拟常曲率流形中有平行平均曲率向量的子流形

研究了拟常曲率流形中具有平行平均曲率向量的子流形,给出了两个积分不等式.     

具有吸附项的渗流方程有界弱解的广义Harnack不等式

具有吸附项的渗流方程有界弱解的广义Harnack不等式@袁洪君@王波...     

Inequality constrained ridge regression estimator

We carry out the idea of inequality constrained least squares (ICLS) estimation of Liew (1976) to the inequality constrained ridge regression (ICRR) estimation. We propose ICRR estimator by reducing the primal–dual relation to the fundamental problem of Dantzig and Cottle, 1967, Cottle and Dantzig, 1974 with Lemke (1962) algorithm. Furthermore, we conduct a Monte Carlo experiment.     

Inequality averse multi-utilitarian bargaining solutions

This paper introduces and analyzes the class of inequality averse multi-utilitarian solutions for cooperative bargaining problems. We show that generalized Gini solutions and inequality averse Choquet solutions are particular cases of this new multi-valued solution concept and provide a complete characterization in which an invariance property, consisting of a weakening of both the linear invariance axiom in Blackorby et al. (Econometrica 62:1161–1178, 1994) and the restricted invariance axiom in Ok and Zhou (Games Econ Behav 33:249–264, 2000), plays an important role. Moreover, by relaxing the assumptions involved in the characterization, the class is extended to include inequality loving multi-utilitarian solutions which are also studied in the paper.     

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.     

The FKG Inequality for Partially Ordered Algebras

The FKG inequality asserts that for a distributive lattice with log-supermodular probability measure, any two increasing functions are positively correlated. In this paper we extend this result to functions with values in partially ordered algebras, such as algebras of matrices and polynomials. This research was supported by an NSF grant.     

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．     

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.