Photometric and fluorimetric study of the acid-base behavior of 2,2′-diquinolyl and 2,2′,2″-terpyridyl

A photometric and fluorimetric study of the acid-base behavior of 2,2-diquinolyl and 2,2,2-terpyridyl was performed. In sulfuric acid medium, the doubly charged 2,2-diquinolynium ion undergoes the first dissociation atH ₀=0.20±0.09, as determined by fluorimetry (_ex=336 nm, _em=424 nm). Photometric titration is less accurate because of the overlapping of the absorption spectra. The second dissociation constant of 2,2-diquinolyl was determined by fluorimetric titration (_ex=336 nm, _em=420 nm), obtaining a value of 3.67±0.03. The triply charged 2,2,2-terpyridyl molecule was found to undergo the first dissociation atH ₀=–7.17±0.04, as determined by fluorimetric titration (_ex=316 nm, _em=350 nm), in aqueous sulfuric acid medium. Photometric titration (=335 nm) was performed in the presence of 6.5% ethanol because of the low solubility of the compound in water. In this ethanolicwater medium, a value of the dissociation constant atH ₀=–7.39±0.03 was calculated. The second dissociation constant was determined to be 2.81±0.12 by photometric titration at 285 nm, and values of 4.03±0.26 and 4.16±0.20 were found for the third dissociation constant by photometric titrations at 320 and 295 nm, in 10% ethanol, in close agreement with previously reported values. The fluorimetric titration profile obtained by exciting at 274 nm and measuring the fluorescence emission at 350 nm, in the zone betweenH ₀=–3 and pH=10, is complicated by the several equilibria involved.     

Nature of 2-Aminoxanthone Fluorescence

Absorption and fluorescence spectra of 2-aminoxanthone in solutions of different types at 77–350 K were studied. The existence of three bands (_{1 max} = 417 nm, ₁ = 14 ns; _{2 max} = 528 nm, ₂ = 13 ns; and _{3 max} = 565 nm, ₃ = 6 ns) in fluorescence of 2-aminoxanthone solutions has been established. It was shown that the first short-wave band was determined by deactivation of singlet excitation of an aminoxanthone molecule. The band with _{3 max} = 565 nm (depending on the concentration) is connected with excimer-type aggregates, which are formed by aminoxanthone molecules grouped with the help of dipole molecules of solvent or by weak hydrogen bonds between aminoxanthone molecules. The emission in band _{2 max} = 528 nm is caused by reversible changes in the 2-aminoxanthone molecule and probably is connected with an intramolecular proton transfer.     

Parametrization of the cosmological scale factor

We show that the growth of the cosmological scale factorR() can be conveniently parametrized as a function of a space-time-dependent cosmological function(x). To show the parametrization, we introduce a simple heuristic model of the cosmological function(x) during the inflationary period by assuming that it is spatially uniform but time dependent with an exponential growth phase followed by a rapid decay. Based upon this relatively simple empirical model we are able to calculate directly all the required features of an inflationary period such as exponential growth of the scale factor plus a natural relaxation (graceful exit) of to apositive present-day cosmological constant. The model also predicts the presence of a very large, negative Planckian cosmological constant at the Planck time.     

Effect of chemical structure on the radioactive decay rate of71Ge

The influence of the chemical structure on the electron capture radioactive decay rate of⁷¹Ge was observed.⁷¹Ge nuclei in bivalent sulphide GeS decay faster than in quadrivalent sulphide GeS₂. The relative change / of the decay constant is+(11.4±1.7) · 10^–4.A possibility to use the experimental values of / to determine the chemical changes in the electron density at germanium nuclei in germanium chemical compounds is discussed. Quantitative determination of the changes in the electron density is complicated because of insufficient reliability of the published values of exchange and overlap corrections to the electron capture probabilities.     

Electron-optical phonon coupling in superconductors

We investigate the role of the optical phonons in superconductivity in the case of compounds with different atomic massesM _k . We show that the electron mass enhancement factor is independent ofM _k if the force constant matrix is mass independent. However, when using to calculateT _c , it must be decomposed into its acoustical and optical contributions, which depend separately onM _k . We study interference scattering from a light and a heavy mass and its contributions to within the free electron approximation. Numerical results are presented for a rocksalt structure crystal with nearest and next nearest neighbour coupling. These results indicate that the optical phonon contributions to may substantially increaseT _c .Address after August 1975: Institut für Angew. Kernphysik, Kernforschungszentrum, 75 Karlsruhe, Germany     

Baryonic decay and 1p-shell hypernuclear spectroscopy

The detailed discussion of baryonic decay channels is presented. Levels built on sp^–1, PP^–1 and ss^–1 configurations are considered. The results presented are obtained in the calculations based on the Translationally Invariant Shell Model which automatically includes some intruder states through the kinematic correlations. The role of the intruder states in the proton decay is discussed. The evolution of the baryonic decay width with increasing nucleon number A in the 1p-shell hypernuclei is traced. Hypernuclear decays into the bound excited states either of secondary hypernuclei or nuclei are revealed. Information which could be extracted from the de-excitation of the baryonic decay products whenever they were measured is discussed. From the suggested new set of theN interaction parameters for the sp^–1 configuration some new information on the proton decay of the ¹² C hypernucleus pp^–1 low-lying levels is given.We would like to express our sincere thanks to R. Chrien, D. Davis, H. Ejiri, K. Itonaga, J. Milener, T. Motoba, O. Richter, M. Sotona and Yu. Smirnov for many illuminating discussions. One author (L.M.) is indebted to Prof. T. Motoba for warm hospitality in Kyoto and Osaka, where a part of this report was prepared.     

Soliton mass and surface tension in the (λ|Ø|4)2 quantum field model

The spectrum of the mass operator on the soliton sectors of the anisotropic (|ø|⁴)₂—and the (ø⁴)₂—quantum field models in the two phase region is analyzed. It is proven that, for small enough >0, the mass gapm _s() on the soliton sector is positive, andm _s()=0(^–1). This involves estimatingm _s() from below by a quantity () analogous to the surface tension in the statistical mechanics of two dimensional, classical spin systems and then estimating () by methods of Euclidean field theory. In principle, our methods apply to any two dimensional quantum field model with a spontaneously broken, internal symmetry group.A Sloan Foundation Fellow; Research supported in part by the U.S. National Science Foundation under Grant No. MPS 75-11864.Supported in part by the National Science Foundation under Grant No. PHY 76-17191     

The Experimental Evaluation of Decay Rate Variations of 57Co by the Δλ/λ Method

The measurement of the relative changes / of the radioactive decay by the electron capture process is a direct experimental way to determine the relative changes of the electron charge density on the nucleus. Here we present the results of the experiment with ⁵⁷Co, where the differences of the decay rate were determined for different chemical states of ⁵⁷Co. We analyzed the experimental time dependences of the activity of ⁵⁷Co by means of the direct approximation method and the specialized optimization tool – a genetic algorithm. Using these methods improved the accuracy of the final / values between ⁵⁷Co and ⁵⁷Co(Pd), ⁵⁷CoCl₂,⁵⁷CoS, ⁵⁷CoSO₄7H₂O, which are in good agreement with theoretical considerations reflecting the electron charge rearrangement and screening effects.     

The asymmetric contact process on a finite set

The contact process onZ has one phase transition; let _c be the critical value at which the transition occurs. Let _N be the extinction time of the contact process on {0,...,N}. Durrett and Liu (1988), Durrett and Schonmann (1988), and Durrett, Schonmann, and Tanaka (1989) have respectively proved that the subcritical, supercritical, and critical phases can be characterized using a large finite system (instead ofZ) in the following way. There are constants ₁() and ₂() such that if < _c , lim _{N N} /logN = 1/₁(); if > _c , lim _N log _N /N = ₂(); if = _c , lim _{N N} /N= and lim _{N N} /N ⁴=0 in probability. In this paper we consider the asymmetric contact process onZ when it has two distinct critical values _c1< _c2. The arguments of Durrett and Liu and of Durrett and Schonmann hold for < _c1 and > _c2. We show that for [ _c1< _c2), lim _{N N} /N=-1/, (where _i is an edge speed) and for = _c2, lim _N log _N /logN=2 in probability.     

Steady-state and time-resolved phosphorescence of wild-type and modified bacteriophage λcI repressors

We have measured the steady-state phosphorescence and decay times of wild-type cI repressor and compared it with that of a modified cI repressor in which > 95% of the tryptophans were replaced with 5-hydroxy-l-tryptophan (5-OHTrp). The wild-type and 5-OHTrp-cI repressors are spectroscopically distinct such that we can selectively excite the 5-OHTrp-cI even in the presence of a 15-fold molar excess ofN-acetyltryptophanamide (NATrpA). The phosphorescence band of wild-type cI is red-shifted by 3 nm relative to NATrpA, characteristic of buried tryptophan. Similarly, the phosphorescence of 5-OHTrp-cI repressor is red-shifted relative to the model, 5-OHTrp, showing that according to the phosphorescence, the modified repressor is structurally indistinguishable from the native repressor. While the phosphorescence decay of both NATrpA and 5-OHTrp are single exponentials, the decay of both wild-type and 5-OHTrp-cI repressors is complex, requiring three decay components whose fractional contributions to the phosphorescence are the same for both repressors. Because the 5-OHTrp phosphorescence can be excited at wavelengths outside the absorbance range of tryptophan and DNA, a protein spectrally enhanced with this emitter will aid the investigations of protein-protein or protein-DNA interactions.     

Mean-Field Critical Behavior for the Contact Process

The contact process is a model of spread of an infectious disease. Combining with the result of ref. 1, we prove that the critical exponents take on the mean-field values for sufficiently high dimensional nearest-neighbor models and for sufficiently spread-out models with d>4:()– _c as _c and ()( _c–)^–1 as _c, where () and () are the spread probability and the susceptibility of the infection respectively, and _c is the critical infection rate. Our results imply that the upper critical dimension for the contact process is at most 4.     

Energy level crossings in quantum mechanics

From the eigenvalue equationH \ _n () =E _n ()\ _n () withH H ₀ +V one can derive an autonomous system of first order differential equations for the eigenvaluesE _n () and the matrix elementsV _mn () where is the independent variable. To solve the dynamical system we need the initial valuesE _n ( = 0) and \ _n ( = 0). Thus one finds the motion of the energy levelsE _n (). We discuss the question of energy level crossing. Furthermore we describe the connection with the stationary state perturbation theory. The dependence of the survival probability as well as some thermodynamic quantities on is derived. This means we calculate the differential equations which these quantities obey. Finally we derive the equations of motion for the extended caseH =H ₀ +V ₁ + ² V ₂ and give an application to a supersymmetric Hamiltonian.     

Absolutely continuous invariant measures for one-parameter families of one-dimensional maps

Given a one-parameter familyf (x) of maps of the interval [0, 1], we consider the set of parameter values for whichf has an invariant measure absolutely continuous with respect to Lebesgue measure. We show that this set has positive measure, for two classes of maps: i)f (x)=f(x) where 0<4 andf(x) is a functionC ³-near the quadratic mapx(1–x), and ii)f (x)=f(x) (mod 1) wheref isC ³,f(0)=f(1)=0 andf has a unique nondegenerate critical point in [0, 1].     

Mode selection in a caricature of eutectic solidification

We have studied the problem of mode selection, specifically, selection of the lamellar spacing, in eutectic solidification, by constructing a caricature of a thin-film eutectic solidifying at constant velocity in the presence of a finite temperature gradient and in a slightly noisy environment. Our model incorporates mechanisms which allow termination of substable lamellae and creation of new lamellae by the splitting of lamellae larger than a spacing _max. We have studied this model both by a simple analytic approximation and by computer simulation. We find that both the steady state spacing and the regularity of the pattern are sensitively dependent on the ratio _max/_min, where _min is the minimum spacing required for steady state stability. An additional result to emerge from our investigation is that when _max becomes less than a critical value, the system apparently undergoes a transition into a chaotic state.For a review of the eutectic problem see Ref. 2.     

Metallic mesh properties and design of submillimeter filters

By using a Michelson interferometer in the asymmetric mode with helium cooled bolometer, we have measured with precision the complex transmittance and reflectance of metallic meshes in the wavelength region 0.7–4 at normal incidence. The important variations of the transmittance with the angle of incidence have been thoroughly investigated. Changes around the maximum transmittance are explained by the propagation of diffracted modes. Phase measurements show that a sharp dip appearing at _d with 1<_d/g<1.8 is related to the finite thickness of the mesh. From our measurements as well as other data precedently published it appears that there is a linear dependance between _d/g and the relative width of the slots of the mesh. All these deviations from classical models must absolutely be taken in account when designing high performances far infrared filters.     

Realization of holonomic constraints and freezing of high frequency degrees of freedom in the light of classical perturbation theory. Part II

As in Part I of this paper, we consider the problem of the energy exchanges between two subsystems, of which one is a system of harmonic oscillators, while the other one is any dynamical system ofn degrees of freedom. Such a problem is of interest both for the realization of holonomic constraints of classical mechanics, and for the freezing of the internal degrees of freedom in molecular collisions. The results of Part I, which referred to the particular case =1, are here extended to the more difficult case >1. For the rate of energy transfer we find exponential estimates of Nekhoroshev's type, namely of the form exp (_*/)^1/a , where is a positive real number giving the size of the involved frequencies, and _* anda are constants. For the particularly relevant constanta we find in generala=1/ however, in the particular case when the frequencies are equal (collision of identical molecules), we finda=1 independently of , as conjectured by Jeans in the year 1903.     

On the maximization of the central gravitational red-shift of a schwarzschild sphere with a given surface gravitational red-shift

Following Bondi static, spherically symmetric equilibrium configurations with a core and an envelope have been considered. It has been shown that for any configurations with nonnegative pressure and density and with a surface red-shiftz _s 4.77 arbitrarily large central red-shiftsz _c are possible in the limiting case of arbitrarily large radius. The effects of imposition of further constraints in the form of a real speed of sound not exceeding the speed of light are also examined. It is seen that for a given limiting sound-to-light-speed ratio . (i) There exists a limiting surface red-shiftz _s() 1.71. (ii) A configuration withz _s >z _s() is not possible, (iii) A configuration withz _s=z _s() has a unique and finitez _c=z _c(). (iv) Forz _s<z _s() arbitrarily large central red-shifts can be obtained for configurations with arbitrarily large radii.     

A Double Infinity of Oscillator Massless Boson Resonances

In the simplest coupling of a harmonic oscillator with a massless boson field, we show that a family of coupling functions leads to resonances or bound-states of the form E _{n1 n0}()=n ₁ z ₁()+n ₀ z ₀(), where z ₁(), z ₀() are in and n ₁, n ₀ are any nonnegative integers. This holds for arbitrary values of the coupling constant.     

A contact process with a single inhomogeneous site

The one-dimensional basic contact process is a Markov process for which particles give birth on vacant nearest neighbor sites at rate >0 and particles die at rate one. We introduce a one-dimensional contact process with a single inhomogeneous site: the evolution is as above except that a particle located at the origin does not die. Let _c be the critical value of the basic contact process. We show that for _c the upper invariant measures of the inhomogeneous contact process and the basic contact process coincide except at a finite number of sites. The behavior at = _c is much more intersting: the upper invariant measure of the inhomogeneous contact process concentrates on configurations with infinitely many particles, while it is known that the critical basic contact process dies out. So a single inhomogeneity may provoke a perturbation unbounded in space. As a byproduct of our analysis we prove that the connectivity probabilities of the critical basic contact process are not summable. We also give a biological interpretation of this model.     

Diode-pumped Tm: YAG solid-state lasers with indirect and direct manifold pumping

We study the continuous-wave (cw) characteristics of both two-manifold and three-manifold Tm: YAG laser pumped at _p 1.8 µm or _p = 0.785 µm and lasing at ₁ = 2.02 µm. The three-manifold rate equations are adiabatically reduced to their two-manifold form. For each pumping scheme, the steady-state rate equations are combined with the cw differential equations for the forward- and reverse-lasing fields and the pump-depletion differential equation. These three coupled cw differential equations are solved analytically. This gives the linear flux-conservation law between the input pump and the laser output, the minimum crystal length, and optimal output couplings. We show that the major difference between these two pumping schemes is due to the different pump effective absorption cross sections and not the two-for-one cross relaxation. Our example shows that the minimum intensity threshold and optimal crystal length are smaller for pumping at _tp = 0.785 µm than pumping at _p 1.8 µm.