Study of magnetic after-effect in magnesium manganese ferrites

The magnetic after-effect caused by the diffusion of electrons was studied in detail in MnMg ferrites of the series Mg _x Mn_1.15–x Fe_1.85O₄₊ ; the comparative measurements were also carried out on a sample of MgFe₂O₄₊₍<0). By combining the two methods, (a) investigation of the disaccommodation of initial permeability at different temperatures and (b) measurement of the displacement of the maximum of the temperature dependence tan with the frequency, it was possible to study the relaxation processes whose time constants lay between 0.5 sec and several hours, or between 10^–4 to 10^–7 sec. It was found that the processes taking place at low temperatures and studied by method (a) differ from those observed at high temperatures by method (b), particularly in the lower activation energies and greater dispersion of the time constants. In addition to these two main relaxation processes a weak relaxation superposed over the main disaccommodation was found in ferrites with non-zero content of manganese. An analysis of the intensity of different relaxation effects showed the participation of Mn ions in these relaxation effects and it was found that both main relaxations are probably equivalent as regards the final steady state, to the creation of which they lead; they differ however in the mechanism of electron diffusion by which this state is realized. The main features of the different diffusion mechanisms are discussed.

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, , MnMg Mg _x Mn_1.15–x Fe_1.85O₄₊ . MgFe₂O_{4+ (}<0). ()- , () tg , , 0,5 sec , 10^–4–10^–7 sec. , , () , , (), , , . , . Mn , , , , , ; , , , . .

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In conclusion the author thanks Dr. J. Bro and K. Závta for valuable discussion and F. Vilím for carefully carrying out the measurements.     

Asymptotic theory of multidimensional chaos

A delay-differential equationu(t)+u(t)=f(u(t–1)), 0t < , and its generalization are investigated in the limit 0, when the attractor's dimension increases infinitely. It is shown that a number of statistical characteristics are asymptotically independent of. As for the attractor, it can be regarded as a direct product ofO(1/) equivalent subattractors, their statistical characteristics being asymptotically independent of . The results enable one to predict some characteristics of the attractor with fractal dimensionD 1 for the case 1, when they are inaccessible numerically. The approach developed seems to be applicable for a wide class of spatiotemporal systems.     

Defect annealing of alpha-particle irradiated n-GaAs

The annealing behaviour of irradiation induced defects in n-type GaAs irradiated at 300 K with 5.4 MeV alpha-particles from an americium-241 (Am-241) radio nuclide have been investigated. The annealing kinetics are presented for the alpha-particle induced defects E1–E5 detected in Organo-Metallic Vapor Phase Epitaxially (OMVPE) grown n-GaAs doped with silicon to 1.2×10¹⁶ cm^–3, these kinetics are compared to those obtained for similar defects (E1–E5) detected after electron irradiation. While defects P1 and P2 were detected after removal of the electron defects E4 and E5, respectively, a new defect labelled P0, located 0.152 eV below the conduction band, was introduced by annealing. The thermal behaviour and trap characteristics of these three defects (P0–P2) are presented. In an attempt to further characterise defects P0 and P1 a preiliminary study investigating the emission rate field dependence of these defects was conducted, it was observed that defect P0 exhibited a fairly strong field dependence while P1 exhibited a much weaker dependence.     

Microwave relaxation and phenomenological damping in thin films

The relation between relaxation timeT, frequency swept resonance linewidth , and phenomenological damping is given by =2/T=(_x+_y), where _x,y = (H ₀+(N _x,y –N _z ) 4M _s ).N _x,y,z are sample demagnetizing factors,H ₀ is the effectivez-directed static field, 4M _s is the saturation induction, and is the gyromagnetic ratio. This fairly simple but general relation shows that the numerical relation between damping and relaxation at a given frequency can be quite different for in-plane and normally magnetized thin films. For thesame loss processes, so thatT andT are equal, is larger than . For permalloy films at 1 GHz, =15 . In addition, the conventional field swept linewidth, H=/, is simply related to only forN _x =N _y . Both and H are geometry dependent and do not provide an intrinsic measure of the relaxation. These results are confirmed by both resonance and transient response experiments. The large values of for large angle switching may also be partially explained by this analysis because the relevant magnetization motion is due to a demagnetizing field normal to the film plane.Visiting scientist on leave fromRaytheon Company, U.S.A. Supported by the Japan Society for the Promotion of Science.     

On longitudinal vibrations of thin cylindrical tubes

The method of variable coupling parameters is used for approximatively calculating the frequencies of longitudinal vibrations of isotropic homogeneous tubes. For thin-walled tubes we arrive at the same formula for frequencies as in Love's classical theory.

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НИЗКОЧАСТОТНЫЕ КОЛЕ БАНИЯ ПРЯМОУГОЛЬНЫХ ПЛАСТИНОК ADP

- — . , - NH₄H₂PO₄,- ADP. ; - .     

Harmonic mixing by weakly pinned charge density waves

Third order harmonic mixing voltageE ₀ in case of frequency matching, =₂–₁=0, and third order pseudo harmonic mixing currentj() in the detuned case, 0, are evaluated for the one-dimensional Fukuyama-Lee-Rice model for weakly pinned charge density waves in the region of sub-threshold bias electric fields. After a perturbation expansion of the phase response to the ac driving fields the impurity averaging is performed diagrammatically. Specific statistical properties of the charge density wave phase in the weak pinning limit and a non-trivial result for the pinning of the static phase are utilized to expressE ₀ andj() in terms of the dielectric function (). A recent evaluation of () within the self-consistent Born approximation is used to present the results explicitly in a number of diagrams. In comparison to the overdamped anharmonic oscillator the following differences are found: Randomness leads to interference contributions which increase the amplitudes and decrease the phase shifts. The more realistic form for () at lower frequencies lead to a downward shift in the maximum ofj() when ₁ is decreased below the cross-over frequency _c . The present theory retains inertia in the dynamical equations and remains valid for frequencies near and above the pinning frequency. It fails, however, for small frequencies _{1 c} due to the neglect of metastable states and screening.     

The free energy of a class of Hopfield models

We show that in the limitp ,N 0,=p/N 0 the limit free energy of the Hopfield model equals in probability the Curie-Weiss free energy. We prove also that the free energy of the Hopfield model is self-averaging for any finite .     

The Landau-Lifshitz equation,elliptic curves and the ward transform

The Landau-Lifshitz (LL) equation is studied from a point of view that is close to that of Segal and Wilson's work on KdV. The LL hierarchy is defined and shown to exist using a dressing transformation that involves parameters ₁, ₂, ₃ that live on an elliptic curve . The crucial role of the groupK ₂ × ₂ of translations by the half-periods of and its non-trivial central extension is brought out and an analogue of Birkhoff factorisation for -equivariant loops in is given. This factorisation theorem is given two treatments, one in terms of the geometry of an infinite-dimensional Grassmannian, and the other in terms of the algebraic geometry of bundles over . Further, a Ward-like transform between a class of holomorphic vector bundles on the total spaceZ of a line-bundle over and solutions of LL is constructed. An appendix is devoted to a careful definition of the Grassmannian of the Frechet spaceC (S ¹).     

Four-wave mixing in CO via the C 1Σ+ (υ′=0) state

Coherent vacuum ultraviolet (VUV) radiation was generated by four-wave difference frequency mixing (_VUV=2₁–₂) of pulsed dye laser radiation in carbon monoxide (CO). The frequency ₁ was tuned to the C ¹⁺(=0)X ¹⁺(=0) two-photon transition, while the dye laser frequency ₂ was scaned around 17650 cm^–1 which corresponds to the A ¹(=7)«C ¹⁺(=0) transition energy. The VUV intensity was found to be strongly wavelength dependent. The analysis of the spectrum revealed (i) that the VUV intensity was enhanced by the rotational levels of the A ¹(=7) state and (ii) that the off-resonance excitation in the C ¹⁺(=0)X ¹⁺(=0) two-photon transition greatly contributed to the present four-wave mixing process. The effects of pumping laser detuning, saturation and foreign gases are briefly discussed.     

Superstability estimates for anharmonic systems

We consider an anharmonic crystal described by variablesS _x ,x ^d ,S _x , with one-body interaction ¦S _x ¦ and nearest neighbor (n.n.) two body interaction ¦S _x –S _y ¦. We prove that, for ^d bounded, , where is the correlation function for the free boundary condition Gibbs state in ,>0 and are suitable constants independent of and . This generalizes previous results obtained in the case.Research partially supported by Consiglio Nazionale delle Ricerche.     

A New Method of the High Temperature Series Expansion

We formulate a new method of performing high-temperature series expansions for the spin-half Heisenberg model or, more generally, for SU(n) Heisenberg model with arbitrary n. The new method is a novel extension of the well-established finite cluster method. Our method emphasizes hidden combinatorial aspects of the high-temperature series expansion, and solves the long-standing problem of how to efficiently calculate correlation functions of operators acting at widely separated sites. Series coefficients are expressed in terms of cumulants, which are shown to have the property that all deviations from the lowest-order nonzero cumulant can be expressed in terms of a particular kind of moment expansion. These quasi-moments can be written in terms of corresponding quasi-cumulants, which enable us to calculate higher-order terms in the high-temperature series expansion. We also present a new technique for obtaining the low-order contributions to specific heat from finite clusters.     

Traces,Dispersions of States and Hidden Variables

No Heading The interplay between the tracial property and minimality of dispersions of states on projections of von Neumann algebras and C^*-algebras is investigated. Let be a state on a C^*-algebra A with the projection structure P(A). The dispersion () is defined as () = sup{(p) – (p)² | p P(A)}. It is proved that () 2/9 whenever is a state on a real rank zero C^*-algebra with no nonzero abelian representation. New characterization of traces in terms of dispersions is proved: A state on a von Neumann algebra without abelian and Type I₂ direct summands is a trace if and only if has the minimal dispersion on all 3x3 matrix substructures. A similar characterization of semifinite normal traces on von Neumann algebras is obtained. The connection between unitary invariance of states and minimal dispersion property on C^*-algebras is studied. Besides providing a new characterization of trace in terms of physically relevant properties, the existing results on hidden variables in W^*- and C^*-formalism of quantum mechanics are strengthen.     

Stochastic gravity

We investigate stochastic gravity as a potentially fruitful avenue for studying quantum effects in gravity. Following the approach of stochastic electrodynamics (sed), as a representation of the quantum gravity vacuum we construct a classical state of isotropic random gravitational radiation, expressed as a spin-2 field,h _µ (x), composed of plane waves of random phase on a flat spacetime manifold. Requiring Lorentz invariance leads to the result that the spectral composition function of the gravitational radiation,h(), must be proportional to 1/ ². The proportionality constant is determined by the Planck condition that the energy density consist of/2 per normal mode, and this condition sets the amplitude scale of the random gravitational radiation at the order of the Planck length, giving a spectral composition functionh() =16c ²L_p/². As an application of stochastic gravity, we investigate the Davies-Unruh effect. We calculate the two-point correlation function (R _iojo(O–/2)R _kolo(O,+/2)) of the measureable geodesic deviation tensor field,R _iojo, for two situations: (i) at a point detector uniformly accelerating through the random gravitational radiation, and (ii) at an inertial detector in a heat bath of the random radiation at a finite temperature. We find that the two correlation functions agree to first order ina/c provided that the temperature and acceleration satisfy the relationkT=a/2c.     

The spectrum of a quasiperiodic Schrödinger operator

The spectrum (H) of the tight binding Fibonacci Hamiltonian (H _mn= _m,n+1+ _m+1,n + _m,n v(n),v(n)= ((n–1)), 1/ is the golden number) is shown to coincide with the dynamical spectrum, the set on which an infinite subsequence of traces of transfer matrices is bounded. The point spectrum is absent for any , and (H) is a Cantor set for 4. Combining this with Casdagli's earlier result, one finds that the spectrum is singular continuous for 16.On leave from the Central Research Institute for Physics, Budapest, Hungary     

Kinetic limit of a conservative lattice gas dynamics showing long-range correlations

An anisotropic lattice gas dynamics is investigated for which particles on ^d jump to empty nearest neighbor sites with (fast) rate ^–2 in a specified direction and some particular configuration-dependent rates in the other directions. The model is translation and reflection invariant and is particle conserving. The space coordinate in the fast-rate direction is rescaled by ^–1. It follows that the density field converges in probability, as 0, to the corresponding solution of a nonlinear diffusion-type equation. The microscopic fluctuations about the deterministic macroscopic evolution are determined explicitly and it is found that the stationary fluctuations decay via a power law (1/r ^d ) with the direction dependence of a quadrupole field.     

Logically independent von Neumann lattices

Three definitions of logical independence of two von Neumann latticesP₁,P₂ of two sub-von Neumann algebras ₁, ₂ of a von Neumann algebra are given and the relations of the definitions clarified. It is shown that under weak assumptions the following notion, called logical independence is the strongest:A B 0 for any 0 A P₁, 0 B P₂. Propositions relating logical independence ofP₁,P₂ toC ^*-independence,W ^* independence, and strict locality of ₁, ₂ are presented.     

A contribution to direct processes in the Co59(p,n) reaction forE p ∼ 6·5 MeV

Nuclear emulsions were used to study the energy spectrum and forward-backward asymmetry of neutrons from the Co⁵⁹(p,n) reaction forE _p 6·5 MeV. It was found that the decay of the compound nucleus makes a maximum contribution of 50% to the reaction yield. Energies of some excited states of the Ni⁵⁹ nucleus were also determined.

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Co⁵⁹(p,n) E _p 6,5 MeV

- Co⁵⁹(p,n) E _p 6,5 MeV. , 50%. , Ni⁵⁹.

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The authors would like to thank all those who helped in this work, particularly all members of the cyclotron group of the Nuclear Research Institute of the Czechoslovak Academy of Sciences, who so willingly helped with the irradiation, and H. Koutová from the Faculty of Technical and Nuclear Physics, who carefully measured the emulsions. Our thanks are also due to R. Krejová from the Faculty of Technical and Nuclear Physics for developing the emulsions and J. Kopecký from the Nuclear Research Institute for providing the cobalt target.     

Scaling in the mean of the p+p→π0+X inclusive reaction data and the energy dependence of Feynman variable

We have studied the p+p⁰+X inclusive reaction data of Carey et al. in the framework of the scaling in the mean hypothesis first proposed by Dao et al. These data have been used to obtain the gamma ray spectrum in terms of the average value of the Feynman variablex, written as x.A comparison with the observed gamma ray spectrum at Mt. Chacaltaya by the Japanese and Brazilian Group gives the energy dependence of x at very high energy.     

Absolute Continuity of Vitali–Hahn–Saks Measure Convergence Theorems

In this paper, we prove the following improved Vitali–Hahn–Saks measure convergence theorem: Let (L, 0, 1) be a Boolean algebra with the sequential completeness property, (G, ) be an Abelian topological group, be a nonnegative finitely additive measure defined on L, {_n: n N} be a sequence of finitely additive s-bounded G-valued measures defined on L, too. If for each a L, {_n(a)}_{n N} is a -convergent sequence, for each nN, when { (a)} convergent to 0, {_n(a)} is -convergent, then when { (a)} convergent to 0, {_n(a)} are -convergent uniformly with respect to nN