A class of reduced-order models in the theory of waves and stability

This paper presents a class of approximations to a type of wave field for which the dispersion relation is transcendental. The approximations have two defining characteristics: (i) they give the field shape exactly when the frequency and wavenumber lie on a grid of points in the (frequency, wavenumber) plane and (ii) the approximate dispersion relations are polynomials that pass exactly through points on this grid. Thus, the method is interpolatory in nature, but the interpolation takes place in (frequency, wavenumber) space, rather than in physical space. Full details are presented for a non-trivial example, that of antisymmetric elastic waves in a layer. The method is related to partial fraction expansions and barycentric representations of functions. An asymptotic analysis is presented, involving Stirling's approximation to the psi function, and a logarithmic correction to the polynomial dispersion relation

A WKB approximation of elastic waves travelling on a shell of revolution

This paper is concerned with the elastic waveguide properties of an infinite pipe with circular cross section whose radius varies slowly along its length. The equations governing the elastodynamics of such shells are derived analytically, approximated asymptotically in the limit of slow axial variation, and solved by means of the WKB-method (Wentzel–Kramers–Brillouin). From the derived solution the dispersion relation, modal coefficients, and wave amplification at each location along the structure are extracted, allowing identification of which types of waves are able to propagate along the structure at a given frequency. A key feature in the formulation of the model and the solution is that the radius and its variation are not specified in advance. Two characteristic examples of shells of revolution are presented to illustrate some general features of the waveguide properties, demonstrating how the evolution of the waves depends on the axial variation of the shell radius. It is explained how local resonances can be excited by the travelling waves and how strong amplifications of displacement can be produced. Specifically, for the axial/breathing wave it is shown that a local resonance is excited at the location where the frequency of the travelling wave and the radius of the shell exactly match the ring-frequency.This research has been founded by The Danish Council for Technology and Innovation, under Grant no. 10-083896, which is gratefully acknowledged

Compressed representation of a partially defined integer function over multiple arguments

In OLAP (OnLine Analitical Processing) data are analysed in an n-dimensional cube. The cube may be represented as a partially defined function over n arguments. Considering that often the function is not defined everywhere, we ask: is there a known way of representing the function or the points in which it is defined, in a more compact manner than the trivial one

Observation of the diphoton decay of the Higgs boson and measurement of its properties

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Precise determination of the mass of the Higgs boson and tests of compatibility of its couplings with the standard model predictions using proton collisions at 7 and 8 TeV

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Study of double parton scattering using W+2-jet events in proton-proton collisions at √s=7 TeV

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Search for new physics in the multijet and missing transverse momentum final state in proton-proton collisions at √s=8 Tev

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Search for Dark Matter and Supersymmetry with a Compressed Mass Spectrum in the Vector Boson Fusion Topology in Proton-Proton Collisions at root s=8 TeV

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Mode of socio-economic development and occupational structure: the case of contemporary Russia

The given paper assumes the existence of a correlation between the occupational structure and the mode of social and economic development of a country. It is shown that the modern stage of development in advanced economies could be described by the post-industrial phase with (a) the specific proportions in the occupational structure (predominance of professional managers and technical experts); (b) particular nature of work and the corresponding extent of labor division according to specialization and qualification (highly skilled labor with broad specialization and a new criterion of creativity included within qualifications). Within the certain historical framework these indicators, combined onto the entire scheme, produce the criteria to distinct different types of socio-economic development and arrange them in consistent order. The analysis of occupational structure of Russian population shows that the reforms of 1990s have facilitated the process of deindustrialization alongside with the growth of semi- and low-skilled jobs. According to the scheme, Russia seems to have reached the stage of the development that is similar to one of the 1950–1960s in the USA and the Europe

Measurement of Higgs boson production and properties in the WW decay channel with leptonic final states

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