Cosine methods for a class of semilinear second-order wave equations

AbstractWe analyze fully discrete methods of fourth- or second-order temporal accuracy for the approximation of the solutions of a class of semilinear second-order hyperbolic equations with a nonlinear term ⨍ that depends on x, t, u, ut, ▿u. The methods are based on Galerkin-type discretizations in space and on a class of two-step, cosine time-stepping schemes. By suitably extrapolating from previous values in the nonlinear term we compute the approximations by solving linear systems of equations at each time step L2-optimal error estimates are proved

Enumeration of Rosenberg-type hypercompositional structures defined by binary relations

AbstractEvery binary relation ρ on a set H,(card(H)>1) can define a hypercomposition and thus endow H with a hypercompositional structure. In this paper, binary relations are represented by Boolean matrices. With their help, the hypercompositional structures (hypergroupoids, hypergroups, join hypergroups) that emerge with the use of the Rosenberg’s hyperoperation are characterized, constructed and enumerated using symbolic manipulation packages. Moreover, the hyperoperation given by x∘x={z∈H|(z,x)∈ρ} and x∘y=x∘x∪y∘y is introduced and connected to Rosenberg’s hyperoperation, which assigns to every (x,y) the set of all z such that either (x,z)∈ρ or (y,z)∈ρ

THE TRANSPOSITION AXIOM IN HYPERCOMPOSITIONAL STRUCTURES

The hypergroup (as defined by F. Marty), being a very general algebraic structure, was subsequently quickly enriched with additional axioms. One of these is the transposition axiom, the utilization of which led to the creation of join spaces (join hypergroups) and of transposition hypergroups. These hypergroups have numerous applications in geometry, formal languages, thetheory of automata and graph theory. This paper deals with transposition hypergroups. It also introduces the transposition axiom to weaker structures, which result from the hypergroup by the removal of certain axioms, thus defining the transposition hypergroupoid, the transposition semi-hypergroup and the transposition quasi-hypergroup. Finally, it presents hypercompositional structures with internal or external compositions and hypercompositions, in which the transposition axiom is valid. Such structures emerged during the study of formal languages and the theory of automata through the use of hypercompositional algebra

Real-time contour propagator for high temperature dimensional reduction

We discuss the extension of dimensional reduction in thermal field theory at high temperature to real-time correlation functions. It is shown that the perturbative corrections to the leading classical behavior of a scalar bosonic field theory are determined by an effective contour propagator. On the real-time-branch of the time-path contour the effective propagator is obtained by subtracting the classical propagator from the contour propagator of thermal field theory, whereas on the Euclidean branch it reduces to the non-static Matsubara propagator of standard dimensional reduction.Comment: 6 pages, Revte

Effective Classical Theory for Real-Time SU(N) Gauge Theories at High Temperature

We derive an effective classical theory for real-time SU($N$) gauge theories at high temperature. By separating off and integrating out quantum fluctuations we obtain a 3D classical path integral over the initial fields and conjugate momenta. The leading hard mode contribution is incorporated in the equations of motion for the classical fields. This yields the gauge invariant hard thermal loop (HTL) effective equation of motion. No gauge-variant terms are generated as in treatments with an intermediate momentum cut-off. Quantum corrections to classical correlation functions can be calculated perturbatively. The 4D renormalizability of the theory ensures that the 4D counterterms are sufficient to render the theory finite. The HTL contributions of the quantum fluctuations provide the counterterms for the linear divergences in the classical theory.Comment: 13 pages, 1 figure, title changed, discussion on the classical approximation include

Emergence of coherent motion in aggregates of motile coupled maps

In this paper we study the emergence of coherence in collective motion described by a system of interacting motiles endowed with an inner, adaptative, steering mechanism. By means of a nonlinear parametric coupling, the system elements are able to swing along the route to chaos. Thereby, each motile can display different types of behavior, i.e. from ordered to fully erratic motion, accordingly with its surrounding conditions. The appearance of patterns of collective motion is shown to be related to the emergence of interparticle synchronization and the degree of coherence of motion is quantified by means of a graph representation. The effects related to the density of particles and to interparticle distances are explored. It is shown that the higher degrees of coherence and group cohesion are attained when the system elements display a combination of ordered and chaotic behaviors, which emerges from a collective self-organization process.Comment: 33 pages, 12 figures, accepted for publication at Chaos, Solitons and Fractal

Эффективность современных технологий при ведении преждевременных родов

The article presents data on the effectiveness of various modern perinatal technologies in spontaneus preterm labor at 28—36 weeks of gestation. Combination of modern perinatal technology: ante- and intranatal tocolysis, antenatal corticosteroidtherapy, epidural anesthesia, exlusive breast feeding, Kangaroo Mother Care were improved perinatal outcomes.В работе представлены данные анализа эффективности различных современных перинатальных технологий при преждевременных родах в сроки гестации 28—36 нед. Использование комплекса перинатальных технологий: анте- и интранатальный токолиз, применение кортикостероидов с целью профилактики респираторного дистресс синдрома новорожденного, выжидательная тактика и применение антибиотиков при преждевременном разрыве оболочек плодного пузыря, бережное ведение родов с применением эпидуральной анестезии, улучшение методов вентиляции легких, использование препаратов сурфактанта, улучшение неонатального ухода, тепловая защита новорожденного, применение нативного молозива и молока, — позволяет улучшить перинатальные исходы

The post-Minkowskian limit of f(R)-gravity

We formally discuss the post-Minkowskian limit of $f(R)$-gravity without adopting conformal transformations but developing all the calculations in the original Jordan frame. It is shown that such an approach gives rise, in general, together with the standard massless graviton, to massive scalar modes whose masses are directly related to the analytic parameters of the theory. In this sense, the presence of massless gravitons only is a peculiar feature of General Relativity. This fact is never stressed enough and could have dramatic consequences in detection of gravitational waves. Finally the role of curvature stress-energy tensor of $f(R)$-gravity is discussed showing that it generalizes the so called Landau-Lifshitz tensor of General Relativity. The further degrees of freedom, giving rise to the massive modes, are directly related to the structure of such a tensor.Comment: 9 page