Basis- and partition identification for quadratic programming and linear complementarity problems

Optimal solutions of interior point algorithms for linear and quadratic programming and linear complementarity problems provide maximally complementary solutions. Maximally complementary solutions can be characterized by optimal partitions. On the other hand, the solutions provided by simplex–based pivot algorithms are given in terms of complementary bases. A basis identification algorithm is an algorithm which generates a complementary basis, starting from any complementary solution. A partition identification algorithm is an algorithm which generates a maximally complementary solution (and its corresponding partition), starting from any complementary solution. In linear programming such algorithms were respectively proposed by Megiddo in 1991 and Balinski and Tucker in 1969. In this paper we will present identification algorithms for quadratic programming and linear complementarity problems with sufficient matrices. The presented algorithms are based on the principal pivot transform and the orthogonality property of basis tableaus. Received April 9, 1996 / Revised version received April 27, 1998? Published online May 12, 1999     

An elliptic singularly perturbed problem with two parameters I: Solution decomposition

In this paper we consider a singularly perturbed elliptic problem with two small parameters posed on the unit square. Its solution may have exponential, parabolic and corner layers. We give a decomposition of the solution into regular and layer components and derive pointwise bounds on the components and their derivatives. The estimates are obtained by the analysis of appropriate problems on unbounded domains.     

Two-Parametric Compound Binomial Approximations

We consider two-parametric compound binomial approximation of the generalized Poisson binomial distribution. We show that the accuracy of approximation essentially depends on the symmetry or shifting of distributions and construct asymptotic expansions. For the proofs, we combine the properties of norms with the results for convolutions of symmetric and shifted distributions. In the lattice case, we use the characteristic function method. In the case of almost binomial approximation, we apply Steins method.__________Published in Lietuvos Matematikos Rinkinys, Vol. 44, No. 4, pp. 443–466, October–December, 2004.     

Analysis of a finite-difference scheme for a singularly perturbed problem with two small parameters

We study a model linear convection-diffusion-reaction problem where both the diffusion term and the convection term are multiplied by small parameters ε_d and ε_c, respectively. Depending on the size of the parameters the solution of the problem may exhibit exponential layers at both end points of the domain. Sharp bounds for the derivatives of the solution are derived using a barrier-function technique. These bounds are applied in the analysis of a simple upwind-difference scheme on Shishkin meshes. This method is established to be almost first-order convergent, independently of the parameters ε_d and ε_c.     

Compound Poisson approximation for unbounded functions on a group,with application to large deviations

Summary A second order error bound is obtained for approximating h d by h d , where is a convolution of measures andQ a compound Poisson measure on a measurable abelian group, and the functionh is not necessarily bounded. This error bound is more refined than the usual total variation bound in the sense that it contains the functionh. The method used is inspired by Stein's method and hinges on bounding Radon-Nikodym derivatives related to . The approximation theorem is then applied to obtain a large deviation result on groups, which in turn is applied to multivariate Poisson approximation.Research of the second author was supported by Schweizerischer Nationalfonds     

Widely tunable continuous-wave Raman laser in diatomic hydrogen pumped by an external-cavity diode laser

What is to the authors' knowledge the first experimental demonstration of a nonresonant cw Raman laser pumped by a tunable external-cavity diode laser (ECDL) is presented. The ECDL is phase-frequency locked to a high-finesse Raman laser cavity containing diatomic hydrogen (H(2)) by the Pound-Drever-Hall locking technique. The Stokes lasing threshold occurs at a pump power of 400 +/- 30 muW, and a maximum photon conversion efficiency of 12.0 +/- 1.3% is achieved at 1.6 mW of pump power. A 40-nm tuning range of the cw Stokes emission, 1174-1214 nm, is obtained by tuning of the wavelength of the ECDL pump source.     

Electronic conductivity in La1−xBaxF3−x crystals

The electronic conductivities of solid solutions La_1?xBa_xF_3?x (0 ? x ? 0.0952) were investigated up to 533 K using the Hebb-Wagner dc polarization technique. The electrochemical cell (-)La|La_1?xBa_xF_3?x|Pt(+) has been utilized with Pt as the ion-blocking electrode. Under steady-state conditions the La_1?xBa_xF_3?x solid solutions exhibit electronic conductivity. The electronic conductivity vanishes in pure LaF₃. Together with ac conductivity measurements it appears that the ionic transference number for La_1?xBa_xF_3?x (0 ? x ? 0.0952) is essentially unity over the temperature range studied.     

KMS condition in a Schrödinger picture of the dynamics

Given the C¹-algebra $\text{A}$ of observables, the KMS condition is formulated in terms of the time evolution α¹_t of a set $\text{S}$₀ ? $\text{S}$($\text{A}$) of “physical” states subject to certain natural conditions. α¹_t need not be defined by an automorphism group of $\text{A}$. It is shown that, for a KMS state ω, α¹_t induces a 1-automorphism α^ω_t of the von Neumann algebra π_ω($\text{A}$)″ generated by the representation π_ω belonging to ω.     

A CASSCF-CI study of the coordination of ethylene with iron

Summary Complete active space SCF, CASSCF, and contracted CI calculations have been performed on the -bonded complex between ethylene and an iron atom. An extended basis set of the ANO type was used, which included polarization functions on all centers. The results indicate an attractive interaction between Fe ⁵ F(d⁷s) and ethylene, with an estimated binding energy of 14 kcal/mol. The low spin complex arising from Fe ³ F(d⁷s) was found to be bound with 18 kcal/mol. Both these potential minima are, however, above the ground state of the iron atom. It is concluded that the interaction between atomic ground state iron and ethylene is not of the normal -bonded type, but is dominated by dispersion forces. A preliminary study showed this interaction to be almost isotropic, with no preferred site for the iron atom.