A comparison of complete global optimization solvers

Results are reported of testing a number of existing state of the art solvers for global constrained optimization and constraint satisfaction on a set of over 1000 test problems in up to 1000 variables, collected from the literature.The test problems are available online in AMPL and were translated into the input formats of the various solvers using routines from the COCONUT environment. These translators are available online, too.     

Generalized inverses of cone preserving maps

Let K₁ and K₂ be solid cones in Rⁿ and R^m respectively, and let A be a linear operator such that AK₁?K₂. Necessary and sufficient conditions for the existence of various kinds of generalized inverses of A taking K₂ into K₁ are given. Projections which belong to π(K), the set of all linear operators that preserve a are studied. In particular, it is proved that a projection P in π(K) is a simplicial nonnegative linear combination of its rank-one operators iff Im P∩K is a simplical cone. An open question of Burns, Fiedler, and Haynsworth concerning minimal generating matrices of polyhedral cones is also extended and answered affirmatively.     

The acoustic modes of a two-dimensional rectangular cavity

A theoretical study of the acoustic modes of a two-dimensional rectangular cavity is presented in this paper. It is found that for cavities with length to depth ratio of unity or larger the natural modes are heavily damped due to acoustic radiation. Numerical results for lower order modes are given. The physical significance of strong radiation damping on the onset of cavity tones induced by outside flow at low Mach number is discussed.     

Synthesis of corynantheidine alkaloids—III : The stereoselective total synthesis of (±)-dihydrocorynantheine

Starting from the normal cyano-acetate derivative 3b, obtained from the allo stereoisomer 3a via an unusual epimerization,¹ the stereoselective totalsynthesis of (±)-dihydrocorynantheine (1a) was accomplished.     

Monte Carlo renormalization group study of the percolation problem of discs with a distribution of radii

A real space renormalization group is formulated for continuum (off-lattice) percolation problems. It is applied to the system of overlapping discs with a variety of distributions of disc radii. Monte Carlo method is used for obtaining recursion relations. The results support universality: The Harris criterion seems to work for percolation. The position of the critical point shows stability against introducing a distribution in the disc radii.Supported in part by SFB 125 Aachen-Jülich-Köln     

Hot gluon propagator

In order to match two complementary approaches to quark gluon plasma, namely the classical hamiltonian lattice gauge field simulation which uses the temporal axial gauge, and hot perturbative QCD which rather uses the Coulomb or the covariant gauge, we obtain a general expression for the hard thermal loop gluon propagator for a variety of non-background gauge fixing conditions. The Coulomb energy is shown to be independent of the gauge fixing condition.     

Soliton solutions and Bäcklund transformation for the Kupershmidt five-field lattice: a bilinear approach

The Kupershmidt five-field lattice is considered in this paper. By a dependent variable transformation, the Kupershmidt lattice is transformed into a bilinear form by the introduction of three auxiliary variables. We present a Bäcklund transformation and a nonlinear superposition formula for the Kupershmidt lattice. As an application of the results, soliton solutions are derived.     

Minimum number of generators of the lattice of submodules of a semisimple module

It is proved that the minimum number of generators of the lattice of all subspaces of a finite-dimensional vector space over a field is finite if and only if the field is finitely generated over the prime field. An upper bound is given for this number, which does not depend on the dimension of the space and is linearly dependent on the number of elements generating the field.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 132, pp. 110–113, 1983.