The postulation of a multiple variety

1940 ◽  
Vol 36 (1) ◽  
pp. 27-33 ◽  
Author(s):  
J. A. Todd
Keyword(s):  
Explicit Formula ◽  
Complete Intersection ◽  
Trivial Case ◽  
Multiple Points ◽  
Ordinary Space ◽  
Large Order ◽  
Special Cases

1. The determination of an explicit formula for the postulation of a multiple variety of given characters for primals of sufficiently large order is one which seems to have received attention only in special cases. The postulation of a multiple curve for surfaces in ordinary space is known*, and Roth† has obtained the postulation of a multiple surface in [4], free from singularities, for primals in that space. Apart from these results, and the trivial case of isolated multiple points, the only general results seem to be those of Torelli‡ and Giambelli§ for the case in which the multiple variety is a Vh which is the complete intersection of r − h primals in [r].

Analytical Techniques for the Optimisation of Rocket Trajectories

1963 ◽  
Vol 14 (2) ◽  
pp. 105-124 ◽  
Author(s):  
Derek F. Lawden
Keyword(s):  
Gravitational Field ◽  
Artificial Satellite ◽  
Analytical Techniques ◽  
Present Position ◽  
Mayer Problem ◽  
Special Cases ◽  
Minimum Expenditure ◽  
Law Of Attraction ◽  
Special Case

SummaryThe development during the last two decades of analytical techniques for the solution of problems relating to the optimisation of rocket trajectories is outlined and the present position in this field of research is summarised. It is shown that the determination of optimal trajectories in a general gravitational field can be expressed as a Mayer problem from the calculus of variations. The known solution to such a problem is stated and applied, first to the special case of the launching of an artificial satellite into a circular orbit with minimum expenditure of propellant and, secondly, to the general astronautical problem of the economical transfer of a rocket between two terminals in a gravitational field. The special cases when the field is uniform and when it obeys an inverse square law of attraction to a point are then considered, and the paper concludes with some remarks concerning areas in which further investigations are necessary.

scholarly journals Simple Method for Estimating the Contribution of Neighbouring n-beam Interactions to Two-beam Structure Factors

1988 ◽  
Vol 41 (3) ◽  
pp. 469
Author(s):  
HJ Juretschke ◽  
HK Wagenfeld
Keyword(s):  
Experimental Determination ◽  
Structure Factor ◽  
Beam Structure ◽  
Simple Method ◽  
Experimental Configuration ◽  
Structure Factors ◽  
Special Cases ◽  
Better Than

Unless special precautions are taken, the experimental determination of two-beam structure factors to better than 1 % may include contributions from neighbouring n-beam interactions. In any particular experimental configuration, corrections for such contributions are easily carried out using the modified two-beam structure factor formalism developed recently (Juretschke 1984), once the full indexing of the pertinent n-beam interactions is known. The method is illustrated for both weak and strong primary reflections and its applicability in special cases, as well as for less than perfect crystals, is discussed.

scholarly journals Observations of Binaries and Evolutionary Implications

1984 ◽  
Vol 80 ◽  
pp. 199-227
Author(s):  
C. De Loore
Keyword(s):  
Mass Transfer ◽  
Angular Momentum ◽  
Mass Transfer Process ◽  
Transfer Phase ◽  
X Ray ◽  
Special Cases ◽  
Angular Momentum Loss ◽  
Spectral Ranges ◽  
X Ray Binaries

AbstractComparison of the characteristics of groups of stars in various evolutionary phases and the study of individual systems allow to make estimates of the parameters governing mass loss and mass transfer. Observations enable us in a few cases to determine geometric models for binaries during or after the mass transfer phase (disks, rings, common envelopes, symbiotics, interacting binaries, compact components).From spectra taken at different phases, radial velocity curves can be derived and masses and radii can be determined. In special cases spectra in different spectral ranges (visual, UV, X-ray) are required for the determination of the radial velocities of the two components (for X-ray binaries, for systems with hot and cool components). Information on parameters related to the mass transfer process enables us to consider non conservative evolution - i.e. the computation of evolutionary sequences with the assumption that mass and angular momentum not only are transferred from one of the components towards the other one, but that also mass and angular momentum can leave the system. Careful and detailed analysis of the observations allows in certain cases to determine the parameters governing this mass and angular momentum loss, and for contact phases, to determine the degree of contact.

scholarly journals The interaction of atoms and molecules with solid surfaces VIII—The exchange of energy between a gas and a solid

1937 ◽  
Vol 158 (894) ◽  
pp. 269-279 ◽  
Keyword(s):  
Morse Potential ◽  
Accommodation Coefficient ◽  
Solid Surfaces ◽  
Adsorbed State ◽  
Thermal Accommodation ◽  
Special Cases ◽  
Thermal Accommodation Coefficient ◽  
The Right ◽  
Energy Interchange

In previous papers of this series the problem of energy interchange between a gas atom and a solid has been discussed for the case when the gas atom makes a transition between two adsorbed states or between an adsorbed state and a free state. In this paper we shall discuss the case of a transition between two free states and apply the results to the determination of the thermal accommodation coefficient. In recent years a number of theoretical papers on this subject have appeared, following the new and accurate experimental work of Roberts, who worked with helium and neon on tungsten. The authors, however, neglect, or only roughly take into account, the attractive field which is known to exist between the solid and the gas; the fact that atoms become adsorbed on the surface is clear evidence of the existence of such a field. In this paper we shall suppose that the interaction potentials between solid and gas atom can be represented by a Morse potential function, for it has the right characteristics; in that it is attractive at large distances and repulsive at small ones, and has a minimum in between. The formulae of this paper are accordingly more general than previous ones and contain them as special cases. They are applicable to experimental results such as those of neon on tungsten for which earlier theories would not be adequate.

scholarly journals Problems of Menotactic Orientation According to the Polarized Light of the Sky

1975 ◽  
Vol 30 (1-2) ◽  
pp. 88-90 ◽  
Author(s):  
Kuno Kirschfeld ◽  
M. Lindauer ◽  
H. Martin
Keyword(s):  
Infinite Number ◽  
Polarized Light ◽  
The Sun ◽  
Number Of Solutions ◽  
Special Cases ◽  
Linearly Polarized ◽  
Vector Direction

Abstract It is shown that the knowledge of the E-vector direction of the linearly polarized light at any point of the sky alone is insufficient for the determination of the position of the sun. If the E-vector direction of a second point is not known the knowledge of at least one other parameter is necessary. This parameter might be the height of the sun over the horizon. With the knowledge of the height the infinite number of solutions for the sun’s position becomes reduced to two, or in special cases to one. These cases are derived.

scholarly journals Application of the radionuclide 210Pb in glaciology – an overview

2020 ◽  
Vol 66 (257) ◽  
pp. 447-456 ◽  
Author(s):  
Heinz W. Gäggeler ◽  
Leonhard Tobler ◽  
Margit Schwikowski ◽  
Theo M. Jenk
Keyword(s):  
Half Life ◽  
Arid Regions ◽  
Noble Gas ◽  
Radioactive Decay ◽  
Ice Cores ◽  
Snow Accumulation ◽  
The Earth ◽  
Special Cases ◽  
Glacier Flow

Abstract210Pb is an environmental radionuclide with a half-life of 22.3 years, formed in the atmosphere via radioactive decay of radon (222Rn). 222Rn itself is a noble gas with a half-life of 3.8 days and is formed via radioactive decay of uranium (238U) contained in the Earth crust from where it constantly emanates into the atmosphere. 210Pb atoms attach to aerosol particles, which are then deposited on glaciers via scavenging with fresh snow. Due to its half-life, ice cores can be dated with this radionuclide over roughly one century, depending on the initial 210Pb activity concentration. Optimum 210Pb dating is achieved for cold glaciers with no – or little – influence by percolating meltwater. This paper presents an overview which not only includes dating of cold glaciers but also some special cases of 210Pb applications in glaciology addressing temperate glaciers, glaciers with negative mass balance, sublimation processes on glaciers in arid regions, determination of annual net snow accumulation as well as glacier flow rates.

Profile Determination of Plate Cams with Oscillating Convex Arbitrary-Shaped Followers

1996 ◽  
Vol 210 (4) ◽  
pp. 333-339 ◽  
Author(s):  
G S Hwang ◽  
D M Tsay ◽  
M H Huang
Keyword(s):  
Arbitrary Shape ◽  
Parametric Form ◽  
Convex Shape ◽  
Universal Form ◽  
Profile Equation ◽  
Special Cases ◽  
Oscillating Motion

A universal form of profile equation for a plate cam whose follower has an oscillating motion and a convex arbitrary shape is derived in this study. The applied concept is the theory of envelopes in a parametric form. The derived results can be used to determine the profile of the cam with any kind of convex shape of the followers. It is also shown that the traditional followers, such as flat-faced and roller followers, are special cases of the universal form.

scholarly journals Multiple-Input Multiple-Output (MIMO) Linear Systems Extreme Inputs/Outputs

2007 ◽  
Vol 14 (2) ◽  
pp. 107-131 ◽  
Author(s):  
David O. Smallwood
Keyword(s):  
Density Matrix ◽  
Random Process ◽  
Multiple Input Multiple Output ◽  
Linear Structure ◽  
Multiple Points ◽  
Critical Response ◽  
Special Cases ◽  
Multiple Input ◽  
Input Multiple Output ◽  
Phase Relationships

A linear structure is excited at multiple points with a stationary normal random process. The response of the structure is measured at multiple outputs. If the autospectral densities of the inputs are specified, the phase relationships between the inputs are derived that will minimize or maximize the trace of the autospectral density matrix of the outputs. If the autospectral densities of the outputs are specified, the phase relationships between the outputs that will minimize or maximize the trace of the input autospectral density matrix are derived. It is shown that other phase relationships and ordinary coherence less than one will result in a trace intermediate between these extremes. Least favorable response and some classes of critical response are special cases of the development. It is shown that the derivation for stationary random waveforms can also be applied to nonstationary random, transients, and deterministic waveforms.

scholarly journals Determination of the Stress State of a Piecewise Homogeneous Elastic Body with a Row of Cracks on an Interface Surface Subject to Antiplane Strains with Inclusions at the Tips

2015 ◽  
Vol 2015 ◽  
pp. 1-22 ◽  
Author(s):  
Ali Golsoorat Pahlaviani ◽  
Suren Mkhitaryan
Keyword(s):  
Stress State ◽  
Elastic Body ◽  
Linear Equations ◽  
The Body ◽  
Shear Stresses ◽  
Interface Surface ◽  
Special Cases ◽  
Crack Problems ◽  
Fourier Sine Series

The stress state of a bimaterial elastic body that has a row of cracks on an interface surface is considered. It is subjected to antiplane deformations by uniformly distributed shear forces acting on the horizontal sides of the body. The governing equations of the problem, the stress intensity factors, the deformation of the crack edges, and the shear stresses are derived. The solution of the problem via the Fourier sine series is reduced to the determination of a singular integral equation (SIE) and consequently to a system of linear equations. In the end, the problem is solved in special cases with inclusions. The results of this paper and the previously published results show that the used approach based on the Gauss-Chebyshev quadrature method can be considered as a generalized procedure to solve the collinear crack problems in mode I, II, or III loadings.

scholarly journals On the mutual potential energy of a plane network of doublets

1927 ◽  
Vol 114 (766) ◽  
pp. 67-72 ◽  
Keyword(s):  
Potential Energy ◽  
Magnetic Moment ◽  
Unit Area ◽  
Surface Layers ◽  
Actual Surface ◽  
Special Cases ◽  
Triangular Network ◽  
Mutual Action

1. The object of this note is the determination of the mutual potential energy of a distribution of small electric or magnetic doublets lying in a plane with their axes perpendicular to the plane; reckoning the potential energy from a state of infinite dispersion of the doublets. The doublets are supposed to have a definite electric or magnetic moment, the same for all, whose value is determined by their constitution and does not depend on their mutual action. The problem bears on the energy of a layer of polarised molecules on the surface of a fluid, and the question as to the value of the energy, for a given number of molecules of given moment per unit area, was put by Dr. E. K. Rideal to Prof. S. Chapman, at whose suggestion the writer undertook this investigation. In actual surface layers the mode of packing of the molecules is not always known, and therefore two special cases are considered, in order to determine how the mode of packing influences the energy, the number of doublets per unit area being given. It is supposed that the doublets form either a simple square network, or an equi-triangular network; and it appears that the mutual potential energy differs only by about 2 per cent, in the two cases. It is thereforepossible to give (§ 4) a fairly definite estimate of the energy, which is likelyto be approximately true for any probable mode of packing of the molecules.

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