Principal Formulae Research Articles

A NOTE ON THE SEQUENT CALCULI

AbstractWe show that the replacement rule of the sequent calculi ${\bf G3[mic]}^= $ in [8] can be replaced by the simpler rule in which one of the principal formulae is not repeated in the premiss.

Review of formulae for efficiency calculation of noise barriers in streets

Analysis of principal formulae for calculation of diffraction effects on the top edge of noise barrier and interference effects of sound waves after reflection from impedance surfaces was done. Main criteria of noise barriers efficiency assessment were considered. Model for calculation of building façade impact was analyzed. Assessment of building façade impact on sound field formation on the street was done.

Time Rates of Hill's Strain Tensors

Based on Hill's principal components formulae, two kinds of basis-free time rate formulae for Hill's strain tensors are proposed in this paper, which are obtained for the cases of distinct stretches, double coalescence and triple coalescence. Furthermore, relations between the coefficients in the representation for the strain tensor and its time derivative are disclosed.

Computational aspects of some autonomous differential equations

This paper deals principally with the differential equation ϵ d 4 y / d x 4 + d 2 y / d x 2 = y - y 2 (0 ≤ x < ∞) Subject to the conditions d y (0) / d x = 0, d y / d x < 0 (0 < x < ∞), lim x→∞ y ( x ) = 0. where ϵ > 0 is a prescribed constant. The equation has served as a model for water waves with surface tension. Interest centres on the behaviour of d 3 y / d x 3 at the point x = 0; and we prove that this quantity is strictly positive and investigate its numerical behaviour as a function of ϵ . A summary of principal formulae appears in §4 at the end of the paper, and table 1 gives numerical results. The introductory section of the paper speculates on whether our method might have wider application to similar autonomous differential equations, which involve a small positive multiple of the highest derivative.

(A. S.) Henry Honours and privileges in Athenian decrees: the principal formulae of Athenian honorary decrees. (Subsidia epigraphica, 10.) Hildesheim etc.: Olms. 1983. Pp. xiv + 381. DM 48.

(A. S.) Henry Honours and privileges in Athenian decrees: the principal formulae of Athenian honorary decrees. (Subsidia epigraphica, 10.) Hildesheim etc.: Olms. 1983. Pp. xiv + 381. DM 48.

Honours and Privileges in Athenian Decrees: The Principal Formulae of Athenian Honorary Decrees

Honours and Privileges in Athenian Decrees: The Principal Formulae of Athenian Honorary Decrees

Terminology and concepts in natural evaporation

This paper presents firstly a systematic unified set of terms, definitions and symbols applicable in the title area. These are based largely on previous studies by a Working Group of the International Commission for Irrigation and Drainage. This is followed by a physical discussion of the evaporative process, employing as its main tools the principal formulae used in evaporation measurement. The latter are conveniently tabulated in the paper, using the recommended terminology. For maximum insight into evaporative behaviour under varying circumstances, attention is focussed on the combination-method formulae, which are used to create a general picture of the interactions between evaporation and the many other factors influencing it.

Perspectives in the mechanics of elastoplastic crystals

The mechanics of metal crystals at finite strain is reappraised, when crystallographic slip is solely responsible for inelastic deformation. Arbitrary work-conjugate variables are used throughout, together with a slip measure that is unaffected by lattice distortion. The pioneering analysis of R. Hill and J.R. Rice ( J. Mech. Phys. Solids 20, 401. 1972) is amplified and in part recast. The existence of a plastic potential is proved from a new standpoint, which is believed to be more readily understandable and direct. The effect of lattice strain on slip-system geometry is expressed via an influence tensor ; this has the effect of linking apparently disparate elements of the theory. Subsequently the principal formulae are made explicit in terms of Green's measure of strain, supplemented by equations of transformation to other variables. The unique yield criterion that confers a normality structure is formulated in terms of a generalized Schmid stress, and associated rules of hardening in multislip are detailed. The available experimental data are briefly reviewed, more especially in relation to the ‘simple theory’ of hardening proposed by K.S. Havner and A.H. Shalaby ( Proc. R. Soc. A358, 47. 1977).

THE FUNDAMENTAL FORMULA OF BLASCHKE IN INTEGRAL GEOMETRY AND GEOMETRICAL PROBABILITY, AND ITS ITERATION, FOR DOMAINS WITH FIXED ORIENTATIONS

AbstractThe so‐called “principal formulae” of planar integral geometry are conventionally couched in terms of the “kinematic density”dxdydθ. Here a corresponding theory with respect to the “Lebesgue density”dxdy, that is with rotations suppressed, is developed. The only real difference is that the new “fundamental formula of Blaschke”contains a term depending upon the relative orientations of the two domains involved. In particular, the remarkable iteration property of these formulae carries over. The usual principal formulae follow as a corollary of the formulae given here, upon, averaging over orientations.

A general method for an explicit determination of the shape of the earth from gravimetric data

The principal formulae of the geophysical geodesy are based on the famous explicit expression of Stokes (1849). Up to now, there has been no method for a computation of the corresponding explicit expression of a (non-spherical) surface with masses outside the geoid. In this paper there is a solution of this problem. Another paper on this subject was presented to “Nordiska geodetmotet” in Copenhagen May 1959 (in Swedish).

AN EXPERIMENTAL STUDY OF COUNTING LOSSES DUE TO DEAD-TIME EFFECTS

When using counting methods for studying instantaneous reactions produced with pulsed accelerators such as synchrotrons or synchrocyclotrons, the systematic errors in counting due to dead-time effects may be considerable. One of us has already published a discussion of the simpler cases of pulsed single-channel counting; the present paper describes experimental investigations designed to extend our knowledge of these corrections, especially to cases of coincidence counting. In Part I of the present paper, the method and apparatus are described, together with calibration procedure; in the course of checking results already known from computation, defects in the functioning of the equipment were uncovered and the correction of these defects is described.Part II of the paper deals with the problems of coincidence counting at high speed but without the complication of a pulsed source. Difficulties arise in this case unless the rate of occurrence of coincidences is much smaller than the counting rates in the separate counters, a condition which may not be satisfied in many cases in the study of high energy reactions. The corrections for this case have therefore been investigated experimentally and a relatively simple correction formula obtained when chance coincidences are negligible. The dependence of the number of additional chance coincidences on coincidence gate-width is determined both theoretically and experimentally, with satisfactory agreement.In Part III the investigation is extended to pulsed coincidence counting. A theoretical formula is developed neglecting chance coincidences, for pulse-lengths less than twice the dead-time, and experiments confirm the results and indicate how to extrapolate for longer pulse-durations. A first-order formula for the chance coincidences is also obtained and confirmed.In all cases near-rectangular pulse-forms are used, but the equipment can readily be modified to study other forms. For the guidance of the user, the principal formulae adopted for determining counting corrections are collected in Appendix III at the end of this paper.

Receiver aerial couplings for medium wavelengths

The paper discusses the electrical nature of an outdoor aerial at medium wave frequencies and the problems which arise when such a generator has to be coupled to a tuned circuit as occurs in the aerial input circuit of a receiver. It is shown that those two desirable features, high voltage transfer and high selectivity, are mutually conflicting and that the kind of coupling circuit which favours one, necessarily gives a poor performance with respect to the other, so that a compromise solution has to be adopted in practice. Another point to be considered, when choosing a circuit for aerial coupling purposes, is the capacitance reflected into the tuning circuit; ideally, to permit accurate ganging, this should be constant and independent of frequency but in practice it may vary considerably, depending on the nature and constants of the circuit used. Three simple types of coupling circuit are analysed, namely, by means of mutual inductance, series capacitance and shunt capacitance, and graphs are given illustrating their performance with respect to voltage gain, selectivity and reflected capacitance. The paper ends with two appendices, one devoted to a detailed mathematical analysis of mutual inductance coupling, and the other to a summary of the principal formulae derived in the text.