Flow control in gas networks: Exact controllability to a given demand

We consider a network of pipelines where the flow is controlled by a number of compressors. The consumer demand is described by desired boundary traces of the system state. We present conditions that guarantee the existence of compressor controls such that after a certain finite time the state at the consumer nodes is equal to the prescribed data. We consider this problem in the framework of continuously differentiable states. We give an explicit construction of the control functions for the control of compressor stations in gas distribution networks. Copyright © 2010 John Wiley & Sons, Ltd.     

Existence and qualitative properties of concentrating solutions for the sinh-Poisson equation

We prove the existence of nodal solutions for – u = sinhu with Dirichlet boundary conditions in bounded, 2D, smoothand non-smooth domains. Indeed, for positive and small enough,we show that there exist at least two pairs of solutions, whichchange sign exactly once, whose nodal lines intersect the boundary.     

Twisted vector bundles on pointed nodal curves

Motivated by the quest for a good compactification of the moduli space ofG-bundles on a nodal curve we establish a striking relationship between Abramovich’s and Vistoli’s twisted bundles and Gieseker vector bundles.     

Torsionfree sheaves over a nodal curve of arithmetic genus one

We classify all isomorphism classes of stable torsionfree sheaves on an irreducible nodal curve of arithmetic genus one defined over ℂ. Let X be a nodal curve of arithmetic genus one defined over ℝ, with exactly one node, such that X does not have any real points apart from the node. We classify all isomorphism classes of stable real algebraic torsionfree sheaves over X of even rank. We also classify all isomorphism classes of real algebraic torsionfree sheaves over X of rank one.     

Rational nodal curves with no smooth Weierstrass points

Let denote the rational curve with nodes obtained from the Riemann sphere by identifying 0 with and with for , where is a primitive th root of unity. We show that if is even, then has no smooth Weierstrass points, while if is odd, then has smooth Weierstrass points.

     

Volumes for Eigensections

It is well known that the size, e.g. Hausdorff measure, of a nodal set of an eigenfunction tends to increase with the eigenvalue. However, because of the highly oscillatory behavior, it is unclear what happens to the volume of the sets where the eigenfunctions are small. In this paper, we show that this volume is bounded uniformly from below for eigenfunctions and, at least on average, for eigenforms (a simple example shows that it need not be true uniformly for eigenforms). The results here answer a question of S. T. Yau.     

Picard groups of the moduli spaces of semistable sheaves I

We compute the Picard group of the moduli spaceU′ of semistable vector bundles of rankn and degreed on an irreducible nodal curveY and show thatU′ is locally factorial. We determine the canonical line bundles ofU′ andU _L ′, the subvariety consisting of vector bundles with a fixed determinant. For rank 2, we compute the Picard group of other strata in the compactification ofU′.     

Laplacian第一特征值整体曲率Pinching的一个结果

紧致流形上Laplacian的第一特征值的下界估计一直以来是人们非常感兴趣的问题之一.本文在整体曲率Pinching较小的条件之下考虑这个问题,得到了相应几何条件之下的Laplacian第一特征值的一个下界估计.     

次临界分数阶Laplace方程具有两个bubbles的变号解存在性

考虑次临界分数阶Laplace问题{(-△)~su=︳u︳~(p-1-ε)u,x∈Ω,u=0,x∈?Ω}具有两个bubbles的变号解的存在性,其中Ω是R~N中的有界光滑区域,N2s,0s1,p=(N+2s)/(N-2s),ε0充分小.这个工作可以看作Bartsch,Micheletti,Pistoia在文[On the existence and the profile of nodal solutions of elliptic equations involving critical growth,Calc.Var.Partial Differential Equations,2006,3:265-282]结果的一种非局部形式的推广.     

Inverse nodal problems for the Sturm-Liouville differential operators on a star-type graph

We study inverse nodal problems for the second order differential operators on a star-type graph satisfying the standard matching conditions at the interior vertex. We prove uniqueness theorems and obtain a constructive solution to the inverse problems of this class. Original Russian Text Copyright ? 2009 Yurko V. A. The author was supported by the Russian Foundation for Basic Research (Grant 07-01-00003) and the National Science Council of Taiwan (Grant 07-01-92000-NSC-a). __________ Saratov. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 50, No. 2, pp. 469–475, March–April, 2009.     

On the Multiplicity of Eigenvalues of the Laplacian on Surfaces

We show that the multiplicity of the eigenvalues of the Laplace Beltrami operator on compact Riemannian surfaces with genus zero is bounded by m(k) 2k – 3 for k 3. Here we label the eigenvalues in the following way: 0 = 1 < 2 3 . . ..     

Finite elements using absolute nodal coordinates for large-deformation flexible multibody dynamics

A family of structural finite elements using a modern absolute nodal coordinate formulation (ANCF) is discussed in the paper with many applications. This approach has been initiated in 1996 by A. Shabana. It introduces large displacements of 2D/3D finite elements relative to the global reference frame without using any local frame. The elements employ finite slopes as nodal variables and can be considered as generalizations of ordinary finite elements that use infinitesimal slopes. In contrast to other large deformation formulations, the equations of motion contain constant mass matrices and generalized gravity forces as well as zero centrifugal and Coriolis inertia forces. The only nonlinear term is a vector of elastic forces. This approach allows applying known abstractions of real elastic bodies: Euler–Bernoulli beams, Timoshenko beams and more general models as well as Kirchhoff and Mindlin plate theories.     

convergence of the reconstruction formula for the potential function

It is known that the potential function of the Sturm-Liouville problem can be reconstructed from the nodal data by a pointwise limit. We show that this convergence is in fact .

     

Size of nodal domains of the eigenvectors of a graph

Consider an eigenvector of the adjacency matrix of a G(n,p) graph. A nodal domain is a connected component of the set of vertices where this eigenvector has a constant sign. It is known that with high probability, there are exactly two nodal domains for each eigenvector corresponding to a nonleading eigenvalue. We prove that with high probability, the sizes of these nodal domains are approximately equal to each other.     

Surfaces à points doubles isolés

We give a characterization of the generic projection on P ² of an algebraic surface of P ³ with a finite number of nodes. The construction of an algebraic surface of P ³ with a given number of nodes is thus equivalent to the construction of a plane curve with nodes and cusps in some special position. Received: November 9, 1996