Methodological imperfection and formalizations of scientific activity

Any mathematical formalization of scientific activity allows for imperfections in the methodology that is formalized. These can be of three types, dirty, rotten, and dammed. Restricting mathematical attention to those methods that cannot be construed to be imperfect drastically reduces the class of objects that must be analyzed, and relates all other objects to these more regular ones. Examples are drawn from empirical logic.     

Stationary states of an electron in the field of a hole in an ionic crystal

An approximate solution is given of the Schrödinger equation for S-states of an electron in the field of a hole, when the potential energy of the electron has the form — e²/r [1+exp (–qr].

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s- , –e²/r [1+exp (–qr].

     

ИЗОТОПЫ ФТОРА F19 И F21 В МОДЕЛИ НИЛЬССОНА

Energy levels and electromagnetic properties of fluorin isotopes in the Nilsson's model with Coriolis mixing are investigated. Position of the F¹⁹ levels is satisfactorily explained up to the energy of 4·5 MeV. Concerning the F²¹ it seems that the shell model will better correspond to the F²¹ nucleus.

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. , .     

Radiation losses in completely ionized plasma

The losses caused by bremsstahlung during electron-ion and electron-electron collisions in a completely ionized plasma (in Born's approximation) are calculated. The calculation can be carried out analytically for a sufficiently dilute plasma (plasma with infinitely large Debay-Hückel radius). This assumption is satisfied very well by the known classification to actual controlled thermonuclear reaction. A dependence of the formI=an ². (1+3/2), wherea=0·73×10^–16 MeV.cm³.sec^–1,n is the number of ions per cm³ and =kT/mc ², is determined for the amount of energy radiated from 1 cm³ of plasma per sec. In the relativistic temperature regionkTmc ² the influence of electron-electron collisions begins to predominate. A number of important results concerning radiation losses in relativistic plasma will be published in a later paper.

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, ( ). ( -). . , I=an ². (1+3/2), =0,73. 10^–16 MeVcm²s^–1,n — =kT/mc ². kTmc ² . , .

     

Intersubjectivity,relativistic covariance,and conditionals: response to C. I. J. M. Stuart

A misunderstanding persists between Stuart and me, which I do my best to clarify. Bayesian inverse subjectivities versus relativistic covariance and physical intersubjectivity are discussed. A joint number of chances formalism taking care of the propagation of the probability of causes is proposed.     

Замечание К теории по степенного возникновения подви жных слоев в плазме инертных газов

[1] t _B , t _B . , t _B , . .

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A note on the theory of the successive production of moving striations in the plasma of inert gases

Approximate expressions are derived on the basis of Pekárek's theoretical paper [1] for the period of the maximum t_B of a wave packet produced by the passage of a wave of stratification before the aperture of a photomultiplier, and for its time width in the half-height t_B. The relaxation time of a wave of stratification, following from the theory [1], can thus be calculated by means of the experimentally measured velocity of motion of the maximum of a wave packet u and its width t_B. The calculation is supplemented by numerical data on the magnitude of errors committed by using approximate expressions.

     

О взаимодействии экс итонов с колебаниями кристаллической реш етки

, - . : - . - .     

ЛОКАЛЬНЫЕ КОЛЕБАНлЯ ДВУХАТОМНОЙ ЛлНЕЙНО Й ЦЕПОЧКл С ДЕФЕКТАМл

. n : , . npou u , n . n n npocm .     

ПОГЛОЩЕНИЕ И РАССЕЯНИЕ МОНОКРИСТАЛЛОВ NaCl ∶ Ni

NaCl Cd [10]. , NaCl Ni , .

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Absorption and dispersion on NaCl Ni crystals

The results of measuring the absorption and dispersion of light on NaCl Cd crystals were compared with the X-ray diffraction measurements by Toman [10]. The comparison showed that under certain conditions micro-regions of segregated impurities are produced in NaCl Ni crystals, apparent in an increased dispersion of light in the ultra-violet region.

     

Влияние переменного магнитного поля на остаточное состоя ние магнитно — Мягких материалов

. .

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The influence of an alternating magnetic field on the remanent state of magnetically soft materials

A study is made of the influence of an alternating magnetic field of varying maximum amplitude on the remanent state, or rather, apparent remanent state of toroidal and open samples of metallic and non-metallic magnetically soft ferromagnetics. An interpretation of the corresponding dependences is given on the basis of Kondorski's conception of the composition of a polycrystalline jerromagnetic material.

     

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.     

On the Hamiltonian interpolation of near-to-the identity symplectic mappings with application to symplectic integration algorithms

We reconsider the problem of the Hamiltonian interpolation of symplectic mappings. Following Moser's scheme, we prove that for any mapping , analytic and -close to the identity, there exists an analytic autonomous Hamiltonian system, H such that its time-one mapping _H differs from by a quantity exponentially small in 1/. This result is applied, in particular, to the problem of numerical integration of Hamiltonian systems by symplectic algorithms; it turns out that, when using an analytic symplectic algorithm of orders to integrate a Hamiltonian systemK, one actually follows exactly, namely within the computer roundoff error, the trajectories of the interpolating Hamiltonian H, or equivalently of the rescaled Hamiltonian K=^-1H, which differs fromK, but turns out to be ⁵ close to it. Special attention is devoted to numerical integration for scattering problems.     

Hausdorff dimension and fluctuations for the largest cluster at the two-dimensional percolation threshold

Monte Carlo simulation shows the average mass of the largest cluster to increase asL ^1.9 at the percolation threshold inL × L square lattices,L290. This fractal dimension agrees with the finite-size scaling prediction/v for this exponent, in contrast to results of Halley and Thang Mai. The mean-square fluctuations in the mass of the largest cluster diverge with the same exponent/v1.8 as the susceptibility.     

Characteristic parameters of recombination centres

The paper points to the possibility of describing the properties of recombination centres by means of the quantitiesc _p/c _n ande _n/e _p, in contrast to the existing method based mainly on the so-called energy position of recombination levels. The proposal is supported by a simple statistical analysis and by experimental material and has some advantages over the method used hitherto.

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c _p/c_n e _n/e_p , . .

     

О ВЛИЯНИИ ДИСЛОКАЦИЙ НА КОЭРЦИТИВНУЮ СИЛУ ФЕРРОМАГНЕТИКО В

- . ( + ) - , , - . , . , -, , , - , - . - . (- - ) . .     

К ВОПРОСУ О ФОТОПРОВО ДИМОСТИ ФОТОГРАФИЧЕСКОЙ ЭМУ ЛьСИИ

) . , , , ; , , . . , .     

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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. . , , . , , .

     

О ВЛИЯНИИ НАПЯЖЕНИЯ, ВОЗНИКАЮЩЕГО ПРИ ПРЕ ЦИПИТАЦИИ, НА КОЭРЦИТ ИВНУЮ СИЛУ ФЕРРОМАГНЕТИКО В

, . - , m. . . , , , . , , Fe₃C .     

Новый тип рентгеновс кого спектрографа

. 1', . . .     

Studium der Stationären und Laufenden Schichtung in der Entladung in Neon Mit Hilfe eines Lokalen Hochfrequenzfeldes

Zusammenfassung Es wurde ein Verfahren zur Erregung von stationären Schichten, der Schichtungswelle und der laufenden Schichten in der Gleichstromentladung ausgearbeitet, das auf der Einwirkung eines Hochfrequenzfeldes auf einen kurzen Abschnitt der positiven Säule beruht. Dieses Verfahren wurde zum Studium aller drei angeführten Schichtungsarten in Neon benützt, insbesondere jedoch zum Studium des Zusammenhanges zwischen den laufenden und den stationären Schichten.Bei stationären Schichten wurden zweifache Strukturen festgestellt und es wurde deren Abhängigkeit vom Entladungsstrom und von der Größe des erregenden Hochfrequenzfeldes verfolgt.Bei der Schichtungswelle wurde die Stelle deren Entstehung ermittelt und es wurde nachgewiesen, daß das Hochfrequenzfeld diese Welle lokal an der Stelle dessen Einwirkung auf die positive Säule hervorruft.Bei den laufenden Schichten wurde deren Resonanzfrequenz in Abhängigkeit vom Entladungsstrom und die Abhängigkeit der Wellenlänge der Schichten von der Frequenz untersucht.Es wurde festgestellt, daß der extrapolierte Wert der Wellenlänge für die Nullfrequenz erheblich niedriger ist als die Länge der stationären Schichten. Weiter wurde eine Übereinstimmung der Frequenz der laufenden Schichten in der Schichtungswelle mit der Resonanzfrequenz der künstlich hervorgerufenen laufenden Schichten festgestellt.

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