Esquentian of the mean by three stage procedure

Let X₁, X₂... be i.i.d. observations with mean μ and variance σ², and suppose that given a sample of size n one wishes to estimate μ by X_n, subject to the loss function L_n= A²(X_n-μ)²+n. When σ² is unknown, the optimal sample size n₀ for minimizing the risk R_n = E{L_n} cannotbe found. To resolve this problem, Robbins (1959) proposed a sequential procedure whenX_i is normally distributed, and then the asymptotic properties have been extensively studied. In this paper, we apply Hall's three stage procedure to the problem without specifying the distribution of X_i and derive the second order asymptotic expansions of the expected sample size and the risk.     

Hierarchical percolation and electrical conduction of glasses in the 50WO3-(50 − x)P2O5-xNa2O system

The validity of the proposed concept of hierarchical percolation is demonstrated using glasses in the WO₃-P₂O₅-Na₂O system as an example. The dependence of the electrical conductivity σ = σ₀(ξ ? ξ_crit)^μ (where ξ is the percolation parameter) with an exponent μ ? 1.4 close to the exponent theoretically predicted for two-dimensional percolation is obtained for the first time. This confirms our hypotheses regarding the two-dimensional percolation nature of electrical conduction over the surface of a phosphate cluster after the percolation threshold is overcome.     

A partial sequential t-test

Several authors have proposed sequential test procedures for testing one sided hypotheses about the mean μ of a normal distribution with unknown variance σ². Some of these procedures have concerned themselves with tests for units of (μ/σ). I this work, a sequential test procedure is introduced for hypoth-eses concerned with μ itself. In the present procedure the transformed observa-tions follow a central t-distribution as distinct from the noncentral t-distribution used in pnvious tests. Insights into properties of the operating characteristic and the average sample number functions are found for the present test; specifically, approximations to the theoretical operating characteristic function are derived and the sensitivity of the average sample number function to changes in some of the test parameters is investigated.     

Kinetics of the epitaxy and the over-growth of polyoxymethylene from molten state on needle-like single-crystals

Kinetic studies have been made on the over-crystallisation of polyoxymethylene on needle-like crystals, which takes place cylindrically around the needles by forming a pile of lamellar crystallites, using the ordinary spherulitic crystallisation as reference. The growth kinetics were investigated, by means of microscopy and differential scanning calorimetry (DSC), and the resultant structure was examined by small-angle X-ray scattering and melting temperature measurements. The discontinuity found for their theoretical plot was assumed to be attributable to the difference in the type of crystallisation. The lamellar surface free energies obtained for the over-growth were smaller than those for the spherulitic growth, i.e., σ_e = 42.1 and σ_s = 2.94 erg/cm² against σ_e = 53.4 and σ_s = 4.97 erg/cm². The epitaxy effect was elucidated from the analysis of DSC curves during cooling and the combined free-energy, σ_eσ_s = 89.4 erg²/cm⁴, was estimated for the initial deposit on the needle surface.     

Struktur und elektrische Leitfähigkeit von polymeren organischen Halbleitern

In this review article we want to give information about low molecular and polymer organic semiconductors, which were recently synthesized in our institute. Specific electric conductivities up to σ_298°K = 9.0 · 10^?5Ω^?1 · cm^?1 and thermic activation energies of E = 0.30 eV of polyenearylenes, respectively -heteroarylenes were measured. Polyazomethines have a maximum σ_298°K = 3.3 · 10^?9Ω^?1 · cm^?1 and E = 0.35 eV. Polymers with indophenine units have conductivities up to σ_298°K = 1.1 · 10^?4Ω^?1 · cm^?1 and E = 0.39 eV. A maximum of σ_298°K = 5.0 · 10^?2Ω^?1 · cm^?1 and E = 0.05 eV was found for bis-(1.2-dicyanoethylenedithiolo)-metal salts. Polymers with a phthalocyanine- or hemiporphyrazine-like structure achieve a conductivity of σ_298°K = 2.3 · 10^?2Ω^?1 · cm^?1 and E = 0.15eV. Coordination polymers of dimercaptomaleic acid, respectively their monoamide show a maximum of σ_298°K = 3.2 · l0^?lΩ^?l · cm^?1 and E = 0.20 ev. Polymers with σ_298°K ≤1.5 · 10^?5 Ω^?l · cm^?l and E ≥ 0.5 eV were obtained by the polymerization of succinonitrile. All the investigated substances show an electronic conductivity. The existence of an ionic conductivity could, in all cases, be excluded by using direct current measurements over a long period of time.     

Specific extinction coefficient of flame generated smoke

The experimental results for the mass specific extinction coefficient (σ_s) at λ=633 nm for flame generated smoke are summarized for seven studies involving 29 fuels. The measurements are for post‐flame smoke generated by overventilated burning. From an analysis of variance for the seven studies, it was found that between‐laboratory differences were the major source of variability. The estimated mean value of σ_s is 8.7 m²/g with an expanded uncertainty (95% confidence interval) of 1.1 m²/g. A major implication of this nearly universal value is that one can infer mass concentration of smoke by making light extinction measurements. Published in 2000 by John Wiley & Sons Ltd.     

Théorie et application de la distribution normale de θ1/3 aux temps de séjour des fluides dans les réservoirs agités en régime continu

Statistical models of residence time distributions in ideal stirred tanks in series are well approximated by a normal distribution of θ^1/2, θ^1/2 or θ according as the number of tanks is > 15, > 50 and very large respectively. For one stirred tank, the normal distribution of θ^1/3 approximates well the residence time distribution for both ideal and nonideal mixing. For ideal mixing, the mean x_m and standard deviation σ of the θ^1/2 distribution assume values of 8/9 and 1/3 respectively. For nonideal mixing, x_m is < 8/9 while σ is > 1/3. At constant fluid viscosities, when the rotational speed of the agitator increases, x_m increases gradually to reach its upper limiting value of 8/9 whilst σ decreases to reach its lower limiting value of 1/3. At fixed rotational speeds, if the viscosity increases, x_m decreases whilst σ increases. A simple mixing efficiency criteria derived from the normal distribution of θ^1/3 is proposed and is compatible with Danckwerts' segregation concept.     

Rheological interpretation of heat generation associated with fatigue of polycarbonate

Temperature change was measured of polycarbonate under monotonically increasing tensile and pulsating tensile loads. In the former case, the specimen temperature began to rise when an appreciable amount of viscoelastic strain was noticed on the stress—strain diagram. The rise, θ_v, could be formulated as a function of the viscoelastic strain, εv: In fatigue tests, the average temperature began to rise immediately after the decrease due to the thermoelastic effect. The amount of the heat generation, σ, was nearly constant for each cycle throughout the fatigue process and has a relation to the fatigue life, N_f, (α? a)·N_f = constant, where a is another adjustable constant. From a rheological aspect of dissipation energy, the equation is transformed to a relation between the viscoelastic strain and the fatigue life as εV^1/2 · N_f = constant, which is similar to the one for metals given by Manson and Coffin.⁶ The temperature rise in the fatigue was also related to the viscoelastic strain. The relation is of the same form as for static tension but less by a factor of one order.     

Reverse osmosis separations for some alcohols and phenols in aqueous solutions using aromatic polyamide membranes

The performance of aromatic polyamide membranes for reverse osmosis separations of eight alcohol and four phenol solutes in dilute aqueous solutions has been studied. The Taft polar parameter σ^* for the solutes studied were in the range of ?0.3 to 1.388. Positive solute separations were obtained for each one of the solutes. In the σ^* value range of ?0.3 to 0, data on PR/PWP ratio scattered close to 1, and solute separation decreased with increase in σ^*. For the phenol solutes, PR/PWP ratio decreased and solute separation increased with increase in σ^*. The results are interpreted on the following basis. The aromatic polyamides are more nonpolar than cellulose acetates. In the σ^* range of ?0.115 to ?0.3, solute separation is governed primarily by polar interactions; in this range, solute transport parameter D_AM/Kδ is well correlated by the expression D_AM/Kδ = C^* exp (ρ^*σ^*). The solute separation for ethyl and methyl alcohol solutes (σ^* = ?0.1 and 0, respectively) is reduced by the nonpolar character of the membrane material. Positive solute separation for each of the phenolic solutes is due to preferential sorption of solute at the membrane-solution interface caused by both the nonpolar character of the membrane material and acidity of the solutes.     

Studies of linear polymer dimensions of poly(4-chlorostyrene) in various solvents around the θ temperatures by intrinsic viscosity

Intrinsic viscosities of poly(4-chlorostyrene) solutions in isopropyl-benzene and n-propylbenzene at temperatures above and below the theta (θ) temperatures of these solvents were measured using a capillary viscometer. The viscosity measurements were performed on three poly(4-chlorostyrene) samples having molecular weights (M?;_v) 1.75 × 10⁶, 6.5 × 10⁵ and 2.7 × 10⁵. A smooth and continuous contraction below the θ temperatures was observed for both solvents. The temperature dependence of [/eta] can be represented by a master curve in a plot of α³/eta|/tau|M^1/2 (g^1/2 mol^?1/2) versus |/tau|M^1/2 (g^1/2 mol^?1/2), where α/eta = [/eta(T)]/[/eta(θ)]^1/3 is the expansion factor and /tau = (T - θ)/T is the reduced temperature. A universal plot of reduced viscosity size (α/eta) versus reduced blob parameter (N/N_c) shows the achievement of collapsed state for T<θ. The prediction of thermal blob theory is also verified for T > θ. The temperature dependence of intrinsic viscosity, both below and above the θ temperature, exhibits similar behaviour to the temperature dependence of dipole moments for both of these solvents.     

Zur unverträglichkeit von polymergemischen. 1. Lichtstreuungsmessungen am system polystyrol/polymethylmethacrylat/benzol

A polystyrene (PS) with M?_w = 9,7 · 10⁴ was investigated by means of light scattering in the isorefractive polymer/solvens-mixture polymethylmethacrylate (PMMA)/benzene. It was found, that the second osmotic virial coefficient A₂ of PS was strongly dependent on the average viscosimetric molecular weight M?_v and on the concentration of PMMA, but scarcely on the temperature in the range of 20°C to 60°C. The θ-Point, where A₂ is zero, was independent of the temperature within experimental error. By defining the PMMA concentration at the θ-Point as c_θ, and by reducing the measured PMMA concentration c to c/c_θ, an unequivocal relation was obtained between A₂ and c/c_θ, which is independent of molecular weight and molecular weight distribution of PMMA. PS shows a high second virial coefficient in dimer and trimer MMA as well as in non-hydrogenated and hydrogenated MMA. The investigated PS constitutes a θ-System in PMMA of a degree of polymerisation of P?_w, ～ 17without the use of benzene.     

High-temperature redox-initiated emulsion polymerization of butadiene

The kinetics of the ferric ethylenediaminetetraacetate (EDTA)–diisopropylbenzene hydroperoxide (DIBHP)-sodium formaldehyde sulfoxylate (SFS) redox system were determined. The rate constant is a function of the ionic strength μ. A plot of log₁₀ (rate constant), for the rate-limiting second-order iron—SFS reaction, vs.μ^1/2 has a slope of 1.3 with a limiting rate constant of 295 ± 15 L. mol^?1. min^?1 at μ = 0. The slope of this plot decreases to essentially zero for μ > 0.06M. Incorporation of these results into the Smith-Ewart model for emulsion polymerization correctly predicts the dependence of latex particle size on Fe and DIBHP concentration, but a much lower dependence on SFS concentration is observed.     

Critical Surface Tension of Non-crosslinking Linear Low Density Polyethylene-graft-acrylic Acid by the Contact Angle Method

Abstract

The contact angles θ of polar liquid on surface of non-crosslinking linear low density polyethylene-graft-acrylic acid (LLDPE-g-AA) were measured. The critical surface tension (γ_c) of LLDPE-g-AA films were evaluated by three different plots, the Zisman plot, the Young-Dupre-Good-Girifalco plot, and the log(1 + cos θ) versus log θ _L , plot. The θ _c of LLDPE-g-AA obtained by the 1 + cosθ versus θ _L ^?1/2 plot were higher than those obtained by other plots.     

Isothermal crystallization of iPP in model glass-fiber composites

Isothermal crystallization of iPP in model glass-fiber composites is studied by DSC, and the basic energetic parameters of crystallization are determined. Unsized untreated and thermally treated glass fibers are used in model composites to determine the role of the surface on nucleation and crystallization processes. Thermally treated glass fibers are found to exhibit a predominant nucleating effect as compared to unsized untreated ones, and the crystallization proceeds faster, resulting in lower values for the half-time of crystallization (10–120 s). The energy of formation of a nuclei of critical dimensions at a given T_c is also lower, and it decreases as the content of the fibers in the composite increases. The surface free energy of folding, σ_e = 140 × 10⁻³ J/m², was determined for iPP in the composite containing 50% glass fibers, while for pure iPP, σ_e = 170 × 10⁻³J/m² was found. © 1998 John Wiley & Sons, Inc. J Appl Polym Sci 69: 381–389, 1998     

Strictly two-dimensional self-avoiding walks: Density crossover scaling

The density crossover scaling of thermodynamic and conformational properties of solutions and melts of self-avoiding and highly flexible polymer chains without chain intersections confined to strictly two dimensions (d = 2) is investigated by means of molecular dynamics and Monte Carlo simulations of a standard coarse grained bead-spring model. We focus on properties related to the contact exponent set by the intrachain subchain size distribution. With R ～ N ^ν being the size of chains of length N and ρ the monomer density, the interaction energy e _int between monomers from different chains and the corresponding number n _int of interchain contacts per monomer are found to scale as with ν = 3/4 and θ₂ = 19/12 for dilute solutions and ν = 1/d and θ₂ = 3/4 for N? g(ρ) ≈ 1/ρ². Irrespective of ρ, long chains thus become compact packings of blobs of contour length with d _p = d ? θ₂ = 5/4 being the fractal line dimension. Due to the generalized Porod scattering of the compact chains, the Kratky representation of the intramolecular form factor F(q) reveals a non-monotonous behavior approaching with increasing chain length and density a power-law slope $F(q)q^d /\rho \approx 1/(qR)^{\theta _2 } $ in the intermediate regime of the wavevector q. The specific intermolecular contact probability is argued to imply an enhanced compatibility for polymer blends confined to ultrathin films. We comment briefly on finite persistence length effects.     

The Softness Parameters of Ions. Prediction of the Occurrence of Miscibility Gaps in Molten Salt Mixtures

Softness parameters σ_M for cations and σ_X for anions, have been calculated as dimensionless quantities for approx. 90 cations and 18 anions. They are given by σ_M = [σ_A (M^m+) - σ_A(H⁺)]/σ_A(H⁺) and σ_X = [σ_B(X^a?) - σ_B(OH^?)]/σ_A(H⁺) where σ_A = [σI_i(M) + ΔH⁰_h(M^m+)]/m and σ_B = [-E_a(X) + ΔH⁰_h(X^a?)]/a are Ahrland's parameters. The new normalized and comparative (to the test ions H⁺ and OH^?) softness parameters are positive for soft ions and negative for hard ones. These parameters, obtained independently, are used with a four-coefficient equation to calculate coordinate bond energies for metal halides with acceptable accuracy. Considerations of the average coordination in reciprocal molten salt mixture lead to an expression for the metathesis energy change as proportional to the product of the differences in softness parameters of the two cations and the two anions. An empirical one-coefficient equation involving the softness parameters is proposed to deal with next-nearest-neighbor interactions in binary common-ion molten salt mixtures. These relationships are then used with Blander and Topol's equation to predict the occurrence of irascibility gaps in uni-univalent reciprocal salt mixtures. The gaps found in other systems are also discussed in terms of the softness of the constituent ions.     

1H- und 13C-NMR-Spektren von N-Methyl-chinoliniumchalkonen: Bestimmung von σ-Konstanten für die 2-, 3- und 4-Position des N-Methyl-chinoliniumrings

¹H- and ¹³C-N.M.R. Spectra of N-Methyl-quinolinium Chalcones: Determination of σ-Constants for the 2-, 3- and 4-Position of the N-Methyl-quinolinium Ring For the N-methyl-quinolinium chalcones 1a – c the ¹H- and ¹³C-n.m.r. data are reported. The unambiguous assignment of signals is based upon the ¹H/¹H homoshift and the ¹³C/¹H heteroshift correlated 2D-n.m.r. spectra. Using a Hammett relationship we have determined σ-constants for the 2-, 3- and 4-position of the N-methyl-quinolinium ring from the ¹³C-α chemical shifts of 1a – c . Their comparison with the σ-values for the equivalent positions in the pyridine, N-methyl-pyridinium and quinoline ring indicates the additivity of anellation and quaternization effect.     

Structural disorder effect on the structural and magnetic properties of Pr0.4Re0.1Sr0.5−yBayMnO3 manganites (Re = Pr,Sm, Eu,Gd, Dy and Ho)

The influence of the A-site cation size-disorder σ² on the structural and magnetic properties of the polycrystalline Pr_0.4Re_0.1Sr_0.5−yBa_yMnO₃ (Re = Pr, Sm, Eu, Gd, Dy and Ho) samples with a constant average ionic radius <r_A> = 1.2445 Å, is investigated. All samples were synthesized using the solid-state reaction. Rietveld refinement of the X-ray diffraction patterns shows that the substitution generates a structural transition from tetragonal to orthorhombic symmetry. The temperature dependence of magnetization indicates a weakening of ferromagnetism by the increase of σ². The large difference between the field cooled and zero field cooled magnetization below Curie temperature suggests the presence of an inhomogeneous mixture of a ferromagnetic and antiferromagnetic domains at low temperature. The maximum of the magnetic entropy change decreases with increasing the mismatch effect. However, several peculiarities were observed in the magnetic behavior indicating that σ² is not the only factor controlling the physical properties; the nature and the magnetic moment of the substituent should be taken in consideration.