Variance calculations and the Bessel kernel

In the Laguerre ensembleof n xN Hermitian matrices, it is of interest both theoretically and for applications to quantum transport problems to compute the variance of a linear statistic, denoted var_N f, asN . Furthermore, this statistic often contains an additional parameter a for which the limit is most interesting and most difficult to compute numerically. We derive exact expressions for both lim_N var_N f and lim , lim_N var_N f.     

Spectroscopic study of a TEA CO2 laser of the CO2/X,X=H2; N2/H2 type

The spectral output of a TEA CO₂ laser utilizing nonconventional CO₂/H₂ and CO₂/N₂/H₂ gas mixtures was analysed. A simultaneous multiline output in P-branch of the 00°110°0 transition was recorded. A domination of the P(18) line is typical for the first, and that of the P(20) line for the second gas mixture. The enhancement of the P(18) line intensity in spectra (different from P(20) line domination-CO₂/N₂/H₂ mixture) is explained primarily by a smaller contribution of the R(23) line gain (01¹111¹0 CO₂ band), to P(20) line (00°110°0 band). All measurements were conducted with a nondispersive optical cavity.     

Singular perturbations of piecewise monotonic maps of the interval

Let t: [0, 1] [0, 1] be a piecewise monotonic, C₂, and expanding map. In computing an orbit { ⁱ (x ₀)} _i=0 , we model the roundoff error at each iteration by a singular perturbation; i.e.,X _n+1=(X _n )+W , whereW is a random variable taking on discrete values in an interval (-ε, ). The main result proves that this process admits an absolutely continuous invariant measure which approaches the absolutely continuous measure invariant under the deterministic map t as the precision of computation 0.     

Energy spectrum of electron pairs in a high energy photon-electron cascade

The energy spectrum of electron pairs generated in a high energy photon-electron cascade up to a depth of 1·5 c. u. was measured and the possible influence of the medium on the shape of the spectrum according to Landau-Pomeranuk-Ter Mikaelyan and Migdal was investigated. Two procedures were used for the analysis; no significant deviation from the Bethe-Heitler spectrum could be observed. Different ways of estimating the primary energy were applied; the resulting value, 2×10¹²eV, was accepted as the primary energy.

---

-

, - 1,5 , - . ; - . ; 210¹² eV.

---

---

The authors wish to thank Dr. Lanius for kindly lending them the necessary plate from the Berlin part of the I-stack.     

Metastable states of an asymmetric spin-glass with one stored pattern

The number of metastable states in a spin-glass with asymmetric Gaussian couplings (J _ij J _ji ) is studied. In order to store one pattern a generalized stability condition on the local energies is considered for a part of the system (=n/N) only. The average number of metastable states is calculated analytically as a function of the overlapm in the thermodynamic limit. For the contribution of the storage restriction an approximation is introduced to simplify the calculations. The corresponding saddlepoint equations are solved numerically for two distribution functions of the local energies. For several values of the parameters we find two bands with an exponential number of metastable states. At a critical value _crit the second band disappears. The critical value for the storage parameter is calculated numerically. As expected we find _crit1 for 0.Work performed within the research program of the Sonderforschungsbereich 341, Köln-Aachen-Jülich     

Triple Fluorescence of Substituted Benzanilides in Solution and in Solid States

The competitive triple fluorescence of benzanilide is studied by steady-state fluorescence investigations in dependence on the solvent polarity and the para-substitution of the aniline core as well as by comparison with the fluorescence behavior of 4-methoxy-N-methylbenzanilide. The normal fluorescence of benzanilide S₁(LE) S₀ appears at _max = 345 nm, whereas a superposition of proton transfer (PT) fluorescence S₁(PT) S₀(PT) and intramolecular charge transfer (ICT) flu-orescence S₁(ICT) S₀(FC) is responsible for the long-wavelength fluorescence in the 500-nm region. Different possibilities for the formation of the PT and ICT states are discussed. Investigations of the fluorescence behavior of benzanilides both in solution and as crystals in dependence on the para-substitution of the benzanilide moiety support the PT/ICT model.     

Steady-State Spectroscopic and Fluorescence Lifetime Measurements of New Two-Photon Absorbing Fluorene Derivatives

Steady-state excitation anisotropy, lifetimes, and time-resolved emission spectra of new 2-photon absorbing fluorene derivatives were measured in aprotic solvents at room temperature. Excitation anisotropy spectra in viscous silicon oil allowed the determination of the spectral position of three electronic transitions S₀ S₁, S₀ S₂, S₀ S₃ (S_i, i = 1, 2, 3 are the singlet electronic states) and the angles ( 30°) between absorption S₀ S₁ and emission S₁ S₀ dipole moments for the first electronic transition. Solvate relaxation processes in the first excited state of the investigated fluorene molecules affect the lifetimes of these states, ₁, so that experimental values of ₁ do not correspond to those calculated by Strickler and Berg theory. The influence of the molecular concentration on the fluorescence quantum yields and ₁ have been investigated.     

Experimental study of cw carbon monoxide flame chemical laser of the CS2/O2/CO2 type

The performance of a continuous-wave (cw) CO flame chemical laser (FCL) of the CS₂/O₂/CO₂ type is presented. The laser gives up to 0.7 W cw output power on a number ofP _v (J) lines corresponding to 1110, ..., 76 vibrational bands of CO molecule. The measured values of chemical efficiency based on the reaction O+CSCO^*(v)+S and the specific power are 0.1% and 0.7J/g, respectively. The spectral composition of the CO FCL of the CS₂/O₂/CO₂ type shows lasing in the region from 5.194 to 5.573 m. All experimental measurements are conducted with a nondispersive optical cavity.     

One- and Two-Photon Fluorescence Anisotropy of Selected Fluorene Derivatives

The steady-state excitation anisotropy spectra of fluorene derivatives were measured in viscous solvents, under the one- and two-photon excitation, over a broad spectral range (UV–Visible). The orientation of their absorption transition moments for the first, S₀S₁, and second, S₀S₂, excited states were determined. It was shown experimentally that a decrease in the angle between S₀S₁and S₀S₂ transitions corresponded to an increased value of two-photon absorption (2PA) cross section for these molecules. Two-photon excitation anisotropy was nearly constant over the spectral region investigated (in contrast to one-photon excitation anisotropy spectra) and can be roughly explained by a simple model of 2PA based on the single intermediate state approximation. For comparison, the same trend in two-photon excitation anisotropy was observed for Rhodamine B inglycerol.     

A lower bound for the memory capacity in the Potts-Hopfield model

We consider Potts-Hopfield networks of sizeN. We prove the result: _c >0 such that for all 0<< _c we can find, >0 in such a way that, whenN, we can store N patterns, all of them being sorrounded by -energy barriers at distance.     

Radiation effects in the production and decay of ψ mesons by leptons

A new expression _e is obtained for resonance in the reaction e⁺e^– ar ^+– with allowance for the radiative corrections, which also contain the emission of hard photons by the final leptons and the final value of the energy resolution E. An expression is obtained for the total probability of radiative lepton decay. A numerical analysis of the experimental data is made for the reaction ^+–, and the parameters e⁺e^– (3, 1) e⁺e^–, and _e ² /, _e, and are determined for (3, 1) resonance-with allowance for the radiative corrections.This paper was read (November 17–21, 1975) at a session on high-energy physics of the Department of Nuclear Physics of the Academy of Sciences of the USSR.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 29–34, March, 1977.     

A dual-polarization InSb receiver for 461/492 GHz

A dual-polarization InSb hot-electron bolometer-mixer receiver has been built for the James Clerk Maxwell Telescope, for operation at 461 and 492 GHz (the frequencies of theJ=43 rotational transition of CO and of the³ P ₁³ P ₀ transition of neutral carbon). Receiver noise temperatures of 500K have been obtained at 461 GHz, in observing bandwidths of 3 MHz. The receiver was designed as a common-user or facility instrument. Here we describe those aspects of the design and construction which enabled this goal to be realized.     

On the asymptotics of occurrence times of rare events for stochastic spin systems

We consider translation-invariant attractive spin systems. LetT _,x ^v be the first time that the average spin inside the hypercube reaches the valuex when the process is started from an invariant measure with density smaller thanx. We obtain sufficient conditions for (1) ¦¦^–1 logT _,x ^v (x) in distribution as ¦¦ , and ¦¦^–1 logT _,x ^v (x) as ¦¦ , where (x):= –lim ¦¦^–1 log {(average spin inside ) x. And (2)T _,x ^v /ET _,x ^v converges to a unit mean exponential random variable as ¦¦ . Both (1) and (2) are proven under some type of rapid convergence to equilibrium. (1) is also proven without extra conditions for Ising models with ferromagnetic pair interactions evolving according to an attractive reversible dynamics; in this case is a thermodynamic function. We discuss also the case of finite systems with boundary conditions and what can be said about the state of the system at the timeT _,x ^v .On leave from São Paulo University.     

Estimation of the Sea Level Muon Spectra at Different Zenith Angles below 10 TeV Energy

The moderate energy primary cosmic ray nucleon spectrum has been calculated from the direct measurements of Webber et al., Seo et al., and Menn et al. along with the other results surveyed by Swordy. Using these directly measured primary mass composition results all particle primary nucleon energy spectrum has been constructed using superposition model to estimate the energy spectra of muons from the decay of the cosmic ray non-prompt and prompt mesons in the atmosphere. The Z-factors have been estimated from the CERN LEBC-EHS on the Lorentz invariant cross section results on pp ^±X and pp K^±X inclusive reactions and FNAL data on ^±p ^±X reactions, and duly corrected for A--A collisions. Using these Z-factors the meson energy spectra in the atmosphere have been calculated. The sea level muon energy spectra at zenith angles 0°, 45°, 72°, and 75° have been derived from the decay of non-prompt mesons by adopting standard diffusion equation of hadronic cascades. The contribution of charmed mesons to muon spectrum has also been accounted by adapting the conventional procedure. The derived differential sea level muon energy spectra for energies 10 TeV have been found to follow the power law fits of the form N (E) const. E ^-. Our estimated muon energy spectra at zenith angles 75° have been found comparable with the global spectrograph muon flux results of MARS, DEIS, and MSU groups.     

Energy spectrum and angular distribution of muons from the decay of heavy leptons produced in colliding electron-positron beams

On the basis of an arbitrary (V, A) structure of the neutral weak ¯ee and LL currents (L=^–, M⁰) a study is made of the processes of production in colliding electron-positron beams of pairs of heavy leptons with subsequent decays in accordance with the schemes e⁺e^––(µ^–v_µv) + ⁺( anything) and e⁺e^–M⁰(µ^–e⁺v_e) + M⁰( anything). The energy spectrum and asymmetry of the distribution of the produced muons are investigated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 66–70, February, 1981.     

Effect of electrolytically deposited nickel films on the magnetic properties of iron-silicon alloy

The effect of electrolytically deposited nickel films on the magnetostriction, coercive force, residual induction, and the position with respect to each other of the magnetic susceptibility maxima _max. _max of specimens of iron-silicon alloy is investigated. It is shown that elastic extensions lead to a reduction in the spacing between the maxima _max, _max , and for certain loads this spacing disappears and only one maximum is observed.     

A central limit theorem for the Fourth Wick power of the free lattice field

LetG _a be the free lattice field measure of massm ₀ onaZ ^d , and: _x ⁴ : be the corresponding fourth Wick power of the lattice field _x . LetgC ₀ (R ^d ),g0, be a given function anda=a(a)a satisfy: lim _a0+a=0 andaZ ^d aZ ^d . We prove that ifd3, ord=2 and lim _a0+ a|loga|²=, then satisfies the central limit theorem: there isV(a, a) with lim _a0+ V(a, a)= such that the distribution of underG _a is convergent to the standard normal distribution, asa0⁺.     

Characteristics of Fe2O3 Nanoparticles Prepared by Heat Treatment of a Nonaqueous Powder Precipitate

Nanosized particles of Fe₂O₃ with a narrow size distribution (5–20-nm) were prepared by heat treatment of powder precipitates obtained from a nonaqueous homogeneous solution of stearic acid and iron(III) nitrate. Differential scanning calorimetric studies and infrared spectroscopic studies on the as prepared powder precipitates revealed the presence of Fe–O-stearate intermediate/complex, which subsequently transformed to -Fe₂O₃ when heat treated at 200°C for 30-min. The crystallographic -Fe₂O₃ transformation and the particle size distribution of the nanosized particles were studied with the help of X-ray diffraction and small angle X-ray scattering technique. Crystallographic transformation of nanosized Fe₂O₃ has been found to occur at 200°C, which is well below the temperature reported elsewhere.     

Particle polarizations in decays of5HeΛ and4HΛhypernuclei

Nucleon polarizations are examined in the hypernucleus decays⁵He, ⁴He + p + _–,⁴H, ³H + p + _–, and⁴H, ³He + n + _–. The effect of the strong interaction in the final state is taken into account. A significant role is predicted for the resonance interaction in the p-⁴He system in the formation of the proton polarization in the⁵He decay. It is also shown that in the⁴H, ³H + p + _– decay the proton-polarization components should attain significant magnitudes, while in the charge-exchange decay⁴H, ³He + n + _–, the neutron polarization is expected to be not too large.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 100–103, October, 1988.