The thickness dependence of the permittivity of barium titanate single crystals

A thickness dependence of the permittivity ofc-domain barium titanate single crystals was found. The experimental results were explained by means of a model of a dielectric with surface layers. The thickness of the layer and the permittivity of the surface layer and bulk of the crystal were determined.

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iO₃

iO₃, -. . , .

     

Möbius function for the set of acyclic directed backbone graphs

Consider a two-rooted graphG, the edges of which are directed in such a way that there are no cycles and every edge belongs to some self-avoiding walk from rootu to rootv which follows the direction of the edges. Au-v backbone ofG is a subgraph formed by taking the union of any subset of directed self-avoiding walks fromu tov. Let _uv be the set of all such backbones ofG partially ordered by set-inclusion. We prove the conjecture of Bhatti and Essam that the Möbius function of this set is given, for acyclicb,b _uv withbb, by(b,b)=(–1) ^c-c , wherec andc are the respective cycle ranks ofb andb. The significance of this result in percolation theory is reviewed together with previous results for other sets of subgraphs.     

New two-color dimer models with critical ground states

We define two new models on the square lattice in which each allowed configuration is a superposition of a covering by white dimers and one by black dimers. Each model maps to a solid-on-solid (SOS) model in which the height field is two dimensional. Measuring the stiffness of the SOS fluctuations in the rough phase provides critical exponents of the dimer models. Using this height representation, we have performed Monte Carlo simulations. They confirm that each dimer model has critical correlations and belongs to a new universality class. In the dimer-loop model (which maps to a loop model) one height component is smooth, but has unusual correlated fluctuations; the other height component is rough. In the noncrossing-dimer model the heights are rough, having two different elastic constants; an unusual form of its elastic theory implies anisotropic critical correlations.     

Stationary solutions of the bogoliubov hierarchy equations in classical statistical mechanics. 3

We continue the analysis of the conjugate equation for the generating function of a Gibbs random point field corresponding to a stationary solution of the classical BBGKY hierarchy. This equation was established and partially investigated in the preceding papers under the same title. In the present paper we reduce a general theorem about the form of solutions of the conjugate equation to a statement which relates to a special case where the interacting particles constitute a quasi—one dimensional configuration.     

Implementation of comparative probability by normal states. Infinite dimensional case

Let be an infinite dimensional Hilbert space and () the set of all (orthogonal) projections on . A comparative probability on () is a linear preorder on () such thatOP1,1O and such that ifP┴R,Q┴R, thenPQP+RQ+R for allP, Q, R in (). We give a sufficient and necessary condition for to be implemented in a canonical way by a normal state onB(), the bounded linear operators on .     

Electronic processes andZ centres in NaCl and KC1 crystals

The paper gives the experimental results of the team-work study of coloured pure and Ca doped NaCl and KC1 crystals. The mechanism of the formation ofR centres by coagulation ofF centres and of the formation ofZ centres fromF centres, cation vacancies and Ca ions is discussed. An alternative model forZ ₃ centres is proposed. The possible connections between physical and chemical behaviour are indicated.

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Z- NaCl 1

NaCl KCl . R- F- Z- F-, Ca. Z ₃-. .

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This work was presented by the courtesy of Prof. R. Maurer at the Symposium on Color Centers, Corvallis, Oregon (1959).

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The authors wish to express their gratitude to K. Suk, K. Listoová and M. Javrková for carefully carrying out the measurements and I. Kunzlová and L. Nováková for preparing the crystals.     

Diffusion of electrons by temperature gradient in plasma of positive column

The inhomogeneous distribution of the concentration of charge carriers in a plasma as a rule excites the deflection of the electron temperature from the equilibrium state by means of a series of interconnected phenomena. In addition to the concentration gradient and the electric field, the temperature gradient also has an influence on the diffusion of electrons.It is shown that in the conditions of the positive column of a d-c discharge the influence of diffusion by a temperature gradient on the electron flux is the same in order of magnitude as the influence of diffusion due to a concentration gradient.

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, ,

, , . , , ., , , , , , .

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In conclusion the authors thank V. Dvoák and K. Pátek for carefully reading the paper and for valuable remarks, and K. Wojaczek for valuable discussions.     

Nonlocality in (1/N)-expanded nonrenormalizable interactions

Nonrenormalizable interactions are studied on the example of the (1/N) ₆ ⁴ model with interaction via the collective = ² mode. In 4<d<6 dimensions, the model is nonrenormalizable by power counting but it does not require more subtractions than in the four-dimensional case. In six dimensions, nonrenormalizability is essential: There are two induced couplings ³ and . The ³ coupling strength can be determined from the requirement that the effective potential has a minimum at ² = = 0. The nonlocal formafactor produced by an infinite number of insertions cannot be determined uniquely, however the ambiguity concentrates in the leading order only. We construct this formfactor using the method of Efimov and Mogilevsky. The resulting theory satisfies unitarity, microcausality and correct spectral properties.     

Relationship between (2 + 1) and (3 + 1)-Friedmann–Robertson–Walker cosmologies; linear,non-linear,and polytropic state equations

It is shown that Friedmann–Robertson–Walker (FRW) cosmological models coupled to a single scalar field and to a perfect fluid fitting a wide class of matter perfect fluid state equations, determined in (3+1) dimensional gravity can be related to their (2+1) cosmological counterparts, and vice-versa, by using simple algebraic rules relating gravitational constants, state parameters, perfect fluid and scalar field characteristics. It should be pointed out that the demonstration of these relations for the scalar fields and potentials does not require the fulfilment of any state equation for the scalar field energy density and pressure. As far as to the perfect fluid is concerned, one has to demand the fulfilment of state equations of the form p+ = f(). If the considered cosmologies contain the inflation field alone, then any (3+1) scalar field cosmology possesses a (2+1) counterpart, and vice-versa. Various families of solutions are derived, and we exhibited their correspondence; for instance, solutions for pure matter perfect fluids and single scalar field fulfilling linear state equations, solutions for scalar fields coupled to matter perfect fluids, a general class of solutions for scalar fields subjected to a state equation of the form p + = are reported, in particular Barrow–Saich, and Barrow–Burd–Lancaster–Madsen solutions are exhibited explicitly, and finally perfect fluid solutions for polytropic state equations are given.     

Symmetries and half-sided modular inclusions of von Neumann algebras

LetN, be a von Neumann algebras on a Hilbert space , a common cyclic and separating vector. Assume to be cyclic and also separating forN . Denote by , _N , _N the modular operators to (, ), (N, ), resp (N , ). Assume now ^-it N ^it N for allt 0. (Such type of inclusions ((N U, ) , ) are called half-sided modular.) Then the modular groups ^it , _N ^ir , _N ^is ,t, r, s generate a unitary representation of the group S1(2, )/Z ₂ of positive energy.Another result is related to two half-sided modular inclusions (₁ , ) and (₂ , ). Under proper conditions the three modular groups ^it , ₁ ^ir , ₂ ^is ,t, r, s generate the three-dimensional subgroup of O(2, 1) of two commuting translations and the Lorentz transformation.Partly supported by the DFG, SFB 288 Differentialgeometrie und Quantenphysik.     

Mach's principle and the reciprocal symmetry of nature

This article develops the postulate that spacetime-charge inversion invariance reflects a fundamental reciprocal symmetry in nature between the two long range forces, from which the derivation of Mach's principle (i.e., the principle that the fundamental parameters of the electromagnetically elementary charged particle are related to those describing the electromagnetically observable universe) follows quite easily. Interpreting this result, it is argued that relativity and quantum mechanics can be made conceptually compatible and mathematically consistent by this reciprocal symmetry if one realizes that relativity isboth a macroscopic, semiclassical theory (i.e., the global half of relativity, described by Eq. (1.1), including special and general relativity) and a microscopic theory (i.e., the local half of relativity, described by Eq. (2.1), including relativistic quantum mechanics and field theory). The reciprocal symmetry of nature, then, promises unique (differential and/or integral) relationships between the coordinate variables of the observers of these tworeciprocally related theories, which implies unique, consistent numerical values for the scalar curvatureR, the massM, and the critical density for closure, _c, of the observable universe [derived from the elementary particle parameters (i.e., the electron mass and Coulomb radius)]. With this symmetry we also postulate a plausible mechanism for spontaneous generation of matter from the ubiquitous (zero-mass ether) nothingness of the Dirac sea of filled negative energy states, and can consistently interpret both the positive and negative-energy state solutions of Dirac's equation for massive, spin-1/2 (i.e., fermion) particles and both the advanced and retarded potential solutions of electromagnetic field equations. It is pointed out that, with this interpretation of the advanced potential solutions from electromagnetic field theory, one can actuallyderive causality from electromagnetic theory.     

The change in primary extinction during decomposition of a super saturated solid solution 1. System Al-Ag

On the basis of the correlation of diffraction data (intensity and width) of a precipitate with the intensity of reflection of a matrix solid solution it is shown that the change in primary extinction during the decomposition of a solid solution of Agin Alis caused by the precipitation of the phase Ag₂Aland not by the production of lattice defects (zones, stacking faults).

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I. Al-Ag

( ) , Ag Al Ag₂Al, ( , ).

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Reported in part at the VIth Scientific Technical Conference on the Application of X-rays held in Leningrad in 1958.

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The author thanks M. Mikovský for preparing the single crystals of the alloy Al-Ag having a high primary extinction and J. Laek and Prof. J. Bedná for carefully checking their homogeneity and chemical composition.     

Is the Free Electromagnetic Field a Consequence of Maxwell's Equations or a Postulate?

It is generally accepted that solutions of so called free Maxwell equations for = 0 (null charge density at every point of the whole space) describe a free electromagnetic field for which flux lines neither begin nor end in a charge). In order to avoid ambiguities and unacceptable approximation which have place in the conventional approach in respect to the free field concept, we explicitly consider three possible types of space regions: (i) isolated charge-free region, where a resultant electric field with the flux lines which either begin or end in a charge is zero in every point, for example, inside a hollow conductor of any shape or in a free-charge universe; (ii) non-isolated charge-free region, where this electric [see (i)] field is not zero in every point; and (iii) charge-neutral region, where point charges exist but their algebraic sum is zero. According to these definitions a strict mathematical interpretation of Maxwell's equations gives following conclusions: (1) In isolated charge-free regions electric free field cannot be unconditionally understood neither as a direct consequence of Maxwell's equations nor as a valid approximation: it may be introduced only as a postulate; nevertheless, this case is compatible is the existence of a time-independent background magnetic field. (2) In both charge-neutral and non-isolated charge-free regions, where the condition = function or = 0 respectively holds, Maxwell's equation for the total electric field have non-zero solutions, as in the conventional approach. However, these solution cannot be strictly identified with the electric free field. This analysis gives rise to the reconsideration of the free-electromagnetic field concept and leads to the simplest implications in respect to charge-neutral universe.     

The distribution of ions and their valencies in manganese ferrites II. Mn1+xFe2-xO4+y ferrites

The influence of the oxygen content on the saturation magnetic moment and the Curie temperature was studied experimentally on non-stoichiometric manganese ferrites having a varying excess of manganese. Taking into consideration the results of studying the electrical conductivity and magnetic relaxation effects, a model was elaborated for the distribution of ions in these ferrites, which starts out from the distribution of ions in stoichiometric manganese ferrite. The experimental results obtained by us and those of other authors confirm the justification of this model.

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II. Mn_1+xFe_2-xO_4+y

. , . .

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In conclusion the authors thank members of their technological department for preparing the samples and M. Mikulá for carefully carrying out the chemical analyses.     

Der Exzitonenzerfall im elektrostatischen Felde der Störstellen von Ionenkristallen

Zusammenfassung Es wird theoretisch der Prozeß des Exzitonenzerfalls mit Hilfe der Ionisation durch das elektrostatische Feld der Störstelle untersucht. Die Wirkungsquerschnitte werden in zwei Grenzfällen bestimmt: bei einer kleinen und einer großen mittleren freien Bahn des Exzitons, die durch dessen Wechselwirkung mit den Phononen bedingt ist. Die Ergebnisse werden zum Studium des Exzitonenzerfalls an einer Vakanz nach einem Kupferion in Cu₂O-Kristallen mit einem stöchiometrischen Sauerstoffüberschuß verwendet.

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. : , . Cu₂0 .

     

Diffusion parameters of thermal neutrons in diphenyl

The diffusion length, diffusion coefficient and mean life time of thermal neutrons in rigid, Czechoslovak made, diphenyl were measured by the impulse method at the temperature 20°C. The experimental results are discussed.

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, ( ) 20°C. .

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We thank J. Jadavan and the accelerator group for their co-operation.     

Renewal Sequences and Intermittency

In this paper we examine the generating function (z) of a renewal sequence arising from the distribution of return times in the turbulent region for a class of piecewise affine interval maps introduced by Gaspard and Wang and studied by several authors. We prove that it admits a meromorphic continuation to the entire complex z-plane with a branch cut along the ray (1, +). Moreover, we compute the asymptotic behavior of the coefficients of its Taylor expansion at z=0. From this, we obtain the exact polynomial asympotics for the rate of mixing when the invariant measure is finite and of the scaling rate when it is infinite.     

Solutions without phase-slip for the Ginsburg-Landau equation

We consider the Ginsburg-Landau equation for a complex scalar field in one dimension and consider initial data which have two different stationary solutions as their limits in space asx±. If these solutions are not very different, then we show that the initial data will evolve to a stationary solution by a phase melting process which avoids phase slips, i.e., which does not go through zero amplitude.     

К ВОПРОСУ ВТОРИЧНОЙ Э МИССИИ ОКСИДНЫХ КАТОДОВ

, .     

РАДИАЦИОННЫЙ ЗАХВАТ ТЕПЛОВЫХ НЕЙТРОНОВ ЯДРОМ II

, -, Na, Co, Zn, Ag J 20÷1000 keV. Co, Zn, Te J .

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Radiative capture of thermal neutrons on nucleus II

The energies and intensities of gamma rays from the capture of a neutron on Na, Co, Zn, Ag, Te and I nucleus in the 20–1000 keV energy region were measured with a single-crystal, single-channel scintillation spectrometer. New energies of radiative transition were measured when measuring Co, Zn, Te and I nuclei.