Stabilization of Interior-Point Methods for Linear Programming

The paper studies numerical stability problems arising in the application of interior-point methods to primal degenerate linear programs. A stabilization procedure based on Gaussian elimination is proposed and it is shown that it stabilizes all path following methods, original and modified Dikin's method, Karmarkar's method, etc.     

Nucleation of vortices in superfluid helium-4

Summary Nucleation of vortices and strings is studied in superfluid helium in the context of phase transitions in this system. It is shown that the formation of these structures depends on the homotopy groups of the manifold of degenerate condensed states. The subsequent evolution of these structures is investigated and then impact on the superfluid nature of this system is analysed. The cross-section for the scattering of quasi-particles is estimated. This is exploited to find the effect of scatterings on the dynamics of shrinking vortex. During the editorial procedure we came to know that this author deceased.     

具小全变差拟线性双曲组的整体经典解

对一阶拟线性双曲组具慢衰减小全变差初值的Cauchy问题得到了整体经典解的结果，并且给出一个应用举例．这一结果对紧支集的结果给予了推广．     

Degeneracy graphs: theory and application an updated survey

A survey of various aspects of the theory and application of degeneracy graphs (DGs for short) is given. The notion and some basic properties of DGs are introduced, cycling of the simplex method is discussed, the neighborhood problem is tackled, and the application of the so-called optimum DGs to particular problems which are connected with optimal degenerate solutions of a linear programming problem is presented. The impact of weakly redundant constraints on various postoptimal analyses under degeneracy is briefly described.     

Degeneracy of Resonances, Jordan Blocks, and Gamow-Jordan Eigenfunctions

We show that a degeneracy of resonances is associated with a second rank pole in the scattering matrix and a Jordan chain of generalized eigenfunctions of the radial Schrödinger equation. The generalized Gamow-Jordan eigenfunctions are basis elements of an expansion in complex resonance energy eigenfunctions. In this biorthonormal basis, any operator f(H _r which is a regular function of the Hamiltonian is represented by a nondiagonal complex matrix with a Jordan block of rank 2.     

Alternating signs of quiver coefficients

We prove a formula for the Grothendieck class of a quiver variety, which generalizes the cohomological component formulas of Knutson, Miller, and Shimozono. Our formula implies that the -theoretic quiver coefficients have alternating signs and gives an explicit combinatorial formula for these coefficients. We also prove some new variants of the factor sequences conjecture and a conjecture of Knutson, Miller, and Shimozono, which states that their double ratio formula agrees with the original quiver formulas of the author and Fulton. For completeness we include a short proof of the ratio formula.

     

均匀磁场中氢原子低能级简并度的解除

讨论了均匀强磁场中氢原子哈密顿量中B^2项的影响，指出在忽略自旋－轨道相互作用的情况下，该项可使氢原子低能级简并度完全解除。     

Logarithmic SUMT limits in convex programming

The limits of a class of primal and dual solution trajectories associated with the Sequential Unconstrained Minimization Technique (SUMT) are investigated for convex programming problems with non-unique optima. Logarithmic barrier terms are assumed. For linear programming problems, such limits – of both primal and dual trajectories – are strongly optimal, strictly complementary, and can be characterized as analytic centers of, loosely speaking, optimality regions. Examples are given, which show that those results do not hold in general for convex programming problems. If the latter are weakly analytic (Bank et al. [3]), primal trajectory limits can be characterized in analogy to the linear programming case and without assuming differentiability. That class of programming problems contains faithfully convex, linear, and convex quadratic programming problems as strict subsets. In the differential case, dual trajectory limits can be characterized similarly, albeit under different conditions, one of which suffices for strict complementarity. Received: November 13, 1997 / Accepted: February 17, 1999?Published online February 22, 2001     

斯托克斯和反斯托克斯拉曼位移差与时间反演对称性

The anti-Stokes scattering was defined as the corresponding time-reversed process of the Stokes scattering. Based on the time-reversal symmetry the differences between one Stokes and its corresponding anti Stokes Raman shifts have been theoretically demonstrated for the systems with Kramers-degenerate ground or final states. In the former cases the Stokes and its corresponding anti-Stokes Raman lines should display on the same side of the excited line. In the latter cases, they show major differences on two sides of the excited line. However, the whole normal Stokes Raman spectrum of a system may be still symmetric to the whole anti-Stokes spectrum, except in the cases of resonant, or laser, or circularly polarized excitation Raman scattering. This is a preliminary theoretical predication which needs more experimental and theoretical investigations.