Electromagnetic and Gravitational Radiation of Graviatoms

Graviatom existence conditions have been found. The graviatoms (quantum systems around mini-black-holes) satisfying these conditions contain the following charged particles: the electron, muon, tau lepton, wino, pion and kaon. Electric dipole and quadrupole and gravitational radiations are calculated for the graviatoms and compared with Hawking's mini-hole radiation.Comment: 7 pages, 1 figure, 3 tables; accepted in "Astronomical and Astrophysical Transactions

Two dimensional Berezin-Li-Yau inequalities with a correction term

We improve the Berezin-Li-Yau inequality in dimension two by adding a positive correction term to its right-hand side. It is also shown that the asymptotical behaviour of the correction term is almost optimal. This improves a previous result by Melas.Comment: 6 figure

Lieb-Thirring inequalities for geometrically induced bound states

We prove new inequalities of the Lieb-Thirring type on the eigenvalues of Schr\"odinger operators in wave guides with local perturbations. The estimates are optimal in the weak-coupling case. To illustrate their applications, we consider, in particular, a straight strip and a straight circular tube with either mixed boundary conditions or boundary deformations.Comment: LaTeX2e, 14 page

Who runs the place? : the evolving role of corporate centre in the strategy-making process : an empirical investigation of a major Russian multi-business corporation

This research was inspired by a particular business problem – the search for an optimal model of strategy-making process in Severstal, a major Russian metals and mining company going through a period of rapid growth and transformation. The research reports on the results of a longitudinal explorative case study based on two distinct empirical projects. The first project addressed strategy process nature, participants, roles of corporate centre, time perspective and impact of the external environment. Its results highlighted the importance of CEO leadership and personal traits, which became the principal focus of the second empirical project. The key empirical contribution of the research was definition of "leader-focused decentralisation" as a particular approach to strategy-making in a multi-business group. This approach combines decentralized, bottom-up, business units-led generation of strategic proposals and initiatives with a crucial role of a company leader as a deeply involved decision-maker, presiding over a small and lean corporate centre with minimal corporate rules and bureaucracy. In Severstal’s case, the "leader-focused decentralisation" approach to strategy was a good match to its volatile yet rewarding external environment. The suggested model can be seen as an empirically-derived step towards a theoretical synthesis of "activist" vs. "detached" views of corporate centre roles in relation to strategy process in multi-business firms. It exhibited some distinctive features which were not yet described in other contexts, including co-existence of strong entrepreneurial leadership and organisational decentralisation. From a practical standpoint, the research highlighted weaknesses and limitations of existing strategy-making model and offered a background for the discussion of ways to develop it in the future.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Critical Temperature and Energy Gap for the BCS Equation

We derive upper and lower bounds on the critical temperature $T_c$ and the energy gap $\Xi$ (at zero temperature) for the BCS gap equation, describing spin 1/2 fermions interacting via a local two-body interaction potential $\lambda V(x)$. At weak coupling $\lambda \ll 1$ and under appropriate assumptions on $V(x)$, our bounds show that $T_c \sim A \exp(-B/\lambda)$ and $\Xi \sim C \exp(-B/\lambda)$ for some explicit coefficients $A$, $B$ and $C$ depending on the interaction $V(x)$ and the chemical potential $\mu$. The ratio $A/C$ turns out to be a universal constant, independent of both $V(x)$ and $\mu$. Our analysis is valid for any $\mu$; for small $\mu$, or low density, our formulas reduce to well-known expressions involving the scattering length of $V(x)$.Comment: RevTeX4, 23 pages. Revised version, to appear in Phys. Rev.

Automatic human action recognition in videos by graph embedding

The problem of human action recognition has received increasing attention in recent years for its importance in many applications. Yet, the main limitation of current approaches is that they do not capture well the spatial relationships in the subject performing the action. This paper presents an initial study which uses graphs to represent the actor's shape and graph embedding to then convert the graph into a suitable feature vector. In this way, we can benefit from the wide range of statistical classifiers while retaining the strong representational power of graphs. The paper shows that, although the proposed method does not yet achieve accuracy comparable to that of the best existing approaches, the embedded graphs are capable of describing the deformable human shape and its evolution along the time. This confirms the interesting rationale of the approach and its potential for future performance. © 2011 Springer-Verlag

Magnetic rings

We study functional and spectral properties of perturbations of the operator −(∂s+ia)2 in L2( 1). This operator appears when considering the restriction to the unit circle of a two-dimensional Schrödinger operator with the Bohm-Aharonov vector potential. We prove a Hardy-type inequality on ℝ2 and, on 1 , a sharp interpolation inequality and a sharp Keller-Lieb-Thirring inequality

Eigenvalue estimates for non-selfadjoint Dirac operators on the real line

We show that the non-embedded eigenvalues of the Dirac operator on the real line with non-Hermitian potential $V$ lie in the disjoint union of two disks in the right and left half plane, respectively, provided that the $L^1-norm$ of $V$ is bounded from above by the speed of light times the reduced Planck constant. An analogous result for the Schr\"odinger operator, originally proved by Abramov, Aslanyan and Davies, emerges in the nonrelativistic limit. For massless Dirac operators, the condition on $V$ implies the absence of nonreal eigenvalues. Our results are further generalized to potentials with slower decay at infinity. As an application, we determine bounds on resonances and embedded eigenvalues of Dirac operators with Hermitian dilation-analytic potentials

Sums of magnetic eigenvalues are maximal on rotationally symmetric domains

The sum of the first n energy levels of the planar Laplacian with constant magnetic field of given total flux is shown to be maximal among triangles for the equilateral triangle, under normalization of the ratio (moment of inertia)/(area)^3 on the domain. The result holds for both Dirichlet and Neumann boundary conditions, with an analogue for Robin (or de Gennes) boundary conditions too. The square similarly maximizes the eigenvalue sum among parallelograms, and the disk maximizes among ellipses. More generally, a domain with rotational symmetry will maximize the magnetic eigenvalue sum among all linear images of that domain. These results are new even for the ground state energy (n=1).Comment: 19 pages, 1 figur