Rigid and Complete Intersection Lagrangian Singularities

In this article we prove a rigidity theorem for lagrangian singularities by studying the local cohomology of the lagrangian de Rham complex that was introduced in [SvS03]. The result can be applied to show the rigidity of all open swallowtails of dimension 2. In the case of lagrangian complete intersection singularities the lagrangian de Rham complex turns out to be perverse. We also show that lagrangian complete intersections in dimension greater than two cannot be regular in codimension one.     

Lagrange问题与平均运动

介绍了天体力学中的Lagrange问题,并结合三连杆机构模型,讨论了Weyl解决这个问题的基本思想和关于平均运动的主要结论.     

Inverse Matroid Intersection Problem

LetM ₁ andM ₂ be matroids onS,B be theirk-element common independent set, andw a weight function onS. Given two functionsb 0 andc 0 onS, the Inverse Matroid Intersection Problem (IMIP) is to determine a modified weight functionw such that (a)B becomes a maximum weight common independent set of cardinalityk underw, (b)c¦w — w¦ is minimum, and (c)¦w — w b. Many Inverse Combinatorial Optimization Problems can be considered as the special cases of the IMIP.In this paper we show that the IMIP can be solved in strongly polynomial time, and give a necessary and sufficient condition for the feasibility of the IMIP. Finally we extend the discussion to the version of the IMIP with Multiple Common Independent Sets.Research partially supported by the National Natural Science Foundation of China     

局部C半群与抽象Cauchy问题

在本文中，我们讨论由算子A生成的局部C半群对应的Cauchy问题，将初值x的取值范围从CD（A）推广到（λ-A）~(-1)C（E）．     

Lagrangian Relaxation and the Single-Source Capacitated Facility-Location Problem

Lagrangian relaxation has been widely used in solving a number of hard combinatorial optimization problems. The success of the approach depends on the structure of the problem and on the values assigned to the Lagrange multipliers. A recent paper on the single-source capacitated facility-location problem proposed the use of Lagrangian relaxation in which the capacity constraints were relaxed. In this paper, a class of such problems is defined for which the proposed relaxation is guaranteed to result in an infeasible solution, irrespective of the values assigned to the Lagrange multipliers. In these cases, the bounds on the optimal solution, obtained from the relaxation, are generally poor. It is concluded that, when using Lagrangian relaxation, it may be worthwhile carrying out a preliminary analysis to determine the potential viability of the approach before extensive development takes place.     

Cauchy Problem with Subcritical Nonlinearity

The semilinear parabolic system onRⁿwith subcritical nonlinearity is studied as an abstract evolutionary equation in a Banach spaceX ? ^p(Rⁿ). As in the case of bounded domains the existence of a strongly continuous semigroup of globalX^α-solutions and its dissipativeness is shown to follow from a single estimate of solutions. Despite the lack of compactness of the Sobolev embeddings inRⁿthe compactness of trajectories of the semigroup is proved using the auxiliary estimate of solutions in a weighted space ^p(Rⁿ, (1 + |x|²)^ν), and the existence of a global attractor is also shown. Thus this paper generalizes earlier considerations and provides a basis for further applications.     

Approximation Methods for Solving the Cauchy Problem

In this paper we give some new results concerning solvability of the 1-dimensional differential equation y′ = f(x, y) with initial conditions. We study the basic theorem due to Picard. First we prove that the existence and uniqueness result remains true if f is a Lipschitz function with respect to the first argument. In the second part we give a contractive method for the proof of Picard theorem. These considerations allow us to develop two new methods for finding an approximation sequence for the solution. Finally, some applications are given.     

测不准原理与Cauchy问题的唯一性

本文讨论具非光滑特征的二阶椭圆偏微分算子Cauchy问题的唯一性.借用测不准原理的思想,通过将方程的解的精细微局部分解,把唯一性证明中最关键的Carleman估计在微局部的层次展开,从而可以在相差一个低阶项的意义下“凝固”某些奇异点的系数,克服因非光滑特征带来的困难,在较以往文章更一般的条件下证明了二阶椭圆微分算子Cauchy 问题的唯一性.     

On the Cauchy Problem of the Camassa-Holm Equation

The purpose of this paper is to investigate the Cauchy problem of the Camassa-Holm equation. By using the abstract method proposed and studied by T. Kato and priori estimates, the existence and uniqueness of the global solution to the Cauchy problem of the Camassa-Holm equation in L ^p frame under certain conditions are obtained. In addition, the continuous dependence of the solution of this equation on the linear dispersive coefficient contained in the equation is obtained.     

Periodic Boundary Problem and Cauchy Problem for the Fluid Dynamic Equation in Geophysics

We study periodic boundary problem and Cauchy problem for the fluid dynamic equation in geophysics. The generalized and classical global solution of the mentioned problems are established. The method employed in this paper is Galerkin approximation and integral estimates.     

Orthogonal Trades and the Intersection Problem for Orthogonal Arrays

This work provides an orthogonal trade for all possible volumes \(N \in \mathbb {Z}^+ \setminus \{1,2,3,4,5,7\}\) for block size 4. All orthogonal trades of volume \(N\leqslant 15\) are classified up to isomorphism for this block size. The intersection problem for orthogonal arrays with block size 4 is solved for all but finitely many possible exceptions.     

On the Correct Solvability of One Cauchy Problem

We establish a criterion for convolutors in certain S-type spaces. Using this criterion, we prove the correct solvability (in both directions) of one Cauchy problem in these spaces.     

On the Cauchy Problem Describing an Electron-Phonon Interaction

In this paper, a model is derived to describe a quartic anharmonic interatomic interaction with an external potential involving a pair electron-phonon. The authors study the corresponding Cauchy Problem in the semilinear and quasilinear cases.     

三维Wigner-Poisson方程组的CaUchy 问题

考虑三维Wigner-Poisson方程组的Cauchy问题,将WP问题转化为等价的Schrodinger     

广义Kawahara方程的Cauchy问题

对初值在Besov空间中的广义Kawahara方程(э)tu+αuk(э)xu+β(э)3xu+γ(э)5xu=0进行了研究,其中k是大于4的正整数,证明了对任意的1≤q≤∞,其Cauchy问题在Besov空间Bsk2,q(R)和Bs2,q(R)中局部适定,这里sk=k-8/2k,s＞max(0,sk);对小初值问题几乎整体适定.并证明了如果β=0或βγ＜0,对小初值问题整体适定.     

关于非齐次柯西问题的强解

利用自反Banach空间中弱紧算子的因子分解技巧，对于一类非齐次项具有连续Lipschitz扰动的柯西问题，当其齐次项算子生成强连续算子半群且具有紧豫解式限制时，证明了方程强解的存在性．     

Cauchy Problem for One Pseudohyperbolic System

Computational Mathematics and Mathematical Physics - The Cauchy problem for one pseudohyperbolic system is considered. The unique solvability of this problem in Sobolev spaces is proved. Systems of...