On the significance of Killing tensors

Killing vectors give the linear first integrals of the geodesic equations on Riemannian manifolds and spacetimes, while Killing tensors give the quadratic, cubic, and higher-order first integrals. Here it is shown that the Lie algebra of Killing vectors,, is extended by Killing tensors into a graded algebra,. This sheds some light on the comment by Xanthopoulos [1] on the apparent scarcity of irreducible Killing tensors. Examples are presented of the graded algebras when is abelian and when is nonabelian.     

О ЗАТУХАНИИ ФАЗОВЫХ К ОЛЕБАНИЙ В СИНХРОТРОНЕ СО СЛАБ ОЙ ФОКУСИРОВКОЙ

, , . , . , - , , [1], .

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On the damping of phase oscillations in a weak-focusing synchroton

An equation of the phase oscillations in a weak-focusing synchroton is derived for the case that an arbitrary high-frequency field of sinusoidal time dependence is distributed on the circumference of the accelerator. It is shown that the damping of phase oscillations is practically independent of the shape of the high-frequency field. From this we get the special case that any adjustments to the accelerator gaps, considered for example in [1], are useless.

     

ИЗЛУЧЕНИЕ ЧЕРЕНКОВА ПРОСТРАНСТВЕННОГО З АРЯДА В ВОЛНОВОДАХ И В НЕОГР АНИЧЕННОЙ СРЕДЕ

, - e . -. , .     

Maximal hypersurfaces in stationary asymptotically flat spacetimes

Existence of maximal hypersurfaces and of foliations by maximal hypersurfaces is proven in two classes of asymptotically flat spacetimes which possess a one parameter group of isometries whose orbits are timelike near infinity.. The first class consists of strongly causal asymptotically flat spacetimes which contain no black hole or white hole (but may contain ergoregions where the Killing orbits fail to be timelike). The second class of spacetimes possess a black hole and a white hole, with the black and white hole horizons intersecting in a compact 2-surfaceS.Supported in part by KBN grant #2 1047 9101Supported in part by NSF grant PHY-8918388.     

Wide-range tunable sub-millimetre cyclotron resonance laser

The results of investigation of cyclotron type stimulated emission processes inp-Ge in strong crossedE B fields are presented. Using the optimumE,B field orientation the spectral range of continuous tuning of the emission line frequency was increased substantially. A tunable sub-millimetre laser with the tuning rangev = 25 to 95cm^–1 ( = 105 to 400m), output power 10 to 100mW and emission linewidthv 0.2cm^–1 is described.     

Problems in the interpretation of cosmic ray nuclear interactions

Difficulties in the interpretation of high-energy nuclear interactions are discussed and explanations suggested on the basis of successive or composite nucleon-nucleus collisions, the first predominant below a few 10 ¹¹ eV,the second for higher energies. In the energy region up to about 10 ¹¹ eVsome discrepancies in the frequency of production of strange particles, the small interaction cross-section of iron etc. are explained, taking into account secondary intranuclear collisions. The tunnel model of Heitler and McCusker is replaced by assuming a cone-shaped interaction volume (funnel) even at the highest primary energies. A number of consequences concerning the energies of the primary particles, the multiplicity and asymmetry in the angular distribution of secondaries, coefficient of inelasticity etc. are discussed.

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, , 10¹¹ eV, — . 10¹¹ eV , ., , . () . , , , .

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This paper contains a condensed summary of some of the material presented in a series of lectures given by the author on the occasion of his visit to Prague in December 1957/January 1958. Its publication in this form is intended as an expression of thanks to the Czechoslovak Academy of Sciences and its leading Officers, in particular Prof. V. Procházka, Prof. J. Novák, and Prof. V. Petrílka, whose kind invitation made this visit possible.     

К ВОПРОСУ О ФОТОПРОВО ДИМОСТИ ФОТОГРАФИЧЕСКОЙ ЭМУ ЛьСИИ

) . , , , ; , , . . , .     

The formation of dislocations by a spark discharge

The arrangement of dislocations formed in a single crystal of the alloy Fe-4·2% Si by a spark discharge in air is studied. The dislocations are made visible by etching on the surfaces perpendicular and parallel to the axis of the crater. The results of the observations are explained on the basis of microphysical conceptions of plastic deformation.

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, Fe— 4,2% Si . , . .

     

The elastic coupling between longitudinal and transversal vibrations оf isotropic rods II. Rods of circular cross-section

The new approximative method for calculating the frequencies of longitudinal vibrations of isotropic homogeneous rods described in part I. is used for rods of circular crosssection. Similarly to the rods of rectangular cross-section there does not exist any dead zone of frequencies.

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II.

, I. (. . 366), . , , .

     

Operators with singular continuous spectrum: II. Rank one operators

For an operator,A, with cyclic vector , we studyA+P, whereP is the rank one projection onto multiples of . If [,] spec (A) andA has no a.c. spectrum, we prove thatA+P has purely singular continuous spectrum on (,) for a denseG of 's.Research partially supported by DGAPA-UNAM and CONACYT.This material is based upon work suported by the National Science Foundation under Grant No. DMS-9207071. The Government has certain rights in this material.This material is based upon work supported by the National Science Foundation under Grant No. DMS-9101715. The Government has certain rights in this material.     

СВЯЗЬ МЕЖДУ МЕТОДОМ С ФЕРИЧЕСКИХ ГАРМОНИК И МЕТОДОМ ДИСКРЕТНЫХ КООРДИНАТ

, .

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On the relation between the method of spherical harmonics and the method of discrete coordinates

The relation between the method of spherical harmonics and the method of discrete coordinates is studied from the point of view of the integral Boltzmann equation for neutron diffusion problems which have full plane and cylindrical symmetry.

     

Die halbleitende Vebbindung SiTe

Ohne Zusammenfassung

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SiTe

     

Systematic study of muon transfer to sulphur dioxide

In a systematic study of the transfer process to sulphur dioxide, in seven different H₂ + SO₂ gas mixtures, the time spectra of the muonic sulphur X-rays yield muon transfer rates to the SO₂ molecule, deduced from the lifetimes of the p atoms, which agree all well with each other. The muonic oxygen time spectra show an additional structure as if p atoms of another kind were present. Reduced transfer rates_O are reproducible if one uses the model of ephemeral p atoms. The intensity ratios between the different kinds of p atoms are also discussed in the framework of this model and the one of black and white p atoms.     

Colored noise in activated rate processes

We consider bistable systems driven by stationary wideband Gaussian colored noise. We construct uniform asymptotic expansions of the stationary probability density function and of the activation rate, for small intensity and short correlation time of the noise. We find that for different values of the total power output / of the noise, different terms in the asymptotic expansions become dominant. For we recover previously derived results, while for =O() and new results are obtained.     

Towards slow μ− production via muon catalyzed fusion

Slow ^– production via dd-CF using a two-layer arrangement is investigated. To determine its feasibility, experimental measurements are now in progress using the muonic X-ray detection method. The following experimental steps are being considered: (1) measurement of the number of ^– stopped inside a solid H₂/D₂ layer by detecting p K X-rays, (2) hot d emission detection by placing a secondary target at a distance of 10–30 mm from the layer and by detecting specific delayed X-rays, (3) measurement of the disappearance of d emission as the added D₂ layer is increased, (4) dd-CF measurement by detecting fusion protons, and (5) slow ^– emission detection. Results of the initial test experiment are presented.     

ЗАВИСИМОСТЬ ПОЧЕРНЕ НИЯ ФОТОГРАФИЧЕСКОЙ ЭМУЛЬСИИ ОТ ЭНЕРГИИβ-ИЗЛУЧЕНИЯ

, - - . , - , , :³²P,³⁵S ⁹⁰Sr+⁹⁰Y.     

The movement of single 90° domain walls of BaTiO3 in an alternating electric field

Single crystals of BaTiO₃, containing one 90° domain wall, were used to study the origin and character of the movement of such a wall in an alternating electric field having a frequency of 50 c/s. The experimental results are discussed from the phenomenological point of view.

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90- BaTiO₃

iO₃, 90- , 50 Hz. .

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The authors would like to thank A. Glanc for preparing the crystals for measurement, V. Dvoák, J. Kaczér and V. Janovec for fruitful discussions.     

ИССЛЕДОВАНИЕ ЭРОЗИЙ НОГО ДЕЙСТВИЯ ИМПУЛЬ СНЯХ ЭЛЕКТРИЧЕСКИХ РАЗРЯ ДОВ С СЛАБЫМ ТОКОМ

50–100 , 1–2 1–10 . - . - . , , - . -.     

ОПРЕДЕЛЕНИЕ ПОСТОЯН НЫХ ДВУХПАРАМЕТРОВЫ Х РЕШЕТОК МЕТОДОМ ОТНО ШЕНИЙ

. . - 10^–4.     

The collisions of two plasma streams

The mutual interaction of two colliding plasma streams is investigated by means of the perturbation method. The disordered random motions of electrons are taken into account. It is shown that electron oscillations occur only when certain conditions as to the density and relative velocity of the colliding streams are fulfilled. The order of magnitude of the thickness of the shock generated by the initial relative motion is estimated on various assumptions.

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. . , , . , , .