The infinite time limit for the time-dependent Born-Oppenheimer approximation

We analyze the Schrödinger equation , whereH() is the hamiltonian of the molecular system consisting of nuclei with masses proportional to ^–4 and electrons with masses of order 1. Using the Born-Oppenheimer method we construct the leading order asymptotic expansion to the exact solutions of the equation. We show that if the particles interact through smooth potentials decaying suitably as the distance between particles tends to , then the expansion holds uniformly for all timest[0,). By similar analysis one can show validity of the expansion fort(–,0], thus our results hold for scattering theory.The material in this paper is contained in a dissertation submitted to the faculty of VPI & SU in partial fulfillment of the requirements for the Ph.D. degree.     

On the effect of impurities on the critical resolved shear stress of zinc single crystals

The dependence of the critical resolved shear stress of zinc single crystals on the impurity content and the dislocation density is observed. It is shown that the effect of impurities on the critical resolved shear stress is indirect.

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. , .

     

Lorentz-symmetric solutions of nonlinear equations

Asymptotic properties of a real scalar self-interacting classical field depending on one variablez = t ²–x ² are studied. The field(z) approaches a minimum of the potentialU() for z + and a maximum forz– ifU((0)) is larger than two minima and smaller than two maxima ofU neighbouring to(0).Presented at the International Symposium Selected Topics in Quantum Field Theory and Mathematical Physics, Bechyn, Czechoslovakia, June 14–19, 1981.     

Proof theory for minimal quantum logic: A remark

It is remarked that the inference rule ( ) is superfluous for the sequential system GMQL introduced by H. Nishimura for the minimal quantum logic.     

A Rigorous Derivation of a Linear Kinetic Equation of Fokker–Planck Type in the Limit of Grazing Collisions

We rigorously derive a linear kinetic equation of Fokker–Planck type for a 2-D Lorentz gas in which the obstacles are randomly distributed. Each obstacle of the Lorentz gas generates a potential V( ), where V is a smooth radially symmetric function with compact support, and >0. The density of obstacles diverges as ^– , where >0. We prove that when 0< <1/8 and =2+1, the probability density of a test particle converges as 0 to a solution of our kinetic equation.     

The Gelfand-Levitan equation and its application to the scattering of neutrons on protons

The Gelfand-Levitan equation for the kernelP(r, r) (withrr) is formulated and then applied for determining the scattering potential in the scattering of slow neutrons on protons (for the case when the dependence of the nuclear forces on the spins can be neglected and onlys-scattering need be considered). The potentials obtained are the same as the Bargmann ones, found by a different method.

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-

- P(r, r) ( rr). , ( s- ). , .

     

Bifurcation phenomena near homoclinic systems: A two-parameter analysis

The bifurcations of periodic orbits in a class of autonomous three-variable, nonlinear-differential-equation systems possessing a homoclinic orbit associated with a saddle focus with eigenvalues ( ±i,), where ¦/¦ < 1 (Sil'nikov's condition), are studied in a two-parameter space. The perturbed homoclinic systems undergo a countable set of tangent bifurcations followed by period-doubling bifurcations leading to periodic orbits which may be attractors if ¦/¦ < 1/2. The accumulation rate of the critical parameter values at the homoclinic system is exp(-2¦/¦). A global mechanism for the onset of homoclinicity in strongly contractive flows is analyzed. Cusp bifurcations with bistability and hysteresis phenomena exist locally near the onset of homoclinicity. A countable set of these cusp bifurcations with scaling properties related to the eigenvalues±i of the stationary state are shown to occur in infinitely contractive flows. In the two-parameter space, the periodic orbit attractor domain exhibits a spiral structure globally, around the set of homoclinic systems, in which all the different periodic orbits are continuously connected.     

Gelation and Cluster Growth with Cluster-Wall Interactions

Metallic cluster growth within a reactive polymer matrix is modeled by augmenting coagulation equations to include the influence of side reactions of metal atoms with the polymer matrix: where > 0 and where c _k denotes the concentration of the kth cluster and p denotes the concentration of reactive sites available within the polymer matrix for reaction with metallic atoms. The initial conditions are required to be non-negative and satisfy and p(0) = p ₀. We assume that for 01, which encompasses both bond linking kernels (R _jk = j k ) and surface reaction kernels (R _jk = j + k ). Our analytical and numerical results indicate that the side reactions delay gelation in some cases and inhibit gelation in others. We provide numerical evidence that gelation occurs for the classical coagulation equations ( = 0) with the bond linking kernel (d ) for 1/2<1. We examine the relative fraction of metal atoms, which coagulate compared to those which interact with the polymer matrix, and demonstrate in particular a linear dependence on ^–1 in the limiting case R _{= jk} , p ₀=1.     

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.     

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.     

Central decomposition of invariant states applications to the groups of time translations and of euclidean transformations in algebraic field theory

With aC*-algebra with unit andgG _g a homomorphic map of a groupG into the automorphism group ofG, the central measure of a state of is invariant under the action ofG (in the state space of ) iff is -invariant. Furthermore if the pair { ,G} is asymptotically abelian, is ergodic iff is ergodic. Transitive ergodic states (corresponding to transitive central measures) are centrally decomposed into primary states whose isotropy groups form a conjugacy class of subgroups. IfG is locally compact and acts continuously on , the associated covariant representations of { , } are those induced by such subgroups. Transitive states under time-translations must be primary if required to be stable. The last section offers a complete classification of the isotropy groups of the primary states occurring in the central decomposition of euclidean transitive ergodic invariant states.     

The effect of microsegregation on the generation of dislocations in zinc single crystals

The applicability of Tiller's considerations on the production of dislocations is proved. The density of dislocations appearing during impurity microsegregation increases with increasing rate of growth as a consequence of the corresponding change in the effective distribution coefficient. The real value of C at the microsegregation boundaries is at least twice as great as the average value of the concentration of impurities in the crystal in question.

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. , , . C , .

     

Electromagnetic Modes in Schwarzschild Geometry in an Annular Region

The fundamental electromagnetic modes in a spherical annular cavity with perfectly conducting walls at r = a and r = b are calculated, in the presence of a weak Schwarzschild gravitational field. Explicit expressions are given for the case of a thin shell, (b - a)/a 1. The modified angular frequency for mode ,m can be written as = = ₀ \{ 1 - (GM/a)[2 - ( + 1)/(₀ a)²] where ₀ is the nongravitational frequency. This formula (being independent of m) holds for the magnetic as well as for the electric modes.     

Металлографические методы определепия нлотности дислокаци й В монокристаллах германия

, , . , .1) . .     

Domain structure of cobalt whiskers

An experimental investigation is made into the domain structure of cobalt whiskers by the colloid technique. A new type of domain structure was found; the width of the domains is studied as a function of the thickness of the whisker. This dependence follows a two-thirds power law and does not agree with existing theories which predict a half power law.

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. . , .

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In conclusion the authors wish to thank V. Janovec and F. Kroupa for valuable remarks and A. Tahalová for help in growing the whiskers.     

СВЕТОСИЛА ЭЛЕКТРОНН О-ОПТИЧЕСКИХ СИСТЕМ

, . g - D, D', D ₄ , - , ' - , ' (). , - S, S ( ) - - 2 _k , 2 _k' () - - , ₂ , -      

Influence of saturable absorber on critical phenomenon analogies in single mode laser driven by external coherent field

The influence of the existence of absorbing atoms in a laser cavity on the critical exponents of abrupt transitions between steady states in the system of single mode onephoton laser driven by an external coherent field is discussed. An isolated threshold when ,and a kind of threshold when, where is the pump parameter of the absorbing atoms, is obtained. The asymptotic forms of the families of potential functions for the system near these threshold are also found. The well-known scaling hypothesis in the general homogeneous function form is shown to be a characteristic of these asymptotic families. Four threshold exponents, , , and and four threshold amplitudes,B, D, andA, near each of these thresholds, are obtained. The threshold exponents near each threshold obey the scaling laws of critical phenomena, while the corresponding amplitudes obey the definite relations between exponents and amplitudes.     

Mikrophy'sikalische Vorgänge,die die Entstehung der Schnellen Schichtungswellen in der Neonglimmentladung bedingen

Zusammenfassung Im nachstehenden Artikel werden mikrophysikalische Vorgänge behandelt, die das Auftreten schneller Schichtungswellen in Neonglimmentladungen veranlassen können. Es werden sowohl die qualitativen Abhängigkeiten, als auch die ziffernmäigen Werte der Parameter der Schichtungswellen mit den charakteristischen Gröenwerten der in diesem Entladungstypus vor sich gehenden Vorgänge verglichen. Auf Grund der vorgenommenen Vergleiche kann gesagt werden, da die Relaxationszeiten der schnellen Wellen durch die Diffusionslebensdauer der atomaren, bzw. molekularen Ionen gegeben sind.

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,

, . , . , , .

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Zum Schlu danken wir F. Kroupa und V. Krejí für die aufmerksame Lesung der Arbeit und wertvolle Hinweise.     

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.     

Limiting behavior of asymptotically flat gravitational fields

Couch and Torrence suggest that the vacuum Einstein equations admit a larger class of asymptotically flat solutions than those exhibiting the peeling property. Starting with the assumption that , (d/dr) and (/x ^A ) , wherex ^A (A = 2, 3) are angular coordinates, they show that , where ₁ 2 and ₁<₀; , where ₂ 1 and ₁< ₁; and ₄ and ₃ peel as they would under the stronger peeling conditions. The Winicour-Tamburino energy-momentun and angular momentum integrals for these solutions, in general, diverge. In fact, since Couch and Torrence determine only the radial dependence of the solution, it is not clear that the solutions are well defined. We find that the stronger assumption , (d/dr) , and (/x ^A ) does result in well-defined solutions for which both the energy-momentum and angular momentum intergrals are not only finite but result in the same expressions as are obtained for peeling space-times. This assumption appears to be the minimal assumption that is necessary for investigating outgoing radiation at null infinity.In part based on a dissertation by Stephanie Novak and submitted to Syracuse University in partial fulfillment of the requirement for the Ph.D. degree.