Stabilizer of a function in the gage group

It is proved that, for the dimension d of the stabilizer of an analytic function z(x, y) in the gage pseudogroup G = {z(x, y) → c(z(a(x), b(y))}, there are precisely four possibilities: (1) d = ∞ and the complexity of z is zero, (2) d = 3 and the complexity of z is equal to one, (3) d = 1 and z is equivalent the function r(x + y) ? x of complexity two, (4) d = 0 in all remaining cases.     

Exact asymptotic form for the β function in quantum electrodynamics

It is shown that the asymptotic form of the Gell-Mann-Low function in quantum electrodynamics can be determined exactly: β(g) = g for g → ∞, where g = e ² is the running fine-structure constant. This solves the problem of electrodynamics at small distances L (for which dependence g ∞ L ^?2 holds) and completely eliminates the problem of “zero charge.”     

<Emphasis Type="Italic">η</Emphasis><Superscript>7</Superscript>Li Scattering in the <Emphasis Type="Italic">αt</Emphasis>-Cluster Model

The cross sections for elastic and inelastic η-meson scattering on ⁷Li nuclei are obtained on the basis of the αt-cluster representation of the target nucleus. The experimentally known values of the parameters of elastic ηα and αt scattering are used in exactly solving three-body Faddeev equations with separable two-body potentials. The η⁷Li elastic-scattering scattering length found from respective calculations is a_η7Li = ?0.310 ? i0.198 fm.     

Global transformations preserving Sturm–Liouville spectral data

We show the existence of a real analytic isomorphism between the space of the impedance function ρ of the Sturm–Liouville problem ?ρ ^?2(ρ ² f′)′ +uf on (0, 1), where u is a function of ρ, ρ′, ρ″, and that of potential p of the Schrödinger equation ?y″ +py on (0, 1), keeping their boundary conditions and spectral data. This mapping is associated with the classical Liouville transformation f → ρf, and yields a global isomorphism between solutions of inverse problems for the Sturm–Liouville equations of the impedance form and those of the Schrödinger equations.     

Two-photon production of vector resonance in <Emphasis Type="Italic">e</Emphasis><Superscript>+</Superscript><Emphasis Type="Italic">e</Emphasis><Superscript>−</Superscript> collisions

A parameterization of the amplitude of the two-photon production of 1⁺⁺ and 1^?+ vector resonances V in the e ⁺ e ^? → e ⁺ e ^? V reaction has been obtained. The differential (in momentum transfer) scattering cross section dσ/dQ ² has been found for this reaction in the equivalent-photon approximation. The result obtained is model-independent.     

Resolvent Expansion and Time Decay of the Wave Functions for Two-Dimensional Magnetic Schrödinger Operators

We consider two-dimensional Schrödinger operators H(B, V) given by Eq. (1.1) below. We prove that, under certain regularity and decay assumptions on B and V, the character of the expansion for the resolvent (H(B, V) ? λ)^?1 as λ → 0 is determined by the flux of the magnetic field B through \({\mathbb{R}^2}\) . Subsequently, we derive the leading term of the asymptotic expansion of the unitary group e ^{?i t H(B, V)} as t → ∞ and show how the magnetic field improves its decay in t with respect to the decay of the unitary group e ^{?i t H(0, V)}.     

Multicomponent <Emphasis Type="Italic">n</Emphasis>-(Bi,Sb)<Subscript>2</Subscript>(Te,Se,S)<Subscript>3</Subscript> solid solutions with different atomic substitutions in the Bi and Te sublattices

The thermoelectric properties of n-Bi_{2 ? x} Sb _x Te_{3 ? y ? z} Se _y S _z solid solutions are studied in the temperature range 300–550 K. It is shown that an increase in the parameter β determining the figure-of-merit Z of the material is observed in compositions with the optimally related effective mass of the density of states m/m ₀, the carrier mobility μ₀, and the lattice thermal conductivity κ _L . Within the temperature range 300–350 K, the parameter β and the figure-of-merit Z are found to increase in solid solutions with substitutions in both bismuth telluride sublattices Bi → Sb and Te → Se, S (x = 0.16, y = z = 0.12) for optimum electron concentrations. An increase in the electron concentration and substitutions of atoms only in the tellurium sublattice bring about an increase in the β parameter and the value of Z at higher temperatures. Within the range 350–450 K, the parameters β and Z are observed to increase in a solid solution with a low content of substituted atoms in the tellurium sublattice Te → Se, S for y = z = 0.09 and, at higher temperatures up to 550 K, in compositions with tellurium substituted by selenium only, with increasing content of substituted atoms.     

Mechanisms of ionization of <Emphasis Type="Italic">F</Emphasis><Subscript>2</Subscript>-centers in laser media on the basis of LiF crystals

F₂ color centers with a superhigh concentration (5000-cm^–1 absorption coefficient at 450 nm) were formed by high-density electron beams in a layer of LiF crystals of micrometer thickness. The F₂-centers excited by high-power nanosecond wide-band optical pulses (the “soft” pumping regime) efficiently amplified the laser radiation and showed high stability under these conditions. A low stability of F₂-centers to laser radiation (the “hard” excitation regime) is explained by the dissociation of (F ₂ ⁺ , F^–) pairs induced by two-step ionization of F₂-centers: (2hν > 4.5 eV) → F₂ → (F₂)* → F ₂ ⁺ + e; F + e → F^–; F ₂ ⁺ + F^– → 3F.     

Spectroscopy of optical centers of Eu<Superscript>3+</Superscript> ions in partially stabilized and stabilized zirconium crystals

The structure of the optical centers of Eu³⁺ ions in tetragonal (ZrO₂)_1–x–y (Y₂O₃) _x (Eu₂O₃) _y (х = 2.7–3.6; y = 0.1) and cubic (ZrO₂)_1–x–y (Y₂O₃) _x (Eu₂O₃) _y (х = 8–38; y = 0.1–0.5) crystals of solid solutions on the basis of zirconium dioxide is studied using the methods of optical and Raman-scattering spectroscopy. Characteristic optical centers of Eu³⁺ ions with different crystalline environments are revealed in the above compounds.     

Elastic Deuteron Scattering on the <Superscript>12</Superscript>C Nucleus within a Three-Body Model

The formalism developed earlier for elastic pd scattering on the basis of Glauber theory with allowance for a total spin dependence is modified by replacing pN amplitudes by amplitudes for N¹²C scattering and is applied to elastic deuteron scattering on the ¹²C nucleus. The amplitudes for elastic N¹²C scattering are obtained within the optical model. Respective numerical calculations performed at the kinetic deuteron-beam energy of 270 MeV lead to results that agree well with data on the differential cross section for d¹²C scattering into the forward hemisphere, but the calculated spin observable A _y ^d agrees with experimental data only qualitatively.     

Asymptotic properties of regge trajectories and elastic pseudoscalar-meson scattering on nucleons at high energies

A phenomenological Regge-eikonal model featuring nonlinear monotonic parametrizations of vacuum Regge trajectories, where their asymptotic behavior in the perturbative sector is taken explicitly into account, is proposed for describing the elastic diffractive scattering of light pseudoscalar mesons on nucleons. In analyzing available experimental data on angular distributions, it is shown that, at collision energies in the region √s > 13 GeV, the diffraction pattern of the processes π ^± p → π ^± p and K ^± p → K ^± p at low momentum transfers can be described qualitatively by using the same phenomenological approximations to vacuum Regge trajectories as in the case of nucleon-nucleon scattering. This fact is indicative of the possibility of explicitly relating Regge phenomenology of various hadron-hadron processes to fundamental results obtained within QCD.     

Asymptotics of Self-similar Solutions to Coagulation Equations with Product Kernel

We consider mass-conserving self-similar solutions for Smoluchowski’s coagulation equation with kernel K(ξ,η)=(ξη) ^λ with λ∈(0,1/2). It is known that such self-similar solutions g(x) satisfy that x ^?1+2λ g(x) is bounded above and below as x→0. In this paper we describe in detail via formal asymptotics the qualitative behavior of a suitably rescaled function h(x)=h _λ x ^?1+2λ g(x) in the limit λ→0. It turns out that \(h \sim 1+ C x^{\lambda/2} \cos(\sqrt{\lambda} \log x)\) as x→0. As x becomes larger h develops peaks of height 1/λ that are separated by large regions where h is small. Finally, h converges to zero exponentially fast as x→∞. Our analysis is based on different approximations of a nonlocal operator, that reduces the original equation in certain regimes to a system of ODE.     

Symmetry energy of the nucleus in the relativistic Thomas–Fermi approach with density-dependent parameters

We introduce an inhomogeneous term, f(t,x), into the right-hand side of the usual Burgers equation and examine the resulting equation for those functions which admit at least one Lie point symmetry. For those functions f(t,x) which depend nontrivially on both t and x, we find that there is just one symmetry. If f is a function of only x, there are three symmetries with the algebra s l(2,R). When f is a function of only t, there are five symmetries with the algebra s l(2,R) ⊕ _s 2A ₁. In all the cases, the Burgers equation is reduced to the equation for a linear oscillator with nonconstant coefficient.     

Study of background processes with the formation of neutrons in nuclear reactions in the energy range of 26–32 kev

The nature of background processes accompanying astrophysical nuclear reactions induced by hydrogen, helium, and neon ions in deuterated targets with small cross sections has been studied in calculations and experiments. The experiments have been performed at a Hall pulsed plasma accelerator in the ion energy range of 26–32 keV. The yield of background neutrons and γ-quanta with energies below 4 MeV in the proton-induced D(p, γ)³He reaction is primarily due to the presence of a natural impurity of gaseous deuterium in gaseous hydrogen and the chain of D(D, ³He)n → (n, γ) or (n, n'γ) reactions. A small contribution comes from the chain of D(¹H, ¹H)D → D(D, ³He)n → (n, γ) or (n, n'γ) reactions. It has been shown that background neutrons and γ-quanta from the D(4He, γ)6Li reaction are entirely due to the chain of D(⁴He, ⁴He)D → D(D, ³He)n → (n, γ) or (n, n'γ) reactions. It has been shown that the yield of neutrons and γ-ray photons detected at the interaction of neon ions with deuterated targets is also entirely due to the chain of elastic- scattering reactions of neon ions on deuterons in the target and to subsequent inelastic processes of interaction of deuterons accelerated at elastic scattering with other deuterons of the target. The main contribution to the yields of background neutrons and γ-quanta comes from doubly charged neon ions. The main conclusion is that the explanation of the yield of neutrons and γ-quanta at the interaction of hydrogen, helium, and neon ions with deuterated targets does not require “exotic” theoretical models.     

<Emphasis Type="Italic">η</Emphasis> Physics with the crystal ball detector

The experimental results obtained with the Crystal Ball detector for the physics of η-meson decays are reviewed. The η → 3π ⁰ Dalitz plot slope and the η → π ⁰ γγ decay width are measured with a high accuracy using 3 × 10⁷ η decays. Upper limits on the η → 3γ, η → 2π ⁰ γ, and η → 3π ⁰ γ C-forbidden decays are found. The sensitivity of these upper limits to C violation is estimated. An upper limit on the η → 4π ⁰ C P-forbidden decay is found for the first time and the sensitivity of this value to C P violation is estimated.     

Annihilation semileptonic decays of <Emphasis Type="Italic">B</Emphasis> mesons and the model dependence on the choice of the distribution amplitude

The rare semileptonic B-meson decay B → ??⁺?^? is considered. The partial decay rate integrated over the 1–8 GeV² interval of the dilepton invariant mass squared is computed with a 10% systematic uncertainty arising from the model dependence of the distribution amplitude. The purely perturbative contribution to the decay probability amounts to ? ～ 10^?12, which suggests that the LHC experiments could observe the B → ??⁺?^? decay in a few years of data taking.