HYM-flation: Yang-Mills cosmology with Horndeski coupling

We propose new mechanism for inflation using classical SU(2) Yang-Mills (YM) homogeneous and isotropic field non-minimally coupled to gravity via Horndeski prescription. This is the unique generally and gauge covariant ghost-free YM theory with the curvature-dependent action leading to second-order gravity and Yang-Mills field equations. We show that its solution space contains de Sitter boundary to which the trajectories are attracted for some finite time, ensuring the robust inflation with a graceful exit. The theory can be generalized to include the Higgs field leading to two-steps inflationary scenario, in which the Planck-scale YM-generated inflation naturally prepares the desired initial conditions for the GUT-scale Higgs inflation.Comment: 13 pages, 3 figure

Problems and strategy of the first flight to the comets

Substantiation is given for the urgency of using space equipment to study comets in order to work out the basic problem of the origin and evolution of the solar system. The potentialities and advantages of selecting ballistically-accessible objects among the newly discovered comets are shown (as a preliminary study). The technique of early detection of such objects is discussed

On the Question of Polygonality and Irregularities of the Shape of Certain Craters on the Moon

Evaluation of moon crater polygonality, and irregular shape

Effects of distance dependence of exciton hopping on the Davydov soliton

The Davydov model of energy transfer in molecular chains is reconsidered assuming the distance dependence of the exciton hopping term. New equations of motion for phonons and excitons are derived within the coherent state approximation. Solving these nonlinear equations result in the existence of Davydov-like solitons. In the case of a dilatational soliton, the amplitude and width is decreased as a results of the mechanism introduced here and above a critical coupling strength our equations do not allow for localized solutions. For compressional solitons, stability is increased.Comment: RevTeX 13 pages, 3 Postscript figure

Penetrators (penetrating sondes) and new possibilities for study of the planets

The fields of possible use of penetrators in space research are considered. A survey of the condition of development and plans for use of penetrators abroad is presented and an analysis is given of the significance of scientific problems when probing planets

Directed current in the Holstein system

We propose a mechanism to rectify charge transport in the semiclassical Holstein model. It is shown that localised initial conditions, associated with a polaron solution, in conjunction with a nonreversion symmetric static electron on-site potential constitute minimal prerequisites for the emergence of a directed current in the underlying periodic lattice system. In particular, we demonstrate that for unbiased spatially localised initial conditions, violation of parity prevents the existence of pairs of counter-propagating trajectories, thus allowing for a directed current despite the time-reversibility of the equations of motion. Occurrence of long-range coherent charge transport is demonstrated

Cubic spline prewavelets on the four-directional mesh

In this paper, we design differentiable, two dimensional, piecewise polynomial cubic prewavelets of particularly small compact support. They are given in closed form, and provide stable, orthogonal decompositions of L^2(\RR^2). In particular, the splines we use in our prewavelet constructions give rise to stable bases of spline spaces that contain all cubic polynomials, whereas the more familiar box spline constructions cannot reproduce all cubic polynomials, unless resorting to a box spline of higher polynomial degree

Braided Picard groups and graded extensions of braided tensor categories

We classify various types of graded extensions of a finite braided tensor category $\cal B$ in terms of its $2$-categorical Picard groups. In particular, we prove that braided extensions of $\cal B$ by a finite group $A$ correspond to braided monoidal $2$-functors from $A$ to the braided $2$-categorical Picard group of $\cal B$ (consisting of invertible central $\cal B$-module categories). Such functors can be expressed in terms of the Eilnberg-Mac~Lane cohomology. We describe in detail braided $2$-categorical Picard groups of symmetric fusion categories and of pointed braided fusion categories