On bulk-service MAP/PH L,N /1/N G-Queues with repeated attempts

We consider a retrial queue with a finite buffer of size N, with arrivals of ordinary units and of negative units (which cancel one ordinary unit), both assumed to be Markovian arrival processes. The service requirements are of phase type. In addition, a PH^L,N bulk service discipline is assumed. This means that the units are served in groups of size at least L, where 1≤ L≤ N. If at the completion of a service fewer than L units are present at the buffer, the server switches off and waits until the buffer length reaches the threshold L. Then it switches on and initiates service for such a group of units. On the contrary, if at the completion of a service L or more units are present at the buffer, all units enter service as a group. Units arriving when the buffer is full are not lost, but they join a group of unsatisfied units called “orbit”. Our interest is in the continuous-time Markov chain describing the state of the queue at arbitrary times, which constitutes a level dependent quasi-birth-and-death process. We start by analyzing a simplified version of our queueing model, which is amenable to numerical calculation and is based on spatially homogeneous quasi-birth-and-death processes. This leads to modified matrix-geometric formulas that reveal the basic qualitative properties of our algorithmic approach for computing performance measures. AMS Subject Classification: Primary 60K25 Secondary 68M20 90B22.     

相型同步启动时间的M／M／c排队系统

本文研究带有同步启动时间的Ｍ／Ｍ／ｃ系统，其中启动时间是相型变量，给出了稳态和等待时间分布等结果。     

COMPLETE EXTREMAL SURFACES OF MIXED TYPE IN 3-DIMENSIONAL MINKOWSKI SPACE

ＣＯＭＰＬＥＴＥＥＸＴＲＥＭＡＬＳＵＲＦＡＣＥＳＯＦＭＩＸＥＤＴＹＰＥＩＮ３－ＤＩＭＥＮＳＩＯＮＡＬＭＩＮＫＯＷＳＫＩＳＰＡＣＥ￥ＧＵＣＨＡＯＨＡＯ（ＩｎｓｔｉｔｕｔｅｏｆＭａｔｈｅｍａｔｉｃｓ，ＦｕｄａｎＵｎｉｖｅｒｓｉｔｙ，Ｓｈａｎｇｈａｉ２００...     

Hyperbolic spaces are of strictly negative type

We study finite metric spaces with elements picked from, and distances consistent with, ambient Riemannian manifolds. The concepts of negative type and strictly negative type are reviewed, and the conjecture that hyperbolic spaces are of strictly negative type is settled, in the affirmative. The technique of the proof is subsequently applied to show that every compact manifold of negative type must have trivial fundamental group, and to obtain a necessary criterion for product manifolds to be of negative type.

     

位置参数估计量的损失函数之估计

本文考虑损失函数的估计问题,分别对于球对称分布和均匀分布情形给出了其参数的J-S型估计量的损失之估计,它们满足[1]中提出的条件(Ⅰ)和(Ⅱ).     

~n中有界域上全纯函数的第Ⅰ型 C-F公式

本文得到Ｃｎ中有界域上全纯函数的一种其积分密度函数含有全纯函数导数的 Ｃａｕｃｈｙ－Ｆａｎｔａｐｐｉ　　公式，称之为第Ⅰ型 Ｃ－Ｆ 公式，利用这个公式，通过适当选择其中的向量函数，可以得到许多区域上全纯函数相应的第Ⅰ型积分表示式．     

关于修正的Baskakov算子的Stechin-Marchaud型不等式

利用K-泛函研究了修正的Baskakov型算子的Stechin-Marchaud型不等式,由此不等式,我们得到了关于ω2φλ的逆结果.     

关于Fejer点上的一种复有理型插值的一致逼近阶

设D是一个Jordan,Г为其边界，并设Г满足Aльпер条件。本文得到了一种基于Fejer点的有理型插值算子对于f(z)∈C（Г）的一致逼近阶。     

The Möbius distribution on the disc

A simple new family of distributions is proposed which has support the unit disc in two dimensions. The density functions of the family are unimodal, monotonic or uniantimodal. The bivariate symmetric beta distributions, which include the uniform distribution, are special cases, but many members of the family are skew. The distributions have three parameters, one controlling orientation, one controlling degree of concentration and the third controlling skewness, or more precisely off-centredness. Importantly, these parameters are globally orthogonal. An illustrative example of fitting the model to data is given. Conditional and marginal distributions are considered. The new distributions are compared favourably with an earlier suggestion of the same author.     

Elliptic fibers over non-perfect residue fields

Kodaira and Néron classified and described the geometry of the special fibers of the Néron model of an elliptic curve defined over a discrete valuation ring with a perfect residue field. Tate described an algorithm to determine the special fiber type by manipulating the Weierstrass equation. In the case of non-perfect residue fields, we discover new fiber types which are not on the Kodaira-Néron list. We describe these new types and extend Tate's algorithm to deal with all discrete valuation rings. Specifically, we show how to translate a Weierstrass equation into a form where the reduction type may be easily determined. Having determined the special fiber type, we construct the regular model of the curve with explicit blow-up calculations. We also provide tables that serve as a simple reference for the algorithm and which succinctly summarize the results.