A novel method for extracting oscillator strength of select rare-earth ion optical transitions in nanostructured dielectric materials

A new technique to obtain the oscillator strength of select rare-earth optical transitions in nanostructured dielectric materials (nanophosphors) is presented. It is based on the experimentally observed nanophosphor lifetime dependence on the embedding medium. A constant oscillator strength and parity-allowed electric dipole transitions of the RE ion emission are assumed. The oscillator strength is obtained from the slope of the 1/τ_ij vs. n(n²+2)² plot, where τ_ij is the radiative lifetime of transition between states i and j, and n is the index of refraction of the embedding medium. The use of the technique is illustrated for the Y ₂SiO₅:Ce nanophosphor.     

Harness Processes and Non-Homogeneous Crystals

We consider the Harmonic crystal, a measure on with Hamiltonian H(x)=∑ _i,j J _i,j (x(i)−x(j))²+h∑ _i (x(i)−d(i))², where x, d are configurations, x(i), d(i)∈ℝ, i,j∈ℤ ^d . The configuration d is given and considered as observations. The ‘couplings’ J _i,j are finite range. We use a version of the harness process to explicitly construct the unique infinite volume measure at finite temperature and to find the unique ground state configuration m corresponding to the Hamiltonian.     

On asymptotic behaviour of four spin correlation functions in a linear chain of spins

Second and fourth moments of the four spin frequency correlation functions S^Z_i(t) S^Z_i+1 (t) S^Z_j+1 〉_k,ω and 〈S^x_i(t) S^z_i+1 (t) S^x_jS^z_j+1 〉_kω have been calculated in the high temperature limit for an arbitrary spin with an isotropic Heisenberg Hamiltonian.     

SUSY-QCD corrections to scalar quark pair production in e+e− annihilation

We calculate the supersymmetric O(α_s) QCD corrections to the cross section e⁺e⁻ → q̃_iq̃_j (i, j = 1,2) within the Minimal Supersymmetric Standard Model. We pay particular attention to the case of the left-right squark mixing and to the renormalization of the mixing angle. The corrections due to gluino exchange turn out to be smaller than those due to gluon exchange, but they can be significant at higher energies, even for a gluino mass of a few hundred GeV.     

Limits on the impact parameters occuring in specific K−p interactions at 8.25 GeV/c

We have determined a lower limit of the impact parameter for the reactions associated with the channels K^?p → K^?pπ⁺π^?K^?p → λπ⁺π^?π⁰. The limit was found to be highest for the diffractive parts of the first channel (～ 0.52 fm) and smallest for the forward Λ in the second channel (～0.21 fm).We have also examined the elements of the inverse correlation matrix for the transfer: the off-diagonal elements are small (consistent with zero) for n = 4?7 body products. The log 〈Q_i·Q_j〉 of the correlation matrix as a function of $\text{Гi?jГ}$ falls on a straight line and the eigenvalue λ₁ of the transverse momentum transfer eigenfunction was found to increase slightly from ～0.6 for 4-body to ～0.7 for 7-body products. The 〈cosφ_ij〉 of the Q_i, Q_j shows similar behaviour to the 〈Q_i·Q_j〉     

A phenomenological theory of possible sequences of ferrotoroidal phase transitions in boracites

A phenomenological theory of the sequence of two second-order phase transitions with close temperatures is considered; such transitions occur in the Ni-Br boracite. The thermodynamic potential is written as a function of polarization P _i, magnetization M _i, and toroidal moment T _i vectors and fields E _i and H _i; T _i is treated as an order parameter. It is assumed that only one coefficient of T _i ² passes through zero as T decreases. The possibility of a sequence of two proper ferrotoroidal phase transitions along the T ₁ and T ₂ components is demonstrated. Spontaneous T _i, P _i, and M _i vector values and equations for susceptibility tensors (dielectric χ _ij = dP _i/dE _j, magnetic k _ij = dM _i/dH _j, and magnetoelectric α_ij = dP _i/dH _j = dM _j/dE _i) were obtained for three phases. Some of these values have well-defined anomalies in the vicinity of transitions. All possible sequences of ferrotoroidal phase transitions in boracites are considered. Depending on two potential coefficient values, these sequences may consist of one, two, or three such transitions.     

Collective plasma corrections to thermonuclear reaction rates in dense plasmas

General kinetic equations are derived for nuclear reactions in dense plasmas by taking into account first-order collective plasma effects. We show that, apart from the corrections proportional to the product of the charges Z _i and Z _j of two reacting nuclei i and j, new corrections comparable in magnitude and proportional to the squares of the nuclear charges Z _i ² and Z _j ² arise. The Salpeter corrections [1] to the nuclear reaction probabilities due to the plasma screening of the interaction potential are shown to be at least a factor of r/d (r is the nuclear size and d is the Debye screening length) smaller than those assumed previously. These are zero in the approximation where the terms of order r/d are disregarded. The correlation corrections proportional to Z _iZ_j have a different physical meaning than those in [1], can have a different sign, and arise for reactions with zero Salpeter corrections. For the correlation corrections that substitute for the previously used Salpeter corrections, strong correlations are difficult to describe analytically. The interpolation formulas between weak and strong Salpeter screenings previously used in many astrophysical applications are inapplicable, because the interpolation formulas between weak and strong correlations cannot yet be obtained. We found a new type of corrections that are proportional to the squares of the charges of reacting nuclei. These are attributable to a change in the collective electrostatic self-energy of the plasma system during nuclear reactions. Plasma corrections for the hydrogen-cycle nuclear reactions are numerically calculated for the temperature, density, and abundances in the solar interior.     

Head-on collision of dust-ion-acoustic solitons in electron-dust-ion quantum plasmas

In this paper, we study the head-on collision between two dust-ion-acoustic (DIA) solitons in quantum electron-dust-ion plasma. Using the extended Poincaré–Lighthill–Kuo (PLK) method, we obtain the Korteweg–de Vries (KdV) equations, the phase shifts and the trajectories after the head-on collision of the two DIA solitons. We investigate the effect of quantum diffraction parameters for electrons and ions (H _e, H _i), the Fermi temperature ratio (σ) and the dust charged number density (n _d0) on the phase shifts. Different values of μ?=?z _d0(n _d0/n _i0) and μ _d?=?z _d0(m _i/m _d) are taken to discuss the effects on phase shifts, where z _d0 denotes the dust charge number, n _j0 represents the equilibrium number density and m _j is the mass of the jth species (j?=?e, i, d for electrons, ions and dust particles, respectively). It is observed that the phase shifts are significantly affected by the plasma parameters.     

Integrals involving Euler-Bernoulli flexure and Saint-Venant torsion eigenfunctions

Tables of the integral ∝₀^LX_i(x)θ_j(x) dx where X_i(x) and θ_j(x) are Euler-Bernoulli and Saint-Venant eigenfunctions respectively are presented for 1?i, j?5 for beams with combinations of clamped, pinned and free ends. These integrals arise in application of the Rayleigh-Ritz and Ritz-Galerkin methods to free vibration and dynamic stability problems involving coupled torsion and bending.     

Multilevel systems and generalizations of the superalgebra

A new approach to constructing the various generalizations of the one-dimensional supersymmetric quantum mechanics is proposed, including the parasupersymmetric quantum mechanics constructed by Rubakov and Spiridonov as the special case. In particular, we derive the generalized superalgebra, which possesses the features both of the familiar superalgebra and of the parasuperalgebra. Namely, the generalized supercharges Q_i ^± and the Hamiltonian H forms the generalized superalgebra, where Q_i ^±2=0 (as for ordinary superalgebra), but the triple products of generalized supercharges obey the relations Q₁ ⁺Q_j ^–Q_j ⁺=Q_i ⁺H (i, j=1, 2) and Q_i ⁺Q_i ^–Q_j ⁺=(1/4)kQ_i ⁺, Q_i ⁺Q_i ^–Q_j ⁺=(1/4)kQ_i ⁺(i, j=1, 2; ij) (analogous to the parasuperalgebra). Furthermore, the generalized supercharges are conserved, i.e. [H, Q_i ^±]=0.Presented at the International Workshop on Squeezed and Correlated States, Moscow, December 3–7, 1990.     

Measurement of the D0, D+ and Ds+ meson lifetimes at √s = 10.58 GeV

We have measured the lifetimes of the D⁰, D⁺ and D_s⁺ mesons with data from the CLEO detector. We find τ_D⁰ = (5.0 ± 0.7 ± 0.4) × 10⁻¹³s, τ_D⁺ = (11.4 ± 1.6 ± 0.7) × 10⁻¹³s and τ_Ds⁺ = (4.7 ± 2.2 ± 0.5) × 10⁻¹³s, giving lifetime ratios τ_D⁺/τ_D⁰ = 2.3 ± 0.5 and τ_Ds⁺/τ_D⁰ = 0.9 ± 0.5.     

Ion conduction in proton- and related defect (super) ionic conductors: Mechanical,electronic and structure parameters

We find the relationships among optical dielectric constant ε_∞, activation energy E_ac, averaged atomic mass per a formula unit, ∑_jm_j / N, volume V and transition temperature T_c for various type ion conductors with forms of E_ac = α / (ε_∞ ? β), E_ac = A₀ + δ / [(∑_jm_j / N) ? d], E_ac = A_v / V^2/3, and ln(T_c) = g ? hln(∑_jm_j), where α, β, δ, A₀, d, A_v, g and h are constants depending on the kinds of conduction elements. We derive those proportional forms from a simple equation of motion under the assumption of ion hopping assisted by enhanced vibration displacement of host lattice. The enhancement is induced from the large fourth-order term of the host lattice potential originating from the electronic shielding effect of Coulomb force, heavy atomic mass of constituent ion, and volume expansion under the long-range periodicity of crystal structure. This mechanism is ascertained from characteristic phenomena of various kinds of conduction elements. For impurity-type H⁺-ion or defect conductor, the proportional form is shifted from that of superionic conductor because of weakened effect of host lattice vibration mode on H⁺-ion or O-ion defect. Photo-induced spectra of mobile ion in AgCl are understood, and a small quantum effect of H⁺ -ion is suggested.     

Degree Complexity of Birational Maps Related to Matrix Inversion

For a q × q matrix x = (x _{i, j} ) we let ${J(x)=(x_{i,j}^{-1})}For a q × q matrix x = (x _{i, j} ) we let J(x)=(x_i,j^-1){J(x)=(x_{i,j}^{-1})} be the Hadamard inverse, which takes the reciprocal of the elements of x. We let I(x)=(x_i,j)^-1{I(x)=(x_{i,j})^{-1}} denote the matrix inverse, and we define K=I°J{K=I\circ J} to be the birational map obtained from the composition of these two involutions. We consider the iterates Kⁿ=K°?°K{K^n=K\circ\cdots\circ K} and determine the degree complexity of K, which is the exponential rate of degree growth d(K)=lim_n?￥( deg(Kⁿ) )^1/n{\delta(K)=\lim_{n\to\infty}\left( deg(K^n) \right)^{1/n}} of the degrees of the iterates. Earlier studies of this map were restricted to cyclic matrices, in which case K may be represented by a simpler map. Here we show that for general matrices the value of δ(K) is equal to the value conjectured by Anglès d’Auriac, Maillard and Viallet.     

Untersuchung der Struktur desu-u-Kerns142Pr durch (α, n γ)- und (p,n γ)-Reaktionen und Bestimmung von Matrixelementen der effektiven Proton-Neutron-Restwechselwirkung

The structure of the odd-odd nucleus¹⁴²Pr has been studied at the Erlangen Tandem Van de Graaff accelerator by using the nuclear reactions¹³⁹La(α, nγ) and¹⁴²Ce(p, n γ). Neutron-gamma and gamma-gamma coincidence measurements have been performed. In the frame work of the shell model the low lying states up to energies of 400 keV can be described as two mixed multiplettsC _1i ^I ¦j′ _p ,j _n ;I>+C _2i ^I ¦j″ _p ,'j _n ; I> (i=1, 2;j′ _p =2d5/2,j″ _p =1g 7/2^?1 andj _n =2f 7/2). From a fit of experimentally determinedγ-branching ratios to theoretical transition probabilities we have derived the amplitudes of the wavefunctions. From these wavefunctions and the energies of states and configurations in¹⁴²Pr we have obtained matrixelements of the effective residualp, n-interaction.     

Covariance of light-front models: pair current

We compute the + component, i.e., j⁺=j⁰+j³, of the electromagnetic current of a composite spin-one two-fermion system for vanishing momentum transfer component q⁺=q⁰+q³. In particular, we extract the nonvanishing pair production amplitude on the light-front. It is a consequence of the longitudinal zero momentum mode, contributing to the light-front current in the Breit-frame. The covariance of the current is violated, if such pair terms are not included in its matrix elements. We illustrate our discussion with some numerical examples.     

Spectral methods and cluster structure in correlation-based networks

We investigate how in complex systems the eigenpairs of the matrices derived from the correlations of multichannel observations reflect the cluster structure of the underlying networks. For this we use daily return data from the NYSE and focus specifically on the spectral properties of weight W_ij=|C|_ij−δ_ij and diffusion matrices D_ij=W_ij/s_j−δ_ij, where C_ij is the correlation matrix and s_i=∑_jW_ij the strength of node j. The eigenvalues (and corresponding eigenvectors) of the weight matrix are ranked in descending order. As in the earlier observations, the first eigenvector stands for a measure of the market correlations. Its components are, to first approximation, equal to the strengths of the nodes and there is a second order, roughly linear, correction. The high ranking eigenvectors, excluding the highest ranking one, are usually assigned to market sectors and industrial branches. Our study shows that both for weight and diffusion matrices the eigenpair analysis is not capable of easily deducing the cluster structure of the network without a priori knowledge. In addition we have studied the clustering of stocks using the asset graph approach with and without spectrum based noise filtering. It turns out that asset graphs are quite insensitive to noise and there is no sharp percolation transition as a function of the ratio of bonds included, thus no natural threshold value for that ratio seems to exist. We suggest that these observations can be of use for other correlation based networks as well.     

Z 3-Graded exterior differential calculus and gauge theories of higher order

We present a possible generalization of the exterior differential calculus, based on the operator d such that d³=0, but d²0. The entities dx ⁱ and d² x ^k generate an associative algebra; we shall suppose that the products dx ⁱ dx ^k are independent of dx ^k dx ⁱ , while theternary products will satisfy the relation: dx ⁱ dx ^k dx ^m =jdx ^k dx ^m dx ⁱ =j ²dx ^m dx ^m dx ⁱ dx ^k , complemented by the relation dx ⁱ d² x ^k =jd² x ^k dx ⁱ , withj:=e^2i/3.We shall attribute grade 1 to the differentials dx ⁱ and grade 2 to the second differentials d² x ^k ; under the associative multiplication law the grades add up modulo 3.We show how the notion ofcovariant derivation can be generalized with a 1-formA so thatD:=d+A, and we give the expression in local coordinates of thecurvature 3-form defined as :=d² A+d(A ²)+AdA+A ³.Finally, the introduction of notions of a scalar product and integration of theZ ₃-graded exterior forms enables us to define the variational principle and to derive the differential equations satisfied by the 3-form . The Lagrangian obtained in this way contains the invariants of the ordinary gauge field tensorF _ik and its covariant derivativesD _i F _km .     

A sequence of two ferrotoroidal phase transitions in nickel-bromine boracite Ni3B7O13Br

The phenomenological theory of a sequence of two second-order phase transitions in Ni-Br boracite is presented. Two different components of the toroidal moment vector T _i are the order parameters of these transitions. Expressions are derived for the temperature dependences of the spontaneous values of T _i , polarization P _i , and magnetization M _i and the dielectric χ_ij=dP _i /dE _j , magnetic k _ij =dM _i /H _j , and magnetoelectric α _ij=dP _i /dH _j =dM _j /dE _i susceptibilities. Some of these susceptibilities display sharp temperature peaks in the vicinity of phase transitions.     

Tau decays into kaons

Predictions for semi-leptonic decay rates of theτ lepton into two meson final statesK ^?π⁰ v _τ, $\overline {K^0 } \pi - v_\tau $ ,K ⁰ K ^? v _τ, and three meson final statesK ^?π^? K ⁺ v _τ, $K^0 \pi ^ - \overline {K^0 } v_\tau $ ,K _sπ^? K _s v _τ,K _sπ^? K _L v _τ,K _Lπ^? K _L v _τ,K ^?π⁰ K ⁰ v _τ, π⁰π⁰ K ^? v _τ,K ^?π^?π⁺ v _τ, π^? K ⁰π⁰ v _τ are derived. The hadronic matrix elements are expressed in terms of form factors, which can be predicted by chiral Lagrangians supplemented by informations about all possible low-lying resonances in the different channels. Isospin symmetry relations among the different final states are carefully taken into account. The calculated branching ratios are compared with measured decay rates where data are available.     

Continuous time Black-Scholes equation with transaction costs in subdiffusive fractional Brownian motion regime

In this paper, we study the problem of continuous time option pricing with transaction costs by using the homogeneous subdiffusive fractional Brownian motion (HFBM) Z(t)=X(S_α(t)), 0<α<1, here dX(τ)=μX(τ)(dτ)^2H+σX(τ)dB_H(τ), as a model of asset prices, which captures the subdiffusive characteristic of financial markets. We find the corresponding subdiffusive Black-Scholes equation and the Black-Scholes formula for the fair prices of European option, the turnover and transaction costs of replicating strategies. We also give the total transaction costs.