Entropy estimate for high-dimensional monotonic functions

We establish upper and lower bounds for the metric entropy and bracketing entropy of the class of d-dimensional bounded monotonic functions under L^p norms. It is interesting to see that both the metric entropy and bracketing entropy have different behaviors for p<d/(d-1) and p>d/(d-1). We apply the new bounds for bracketing entropy to establish a global rate of convergence of the MLE of a d-dimensional monotone density.     

Zero-cycles on self-product of modular curves

We use the elements in K-cohomology groups which are constructed by Flach and Mildenhall to obtain a finiteness result for the torsion part of the Chow group of a self-product of a modular curve.     

Multiple periodic solutions of a delayed stage-structured predator–prey model with non-monotone functional responses

A delayed stage-structured predator–prey model with non-monotone functional responses is proposed. It is assumed that immature individuals and mature individuals of the predator are divided by a fixed age, and that immature predators do not have the ability to attack prey. Some new and interesting sufficient conditions are obtained for the global existence of multiple positive periodic solutions of the stage-structured predator–prey model. Our method is based on Mawhin’s coincidence degree and novel estimation techniques for the a priori bounds of unknown solutions to Lx = λNx. An example is given to illustrate the feasibility of our main result.     

On Genuine Bernstein–Durrmeyer Operators

We continue the studies on the so–called genuine Bernstein–Durrmeyer operators U _n by establishing a recurrence formula for the moments and by investigating the semigroup T(t) approximated by U _n . Moreover, for sufficiently smooth functions the degree of this convergence is estimated. We also determine the eigenstructure of U _n , compute the moments of T(t) and establish asymptotic formulas. Received: January 26, 2007.     

Second order evolution equations with time-dependent subdifferentials

We study an abstract second order nonlinear evolution equation in a real Hilbert space. We consider time-dependent convex functions and their subdifferentials operating on the first derivative of the unknown function. Introducing appropriate assumptions on the convex functions and other data, we prove the existence and uniqueness of a strong solution, and give some applications of the abstract theorem to hyperbolic variational inequalities with time-dependent constraints.      

The Sheffer group and the Riordan group

We define the Sheffer group of all Sheffer-type polynomials and prove the isomorphism between the Sheffer group and the Riordan group. An equivalence of the Riordan array pair and generalized Stirling number pair is also presented. Finally, we discuss a higher dimensional extension of Riordan array pairs.     

An explosion point space without the fixed point property

In 1988 A. Gutek proved that there exist one-point connectifications of hereditarily disconnected spaces that do not have the fixed point property. We improve on this result by constructing a one-point connectification of a totally disconnected space without the fixed point property.     

Irn(n=2-25)团簇基态结构的遗传算法研究

用遗传算法结合Gupta紧束缚模型势研究了Irn(n=2-25)团簇的基态结构.分析了Irn(n=2-25)团簇的基态结构随团簇尺寸的变化规律.计算结果表明,Irn(n=2-25)团簇的每个原子的平均束缚能和平均第一近邻随团簇尺寸的增加而增大,以总束缚能的二阶差分为判据,Irn(n=2-25)团簇的幻数是4、7、9、13、15、19、23.     

Complete systems, elementary submodels and the tightness of upper hyperspaces

We introduce and study some completeness properties for systems of open coverings of a given topological space. A Hausdorff space admitting a system of cardinality κ satisfying one of these properties is of type Gκ. Hence, we define several new variants of the ?ech number and use elementary submodels to determine further results. We introduce M-hulls and M-networks, for M elementary submodel. As an application, we give estimates for both the tightness and the Lindelöf number of a generic upper hyperspace. Two recent results of Costantini, Holá and Vitolo on the tightness of co-compact hyperspaces follow from ours as corollaries.     

Aldo Cossu’s Work in Finite Geometry

A survey of the contributions of Aldo Cossu in finite geometry is given. Dedicated to the memory of Professor Aldo Cossu