Anomalous dimension and local charges

AdS space is the universal covering of a hyperboloid. We consider the action of the deck transformations on a classical string worldsheet in $AdS_5\times S^5$. We argue that these transformations are generated by an infinite linear combination of the local conserved charges. We conjecture that a similar relation holds for the corresponding operators on the field theory side. This would be a generalization of the recent field theory results showing that the one loop anomalous dimension is proportional to the Casimir operator in the representation of the Yangian algebra.Comment: 10 pages, LaTeX; v2: added explanations, reference

Analysis of segregated boundary-domain integral equations for mixed variable-coefficient BVPs in exterior domains

This is the post-print version of the Article. The official published version can be accessed from the link below - Copyright @ 2011 Birkhäuser Boston.Some direct segregated systems of boundary–domain integral equations (LBDIEs) associated with the mixed boundary value problems for scalar PDEs with variable coefficients in exterior domains are formulated and analyzed in the paper. The LBDIE equivalence to the original boundary value problems and the invertibility of the corresponding boundary–domain integral operators are proved in weighted Sobolev spaces suitable for exterior domains. This extends the results obtained by the authors for interior domains in non-weighted Sobolev spaces.The work was supported by the grant EP/H020497/1 ”Mathematical analysis of localised boundary-domain integral equations for BVPs with variable coefficients” of the EPSRC, UK

Zero curvature representation for a new fifth-order integrable system

In this brief note we present a zero-curvature representation for one of the new integrable system found by Mikhailov, Novikov and Wang in nlin.SI/0601046.Comment: 2 pages, LaTeX 2e, no figure

Theoretical backgrounds of durability analysis by normalized equivalent stress functionals

Generalized durability diagrams and their properties are considered for a material under a multiaxial loading given by an arbitrary function of time. Material strength and durability under such loading are described in terms of durability, safety factor and normalized equivalent stress. Relations between these functionals are analysed. We discuss some material properties including time and load stability, self-degradation (ageing), and monotonic damaging. Phenomenological strength conditions are presented in terms of the normalized equivalent stress. It is shown that the damage based durability analysis is reduced to a particular case of such strength conditions. Examples of the reduction are presented for some known durability models. The approach is applicable to the strength and durability description at creep and impact loading and their combination

Enhanced graphene nonlinear response through geometrical plasmon focusing

We propose a simple approach to couple light into graphene plasmons and focus these excitations at focal spots of a size determined by the plasmon wavelength, thus producing high optical field enhancement that boosts the nonlinear response of the material. More precisely, we consider a graphene structure in which incident light is coupled to its plasmons at the carbon edges and subsequently focused on a spot of size comparable to the plasmon wavelength. We observe large confinement of graphene plasmons, materializing in small, intense focal spots, in which the extraordinary nonlinear response of this material leads to relatively intense harmonic generation. This result shows the potential of plasmon focusing in suitably edged graphene structures to produce large field confinement and nonlinear response without involving elaborated nanostructuring.Peer ReviewedPostprint (published version

Analysis of some localized boundary-domain integral equations for transmission problems with variable coefficients

This is the post-print version of the Article. The official published version can be found at the links below - Copyright @ 2011 Birkhäuser Boston.Some segregated systems of direct localized boundary-domain integral equations (LBDIEs) associated with several transmission problems for scalar PDEs with variable coefficients are formulated and analyzed for a bounded domain composed of two subdomains with a coefficient jump over the interface. The main results established in the paper are the LBDIE equivalence to the original transmission problems and the invertibility of the corresponding localized boundary-domain integral operators in corresponding Sobolev spaces function spaces.This research was supported by the EPSRC grant EP/H020497/1: ”Mathematical analysis of Localized Boundary-Domain Integral Equations for Variable-Coefficient Boundary Value Problems” and partly by the Georgian Technical University grant in the case of the third author

Ground experiments for finding principles and working out methods for preventing adverse effects of weightlessness on the human organism

A comparative assessment of the effectiveness of different prophylactic procedures to prevent the adverse effects of weightlessness is presented. It is concluded that: physical training is most effective but no single method by itself produces the full effect, and an adjustment of regimes to one another enhances the effect. The approved complex of prophylactic procedures affected basic changes occurring in hypokinesia: deficit of muscular activity, no or reduced BP hydrostatic component, reduced volume of blood circulation, reduced hydration level, and the application of various prophylactic complexes during 49 day antiorthostatic hypodynamia eliminated or reduced the adverse effects of weightlessness in simulation

Localized boundary-domain singular integral equations based on harmonic parametrix for divergence-form elliptic PDEs with variable matrix coefficients

This is the post-print version of the Article. The official publised version can be accessed from the links below. Copyright @ 2013 Springer BaselEmploying the localized integral potentials associated with the Laplace operator, the Dirichlet, Neumann and Robin boundary value problems for general variable-coefficient divergence-form second-order elliptic partial differential equations are reduced to some systems of localized boundary-domain singular integral equations. Equivalence of the integral equations systems to the original boundary value problems is proved. It is established that the corresponding localized boundary-domain integral operators belong to the Boutet de Monvel algebra of pseudo-differential operators. Applying the Vishik-Eskin theory based on the factorization method, the Fredholm properties and invertibility of the operators are proved in appropriate Sobolev spaces.This research was supported by the grant EP/H020497/1: "Mathematical Analysis of Localized Boundary-Domain Integral Equations for Variable-Coefficient Boundary Value Problems" from the EPSRC, UK

Threshold photoelectron photoion coincidence spectroscopy and selected ion flow tube reactions of CHF3: comparison of product branching ratios

The threshold photoelectron and threshold photoelectron photoion coincidence spectra of CHF$_3$ in the range 13.5 – 24.5 eV have been recorded. Ion yields and branching ratios have been determined for the three fragments CF$_3^+$, CHF2$^+$ and CF$^+$. The mean kinetic energy releases into fragment ions involving either C-H or C-F bond cleavage have been measured, and compared with statistical and impulsive models. CHF$_3^+$ behaves in a non-statistical manner characteristic of the small-molecule limit, with the ground electronic state and low-lying excited states of CHF$_3^+$ being largely repulsive along the C-H and C-F coordinates, respectively. The rate coefficients and product ion branching ratios have been measured at 298 K in a selected ion flow tube for the reactions of CHF$_3$ with a large number of gas-phase cations whose recombination energies span the range 6.3 through 21.6 eV. A comparison between the branching ratios from the two experiments, together with an analysis of the threshold photoelectron spectrum of CHF$_3$, shows that long-range charge transfer probably occurs for the Ar$^+$ and F$^+$ atomic ions whose recombination energies lie above ca. 15 eV. Below this energy, the mechanism involves a combination of short-range charge transfer and chemical reactions involving a transition state intermediate