Anomalous change in the photoacoustic phase near superconducting transition in YBa2Cu3O7

Photoacoustic amplitude and phase measurements have been carried out near the superconducting transition temperature in the highT _csuperconductor YBa₂Cu₃O₇. In both the samples investigated, the photoacoustic phase undergoes an anomalous step-like decrease aroundT _c≈ 96 K and increases at lower temperatures. A clear temperature hysteresis for the phase change has been noticed. No anomalous variation has been observed in the amplitude values. Neither phase nor amplitude shows any anomaly in a non-superconducting sample of the same composition.     

Solution of Shapirovskii's question

Boris Shapirovskii posed the following question: “Suppose a continuous mapping from one compact space onto another is given. Suppose that the π-character of any point in the domain is greater than the weight of the target space. Will there be two disjoint closed sets in the domain mapping onto?”. There is a zero-dimensional counterexample (Corollary 12), but the one cardinal up version is true in zero-dimensional case (Corollary 14). Nevertheless, there always will be two disjoint open sets mapping densely (Theorem 7).     

Characterization of the ground state pyrene complex in ethylene-propylene copolymer solutions

Pyrene-labeled functionalized ethylene-propylene (EP) copolymer was prepared by grafting 1-pyrenebutyrylhydrazine onto EP copolymer through maleic anhydride pendants. The EP copolymer contained 60 mol % ethylene; its weight-average molecular weight (M^w) was 148,000. The pyrene-labeled amide functionalized EP copolymer, PA-EP(60/40), was made to simulate the amine functionalized EP copolymers that are commonly used as dispersant additives in motor oils. UV absorption spectra, fluorescence emission and excitation spectra, and fluorescence decay profiles of the pyrene were studied to determine the copolymer conformation and dynamics in methylcyclohexane and tetrahydrofuran (THF). The pyrene fluorescence characteristics of PA-EP(60/40) were highly dependent on the solvent. The dependence of fluorescence emission intensity on the excitation wavelength was large in methylcyclohexane and moderate in THF. A frequency shift of about 2 nm was observed between the excitation spectrum obtained with the emission line at 377 nm and that at 550 nm in the methylcyclohexane solutions, but no shift was found in the corresponding tetrahydrofuran solutions. The ratios of the preexponential factors (a₂₁/a₂₂) of the excimer decays obtained in both methylcyclohexane and THF solutions were different from ?1.0. However, the deviation of the excimer formation process from the Birks scheme is small in THF but large in methylcyclohexane. In addition, the Huggins constants obtained from intrinsic viscosity measurements of the PA-EP(60/40) copolymer solutions suggest that copolymer aggregation occurs in methylcyclohexane but not in THF. H-bonding between two pyrene-containing pendants is apparently the main driving force for the formation of the ground state pyrene complex. THF is found to be effective in inhibiting the H-bonding formation. © 1995 John Wiley & Sons, Inc.     

Determinants of Laplacians on surfaces of finite volume

Determinants of the Laplace and other elliptic operators on compact manifolds have been an object of study for many years (see [MP, RS, Vor]). Up until now, however, the theory of determinants has not been extended to non-compact situations, since these typically involve a mixture of discrete and continuous spectra. Recent advances in this theory, which are partially motivated by developments in mathematical physics, have led to a connection, in the compact Riemann surface case, between determinants of Laplacians on spinors and the Selberg zeta function of the underlying surface (see [DP, Kie, Sar, Vor]).Our purpose in this paper is to introduce a notion of determinants on non-compact (finite volume) Riemann surfaces. These will be associated to the Laplacian shifted by a parameters(1–s), and will be defined in terms of a Dirichlet series (w, s) which is a sum that represents the discrete as well as the continuous spectrum. It will be seen to be regular atw=0, and our main theorem (see Sect. 1) will express exp as the Selberg zeta function of the surface times the appropriate -factor.A Sloan Fellow and partially supported by NSF grant DMS-8701865     

The direct and inverse problem for sub-diffusion equations with a generalized impedance subregion

Applications of Mathematics - In this paper, we consider the direct and inverse problem for time-fractional diffusion in a domain with an impenetrable subregion. Here we assume that on the boundary...     

On Generalized Affine Rotation Surfaces

From group-theoretical point of view, we discuss affine rotation surfaces in R³ and projective rotation surfaces in RP³. These pave a way toward generalized affine rotation surfaces in R³. We will follow closely the modern approach introduced by Nomizu in the study affine differential geometry [N]. In this paper, we have the following results on generalized affine rotation surfaces:

1. Many nice properties showing duality between x² + y² = g²(z) and x² ? y² = g²(z).
2. In this set, any surface with zero Pick invariant is a quadratic surface.
3. Excluding the Caley surface z = xy ? x³/3 and the surface z = xy + log x, any affine unimodular homogeneous surface belongs to this set.
4. In this set, the following surfaces are characterized by some affine invariants: $${\matrix{x^{2}+\epsilon\ y^{2}=z \cr \qquad \qquad \qquad \qquad \qquad \qquad \qquad y^{2}=z(x+\epsilon\ (z+a)^{2/3}(z+6a)),\cr \qquad \qquad \qquad \ \ \ y^{2}=z(x+\epsilon\ z^{3}),\cr \qquad \qquad \ \ \ \ \ \ y^{2}=x+\epsilon\ z^{2/3},\cr \qquad \qquad \ \ \ \ \ \ \ y^{2}=x+\epsilon\ z^{-2/3},\cr \qquad \qquad \ \ \ y^{2}=x+\epsilon\ {\rm log}z,\cr}} $$ where ? represents 1 or ?1 in this paper.

     

The Internal Bremsstrahlung following the Electron Capture decay of55Fe

The Internal Bremsstrahlung Electron Capture spectrum from⁵⁵Fe was measured with a HPGe detector. The total spectrum was unfolded taking into account the secondary detection effects and agrees with Glauber and Martin calculations. The measured intensity relative to K capture in the range 35 to 231 keV is 3.24(6)·10^?5 while the calculated one is 3.20·10^?5. TheQ value for the electron capture was deduced as 230.7(19) keV.     

Hydrophile-lipophile balance of alkyl ethoxylated surfactants as a function of intermolecular energies

Summary The semiempirical MNDO method has been used in order to examine the variation of the molecular properties of hydrocarbons C_nH_2n+2 (with 1n19) and ethylene oxide chains CH₃(CH₂CH₂O)_mCH₃ (with 1m19) as a function of their molecular length. Least-square fits of those properties have been calculated, along with two mathematical relations between the hydrophile-lipophile balance of alkyl-phenol ethoxylated surfactants and (1) the ratio of molecular lengths between their lipophilic and hydrophilic branches; (2) the intermolecular energies between the molecules of surfactant, water and hexane.     

THE QUENCHING OF TYROSINE AND TRYPTOPHAN FLUORESCENCE BY H2O AND D2O*

Abstract— The quantum yields and lifetimes of the fluorescence of tyrosine and tryptophan were determined in D₂O-H₂O and glycerol-H₂O solvent mixtures of varying composition from 10 vol.% to 100% H₂O at 15°C. Forboth amino acids the ratio of the quantum yields in D₂O and H₂O (i.e., q_D/q_H) was smaller than the ratio of the corresponding lifetimes (_D/_H). For tyrosine the ratio of the quantum yields in glycerol and H₂O (q_G/q_H) was also smaller than the corresponding _G/_H ratio, but for tryptophan q_G/g_HG/_H. The proximity of the q vs. plots for tyrosine in the two solvent mixtures indicates that at 15°C neither D₂O nor glycerol, in the pure state or when diluted with H₂O, quench tyrosine significantly. However, H₂O quenches tyrosine by a dynamic process, which increases both the radiative and the nonradiative rate constant. The quenching action is attributed to a tyrosine-H₂O exciplex, whose formation is independent of bulk viscosity and dielectric constant. Unlike tyrosine, tryptophan is quenched weakly by D₂O by a static process at 15°C (i.e., involving no change in), but H₂O quenches tryptophan much more efficiently by a dynamic process, which involves the nonradiative rate constant, but not the radiative constant. These results are explained on the basis of electrostatic complexation of the ammonium group to the carbon atom adjacent to the ring nitrogen with a lifetime which is longer thanin D₂O but shorter thanin H₂O, with solvent reorientation possibly also being an important factor in the quenching. This explanation is consistent with the fact that concentrated (8 M) urea increases q andof aqueous tryptophan ? 15–20%, while guanidine hydrochloride (6.4 M) has the opposite effect, i.e., it decreases q and t of tryptophan ? 15–20%, and with the fact that neither 8 M urea nor 6.4 M guanidine hydrochloride affects any fluorescence parameter of tyrosine at all.