An analytic finite capacity queueing network model capturing the propagation of congestion and blocking

Analytic queueing network models often assume infinite capacity queues due to the difficulty of grasping the between-queue correlation. This correlation can help to explain the propagation of congestion. We present an analytic queueing network model which preserves the finite capacity of the queues and uses structural parameters to grasp the between-queue correlation. Unlike pre-existing models it maintains the network topology and the queue capacities exogenous. Additionally, congestion is directly modeled via a novel formulation of the state space of the queues which explicitly captures the blocking phase. The model can therefore describe the sources and effects of congestion.     

Uniqueness of conformal metrics with prescribed total curvature in R^2

In this paper, we investigate the solution structure of solutions of where K(x) is a H?lder function in . For a given positive total curvature, we consider the problem of the uniqueness of solutions with this prescribed total curvature. We apply various methods such as the method of moving spheres and the isoperimetric inequality to show the uniqueness for several classes of K. Received December 15, 1998 / Accepted April 23, 1999     

Conformal metrics with prescribed Q-curvature on S n

In this paper we prescribe a fourth order conformal invariant on the standard n-sphere, with n????5, and study the related fourth order elliptic equation. We prove new existence results based on a new type of Euler?CHopf type formula. Our argument gives an upper bound on the Morse index of the obtained solution. We also give a lower bound on the number of conformal metrics having the same Q-curvature.     

Real analytic structures on a symplectic manifold

We prove that every symplectic manifold possesses a real analytic structure. Moreover this structure is unique up to isomorphism.

     

Real analytic solutions of parabolic equations with time-measurable coefficients

We use Bernstein's technique to show that for any fixed , strong solutions of the uniformly parabolic equation in are real analytic in . Here, is a bounded domain and the coefficients are measurable. We also use Bernstein's technique to obtain interior estimates for pure second derivatives of solutions of the fully nonlinear, uniformly parabolic, concave equation in , where is measurable in .

     

Real closed fields with non-standard and standard analytic structure

We consider the ordered field which is the completion of thePuiseux series field over equipped with a ring of analyticfunctions on [–1, 1]ⁿ which contains the standard subanalyticfunctions as well as functions given by t-adically convergentpower series, thus combining the analytic structures of Denefand van den Dries [Ann. of Math. 128 (1988) 79–138] andLipshitz and Robinson [Bull. London Math. Soc. 38 (2006) 897–906].We prove quantifier elimination and o-minimality in the correspondinglanguage. We extend these constructions and results to rankn ordered fields _n (the maximal completions of iterated Puiseuxseries fields). We generalize the example of Hrushovski andPeterzil [J. Symbolic Logic 72 (2007) 119–122] of a sentencewhich is not true in any o-minimal expansion of (shown in [Bull.London Math. Soc. 38 (2006) 897–906] to be true in ano-minimal expansion of the Puiseux series field) to a towerof examples of sentences _n, true in _n, but not true in any o-minimalexpansion of any of the fields , ₁, ..., _n–1.     

可允许度量下有限能量辛涡旋的渐近行为献给钱敏教授90华诞

假设(X,ω)是一个具有紧致单连通Lie群G Hamilton作用的紧致光滑辛流形.本文证明只要Riemann面的柱形端口具有一个比标准柱形度量增长速度快的线性度量,那么任何一个有限能量辛涡旋将以指数衰减的速度收敛到辛流形X在正则值辛约化的扭曲分支或非扭曲分支上.本文结果无需假设群G在正则水平集上的作用是自由的.因此,它直接推广了Ziltener在群作用自由的假设下得出的相关结果.本文结果在作者关于量子化Kirwan同态的系列工作中有重要应用.     

Sharp trace theorems for null hypersurfaces on Einstein metrics with finite curvature flux

The main objective of the paper is to prove a geometric version of sharp trace and product estimates on null hypersurfaces with finite curvature flux. These estimates play a crucial role to control the geometry of such null hypersurfaces. The paper is based on an invariant version of the classical Littlewood–Paley theory, in a noncommutative setting, defined via heat flow on surfaces. Received: April 2004 Revision: June 2005 Accepted: July 2005 The first author is partially supported by NSF grant DMS-0070696. The second author is a Clay Prize Fellow and is partially supported by NSF grant DMS-01007791.     

Harmonic maps with finite total energy

We will give a criteria for a nonnegative subharmonic function with finite energy on a complete manifold to be bounded. Using this we will prove that if on a complete noncompact Riemannian manifold , every harmonic function with finite energy is bounded, then every harmonic map with finite total energy from into a Cartan-Hadamard manifold must also have bounded image. No assumption on the curvature of is required. As a consequence, we will generalize some of the uniqueness results on homotopic harmonic maps by Schoen and Yau.

     

Spherical metrics with conical singularities on 2-spheres

Suppose that \(\theta _1,\theta _2,\ldots ,\theta _n\) are positive numbers and \(n\ge 3\). We want to know whether there exists a spherical metric on \(\mathbb {S}^2\) with n conical singularities of angles \(2\pi \theta _1,2\pi \theta _2,\ldots ,2\pi \theta _n\). A sufficient condition was obtained by Mondello and Panov (Int Math Res Not 2016(16):4937–4995, 2016). We show that their condition is also necessary when we assume that \(\theta _1,\theta _2,\ldots ,\theta _n \not \in \mathbb {N}\).     

Randers metrics on CP2

The complex projective space CP² is a classical example of Einstein metric in Riemannian geometry. Moreover, beside this property, it has other interesting geometrical properties: it is a symmetric space, and a C manifold. We would like to know whether there is an Einstein metric of Randers type on CP² with similar properties. Based on some the generalization of Zermelo navigation problem for Finsler manifolds we construct such Randers metric on CP² and study some of its geometrical properties.     

The prescribed scalar curvature problem for metrics with unit total volume

We solve the modified Kazdan–Warner problem of finding metrics with prescribed scalar curvature and unit total volume.