Universally-Convergent Squared-Operator Iteration Methods for Solitary Waves in General Nonlinear Wave Equations

Three new iteration methods, namely the squared-operator method, the modified squared-operator method, and the power-conserving squared-operator method, for solitary waves in general scalar and vector nonlinear wave equations are proposed. These methods are based on iterating new differential equations whose linearization operators are squares of those for the original equations, together with acceleration techniques. The first two methods keep the propagation constants fixed, while the third method keeps the powers (or other arbitrary functionals) of the solution fixed. It is proved that all these methods are guaranteed to converge to any solitary wave (either ground state or not) as long as the initial condition is sufficiently close to the corresponding exact solution, and the time step in the iteration schemes is below a certain threshold value. Furthermore, these schemes are fast-converging, highly accurate, and easy to implement. If the solitary wave exists only at isolated propagation constant values, the corresponding squared-operator methods are developed as well. These methods are applied to various solitary wave problems of physical interest, such as higher-gap vortex solitons in the two-dimensional nonlinear Schrödinger equations with periodic potentials, and isolated solitons in Ginzburg–Landau equations, and some new types of solitary wave solutions are obtained. It is also demonstrated that the modified squared-operator method delivers the best performance among the methods proposed in this article.     

Seeing small

This paper reviews a number of used and/or proposed ideas for optical detection of small particles including single-molecules. Different techniques (direct absorption and scattering, interferometry, use of sub Poissonian statistics, cavity enhancement, and thermal lens detection) are compared in terms of signal-to-noise (SNR) ratio. It is shown that scattering (resonance and non-resonance) remains the method of choice for most practical applications. Thermal lens detection can do potentially better, but its performance critically depends on the thermal properties of the particle surroundings.     

The Direct Limits Of The Banach-mazur Compacta

Let 1 p . For each n-dimensional Banach space E = (E, || ·||), we define a norm || · ||_p on E x R as follows: [formula] It is shown that the correspondence (E, || · ||) (Ex R, || · ||_p) defines a topological embedding of oneBanach–Mazur compactum, BM(n), into another, BM(n 1),and hence we obtain a tower of Banach–Mazur compacta:BM(1) BM(2) BM(3) ···. Let BM_p be thedirect limit of this tower. We prove that BM_p is homeomorphicto Q = dir lim Qⁿ, where Q = [0, 1] is the Hilbert cube. 1991Mathematics Subject Classification 46B04, 46B20, 52A21, 57N20,54H15.     

High-spin yrast states in Ce

Yrast states up to spin 18 have been identified in ¹³²Ce. The energies and spins of the levels suggest the existence of two fairly well-behaved collective bands. The results are compared with those obtained in the rare-earth deformed region.     

Functionalized carbo- and heterocycles via Pt-catalyzed asymmetric alkoxycyclization of 1,6-enynes

This paper describes the asymmetric version of highly atom-economical alkoxycyclization of 1,6-enynes, using a combination of silver salts with the Pt(II)/(R)-Ph-BINEPINE system.     

Determination and estimation of risk aversion coefficients

Computational Management Science - In the paper we consider two types of utility functions often used in portfolio allocation problems, i.e. the exponential utility and the quadratic utility. We...     

Moment-angle complexes from simplicial posets

We extend the construction of moment-angle complexes to simplicial posets by associating a certain T ^m -space Z _S to an arbitrary simplicial poset S on m vertices. Face rings ℤ[S] of simplicial posets generalise those of simplicial complexes, and give rise to new classes of Gorenstein and Cohen-Macaulay rings. Our primary motivation is to study the face rings ℤ[S] by topological methods. The space Z _S has many important topological properties of the original moment-angle complex Z _K associated to a simplicial complex K. In particular, we prove that the integral cohomology algebra of Z _S is isomorphic to the Tor-algebra of the face ring ℤ[S]. This leads directly to a generalisation of Hochster’s theorem, expressing the algebraic Betti numbers of the ring ℤ[S] in terms of the homology of full subposets in S. Finally, we estimate the total amount of homology of Z _S from below by proving the toral rank conjecture for the moment-angle complexes Z _S .     

Topological groups and convex sets homeomorphic to non-separable Hilbert spaces

Let X be a topological group or a convex set in a linear metric space. We prove that X is homeomorphic to (a manifold modeled on) an infinite-dimensional Hilbert space if and only if X is a completely metrizable absolute (neighborhood) retract with ω-LFAP, the countable locally finite approximation property. The latter means that for any open cover of X there is a sequence of maps (f _n : X → X) _nεgw such that each f _n is -near to the identity map of X and the family {f _n (X)} _n∈ω is locally finite in X. Also we show that a metrizable space X of density dens(X) < is a Hilbert manifold if X has gw-LFAP and each closed subset A ⊂ X of density dens(A) < dens(X) is a Z _∞-set in X.      

Acclimation Response of Green Microalgae Chlorella Sorokiniana to 2,3′,4,4′,6-Pentachlorobiphenyl

The effect of the toxicant 2,3′,4,4′,6-pentachlorobiphenyl (PCB-119) on the growth, chlorophyll content, and PSII activity of C. sorokiniana cells was investigated. A strong negative effect of the toxicant was observed at PCB concentration of 0.05 μg mL⁻¹, when culture growth ceased, chlorophyll strongly bleached, and cell death occurred. The use of original highly sensitive fluorimeter to measure three types of high-resolution chlorophyll fluorescence kinetics allowed us to detect an initial dramatic decrease in the activity of primary photosynthetic reactions, followed by their almost complete recovery at the end of the incubation period when most cells were dead. The study of the distribution of individual cells in culture in terms of F_v/F_m parameter, which reflects the quantum yield of PSII photochemistry, revealed the existence of 2–3% of cells retaining high F_v/F_m (>0.7) in the presence of the toxicant. The treated cultures were able to resume growth after prolonged incubation in fresh medium. The high sensitivity fluorescence methods used made it possible to identify stress-resistant cells which maintain high photosynthetic activity in the presence of lethal doses of toxic substances; these cells provide recovery of the population after stress.