Vortex Counting and Lagrangian 3-Manifolds

To every 3-manifold M one can associate a two-dimensional ${\mathcal{N}=(2, 2)}$ supersymmetric field theory by compactifying five-dimensional ${\mathcal{N}=2}$ super-Yang?CMills theory on M. This system naturally appears in the study of half-BPS surface operators in four-dimensional ${\mathcal{N}=2}$ gauge theories on one hand, and in the geometric approach to knot homologies, on the other. We study the relation between vortex counting in such two-dimensional ${\mathcal{N}=(2, 2)}$ supersymmetric field theories and the refined BPS invariants of the dual geometries. In certain cases, this counting can also be mapped to the computation of degenerate conformal blocks in two-dimensional CFT??s. Degenerate limits of vertex operators in CFT receive a simple interpretation via geometric transitions in BPS counting.     

Fullerene C<Subscript>70</Subscript> Triplet Zero-Field Splitting Parameters Revisited by Light-Induced EPR at Thermal Equilibrium

Continuous-wave (CW) electron paramagnetic resonance (EPR) and echo-detected (ED) EPR spectra of triplet state of fullerene C₇₀ in molecular glasses of decalin, o-terphenyl and toluene, and in polymethylmethacrylate polymer were obtained under continuous light illumination. Temperature was high enough so that the EPR spectra corresponded to thermal equilibrium between the spin sublevels. The comparison of CW EPR and ED EPR data has shown that pseudorotation in the ³C₇₀ frame does not remarkably affect deriving the zero-field splitting (ZFS) D and E parameters from the EPR spectra. ³C₇₀ EPR spectra were simulated at 77 K fairly well using the distribution of the ZFS D and E parameters. These distributions may be caused by the inhomogeneity of the glassy matrix surrounding, which affects the Jahn–Teller distortions of ³C₇₀ molecules (D-strain and E-strain).     

Electron field emission properties of highly dense carbon nanotube arrays

In this paper, we have studied field emission properties of highly dense arrays of multi-walled carbon nanotubes (CNTs) used as cathodes in diode-type field emission devices with a phosphor screen. For the high-density CNT emitters it is demonstrated that the emission sites are located on the CNT-cathode edges, which is direct experimental evidence of the ‘edge effect’. The results of computer simulations (using ‘ANSYS Electromagnetic’ software) are presented to confirm the experimental data and to analyze the effect of patterning on the electric field distribution for high-density CNT arrays. It is shown that selective-area removal of nanotubes in the arrays leads to the formation of additional edges characterized by the high field enhancement factor and enhanced emission from the CNT cathodes. In addition, scanning probe microscopy techniques are employed to examine surface properties of the high-density CNT arrays. For CNT arrays of ‘short’ nanotubes, the work function distribution over the sample surface is detected using a scanning Kelvin microscopy method.     

New hexanuclear group 11 pyrazolate complexes: synthesis and photophysical features

The treatment of 2,2'-di(1,2-pyrazol-3-yl)-1,1'-binaphthyl with two equivalents of appropriate monovalent group 11 precursors in the presence of a base leads to a complete exchange of the pyrazole NH protons with M(+) cations. Structural characterisation of the copper(I) complex revealed a hexanuclear complex with a pelton-wheel-like arrangement of the binaphthyl unit. As indicated by their spectroscopic data, all three complexes are isostructural. The complexes show a complex fluorescence behaviour that can be partially related to the ligand system and also to the metal sites, as indicated by the position of the fluorescence peaks and their temperature dependence and lifetimes.     

Polyhedral Finsler spaces with locally unique geodesics

We study Finsler PL spaces, that is simplicial complexes glued out of simplices cut off from some normed spaces. We are interested in the class of Finsler PL spaces featuring local uniqueness of geodesics (for complexes made of Euclidean simplices, this property is equivalent to local CAT(0)). Though non-Euclidean normed spaces never satisfy CAT(0), it turns out that they share many common features. In particular, a globalization theorem holds: in a simply-connected Finsler PL space local uniqueness of geodesics implies the global one. However the situation is more delicate here: some basic convexity properties do not extend to the PL Finsler case.     

On exact recovery of sparse vectors from linear measurements

Let 1 ≤ k ≤ n < N. We say that a vector x ∈ ? ^N is k-sparse if it has at most k nonzero coordinates. Let Φ be an n × N matrix. We consider the problem of recovery of a k-sparse vector x ∈ ? ^N from the vector y = Φx ∈ ? ⁿ . We obtain almost-sharp necessary conditions for k, n, N for this problem to be reduced to that of minimization of the ?₁-norm of vectors z satisfying the condition y = Φz.     

The Composition Structure of Alternative and Malcev Algebras

We construct a polynomial of degree 5 from the associative nucleus (kernel) of the free alternative algebra. We show that this polynomial is of minimal degree. Using this polynomial, we obtain decompositions of the varieties of alternative and Malcev algebras.     

Influence of an intense pulsed electromagnetic field on nonresonant scattering of a photon by an electron for the nonrelativistic energy

The theory of nonresonant scattering of a photon by an electron in the field of an intense pulsed light wave is developed. The approximation when a pulse width is considerably greater than the characteristic time of wave oscillation is considered. The nonresonant kinematic region is determined. The general relativistic expression for the nonresonant cross-section is derived for the range of the external field intensities if η ₀ ? 1, η₀ ² ? 1 (see Eq. (12)) is valid. The obtained differential cross-section of the process has form of a sum over partial differential cross-sections. Each of them corresponds to the process with emission (absorption) of a certain number of wave photons. It is shown, that for nonrelativistic energy the cross-section summed over all possible partial processes differs considerably from the cross-section of Compton scattering if the external field is absent and may exceed the latter over than 200%.