Individual blocking probabilities in the loss systemGI + M|\vec M|N|0

In this paper we investigate anN server loss system, where the input is a superposition of two types of traffics, namely of a renewal process and a Poisson process. The holding times of the two customer types are exponentially distributed with different parameters. For this model, denoted by , we derive a numerical algorithm for computing the individual blocking (loss) probabilities. The analysis is given by constructing a two-dimensional embedded Markov chain and by using the intensity conservation principle as well as point process arguments. The results generalize those of Kuczura [8] and Willie [11]. Finally, for the loss system we give a system of partial differential equations for the densities of the steady state distribution and discuss a special case.     

关于排队过程GI/E_k/l的若干結果

<正> §1.引言 采用Kendall的記号,所謂GI/E_k/1是指由下述条件規定的一个排队过程: (i)若用t_n表第n个顾客来到服务系统的时刻,而用ui=ti-t_(i-1)山表示相紕两顾客到达时刻間的間隔(簡称到达間隔),則这些u互相独立,并且服从同一分布     

有限群的ss-置换子群

设G为有限群,称G的子群H为ss-置换子群,如果存在G的次正规子群B使得G=HB,且H与B的任意Sylow子群可以交换,即对任意X∈Syl（B）有XH=HX.利用子群的ss-置换性来研究有限群的结构,得到有限群超可解的两个充分条件.     

Semisummands and semiideals in banach spaces

Let |·| be a fixed absolute norm onR ². We introduce semi-|·|-summands (resp. |·|-summands) as a natural extension of semi-L-summands (resp.L-summands). We prove that the following statements are equivalent. (i) Every semi-|·|-summand is a |·|-summand, (ii) (1, 0) is not a vertex of the closed unit ball ofR ² with the norm |·|. In particular semi-L ^p-summands areL ^p-summands whenever 1<p≦∞. The concept of semi-|·|-ideal (resp. |·|-ideal) is introduced in order to extend the one of semi-M-ideal (resp.M-ideal). The following statements are shown to be equivalent. (i) Every semi-|·|-ideal is a |·|-ideal, (ii) every |·|-ideal is a |·|-summand, (iii) (0, 1) is an extreme point of the closed unit ball ofR ² with the norm |·|. From semi-|·|-ideals we define semi-|·|-idealoids in the same way as semi-|·|-ideals arise from semi-|·|-summands. Proper semi-|·|-idealoids are those which are neither semi-|·|-summands nor semi-|·|-ideals. We prove that there is a proper semi-|·|-idealoid if and only if (1, 0) is a vertex and (0, 1) is not an extreme point of the closed unit ball ofR ² with the norm |·|. So there are no proper semi-L ^p-idealoids. The paper concludes by showing thatw*-closed semi-|·|-idealoids in a dual Banach space are semi-|·|-summands, so no new concept appears by predualization of semi-|·|-idealoids.     

Explicit Formulas of the Bergman Kernel for Some Reinhardt Domains

In this paper we obtain the closed forms of some hypergeometric functions. As an application, we obtain the explicit forms of the Bergman kernel functions for Reinhardt domains \(\{|z_3|^{\lambda } < |z_1|^{2p} + |z_2|^2, \ |z_1|^{2p} + |z_2|^2 < |z_1|^{p} \}\) and \(\{|z_4|^{\lambda } < (|z_1|^2 + |z_2|^2)^{p} + |z_3|^2, \ (|z_1|^2 + |z_2|^2)^{p} + |z_3|^2 < (|z_1|^2 + |z_2|^2 )^{p/2} \}\).     

Fluid queue driven by aGI/GI/1 queue

Consider a model consisting of two phases: the GI/GI/1 queue and a buffer which is fed by a fluid arriving from a single-server queue. The fluid output from the GI/GI/1 queue is of the on/off type with on- and off-periods distributed as successive busy and idle periods in the GI/GI/1 queue. The fluid pours out of the buffer at a constant rate. The steady-state performance of this model is studied. We derive the Laplace-Stieltjes transform of the stationary distribution function of the buffer content in the case of the M/GI/1 queue in the first phase. It is shown that this distribution depends on the form of the service-time distribution. Therefore, the replacement of an M/GI/1 queue by an M/M/1 queue is not correct, in general. Continuity estimates are derived in the cast where the buffer is fed from the GI/GI/1 queue. Proceedings of the Seminar on Stability Problems for Stochastic Models, Moscow Russia, 1996, Part II.     

具临界指数和临界非线性边界条件的拟线性椭圆型方程Neumann问题

本文给出ＲＮ（Ｎ３）中有界光滑区域Ω上的拟线性椭圆型方程：－∑Ｎｉ＝１ｘｉ·｜Ｄｕ｜ｐ－２ｕｘｉ＝λ｜ｕ｜ｐ－２ｕ＋ａ（ｘ）｜ｕ｜ｐ－２ｕ＋ｆ（ｘ，ｕ），ｘ∈Ω（λ＞０，ｐ＝Ｎｐ／（Ｎ－ｐ），２ｐ＜Ｎ）在边界条件：－｜Ｄｕ｜ｐ－２Ｄνｕ｜Ω＝ψ（ｘ）｜ｕ｜ｑ－２ｕ（ｑ＝（Ｎ－１）ｐ／（Ｎ－ｐ））下的多解性结果．     

关于Aluthge变换的数值域

设A是作用在希耳伯特空间H上的有界线性算子,如果A=V A是算子A的极分解,则定义A~=A 12V A 21和A~(*)=A*21V A*21分别为算子A的Aluthge变换A~和*-Aluthge变换A~(*).记A~和A~(*)的数值域分别为W(A~)和W(A~(*)).证明了W(A~)=W(A~(*)),即肯定了吴提出的一个猜想.     

Nonexistence of Blow-up Flows for Symplectic and Lagrangian Mean Curvature Flows

In this paper we mainly study the relation between $|A|^2, |H|^2$ and cosα (α is the Kähler angle) of the blow up flow around the type II singularities of a symplectic mean curvature flow. We also study similar property of an almost calibrated Lagrangian mean curvature flow. We show the nonexistence of type II blow-up flows for a symplectic mean curvature flow satisfying $|A|^2≤λ|H|^2$ and $cosα≥δ>1-\frac{1}{2λ}(½≤α≤ 2)$, or for an almost calibrated Lagrangian mean curvature flow satisfying $|A|^2≤λ|H|^2$ and $cosθ≥δ>max\ {0,1-\frac{1}{λ}}(\frac34≤λ≤ 2)$, where θ is the Lagrangian angle.     

Solutions to the $\sigma_k$-Loewner-Nirenberg Problem on Annuli are Locally Lipschitz and Not Differentiable

We show for $k \geq 2$ that the locally Lipschitz viscosity solution to the $\sigma_k$-Loewner-Nirenberg problem on a given annulus $\{a < |x| < b\}$ is $C^{1,\frac{1}{k}}_{\rm loc}$ in each of $\{a < |x| \leq \sqrt{ab}\}$ and $\{\sqrt{ab} \leq |x| < b\}$ and has a jump in radial derivative across $|x| = \sqrt{ab}$. Furthermore, the solution is not $C^{1,\gamma}_{\rm loc}$ for any $\gamma > \frac{1}{k}$. Optimal regularity for solutions to the $\sigma_k$-Yamabe problem on annuli with finite constant boundary values is also established.     

CONVERGENCE OF THE WEIGHTED NONLOCAL LAPLACIAN ON RANDOM POINT CLOUD

We analyze the convergence of the weighted nonlocal Laplacian (WNLL) on the high dimensional randomly distributed point cloud.Our analysis reveals the importance of the scaling weight,μ ～ |P|/|S| with |P| and |S| being the number of entire and labeled data,respectively,in WNLL.The established result gives a theoretical foundation of the WNLL for high dimensional data interpolation.     

偶图的K3.3剖分

设G＝（X，Y；E）是一个偶图。如果|X|≥2|Y|-3且d(v)=3对任意v∈X,那么G含有K3.3的剖分。有例子表明|X|的下界在一定程度上是不可改进的。     

A NOTE ON A PROBLEM OF BOAS R.P.

To answer the rest part of the problem of Boas R. P. on derivative of polynomial, it is shown that if $\[p(z)\]$ is a polynomial of degree n such that $\[\mathop {\max }\limits_{\left| z \right| \le 1} \left| {p(z)} \right| \le 1\]$ and $\[{p(z) \ne 0}\]$ in $\[\left| z \right| \le k,0 < k \le 1\]$, then $\[\left| {{p^''}(z)} \right| \le n/(1 + {k^n})\]$ for $\[\left| z \right| \le 1\]$. The above estimate is sharp and the equation holds for $\[p(z) = ({z^n} + {k^n})/(1 + {k^n})\]$.     

COMPLETE HYPERSURFACES WITH CONSTANT SCALAR CURVATURE AND CONSTANT MEAN CURVATURE IN R~4

Let M be a 3-dimersional complete and connected hypersurface immersed in R~4. If thescalar curvature R and the mean curvature |H| of M are constants, where |H|≠0, R≥0,then there are only three cases: R=6|H|~2, 9/2|H|~2 and 0. Moreovon we can find somehypersurfaces appropriate to these cases.     

On the Strong Law of Large Numbers for φ-Sub-Gaussian Random Variables

Ukrainian Mathematical Journal - For p ≥ 1, let φp(x) = x2/2 if |x| ≤ 1 and φp(x) = 1/p|x|p ? 1/p + 1/2 if |x| &gt; 1. For a random variable ξ, let $$...     

面积平均p叶函数的最小模估计及其应用

假设,在单位圆盘△={z:|z|<1}内是面积平均p叶函数.关于|f'/f|2的平均增长,Hayman和Duren等对其进行了详细的研究.注意到,这种增长涉及到f(z)的最小模m(r)=min|z|=r|f(z)|.本文首先估计m(r),然后给出一些相关的应用,其中包括|f'/f|2的平均增长估计,|f(eiθ)|-λ的可积性以及一个新的Bazilevic定理,这个新的定理涉及到f的最大增长方向和最小增长方向.我们得到的某些结果是不可改进的.     

Lu Qi-Keng’s Problem for Intersection of Two Complex Ellipsoids

In this paper we investigate the Lu Qi-Keng problem for intersection of two complex ellipsoids \(\{z \in \mathbb {C}^3 :|z_1|^2 + |z_2|^q < 1, |z_1|^2 + |z_3|^r < 1\}\).     

On approximation of smooth functions from null spaces of optimal linear differential operators with constant coefficients

For a real valued function f defined on a finite interval I we consider the problem of approximating f from null spaces of differential operators of the form Ln(ψ) = n ∑ k=0 akψ(k), where the constant coefficients ak ∈ R may be adapted to f . We prove that for each f ∈ C(n)(I), there is a selection of coefficients {a1, ,an} and a corresponding linear combination Sn( f ,t) = n ∑ k=1 bkeλkt of functions ψk(t) = eλkt in the nullity of L which satisfies the following Jackson’s type inequality: f (m) Sn(m )( f ,t) ∞≤ |an|2n|Im|1/1q/ep|λ|λn|n|I||nm1 Ln( f ) p, where |λn| = mka x|λk|, 0 ≤ m ≤ n 1, p,q ≥ 1, and 1p + q1 = 1. For the particular operator Mn(f) = f + 1/(2n) f(2n) the rate of approximation by the eigenvalues of Mn for non-periodic analytic functions on intervals of restricted length is established to be exponential. Applications in algorithms and numerical examples are discussed.     

Quantitative Stability of the Brunn-Minkowski Inequality for Sets of Equal Volume

The authors prove a quantitative stability result for the Brunn-Minkowski inequality on sets of equal volume:If |A| =|B| ＞ 0 and |A + B|1/n =(2 + δ)|A|1/n for some small δ,then,up to a translation,both A and B are close (in terms of δ) to a convex set K.Although this result was already proved by the authors in a previous paper,the present paper provides a more elementary proof that the authors believe has its own interest.Also,the result here provides a stronger estimate for the stability exponent than the previous result of the authors.     

關於平均P葉函數

<正> §1.設函數f(z)=在單位圓|z|<1中是正則的;W表示w=f(z)將|z|>1照像到w平面上的黎曼面;以w(R)表示圓|w|≤R所掩蓋W的面積(重叠的黎曼面以重叠的次數計算)。若對任意的R>0,