On the Newton polygons of twisted L-functions of binomials

Let χ be an order c multiplicative character of a finite field and $f(x)=x^d+\lambda x^e$ a binomial with $(d,e)=1$. We study the twisted classical and T-adic Newton polygons of f. When $p>(d-e)(2d-1)$, we give a lower bound of Newton polygons and show that they coincide if p does not divide a certain integral constant depending on $p\mathrm{mod}cd$.We conjecture that this condition holds if p is large enough with respect to $c,d$ by combining all known results and the conjecture given by Zhang-Niu. As an example, we show that it holds for $e=d-1$.     

An admissible minimax estimator of a bounded scale-parameter in a subclass of the exponential family under scale-invariant squared-error loss

A subclass of the scale-parameter exponential family is considered and for the rth power of the scale parameter, which is lower bounded, an admissible minimax estimator under scale-invariant squared-error loss is presented. Also, an admissible minimax estimator of a lower-bounded parameter in the family of transformed chi-square distributions is given. These estimators are the pointwise limits of a sequence of Bayes estimators. Some examples are given.     

Dynamics of the periodic type-K competitive Kolmogorov systems

For time-periodic dissipative and irreducible type-K competitive Kolmogorov systems, it is proved that there is a canonically defined countable family F of unordered, disjoint invariant sets with the property that, for every persistent trajectory whose ω-limit set is not a cycle, there exists a unique trajectory in some element of F such that these two trajectories are asymptotic and the corresponding points in these two trajectories are K-related.     

The exponential power law: partial wetting kinetics and dynamic contact angles

An equation for the kinetics of partial drop spreading is proposed. This equation was empirically derived from experimental data for the spreading kinetics of partially wetting liquids in terms of the wet area versus time. The equation has the form of an exponential power law (EPL), and transforms into the well-known power law for complete wetting, when the equilibrium contact angle approaches zero. The EPL fits very well available experimental data. To lend additional support to the validity of this generalized equation, it will be demonstrated that when it is transformed to present the dynamic contact angle (DCA), it fits very well DCA experimental data for other wetting processes, such as capillary flow and tape coating.     

Melnikov向量与退化情形下的横截异宿轨道

利用指数二分性和泛函分析方法,我们研究了当未扰动系统不具有异宿流形的退化异宿分支.我们利用Melnikov型向量给出了系统在退化情形下的横截异宿轨道存在的充分条件.     

ON THE SINGULAR DIRECTIONS OF VALUE DISTRIBUTION OF HOLOMORPHIC CURVES IN P^n（C）

This article proves the existence of singular directions of value distribution theory for some transcendental holomorphic curves in the n-dimensional complex projective space Pn(C). An example is given to complement these results.     

Existence Results for Semilinear Neutral Functional Differential Inclusions via Analytic Semigroups

In this paper we prove existence results for semilinear neutral functional differential inclusions with finite or infinite delay in Banach spaces. Our theory makes use of analytic semigroups and fractional powers of closed operators, integrated semigroups and cosine families.      

Constructions of External Difference Families and Disjoint Difference Families

External difference families (EDFs) are a type of new combinatorial designs originated from cryptography. In this paper, some earlier ideas of recursive and cyclotomic constructions of combinatorial designs are extended, and a number of classes of EDFs and disjoint difference families are presented. A link between a subclass of EDFs and a special type of (almost) difference sets is set up.     

Commutators, C0-semigroups and resolvent estimates

We study the existence and the continuity properties of the boundary values on the real axis of the resolvent of a self-adjoint operator H in the framework of the conjugate operator method initiated by Mourre. We allow the conjugate operator A to be the generator of a C₀-semigroup (finer estimates require A to be maximal symmetric) and we consider situations where the first commutator [H,iA] is not comparable to H. The applications include the spectral theory of zero mass quantum field models.     

Eigenvalue and stability of singular differential delay systems

The eigenvalue and the stability of singular differential systems with delay are considered. Firstly we investigate some properties of the eigenvalue, then give the exact exponential estimation for the fundamental solution, and finally discuss the necessary and sufficient condition of uniform asymptotic stability.