非线性等重码的一个上界

本文给出等重码的一个上界，并且举例说明这个上界是可以达到的，作为直接推论，我们推导出等重等距码的几个结果。     

色散长波方程簇的Hamilton结构

本文导出了色散长波方程簇,并利用屠规彰迹恒等式方法,讨论它们的Hamil-ton结构。     

The next step of the word problem over monoids

It is known that a group presentation P can be regarded as a 2-complex with a single 0-cell. Thus we can consider a 3-complex with a single 0-cell which is known as a 3-presentation. Similarly, we can also consider 3-presentations for monoids. In this paper, by using spherical monoid pictures, we show that there exists a finite 3-monoid-presentation which has unsolvable “generalized identity problem” that can be thought as the next step (or one-dimension higher) of the word problem for monoids. We note that the method used in this paper has chemical and physical applications.     

A new identity for Parseval frames

In this paper we establish a surprising new identity for Parseval frames in a Hilbert space. Several variations of this result are given, including an extension to general frames. Finally, we discuss the derived results.

     

On some applications of Wald's identity to dams

It is known that the main difficulty in applying the Markovian analogue of Wald's Identity is the presence, in the Identity, of the last state variable before the random walk is terminated. In this paper we show that this difficulty can be overcome if the underlying Markov chain has a finite state space. The absorption probabilities thus obtained are used, by employing a duality argument, to derive time-dependent and limiting probabilities for the depletion process of a dam with Markovian inputs.The second problem that is considered here is that of a non-homogeneous but cyclic Markov chain. An analogue of Wald's Identity is obtained for this case, and is used to derive time- dependent and limiting probabilities for the depletion process with inputs forming a non- homogeneous (cyclic) Markov chain.     

On the Hybrid Power Mean Involving the Two-Term Exponential Sums and Polynomial Character Sums

The main purpose of this paper is using the analytic method and the properties of trigonometric sums and character sums to study the computational problem of one kind hybrid power mean involving two-term exponential sums and polynomial character sums. Then the authors give some interesting calculating formulae for them.     

Hilbert空间H中G-框架等式

框架已获得广泛的应用,g-框架是框架的推广.本文运用算子理论方法,根据Hilbert空间H中的g-框架和g-框架算子的性质,得到有关g-框架的几个等式,给出一些有意义的结果.     

A note on the α-quantile option

Some properties of a class of path-dependent options based on the α-quantiles of Brownian motion are discussed. In particular, it is shown that such options are well behaved in relation to standard options and comparatively cheaper than an equivalent class of lookback options.     

Hilbert’s Nullstellensatz for analytic trigonometric polynomials

This paper proves such a new Hilbert’s Nullstellensatz for analytic trigonometric polynomials that if ${\left\{f_j\right\}}_{j=1}^{n\ge 2}$ are analytic trigonometric polynomials without common zero in the finite complex plane $?$ then there are analytic trigonometric polynomials ${\left\{g_j\right\}}_{j=1}^{n\ge 2}$ obeying ${\sum }_{j=1}^{n\ge 2}{f}_j{g}_j=1$ in $?$, thereby not only strengthening Helmer’s Principal Ideal Theorem for entire functions, but also finding an intrinsic path from Hilbert’s Nullstellensatz for analytic polynomials to Pythagoras’ Identity on $?$.     

On an identity associated with Weil's estimate and its applications

In this paper we study the fourth mean value of generalized quadratic Gauss sums, and get an interesting identity associated with Weil's estimate,