On Methods of Constructing Sets of Mutually Orthogonal Latin Squares Using a Computer. I

This paper deals with the problem of finding sets of mutually orthogonal Latin squares of order 4t (where 4t – 1 is a prime power) based on orthogonal mappings of a group. For the group G we take the module G(2, 2t) whose elements are vectors (a ₁, a ₂,) where a ₁ is a residue class (mod 2) and a ₂ is a residue class (mod 2t), the addition being defined by (a ₁, a ₂) + (b ₁, b ₂) = (c ₁, c ₂) where a ₁ + b ₁ = C ₁ (mod 2) and a ₂ + b ₂ = c ₂ (mod 2t). Then the search for orthogonal mappings is materially simplified by using a configuration based on the balanced incomplete block design with parameters v = b = 4t – 1, r = k = 2t – 1, λ = t – 1. Using this method, two sets of five mutually orthogonal Latin squares of order 12 were obtained.     

A linear representation of the diffusion of solvents into insoluble polymers

The amount,q, of a solvent taken up by a sample of an insoluble polymer during a time,t, can be represented accurately by the relationq=t/(at + b), which has a very simple linear equivalent: (t/q)=at+b, wherea andb are constants. The same behaviour is also shown by the exchange of ions in an ion-exchange resin and in the case of a swell process, whereq may be measured as a volume increase. The kinetic relationq=k(Q−q) ², where Q=a⁻¹ andk=Q ⁻²b⁻¹, is compared with Fick's first law of diffusion and the dependence of the diffusion coefficient and the concentration gradient onq is discussed.     

A New Balanced Design for Eighteen Varieties

A new balanced incomplete block design for v = |8, b = 5|, r = 17, k = 6. λ = 5 is presented. The design is resolvable and can be split into useful partially balanced suhdesigns. When these designs are used for the 2 × 3² factorial experiment they all have factorial structure.     

Optical absorption and photoconductivity in gamma-irradiated zinc selenide crystals

The possibility of radiation-induced enhancement of photoconductivity (σ_ph) in crystalline zinc selenide (ZnSe) has been studied. The electron concentration in the initial ZnSe:O crystal was N _Eg = 1.26 × 10¹⁶ cm⁻³ as determined from the optical density of the sample at E _g = 2.58 eV. The irradiation of the ZnSe:O crystal by gamma-photons from ⁶⁰Co source to a dose of 10⁶ Gy leads to the creation of five new energy levels (Γ_6v, 5.76 eV; L _1.3v, 4.85 eV; Zn_i, 3.34 eV; O_Se, 3.13 eV; X, 2.72 eV), a decrease in the electron concentration to N _Eg = 0.63 × 10¹⁶ cm⁻³, and a twofold increase in σ_ph. The doping with Te to 0.2 wt % also creates the L _1.3v level and increases N _Eg to 2.02 × 10¹⁶ cm⁻³ and σ_ph to 2.01 × 10⁻¹⁰ Ω⁻¹. The irradiation of Te-doped crystals leads to the creation of an additional resonant level (Zn_i, 3.34 eV) and a two-fold increase in σ_ph. An increase in the content of Te to 0.5 wt % results in a shift of the Zn_i level to 3.39 eV and a growth in the conductivity to σ_ph = 7.64 × 10⁻¹⁰ Ω⁻¹. However, the gamma-irradiation of these crystals leads to decomposition of this center and to a decrease in the photoconductivity.     

Global existence and blow-up analysis for a nonlinear diffusion equation with inner absorption and boundary flux

This article deals with a nonlinear diffusion equation with inner absorption u _t ?=?(log^σ(1?+?u)u _x ) _x ???λ(1?+?u)log ^p (1?+?u), in ?₊?×?(0,?+∞), subject to a logarithmic boundary flux ? log^σ(1?+?u)u _x (0,?t)?=?(1?+?u)log ^q (1?+?u)(0,?t), t?∈?(0,?+∞). We establish the critical global existence curve and give the asymptotic behaviour close to the blow-up time.     

Calculation of the process of blast wave diffraction in a cylindrical channel

We performed a numerical investigation of the process of transition of a spherical leading front into a plane one in a cylindrical channel. The processes of the collision of reflected shock waves, formation of a nonstationary grating-like structure of flow, and of the overtaking interaction of shock waves are investigated. We found that in the presence of hot gas layers on the walls of the channel a plane head front is not formed.Notation r,z radial and axial coordinates - t time - p pressure - T temperature - u,v radial and axial velocity components - a distance between the planes - b half-distance between the planes - d channel diameter (in experimental data) - R ₀ inital radius of the shock wave front - p ^*(r, z),u ^*(r, z),v ^*(r, z),T ^*(r, z) distributions of pressure, radial, and axial velocity, and temperature at the initial time moment - L length of the zone of formation of a plane front - T ₁,T ₂ temperature of gas in the lower and upper thermal layers - h ₁,h ₂ thicknesses of the lower and upper thermal layers Department of Theoretical Problems of the Russian Academy of Sciences, Moscow Physicotechnical Institute, Moscow. Translated from Inzhernerno-Fizicheskii Zhurnal, Vol. 68, No. 4, pp. 583–588, July–August, 1995.     

Angle-of-incidence Derivatives of the Complex Parallel and Perpendicular Reflection Coefficients and Their Ratio for a Film-substrate System

Angle-of-incidence derivatives of the complex parallel (p) and perpendicular (s) reflection coefficients R _p and R _s, and their ratio ρ = R _p/R _s, for an absorbing substrate coated by a transparent film are investigated as functions of the angle of incidence φ and film thickness d. Such derivatives are of importance to AIDER (angle-of-incidence derivative ellipsometry and reflectometry).R′ _p/R _p,R′ _s/R _s,and ρ′/ρ (where the prime indicates ?/?φ) are shown to be aperiodic spiral functions of d at constant φ, except in the limiting cases of normal and grazing incidence when they become periodic. In the latter case (φ= 90°), the locus of R′ _v/R _v(v = p or s) is found and proved to be exactly a circle. The complementary family of constant-thickness contours of these derivative functions are also plotted in the complex plane. Finally, graphs representing the real AIDER signals ?′_p /?_p, ψ′ and Δ′ (where ?= |R|², tan ψ exp (jΔ) = ρ) versus d at constant φ, and versus φ at constant d, are given.     

Salt effect of lithium bromide on the solution polymerization of acrylonitrile

Abstract

In this paper, the salt effect of lithium bromide (LiBr) on the dimethyl formamid (DMF) solution polymerization of acrylonitrile was studied. From the experimental data, we proposed a possible mechanism and derived its rate expression to determine the kinetic parameters for this system. The results show that the values of k_v/k_tr (1.984～79.365) and k_t/k² _tr (3.311×l0²～3.156×l0⁵ sec·mole/1) of the DMF‐LiBr solution polymerization of acrylonitrile are larger than those of the DMF‐LiCl solution polymerization of acrylonitrile shown by Bamford and others. These results can be explained by the basicity of salt and the dissociation of polyacrylonitrile in the DMF‐LiBr solution.     

Applied Time Series Analysis II

The problem of identification and construction of optimal designs for comparing several test treatments with a control treatment is studied. Two-way heterogeneity in the experimental units is considered under the usual additive model. A general class of designs—named balanced treatment row-column designs—appears to be natural candidates for the A-optimality criterion. Catalogs of A-optimal balanced treatment row-column designs have been prepared and tabulated for a practical range of parameter values. The use of the catalogs is explained with examples.     

Structure and properties of the layered oxide GdBaFeNiO<Subscript>5 + δ</Subscript>

GdBaFeNiO_5+δ has been synthesized, and its crystal structure, thermal expansion, and electrical properties have been studied. It has a tetragonal structure (sp. gr. P4/mmm) with unit-cell parameters a = 0.3910(2) nm, c = 0.7582(6) nm, and V = 115.9(2) × 10⁻³ nm³ (δ = 0.53) and is a p-type semiconductor. The linear thermal expansion coefficient of GdBaFeNiO_5+δ is 1.32 × 10⁻⁵, 1.72 × 10⁻⁵, and 1.37 × 10⁻⁵ K⁻¹ in the temperature ranges 340–655, 655–870, and 870–1080 K, respectively.     

Preparation and characterization of indium oxide (In2O3) films by activated reactive evaporation

The electrical and optical properties of In₂O₃ films prepared at room temperature by activated reactive evaporation have been studied. Hall effect measurements at room temperature show that the films have a relatively high mobility 15 cm²v⁻¹s⁻¹, high carrier concentration 2·97 × 10²⁰/cm³, with a low resistivityρ = 1·35 × 10⁻³ ohm cm. As-prepared film is polycrystalline. It shows both direct and indirect allowed transitions with band gaps of 3·52eV and 2·94eV respectively.     

Influence of impurities on the etching of NaCl crystals

The effect of CdCl₂, CuCl₂·2H₂O, MnCl₂·4H₂O and FeCl₃·6H₂O impurities and undersaturation on the rates of macroscopic dissolution,v _p, lateral etching away from a dislocation line,v _t, and normal etching along the dislocation line,v _n, and on the surface micromorphology of the {100} face of NaCl single crystals in water, methanol and 96% ethanol is investigated. The dependence of etch rates on impurity concentration,c _i, showed that the addition of a salt to the solvent always leads to a decrease inv _p, which attains a minimum value after a particular value ofc _i. The concentration dependence ofv _t andv _n is relatively complex, but often both decrease or increase simultaneously. A change in etch-pit morphology is caused by increasing the concentrations of all additives in ethanol and methanol. The dependence of etch rates on the undersaturation of methanol and methanol containing 10^–3 M CdCl₂ showed that dislocation etch pits are formed only for undersaturations greater than 0.02 and 0.06, respectively. These results as well as the roughening of etched surfaces at low impurity concentrations, the formation of terraced etch pits and the difference between etch pits at aged and fresh dislocations are discussed.     

A Note on Estimation from a Type I Extreme-Value Distribution

If the random variable T has the ta-o-parameter Weibull distribution with cumulative distribution function F(t; θ, K) = 1 – exp[–(t/θ) ^k ], where θ is the scale parameter and K is the shape parameter, then the random vatiable X = In T has the Type I extreme-value distribution of smallest values with cumulative distribution function F(x; u, b) = 1 – exp {–exp [(x – u)/b}, where u = In θ is the location parameter (mode) and b = 1/K is the scale parameter. It is therefore possible to obtain the maximum-likelihood estimator û _mn | b of u, based on the first m order statistics of a sample of size n, when b is known, by a simple transformation of the corresponding estimator of θ when K is known. Use is made of the fact that û _mn | b = In _mn | K, where 2m( _mn | K) ^k /θ ^k has the chi-square distribution with 2m degrees of freedom, to set confidence bounds on u. The probability density function of û _mn | b which for given m is the same for any n ≥ m, is obtained by a simple transformation of that of _mn | K. Integration yields expressions, involving digamma and trigamma functions, for the bias E = E[(û _mn |b) – u] and the variance V = V(û _mn | b). By subtracting the bias E](û _mn |b) – u] from û _mn |b, one obtains an unbiased estimator û|b which has the same variance as the maximum-likelihood estimator. Values of E/b(6DP) and of V/b ²(6DP) are tabulated for m = 1(1)100. The use of the table is discussed and illustrated by a numerical example.     

The Characters of a Sylow p-Subgroup of the Group G2(pn), p≠2, 3

 We compute the irreducible complex characters of a Sylow p-subgroup of the Chevalley group G ₂(q), q=p ⁿ , p≠2, 3 and show that the non linear irreducible characters are induced from linear characters of subgroups of order q ⁵ and q ⁴. Received April 6, 1995     

Structure and electrical conductivity of selenium-ion-implanted CdSe films

We have studied the effect of annealing on the spectral and photoelectric properties of polycrystalline CdSe films produced by thermal evaporation and implanted with Se ions to doses from 5 × 10¹⁵ to 5 × 10¹⁶ cm⁻². The results demonstrate that, when cadmium vacancies and selenium interstitials are major defects, annealing leads to the formation of microcrystalline two-phase layers during recrystallization, which have low p-type conductivity due to a shallow acceptor at E _v + 0.04–0.05 eV, related to interstitial selenium.     

Directional solidification of eutectic and off-eutectic Au-Co composites with and without magnetic field

A fibrous eutectic with Co fibres embedded in a Au-matrix can be obtained at G/v ≥ 2×10⁵ deg/cm² whereG = temperature gradient andv = growth velocity. Interfibre spacing 2R can be described byR ² v=1.2×10⁻¹¹ cm³/sec. Below G/v=2×10⁵ deg/cm² cellular growth is observed. Fibre to blade transitions have been found over the entire range of growth velocities employed, i.e. between 10⁻⁵ and 10⁻²cm/sec and are thought to be due to local growth perturbations. Composite growth under the influence of a magnetic field produces two effects: an orienting effect and a shape and size modification. Orienting occurs at slow growth rates, preferably, in hypereutectic alloys and is explained as a magnetic aligning of the ferromagnetic primary Co-precipitates. The shape and size modification which results in thick and segmented, caterpillar-like Co fibres, appears to be independent of growth rate (within the limits indicated above), occurs mainly in cell boundaries at all compositions, including hypoeutectic ones, and is thought to be due to a field induced enhancement of local temperature gradients.     

MnNb2O4.33: A new compound in the MnO-NbO-NbO2 system

A new compound of composition MnNb₂O_4.33 with an orthorhombic structure was identified in the MnO-NbO-NbO₂ system by x-ray diffraction. Its lattice parameters area = 5.833 ± 0.001 å,b = 5.479 ± 0.001 å, and c = 10.223 ± 0.0O₂ A; p_x = 6.3 g/cm³, p_meas = 5.85 g/cm³.     

Maximum-Likelihood Estimation of the Parameters of a Four-Parameter Generalized Gamma Population from Complete and Censored Samples

Consider the four-parameter generalized Gamma population with location parameter c, scale parameter a, shape/power parameter b, and power parameter p (shape parameter d = bp) and probability density function f(x; c, a, b, p) = p(x — c) ^bp–1 exp {–[(x – c)/a] ^p }/a ^bp Γ(b), where a, b, p > 0 and x ≥ c ≥ 0. The likelihood equations for parameter estimation are obtained by equating to zero the first partial derivatives, with respect to each of the four parameters, of the natural logarithm of the likelihood function for a complete or censored sample. The asymptotic variances and covariances of the maximum-likelihood estimators are found by inverting the information matrix, whose components are the limits, as the sample size n → ∞, of the negatives of the expected values of the second partial derivatives of the likelihood function with respect to the parameters. The likelihood equations cannot be solved explicitly, but an iterative procedure for solving them on an electronic computer is described. The results of applying this procedure to samples from Gamma, Weibull, and half-normal populations are tabulated, as are the asymptotic variances and covariances of the maximum-likelihood estimators.     

Molecular Dynamics Calculation of Critical Point of Nickel

The critical point of nickel and the phase diagram near the critical point are numerically evaluated using molecular dynamics (MD) computations. Thermodynamic states on the phase diagram are calculated for a homogeneous material at equilibrium states. Isothermal lines on p–v diagrams are constructed at temperatures below and above the critical temperature, and the liquid-gas coexistence lines and regimes are obtained. The critical point of nickel is obtained as T _c = 9460± 20 K, ρ _c = 2560± 100 kg· m⁻³, and p _c = 1.08± 0.01 GPa. The method used in this work can be used to estimate thermodynamic properties of other materials at high temperature/pressure.     

Some characteristics of electric explosion of zinc wires

Some physical characteristics necessary for calculating the circuit of and selecting the optimum conditions for the electric explosion of zinc wires have been experimentally determined, including the specific action of zinc h _b = (0.70 ± 0.15) × 10⁵ A² s/mm⁴ (for maximum current densities 2.5 × 10⁵ A/mm² < j _M < 4.5 × 10⁵ A/mm²) and the critical length of exploding wire λ_cr = 1.8 × 10³ (ɛν × 10⁻⁶)^0.56.