Lyapunov函数和线性矩阵不等式方法,证明了模糊输入时滞系统的渐近稳定性,同时给出了控制和观测增益矩阵的分离设计算法.仿真结果进一步验证了所提出的方法和条件的有效性.     

Simulating the effect of nepotism on political risk taking and social unrest

Nepotism has been the primary influence on political behavior throughout human history. Despite the spread of democracy in the 20th century, nepotistic regimes have hardly disappeared. Nepotism heavily influences political activity throughout the developing world, Middle East, and central Asia where family ties are essential for gaining access to power, state resources, and privileges. Rebelling against such nepotistic regimes is difficult and risky. RiskTaker is an agent-based model we developed for testing the influences of various social forces on risk taking behavior, including the formulation of rebellious coalitions. We use RiskTaker to examine the influence of nepotism on the distribution of wealth and social status. Nepotism heavily skews the distribution of wealth and status, leading to the formation of opposing coalitions and exacerbating social unrest.This paper was tied for Best Paper, NAACSOS (North American Association for Computational Social and Organizational Science) Annual Conference 2005, June 26–28, Notre Dame. Robert Sedlmeyer, Department of Computer Science, Indiana University – Purdue University, Fort Wayne provided programming for the RiskTaker model. Lawrence A. Kuznar is a professor of anthropology and director of the Decision Sciences and Theory Institute at Indiana University—Purdue University, Fort Wayne. He has conducted fieldwork among Aymara Indians in Andean Peru and the Navajo of the American southwest. His research interests include computer modeling, theories of risk taking and conflict, terrorism, social evolution, and scientific epistemology. He has authored articles in Ecological Economics (with W. Frederick), Current Anthropology, American Anthropologist, Mathematical Anthropology and Culture Theory and Journal of Anthropological Research, and published two books (Awatimarka Harcourt Brace, 1995 and Reclaiming a Scientific Anthropology Altamira Press, 1997) and two edited volumes. William Frederick has served as a faculty member in the departments of mathematical sciences and the department of computer sciences at Indiana University—Purdue University, Fort Wayne since 1979. His primary interests include mathematical modeling, game theory, and genetic algorithms.