On binomial Thue-Mahler equations

We give a rather sharp upper bound for the degree of a binomial Thue--Mahler equation in terms of the coefficients and the primes involved. Further, we establish explicit lower bounds for the greatest prime factor of a binomial binary form at integral points. Our estimates considerably generalize and improve the earlier results obtained in this direction.     

Uniqueness of the uniform norm and adjoining identity in Banach algebras

LetA _e be the algebra obtained by adjoining identity to a non-unital Banach algebra (A, ∥ · ∥). Unlike the case for aC*-norm on a Banach *-algebra,A _e admits exactly one uniform norm (not necessarily complete) if so doesA. This is used to show that the spectral extension property carries over fromA to A _e . Norms onA _e that extend the given complete norm ∥ · ∥ onA are investigated. The operator seminorm ∥ · ∥_op onA _e defined by ∥ · ∥ is a norm (resp. a complete norm) iffA has trivial left annihilator (resp. ∥ · ∥_op restricted toA is equivalent to ∥ · ∥).     

Graded Multiple Analogs of Lie Algebras

Graded analogs of (n,k,r)-Lie algebras (in particular, of Nambu–Lie algebras), introduced by the authors, are defined and their general property are studied.     

关于log2的无理性测量

利用ＤｖｏｒｎｉｃｉｃｈＲ和ＶｉｏｌａＣ关于ξ（２）＝和ξ（３）＝无理性测量的证明方法，给出了一个关于ｌｏｇ２的无理性测量的新的证明方法．     

On the compounded bivariate Poisson distribution: A unified treatment

A unified treatment is presented here of compounding with the bivariate Poisson distribution. Exploiting the exponential nature of its probability generating function, it is shown that the pgf of the compound distribution is the moment generating function of the compounding random variable. This relationship leads to rather interesting general results. Particularly, the development of the conditional distribution is simplified. Four cases are presented in detail.     

An identity involving partitional generalized binomial coefficients

Define coefficients (_κ^λ) by C_λ(I_p + Z)/C_λ(I_p) = Σ_k=0^l Σ_{?∈$\text{P}$k} (_?^λ) C_κ(Z)/C_κ(I_p), where the C_λ's are zonal polynomials in p by p matrices. It is shown that C_?(Z) etr(Z)/k! = Σ_l=k^∞ Σ_{λ∈$\text{P}$l} (_?^λ) C_λ(Z)/l!. This identity is extended to analogous identities involving generalized Laguerre, Hermite, and other polynomials. Explicit expressions are given for all (_?^λ), ? ∈ $\text{P}$_k, k ≤ 3. Several identities involving the (_?^λ)'s are derived. These are used to derive explicit expressions for coefficients of $\text{C}{}_{\mathrm{\lambda }}\text{(Z)}\text{l}\text{!}$ in expansions of P(Z), $\text{etr}\text{(Z)}\text{k!}$ for all monomials P(Z) in s_j = tr Z^j of degree k ≤ 5.     

“f二项近似式”在蚕种检验计算中的应用

本文对蚕种检验中的超几何分布用“ｆ二项近似式”进行计算,既方便,又准确率高。     

Analytic wavelets generated by radial functions

In this paper, we deal with a class of non-stationary multiresolution analysis and wavelets generated by certain radial basis functions. These radial basis functions are noted for their effectiveness in terms of projection, such as interpolation and least-squares approximation, particularly when the data structure is scattered or the dimension of ^s is large. Thus projecting a functionf onto a suitable multiresolution space is relatively easy here. The associated multiresolution spaces approximate sufficiently smooth functions exponentially fast. The non-stationary wavelets satisfy the Littlewood-Paley identity so that perfect reconstruction of wavelet decompositions is achieved. For the univariate case, we give a detailed analysis of the time-frequency localization of these wavelets. Two numerical examples for the detection of singularities with analytic wavelets are provided.Supported by NSF Grant #DMS-92-06928, Air Force Grant #F49620-92-J-0403DEF and NATO Grant #CR-900158.     

拟除虫菊酯分子设计中的生物同一性

讨论了在拟除虫菊酯分子设计中利用生物同一性，对先导化合物进行一系列化 学改造和修饰，以获得新的拟除虫菊酯。     

On the GI/M/∞ queue with batch arrivals of constant size

In this note, the GI/M/ queue with batch arrivals of constant sizek is investigated. It is shown that the stationary probabilities that an arriving batch findsi customers in the system can be computed in terms of the corresponding binomial moments (Jordan's formula), which are determined by a recursive relation. This generalizes well-known results by Takács [12] for GI/M/. Furthermore, relations between batch arrival- and time-stationary probabilities are given.