Driven nonequilibrium lattice systems with shifted periodic boundary conditions

We present the first study of a driven nonequilibrium lattice system in the two-phase region, withshifted periodic boundary conditions, forcing steps into the interface. When the shift corresponds to small angles with respect to the driving field, we find nonanalytic behavior in the (internal) energy of the system, supporting numerical evidence that interface roughness is suppressed by the field. For larger shifts, the competition between the driving field and the boundary induces the breakup of a single strip with tilted interfaces into many narrower strips with aligned interfaces. The size and temperature dependences of the critical angles of such breakup transitions are studied.     

An asymptotic approximation scheme for the concave cost bin packing problem

We consider a generalized one-dimensional bin packing model in which the cost of a bin is a nondecreasing concave function of the utilization of the bin. We show that for any given positive constant ?, there exists a polynomial-time approximation algorithm with an asymptotic worst-case performance ratio of no more than 1 + ?.     

Monotone schemes for semilinear elliptic systems related to ecology

Semilinear elliptic systems of partial differential equations related to ecology are studied, with Dirichlet boundary conditions. Monotone sequences of functions which satisfy scalar equations are constructed so that they will converge to upper and lower bounds for the solutions of the systems. In case a related system has a unique positive solution, then these sequences will converge to the solution of the original system. Applications of the monotone sequences to uniqueness and stability are also given.     

Binary (e,2e) spectroscopic study of carbonyl sulfide and the momentum-space chemistry of CO2, CS2 and OCS

The valence-shell binding energy spectra (8–44 eV) and molecular orbital momentum distributions of OCS have been studied by non-coplanar symmetric binary (e,2e) spectroscopy. Existing theoretical binding energy spectra calculated using the many-body 2ph-TDA Green's function (GF) method and using the symmetry-adapted cluster (SAC) on method are compared with the experiment. Intense many-body structure in the measured and calculated binding energy spectra indicates the general breakdown of the independent particle ionization picture. Experimental momentum distributions are compared with those calculated using ab initio SCF wavefunctions of minimal basis set quality and of near Hartree—Fock quality. Excellent agreement between the experimental momentum distributions and those calculated by the near Hartree—Fock wavefunction is obtained for the three innermost valence orbitals: 8σ, 7σ and 6σ. The correct order of the close lying outer-valence 2π and 9σ orbitals is unambiguously identified from the shapes of the measured momentum distributions. Momentum and position contour density maps computed from theoretical wavefunctions of near Hartree—Fock quality are used to interpret the shapes and atomic characters of the observed momentum distributions. The momentum densities of the outermost-valence antibonding π orbitals and of the outermost-valence bonding σ orbitals of the linear triatomic group: CO₂, CS₂ and OCS are compared respectively with each other. The associated chemical trends are discussed within the existing framework of momentum-space chemical principles.     

Estimating functions of canonical correlation coefficients

Let ρ²₁,…,ρ²_p be the squares of the population canonical correlation coefficients from a normal distribution. This paper is concerned with the estimation of the parameters δ₁,…,δ_p, where $\text{δ}{}_{\mathrm{i}}\text{=}\text{ρ}{}^2{}_{\mathrm{i}}\text{(1 ? ρ}{}^2{}_{\mathrm{i}}\text{)}$, i = 1,…,p, in a decision theoretic way. The approach taken is to estimate a parameter matrix Δ whose eigenvalues are δ₁,…,δ_p, given a random matrix F whose eigenvalues have the same distribution as $\text{r}{}^2{}_{\mathrm{i}}\text{(1 ? r}{}^2{}_{\mathrm{i}}\text{)}$, i = 1,…,p, where r₁,…,r_p are the sample canonical correlation coefficients.     

Monotone scheme for finite difference equations concerning steady-state prey-predator interactions

In this article a system of semilinear elliptic partial differential equations is studied. This system determines the equilibria of the Volterra-Lotka equations describing prey-predator interactions with diffusion. To analyze the system, a new monotone scheme is presented. A rigorous foundation is given for numerical calculations by adapting a suitable finite difference method to the new monotone scheme. Earlier theories in finite differences are not successful in solving the system without this scheme.     

Adiabatic invariants for linear Hamiltonian systems

n independent adiabatic invariants in involution are found for a slowly varying Hamiltonian system of order 2n × 2n. The Hamiltonian system considered is $\text{?}\text{u}\text{?}\text{= A(t)u}\text{as}\text{? → 0}{}^{\mathrm{+}}$, where A(t) is a 2n × 2n real matrix with distinct, pure imaginary eigen values for each t? [?∞, ∞], and $\text{d}{}^{\mathrm{(j)}}\text{A}\text{dt}{}^{\mathrm{(j)}}\text{? L}{}_{\mathrm{j}}\text{(?∞, ∞)}$, for all j > 0. The adiabatic invariants I_s(u, t), s = 1,…, n are expressed in terms of the eigen vectors of A(t). Approximate solutions for the system to arbitrary order of ? are obtained uniformly for t? [?∞, ∞].