Reduced expression of <Emphasis Type="Italic">TAC1</Emphasis>, <Emphasis Type="Italic">PENK</Emphasis> and <Emphasis Type="Italic">SOCS2</Emphasis> in <Emphasis Type="Italic">Hcrtr-2</Emphasis> mutated narcoleptic dog brain

Background  

Narcolepsy causes dramatic behavioral alterations in both humans and dogs, with excessive sleepiness and cataplexy triggered by emotional stimuli. Deficiencies in the hypocretin system are well established as the origin of the condition; both from studies in humans who lack the hypocretin ligand (HCRT) and in dogs with a mutation in hypocretin receptor 2 (HCRTR2). However, little is known about molecular alterations downstream of the hypocretin signals.     

The determination of <Emphasis Type="Italic">α</Emphasis><Subscript><Emphasis Type="Italic">S</Emphasis></Subscript> from <Emphasis Type="Italic">τ</Emphasis> decays revisited

We revisit the determination of α _S (m _τ ²) using a fit to inclusive τ hadronic spectral moments in light of (1) the recent calculation of the fourth-order perturbative coefficient K ₄ in the expansion of the Adler function, (2) new precision measurements from BABAR of e⁺e⁻ annihilation cross sections, which decrease the uncertainty in the separation of vector and axial-vector spectral functions, and (3) improved results from BABAR and Belle on τ branching fractions involving kaons. We estimate that the fourth-order perturbative prediction reduces the theoretical uncertainty, introduced by the truncation of the series, by 20% with respect to earlier determinations. We discuss to some detail the perturbative prediction of two different methods: fixed-order perturbation theory (FOPT) and contour-improved perturbative theory (CIPT). The corresponding theoretical uncertainties are studied at the τ and Z mass scales. The CIPT method is found to be more stable with respect to the missing higher order contributions and to renormalization scale variations. It is also shown that FOPT suffers from convergence problems along the complex integration contour. Nonperturbative contributions extracted from the most inclusive fit are small, in agreement with earlier determinations. Systematic effects from quark-hadron duality violation are estimated with simple models and found to be within the quoted systematic errors. The fit based on CIPT gives α _S (m _τ ²)=0.344±0.005±0.007, where the first error is experimental and the second theoretical. After evolution to M _Z we obtain α _S (M _Z ²)=0.1212±0.0005±0.0008±0.0005, where the errors are respectively experimental, theoretical and due to the evolution. The result is in agreement with the corresponding N³LO value derived from essentially the Z width in the global electroweak fit. The α _S (M _Z ²) determination from τ decays is the most precise one to date.     

Dual properties of orthogonal polynomials of discrete variables associated with the quantum algebra <Emphasis Type="Italic">U</Emphasis><Subscript><Emphasis Type="Italic">q</Emphasis></Subscript>(<Emphasis Type="Italic">su</Emphasis>(2))

We show that for every set of discrete polynomials y _n (x(s)) on the lattice x(s), defined on a finite interval (a, b), it is possible to construct two sets of dual polynomials z _k (ξ(t)) of degrees k = s-a and k = b-s-1. Here we do this for the classical and alternative Hahn and Racah polynomials as well as for their q-analogs. Also we establish the connection between classical and alternative families. This allows us to obtain new expressions for the Clerbsch-Gordan and Racah coefficients of the quantum algebra U _q (su(2)) in terms of various Hahn and Racah q-polynomials. Dedicated to the memory of our teacher and friend Arnold F. Nikiforov (18.11.1930–27.12.2005).     

A general <Emphasis Type="Italic">Z</Emphasis>-scan theory

A novel Z-scan theory based on the solution of the nonlinear paraxial wave equation, completed by the Huygens–Fresnel principle is introduced. This theory is valid for the general case, i.e. for thick samples and large nonlinearities including both nonlinear refraction and absorption. In both limiting cases of thin sample and weak nonlinearity, predictions of this model are in good agreement with theories not using parabolic approximation for the beam profile. It is shown that the widely used parabolic approximation leads to inadequate results when evaluating Z-scan measurements.     

Glueballs,gluerings, and gluestars in the <Emphasis Type="Italic">d</Emphasis> = 2 + 1 <Emphasis Type="Italic">SU</Emphasis>(<Emphasis Type="Italic">N</Emphasis>) gauge theory

The 3d gluodynamics which governs the large-T quark—gluon plasma is studied in the framework of the field correlator method. Field correlators and spacial string tension are derived through the gluelump Green’s functions. The glueball spectrum is calculated both in C = −1 as well as in C = +1 sectors, and multigluon bound states in the form of “gluon rings” and “gluon stars” are computed explicitly. Good overall agreement with available lattice data is observed. The text was submitted by the author in English.     

Little Higgs model effects in <Emphasis Type="Italic">γγ</Emphasis> → <Emphasis Type="Italic">γγ</Emphasis>

Though the predictions of the standard model (SM) are in excellent agreement with experiments, there are still several theoretical problems associated with the Higgs sector of the SM, where it is widely believed that some new physics will take over at the TeV scale. One beyond the SM theory which resolves these problems is the Little Higgs (LH) model. In this work we have investigated the effects of the LH model on γγ → γγ scattering [1].      

GaSe<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript><Emphasis Type="Italic">S</Emphasis><Subscript><Emphasis Type="Italic">x</Emphasis></Subscript> solid solutions

The most probable parameters of the pure, doped, and mixed GaSe_1−xS_x (x ≤ 0.4) crystals (solid solutions) are presented together with the results of investigations of their crystal structure and defects, optical and mechanical properties, and damage thresholds. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 35–40, June, 2007.     

A <Emphasis Type="Italic">CR</Emphasis>-manifold in general position as an {<Emphasis Type="Italic">e</Emphasis>}-structure

In the paper, it is proved that a “generic” CR-structure is reduced to an {e}-structure. Using the invariant frames obtained as a result of this reduction (an analog of the Darboux frame of classical differential geometry), we give a simple proof of an analog of the Vitushkin theorem on the extension of a germ for a rather broad class of real submanifolds of complex spaces. Partially financially supported by the RFBR grants nos. 05-01-0981 and NSh-2040.2003.1.     

<Emphasis Type="Italic">X</Emphasis>(3): An exactly separable <Emphasis Type="Italic">γ</Emphasis>-rigid version of the <Emphasis Type="Italic">X</Emphasis>(5) critical point symmetry

A γ-rigid version (with γ = 0) of the X(5) critical point symmetry is constructed. The model, to be called X(3) since it is proved to contain three degrees of freedom, utilizes an infinite well potential, is based on exact separation of variables, and leads to parameter-free (up to overall scale factors) predictions for spectra and B(E2) transition rates which are in good agreement with existing experimental data for ¹⁷²Os and ¹⁸⁶Pt. An unexpected similarity of the β ₁ bands of the X(5) nuclei ¹⁵⁰Nd, ¹⁵²Sm, ¹⁵⁴Gd, and ¹⁵⁶Dy to the X(3) predictions is observed. The text was submitted by the authors in English.     

<Emphasis Type="Italic">Y</Emphasis> and <Emphasis Type="Italic">Z</Emphasis> luminescence of polycrystalline cadmium telluride

The properties of polycrystalline CdTe with a grain size of 5–30 μm have been investigated using the microphotoluminescence methods of spectral analysis and topography. This material has been prepared by direct synthesis in a vapor flow of components at a low temperature. The dominance of the Y and Z bands in the spectra reflects a nonequilibrium character of the crystallization processes. The superlinear dependences of the luminescence intensity on the level of the band-to-band excitation indicate the exciton nature of the corresponding transitions. The activation energies for temperature quenching of luminescence in the temperature range T = 100–150 K are found to be 120 meV for the Y luminescence and 180 meV for the Z luminescence, which correspond to the dissociation of excitons bound to defects with the transition of charge carriers to the conduction and valence bands. The monochromatic topography data indicate that Y and Z defects have different material bases.     

<Emphasis Type="Italic">SU</Emphasis><Subscript><Emphasis Type="Italic">L</Emphasis></Subscript>(4)×<Emphasis Type="Italic">U</Emphasis>(1) model for electroweak unification and sterile neutrinos

Some of the basic problems in neutrino physics, such as new energy scales, the enormous gap between the neutrino masses and the lightest charged fermion mass, and the possible existence of sterile neutrinos in the eV mass range are studied in the local gauge group SU _L (4)×U(1) for electroweak unification, which does not contain fermions with exotic electric charges. It is shown that the neutrino mass spectrum can be decoupled from that of the other fermions. The further normal seesaw mechanism for neutrinos, with right-handed neutrino Majorana masses of order M≫M _weak as well a new eV-scale can be accommodated. The eV-scale seesaw may manifest itself in experiments like the Liquid Scintillation Neutrino Detector (LSND) and MiniBooNE (MB) experimental results and future neutrino experiments.     

<Emphasis Type="Italic">N</Emphasis> = 4 supersymmetric Eguchi-Hanson sigma model in <Emphasis Type="Italic">d</Emphasis> = 1

We show that it is possible to construct a supersymmetric mechanics with four supercharges possessing not conformally flat target space. A general idea of constructing such models is presented. A particular case with Eguchi-Hanson target space is investigated in detail: we present the standard and quotient approaches to get the Eguchi-Hanson model, demonstrate their equivalence, give a full set of nonlinear constraints, study their properties and give an explicit expression for the target space metric. Presented at the International Colloquium “Integrable Systems and Quantum Symmetries”, Prague, 16–18 June 2005.     

The <Emphasis Type="Italic">Φ</Emphasis>→K<Superscript>0</Superscript>¯<Emphasis Type="Italic">γ</Emphasis> decay

The scalar contributions to the radiative decay φ→K ⁰ˉ⁰ γ are studied within the framework of the Linear Sigma Model (LσM). Theoretical predictions for the associated subprocesses φ→f ₀ γ and φ→a ₀ γ as well as the ratio φ→f ₀ γ/a ₀ γ are also given.     

Mean Field Magnetic Phase Diagrams for the Two Dimensional <Emphasis Type="Italic">t</Emphasis> — <Emphasis Type="Italic">t</Emphasis>′ — <Emphasis Type="Italic">U</Emphasis> Hubbard Model

We study the ground state phase diagram of the two dimensional t — t′ — U Hubbard model concentrating on the competition between antiferro-, ferro-, and paramagnetism. It is known that unrestricted Hartree–Fock- and quantum Monte Carlo calculations for this model predict inhomogeneous states in large regions of the parameter space. Standard mean field theory, i.e., Hartree–Fock theory restricted to homogeneous states, fails to produce such inhomogeneous phases. We show that a generalization of the mean field method to the grand canonical ensemble circumvents this problem and predicts inhomogeneous states, represented by mixtures of homogeneous states, in large regions of the parameter space. We present phase diagrams which differ considerably from previous mean field results but are consistent with, and extend, results obtained with more sophisticated methods. PACS: 71.10.Fd, 05.70.Fh, 75.50.Ee     

Super <Emphasis Type="Italic">D</Emphasis>-Differentiation for <Emphasis Type="Italic">R</Emphasis><Superscript> ∞ </Superscript>-Supermanifolds

The concept of ‘D-Differentiation’, which, in the context of smooth manifolds, generalises Lie and covariant differentiation, is extended to R ^∞-supermanifolds under the name of ‘Super D-Differentiation’. This is done by defining new (non-linear) mappings, called ‘μ-mappings’ and by relating their non-linearity to the Leibniz rule that a derivation must satisfy when it acts on a tensor product. The resulting axiomatics, which is basis-independent and coordinate-free, is then expressed in a general basis (not necessarily holonomic). Super Lie and Super covariant differentiation are, amongst others, special cases of Super D-Differentiation. In particular, the transformation rules for the connection coefficients and the commutation coefficients of non-holonomic bases are obtained. These special cases are found to be in agreement with the DeWitt Super covariant and Super Lie derivatives.