Non-empirical calculations of NMR indirect carbon-carbon coupling constants. Part 6: propellanes

A full set of carbon-carbon coupling constants have been calculated at the SOPPA level in the series of six most representative propellanes. Special attention was focused on spin-spin couplings involving both bridgehead carbons, and these data were rationalized in terms of the multipath coupling mechanism and hybridization effects. Many unknown couplings in the propellane frameworks were predicted with high reliability.     

Random perturbations of 2-dimensional hamiltonian flows

We consider the motion of a particle in a periodic two dimensional flow perturbed by small (molecular) diffusion. The flow is generated by a divergence free zero mean vector field. The long time behavior corresponds to the behavior of the homogenized process - that is diffusion process with the constant diffusion matrix (effective diffusivity). We obtain the asymptotics of the effective diffusivity when the molecular diffusion tends to zero.     

Electron transport in granular metals

We consider thermodynamic and transport properties of a long granular array with strongly connected grains (intergrain conductance g>1). We find that the system's conductance and differential capacitance exhibits activated behavior, approximately exp([-T(*)/T]. The gap T(*) represents the energy needed to create a long single-electron charge soliton propagating through the array. This scale is parametrically larger than the energy at which conventional perturbation theory breaks down.     

Magnetic properties of C60 polymers

Magnetic properties of various C60 polymers are calculated using tight-binding molecular-dynamics and ab initio methods. Our results suggest a mechanism involving an interplay between structural defects and sp(3) hybridization to be responsible for the origin of this magnetism. The onset of magnetism is found to occur much more readily for the Rh-C60 polymeric phase with defects than for any of the other polymers, in agreement with the recent experiment. Our estimate of the magnetic moment is also in very good agreement with the value observed in experiment.     

Magnetic propulsion of intense lithium streams in a tokamak magnetic field

This paper describes the effect and gives the theory of magnetic propulsion which allows driving free surface plasma facing liquid lithium streams in tokamaks. In the approximation of a thin flowing layer the MHD equations are reduced to one integrodifferential equation which takes into account the propulsion effect, viscosity, and the drag force due to magnetic pumping and other interactions with the magnetic field. A stability criterion is obtained for stabilization of the "sausage" instability of the streams by centrifugal force.     

Carbon nanotube "T Junctions": formation pathways and conductivity

Using tight-binding molecular dynamics we simulate the formation of single wall carbon nanotube T junctions via the fusing of two nanotubes. We propose energetically efficient pathways for this process in which all atoms maintain their sp(2) arrangements throughout. Recent experimental advances have greatly increased the plausibility of synthesizing T junctions as proposed in the simulations. We further report I-V characteristics of the formed junctions.     

Extending the Balas-Yu bounds on the number of maximal independent sets in graphs to hypergraphs and lattices

A result of Balas and Yu (1989) states that the number of maximal independent sets of a graph G is at most ^p+1, where is the number of pairs of vertices in G at distance 2, and p is the cardinality of a maximum induced matching in G. In this paper, we give an analogue of this result for hypergraphs and, more generally, for subsets of vectors in the product of n lattices =₁××_n, where the notion of an induced matching in G is replaced by a certain binary tree each internal node of which is mapped into . We show that our bounds may be nearly sharp for arbitrarily large hypergraphs and lattices. As an application, we prove that the number of maximal infeasible vectors x=₁××_n for a system of polymatroid inequalities does not exceed max{Q,^logt/c(2Q,)}, where is the number of minimal feasible vectors for the system, , , and c(,) is the unique positive root of the equation 2^c(^c/log–1)=1. This bound is nearly sharp for the Boolean case ={0,1}ⁿ, and it allows for the efficient generation of all minimal feasible sets to a given system of polymatroid inequalities with quasi-polynomially bounded right-hand sides . This research was supported by the National Science Foundation (Grant IIS-0118635), and by the Office of Naval Research (Grant N00014-92-J-1375). The second and third authors are also grateful for the partial support by DIMACS, the National Science Foundation's Center for Discrete Mathematics and Theoretical Computer Science.Mathematics Subject Classification (2000):20E28, 20G40, 20C20     

Primal-dual algorithms and infinite-dimensional Jordan algebras of finite rank

We consider primal-dual algorithms for certain types of infinite-dimensional optimization problems. Our approach is based on the generalization of the technique of finite-dimensional Euclidean Jordan algebras to the case of infinite-dimensional JB-algebras of finite rank. This generalization enables us to develop polynomial-time primal-dual algorithms for ``infinite-dimensional second-order cone programs.' We consider as an example a long-step primal-dual algorithm based on the Nesterov-Todd direction. It is shown that this algorithm can be generalized along with complexity estimates to the infinite-dimensional situation under consideration. An application is given to an important problem of control theory: multi-criteria analytic design of the linear regulator. The calculation of the Nesterov-Todd direction requires in this case solving one matrix differential Riccati equation plus solving a finite-dimensional system of linear algebraic equations on each iteration. The number of equations and unknown variables of this algebraic system is m+1, where m is a number of quadratic performance criteria. Key words.polynomial-time primal-dual interior-point methods – JB-algebras – infinite-dimensional problems – optimal control problemsThis author was supported in part by DMS98-03191 and DMS01-02698.This author was supported in part by the Grant-in-Aid for Scientific Research (C) 11680463 of the Ministry of Education, Culture, Sports, Science and Technology of Japan.Mathematics Subject Classification (1991):90C51, 90C48, 34H05, 49N05     

A New Inertia Theorem for Stein Equations,Inertia of Invertible Hermitian Block Toeplitz Matrices and Matrix Orthogonal Polynomials

In this paper we present an inertia result for Stein equations with an indefinite right hand side. This result is applied to establish connnections between the inertia of invertible hermitian block Toeplitz matrices and associated orthogonal polynomials.