A global optimization algorithm for solving the minimum multiple ratio spanning tree problem

This paper studies the sum-of-ratios version of the classical minimum spanning tree problem. We describe a branch-and-bound algorithm for solving the general version of the problem based on its image space representation. The suggested approach specifically addresses the difficulties arising in the case when the number of ratios exceeds two. The efficacy of our approach is demonstrated on randomly generated complete and sparse graph instances.     

Computational study of the US stock market evolution: a rank correlation-based network model

This paper presents a computational study of global characteristics of the US stock market using a network-based model referred to as the market graph. The market graph reflects similarity patterns between stock return fluctuations via linking pairs of stocks that exhibit “coordinated” behavior over a specified period of time. We utilized Spearman rank correlation as a measure of similarity between stocks and considered the evolution of the market graph over the recent decade between 2001–2011. The observed market graph characteristics reveal interesting trends in the stock market over time, as well as allow one to use this model to identify cohesive clusters of stocks in the market.     

Cubic Nonlinearity in Elastic Materials: Theoretical Prediction and Computer Modelling of New Wave Effects

Our object of interest is nonlinear interaction of waves in elastic materials. The new model of a material is proposed that takes into account the mechanism of simultaneous quadratic and cubic nonlinear deformations. Introduction of cubic nonlinearity into the model makes the general wave picture more complicated and creates new possibilities for the wave analysis. We present four possibilities for the evolution of profiles of plane harmonic waves. It is noted that quadratic and cubic nonlinearities emerge first of all in the second and third harmonics generation, respectively. Further, we discuss the results of computer modelling of the wave profile evolution. The influence of the progress of second and third harmonics on the wave profile evolution is studied separately. We study separately how second and third harmonics influence the evolution of the wave profile. We also investigate how the progress of harmonics depends on the initial frequency and amplitude. We find two distinct schemes of the evolution progress: the scheme (in) with four stages for the second harmonics and the scheme with three stages for the third harmonics. As a result the influence of both harmonics could be observed simultaneously, and such a case is demonstrated in the paper. Nevertheless this phenomenon is not necessarily present in every material which explains the absence of experimental observations of the third harmonics by this time.     

Cluster glass magnetism in the phase-separated Nd2/3Ca1/3MnO3 perovskite

A detailed study of the low-temperature magnetic state and the relaxation in the phase-separated colossal magnetoresistance Nd_2/3Ca_1/3MnO₃ perovskite has been carried out. Clear experimental evidence of the cluster-glass magnetic behavior of this compound has been revealed. Well defined maxima in the in-phase linear ac susceptibility χ′(T) were observed, indicative of the magnetic glass transition at T_g∼60 K. Strongly divergent zero-field-cooled and field-cooled static magnetizations and frequency dependent ac susceptibility are evident of the glassy-like magnetic state of the compound at low temperatures. The frequency dependence of the cusp temperature T_max of the χ′(T) susceptibility was found to follow the critical slowing down mechanism. The Cole–Cole analysis of the dynamic susceptibility at low temperature has shown extremely broad distribution of relaxation times, indicating that spins are frozen at “macroscopic” time scale. Slow relaxation in the zero-field-cooled magnetization has been experimentally revealed. The obtained results do not agree with a canonical spin-glass state and indicate a cluster glass magnetic state of the compound below T_g, associated with its antiferromagnetic–ferromagnetic nano-phase segregated state. It was found that the relaxation mechanisms below the cluster glass freezing temperature T_g and above it are strongly different. Magnetic field up to about μ₀H∼0.4 T suppresses the glassy magnetic state of the compound.     

Global Well-Posedness for the Generalized Large-Scale Semigeostrophic Equations

We prove existence and uniqueness of global classical solutions to the generalized large-scale semigeostrophic equations with periodic boundary conditions. This family of Hamiltonian balance models for rapidly rotating shallow water includes the L ₁ model derived by R. Salmon in 1985 and its 2006 generalization by the second author. The results are, under the physical restriction that the initial potential vorticity is positive, as strong as those available for the Euler equations of ideal fluid flow in two dimensions. Moreover, we identify a special case in which the velocity field is two derivatives smoother in Sobolev space as compared to the general case. Our results are based on careful estimates which show that, although the potential vorticity inversion is nonlinear, bounds on the potential vorticity inversion operator remain linear in derivatives of the potential vorticity. This permits the adaptation of an argument based on elliptic L ^p theory, proposed by Yudovich in 1963 for proving existence and uniqueness of weak solutions for the two-dimensional Euler equations, to our particular nonlinear situation.     

Checking solvability of systems of interval linear equations and inequalities via mixed integer programming

This paper deals with the problems of checking strong solvability and feasibility of linear interval equations, checking weak solvability of linear interval equations and inequalities, and finding control solutions of linear interval equations. These problems are known to be NP$\mathit{NP}$-hard. We use some recently developed characterizations in combination with classical arguments to show that these problems can be equivalently stated as optimization tasks and provide the corresponding linear mixed 0–1 programming formulations.     

Effect of anion substitution onto structural and magnetic properties of chromium chalcogenides

We investigated experimentally and theoretically the effect of the substitution of Te by Se onto the structural, magnetic and electronic properties of ferromagnetic Cr_5±xTe₈ as parent material. Whereas Cr₅Te₈ is dimorphic crystallizing in a monoclinic and trigonal modification, Se substituted samples crystallize in two different trigonal modifications depending on the synthesis conditions. One of the modifications can be viewed as self-intercalated dichalcogenides Cr_1+xQ₂ (Q = Te, Se) and the other is a superstructure which is isostructural to one of the Cr_5±xTe₈ modifications. For the Se richest samples (Te:Se = 1:7) a new modification is identified which was formerly reported for Cr_3+xSe₄. For a distinct Cr content the replacement of Se by Te induces a reduction of the unit cell volumes, of the Cr-Cr and Cr-Te/Se distances. Increasing the Cr content for a constant Te:Se ratio has the opposite effect. The results also suggest that the homogeneity range extends to more Cr rich compounds with decreasing Te content. For a given Cr content the substitution of Te by Se weakens the ferromagnetic exchange interactions and strengthens the antiferromagnetic exchange. With increasing Cr content and a fixed Te:Se ratio ferromagnetic properties become more pronounced. The low temperature magnetic behavior is characterized by spin-glass, spin-glass like or cluster-glass properties depending on the Cr content and the Te:Se ratio. Electronic structure calculations done within the framework of LSDA (local spin density approximation) gave a detailed insight into the electronic and magnetic properties of the investigated systems supporting the interpretation of the achieved experimental results. This applies in particular for the calculated exchange coupling constants that provided the necessary input for Monte Carlo simulations used for theoretical investigations on the magnetic properties at finite temperatures.     

Synthesis of (2,2,2-trifluoroethyl) substituted pyridazin-3(2H)-ones and 1,5-dihydropyrrol-2-ones from α,β-unsaturated γ-lactones and hydrazines

This paper presents the transformation of α,β-unsaturated γ-lactones into 2,2,2-trifluoroethyl substituted pyridazin-3(2H)-ones and 1,5-dihydropyrrol-2-ones starting from various hydrazines. The influence of the γ-lactone substitution (sulfanyl versus sulfonyl moiety) and the nature of the hydrazines (unsubstituted, alkyl- or aryl-substituted) on the outcome of the reaction were studied. All new heterocycles were characterized using 1D NMR, IR, MS and their data was compared with those of two reported X-ray diffraction structures. The two possible competitive pathways leading to pyridazin-3(2H)-ones and/or 1,5-dihydropyrrol-2-ones are discussed. Abinitio DFT calculations were also performed in order to rationalize several experimental results.     

Spatiotemporal airy light bullets in the linear and nonlinear regimes

We demonstrate the realization of intense Airy-Airy-Airy (Airy(3)) light bullets by combining a spatial Airy beam with an Airy pulse in time. The Airy(3) light bullets belong to a family of linear spatiotemporal wave packets that do not require any specific tuning of the material optical properties for their formation and withstand both diffraction and dispersion during their propagation. We show that the Airy(3) light bullets are robust up to the high intensity regime, since they are capable of healing the nonlinearly induced distortions of their spatiotemporal profile.     

Convergence of experiment and theory on the pure vibrational spectrum of HeH(+)

Very accurate quantum mechanical calculations of the pure vibrational spectrum of the molecular ion are reported and compared with newly obtained pure vibrational transitions extracted from the available experimental data. The calculations are performed without assuming the Born-Oppenheimer approximation regarding separability of the nuclear and electronic motions and include the first order relativistic mass-velocity and Darwin corrections. For the two lowest transitions, whose experimental energies are established with the highest precision, the calculated and the experimental results show very good agreement.