A Generalized Hypergeometric Function II. Asymptotics and <Emphasis Type="Italic">D</Emphasis><Subscript><Emphasis Type="Italic">4</Emphasis></Subscript> Symmetry

In previous work we introduced and studied a function that generalizes the hypergeometric function. In this paper we focus on a similarity-transformed function , with parameters ⁴ related to the couplings c⁴ by a shift depending on a ₊ , a _– . We show that the -function is invariant under all maps w(), with w in the Weyl group of type D ₄ . Choosing a ₊ , a _– positive and real, we obtain detailed information on the |Re v| asymptotics of the -function. In particular, we explicitly determine the leading asymptotics in terms of plane waves and the c-function that implements the similarity R.     

The quantum efficiency of the internal photo-electric effect in indium antimonide

A method is described for measuring the relative quantum efficiency of the internal photo-electric effect in semi-conductors by simultaneously measuring the photo-magnetoelectric and photo-conductive effect. The results of measurements on indium antimonide are given. The quantum efficiency begins to increase if the energy of the photon exceeds 0·47 eVat room temperature. The quantum efficiency as a function of the energy of the photon is analysed on the basis of the conception of impact ionization and it is shown that a study of the structure of this curve can supply information on the, band structure of a semi-conductor in the region of high energies of electrons and holes.

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. . , 0,47 eV . , .

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The authors thank M. Závtová and M. Vantuchová for efficient help with the measurements, K. mirous and V. Vrchovská for preparing the material, E. Antoník for critical remarks and M. Matyá and A. Müller for determining the constants of the material.     

СЕРНИСТЫЙ ТЕЛЛУР — ПО ЛУПРОВОДИОЕ СОЕДИНЕ НИЕ

, , , , .     

Trigonometric Dynamical <Emphasis Type="Italic">r</Emphasis>-Matrices Over Poisson Lie Base

Let be a finite dimensional complex Lie algebra and a Lie subalgebra equipped with the structure of a factorizable quasitriangular Lie bialgebra. Consider the Lie group Exp with the Semenov-Tjan-Shansky Poisson bracket as a Poisson Lie manifold for the double Lie bialgebra . Let be an open domain parameterizing a neighborhood of the identity in Exp by the exponential map. We present dynamical r-matrices with values in over the Poisson Lie base manifold .*This research is partially supported by the Emmy Noether Research Institute for Mathematics, the Minerva Foundation of Germany, the Excellency Center Group Theoretic Methods in the study of Algebraic Varieties of the Israel Science foundation, and by the RFBR grant no. 03-01-00593.     

Structure,transport and magnetic properties of the double perovskite (Ca<Subscript>2-2x</Subscript>Sr<Subscript>2x</Subscript>)FeMoO<Subscript>6</Subscript>

In this paper we report the results of a detailed investigation of the double perovskite (Ca_2-2xSr_2x)FeMoO₆ system. Chemical size effects on structural, electrical, and magnetic properties caused by the substitution of isovalent, larger Sr ions into the smaller Ca sites, resulting in (Ca_2-2xSr_2x)FeMoO₆, have been examined. The compounds crystallize in the monoclinic space group P2₁/n for 0.0x<0.2, the orthorhombic space group Pbnm for 0.2x<0.4, and the tetragonal space group I4/m and I4/mmm for x0.4. Examination of the resistivity of all compounds reveals a metallic behavior which is well described by a Tⁿ dependence except for x=1.0. These n values change from 1 to 2 as T decreases lower than T_c. This is indicative of a variation in the transport mechanism at T_c. The ferrimagnetic transition temperature T_c increases with increasing x from 318 (x=0.0) to 393 K (x=1.0). For all samples, the saturation magnetization at 82 K obeys M_s3.5_B/(formula unit), compared to a theoretical spin-only moment of 4_B/(formula unit) for a perfectly ordered compound. PACS 74.25.Fy; 74.25.Ha     

Relationship between low frequency dielectric dispersion and ferroelectric phase transition in pulsed-laser-deposited Bi<Subscript>4-x</Subscript>La<Subscript>x</Subscript>Ti<Subscript>3</Subscript>O<Subscript>12</Subscript> thin film

The frequency and temperature dependence of the complex dielectric constant of Bi_4-xLa_xTi₃O₁₂ (BLT, x=0.9) ferroelectric thin film was studied in the frequency range of 10^-110⁶ Hz and the temperature range of 298673 K. A low frequency dielectric dispersion (LFDD) was found. A model was proposed to account for this observed phenomena. The complex dielectric constant data obtained in the measured frequency and temperature ranges have been found to fit very well to the dielectric dispersion relation: ^*=+i/₀+[B(i)^n-1]/₀. The knee in the log of the electrical conductivity versus the reciprocal temperature curve occurs at T_c. The activation energies associated with charge conduction are E_a,II=0.73 eV below T_c and E_a,I=0.95 eV above T_c. The occurrence of an anomaly in both the n and parameters near T_c indicates a coupling between charge carries and phonons. PACS 77.55.+f; 77.80.-e; 77.22.Jp     

Ergodic states in a non commutative ergodic theory

Using the Godement mean of positive-type functions over a groupG, we study -abelian systems { , } of aC*-algebra and a homomorphic mapping of a groupG into the homomorphism group of . Consideration of the Godement mean off(g)U _g withf a positive-type function overG andU a unitary representation ofG first yields a generalized mean-ergodic theorem. We then define the Godement mean off(g) ( _g (A)) withA and a covariant representation of the system { , } for which theG-invariant Hilbert space vectors are cyclic and study its properties, notably in relation with ergodic and weakly mixing states over . Finally we investigate the discrete spectrum of covariant representations of { , } (i.e. the direct sum of the finite-dimensional subrepresentations of the associated representations ofG).On leave of absence from Istituto di Fisica G. Marconi Piazzale delle Scienze 5 — Roma.     

A\overline {Poincar\acute{e}} gauge theory of gravity

We develop a gauge theory of gravity on the basis of the principal fiber bundle over the four-dimensional space-timeM with the covering groupP¯ ₀ of the proper orthochronous Poincaré group. The field components are constructed with the connection coefficients , and with a Higgs-type field. A Lorentz metricg is introduced with , which are then identified with the components of duals of the Vierbein fields. Associated with there is a spinor structure onM. For Lagrangian densityL, which is a function of , ,, matter field , and oftheir first derivatives, we give the conditions imposed by the requirement of the gauge invariance. The Lagrangian densityL is restricted to be of the formL =L ^tot (, T ^klm ,R ^klmn , _k , ), in whichT ^klm ,R ^klmn are the field strengths of , , respectively. Identities and conservation laws following from the gauge invariance are given. Particularly noteworthy is the fact that the energy momentum conservation law follows from theinternal translational invariance. The field equation of is automatically satisfied, if those of and of are both satisfied. The possible existence of matter fields with intrinsic energy momentum is pointed out. When is a field with vanishing intrinsic energy momentum, the present theory practically agrees with the conventional Poincaré gauge theory of gravity, except for the seemingly trivial terms in the expression of the spin-angular momentum density. A condition leading to a Riemann-Cartan space-time is given. The field holds a key position in the formulation.     

Complex conformal rescalings and complex Lorentz transformations

Complex Lorentz transformations and complex conformal rescalings with independent conformal factors and are investigated in terms of elements of the group GL(2,C) G (2,C). It is shown how a general element of this group decomposes into a standard conformal rescaling (with =), a pure spin transformation, complex null rotations, and a complex boost-rotation. Of particular interest are the pure spin transformations that leave invariant the metric but transform the permutation spinors. It is these transformations that, when , are responsible for seemingly complicating the transformation law of the derivative operator and of spinors dependent thereon. It has been suggested that to avoid this complication one should allow the rescaled metric to have torsion. It is argued here that simplicity can be achieved even when the torsion-free condition is imposed.     

The physical nature of the production of moving striations in a d-c discharge plasma

The physical nature of the stratification of the d-c discharge plasma is found and physically interpreted. The interpretation is based on the mathematical expression of the production of periodic structure in plasma after an aperiodic disturbance, derived from an extremely simplified system of equations. Only three basic phenomena occurring in the plasma of each d-c discharge are included: a) the dependence of the rate of ionization on the electron temperature and hence on the electric field, b) the production of space charges due to the different rates of diffusion of the electrons and ions, c) the creation of additional electric fields due to the creation of space charges. The interactions of these phenomena gives rise to a chain, expanded in time and space, which leads to the production of moving striations. In agreement with experiment this structure is developed only on the side towards the anode from the place where the equilibrium state is disturbed.

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. (9, 10) (4, ), . , , : ) , , ; ) , ; ) , . , , — — . , .

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In conclusion the authors thank J. Fousek, J. Kaczér and M. Novák for carefully reading this paper and for valuable remarks, and J. Holub for carrying out the numerical and graphical work.     

A note on the Watanabe theory of weak interactions

It is shown that according to the Watanabe theory of weak interactions a resonant scattering of electrons by protons must take place. The resonant energy depends on the massm _B of the intermediate boson. Form _B=2300m _e this energy is about 213 MeV in the centre of the mass system (c. m. s.). The energy width at resonance is 1·4 MeV.

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, . , , . _{m B}=2300_{m B} , 213 MeV -. 1,4 MeV.

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The author would like to thank Professor V. Votruba for suggesting this note and for valuable advice and help during the work.     

ВлИьНИЕ Cd НА пОглОЩЕН ИЕ NaCl

NaCl Cd , .

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The influence of Cd on the absorption of NaCl

Absorption measurements on uncoloured and X-rayed crystals of NaCl with different Cd-concentrations were made to show under what conditions the non-active form of this impurity may become the active form.

     

Equilibrium state of toroidal electron beam

The paper deals with the collective behaviour of electrons which rotate in a magnetic field used in a betatron. It is shown experimentally that there exists strong interaction between the electrons, which leads to the rapid formation of the equilibrium state with characteristic distribution of the charge density in the cross-section of the toroidal beam. The corresponding relaxation time is of the order of 1 sec. A statistical theory of the equilibrium beam is elaborated. Its main result is that the effective radius of the beam is a function of two parameters, one of which is proportional to the thermal energy of the electrons and the other to the perveance of the beam. The charge contained in a toroidal beam of given effective cross-section is equal to the product of the charge the beam would contain at zero temperature and a coefficient, which is a function of the temperature of the beam. Its value is unity at zero temperature and rapidly decreases with increasing temperature. The cause of cooling of the beam is shown.

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, . , , . 1S. . , , — I/(E₀/q)^3/2 (I — , ₀ — q ). , , , , , . . .

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Now Institute of Vacuum Electronics, Czechosl. Acad. Sci., Prague.

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In conclusion the author thanks J. Luká and L. Hyttych for invaluable help in the experiments, A. Rajský for constructing the electronic apparatus and J. Sokol for preparing the miniature probe.     

ОДНОНУКЛОННАЯ МОДЕЛ Ь ЯДРА. ЧАСТЬ I

. . , - , - , - .     

High-spin states and band structures in the doubly odd <Superscript>136</Superscript>La nucleus

High-spin states of ¹³⁶La have been investigated with the reaction ¹³⁰Te( ¹¹B, 5n) at a beam energy of 60 MeV. The level scheme with three collective bands has been updated with spin up to 20 . The observed h_11/2 h_11/2 band shows -instability with increasing spin according to the TRS calculations. The band crossing and the signature splitting and inversion have been discussed. Other two collective bands based on 12^-and 16⁺ levels were proposed as oblate deformation with -60^°. They most probably originate from four- and six-quasiparticle configurations, that is, h_11/2 g_7/2h_11/2² and g_7/2 g_7/2²d_5/2h_11/2² respectively.     

Noncommutative Unification of General Relativity and Quantum Mechanics. A Finite Model

We construct a model unifying general relativity and quantum mechanics in a broader structure of noncommutative geometry. The geometry in question is that of a transformation groupoid given by the action of a finite group on a space E. We define the algebra of smooth complex valued functions on , with convolution as multiplication, in terms of which the groupoid geometry is developed. Owing to the fact that the group G is finite the model can be computed in full details. We show that by suitable averaging of noncommutative geometric quantities one recovers the standard space-time geometry. The quantum sector of the model is explored in terms of the regular representation of the algebra , and its correspondence with the standard quantum mechanics is established.     

Letter: On the Newtonian Limit in Gravity Models with Inverse Powers of R

I reconsider the problem of the Newtonian limit in nonlinear gravity models in the light of recently proposed models with inverse powers of R. Expansion around a maximally symmetric local background with curvature scalar R ₀ > 0 gives the correct Newtonian limit on length scales R ₀ ^–1/2 if the gravitational Lagrangian satisfies f(R ₀)f(R₀) 1, and I propose two models with f(R ₀) = 0.     

TypeN vacuum space-times as special functions in ℂ2

The members of one explicit class of functions in ² are identified with the geodetic shear-free null congruences in Minkowski's space-time. Members of a second explicit class are identified with the type-N vacuum space-times with twist-free rays. These two classes are special subclasses from a larger class of functions associated with the type-N space-times. This larger class is characterized in the following way: If and are holomorphic variables in ², thenu (, , ), a function holomorphic in, belongs to the class provided the function u/ u satisfies the tangential Cauchy-Riemann equation for an antiholomorphic function on the 3-surface whereu (, , ) has real values.This work was supported in part by NSF grant No. MPS74-14191-A01.     

КРУЧЕНИЕ ПРИЗМАТИЧЕ СКИХ СТЕРЖНЕЙ ШВЕЛЛЕ РНОГО ПОПЕРЕЧНОГО СЕЧЕНИЯ

- [3], [4], U(x, y) . - U(x, y) -, . B § 10 - . , - , - D, . - .     

Comparative study of hydrofullerides C<Subscript><Emphasis Type="Bold">60</Emphasis></Subscript>H<Subscript><Emphasis Type="BoldItalic">x</Emphasis></Subscript> synthesized by direct and catalytic hydrogenation

Hydrofullerides with hydrogen content up to 5 wt.% were obtained by direct and catalytic reactions with H₂ gas. Hydrogen content was monitored in situ using a gravimetric system, and verified by chemical analysis ex situ. It was found that pure C₆₀ reacts rapidly when exposed to H₂ gas at 673 K and 50–100 bar. Gravimetric study of this reaction showed that hydrogenation is saturated at about 5 wt.% of hydrogen. The mass of the sample goes through a maximum and with a longer reaction time its weight starts to decrease. This proves that hydrofullerides with high hydrogen content are not stable and strong hydrogenation results in the collapse of C₆₀ molecules. XRD studies showed that samples prepared by direct hydrogenation without a catalyst retain an original fcc structure with an increase of the cell parameter a up to 15.1 Å. Catalytic hydrogenation of C₆₀ with H₂ gas results in a decrease of the reaction temperature and formation of hydrofullerides with different types of crystal structures. PACS 61.48.+c; 61.10.Nz; 81.05.Tp