scholarly journals IV. A general method for exhibiting the value of an algebraic expression involving several radical quantities in an infinite series: wherein Sir Isaac Newton’s theorem for involving a binomial, with another of the same author, relating to the roots of equations, are demonstrated

1752 ◽  
Vol 47 ◽  
pp. 20-27 ◽  
Keyword(s):  
Infinite Series ◽  
Algebraic Expression ◽  
Roots Of Equations ◽  
General Method

Among all the great improvements, which the art of computation hath in these last ages received, the most considerable; since not only the doctrine of chances and annuites, with some other branches of the mathematics, depend almost intirely thereon, but even the business of fluents, of such extensive use, would, without its aid and concurrence, be quite at a stand in a multitude of cases, as is well known to mathematicians.

scholarly journals On the theory of the elliptic transcendents

1837 ◽  
Vol 3 ◽  
pp. 60-60
Keyword(s):  
Elliptic Function ◽  
Elliptic Integral ◽  
Elliptic Functions ◽  
Algebraic Expression ◽  
Algebraic Equations ◽  
Similar Function ◽  
Circular Arcs ◽  
Straight Line ◽  
Regular Theory ◽  
General Method

Fagnani discovered that the two arcs of the periphery of a given ellipse may be determined in many ways, so that their difference shall be equal to an assignable straight line; and proved that any arc of a lemniscate, like that of a circle, may be multiplified any number of times, or may be subdivided into any number of equal parts, by finite algebraic equations. What he had accomplished with respect to the arcs of the lemniscates, which are expressed by a particular elliptic integral, Euler extended to all transcendents of the same class. Landen showed that the arcs of the hyperbola may be reduced, by a proper transformation, to those of an ellipse. Lagrange furnished us with a general method for changing an elliptic function into another having a different modulus; a process which greatly facilitates the numerical calculation of this class of integrals. Legendre distributed the elliptic functions into distinct classes, and reduced them to a regular theory, developing many of their properties which were before unknown, and introducing many important additions and improvements in the theory. Mr. Abel of Christiana happity conceived the idea of expressing the amplitude of an elliptic function in terms of the function itself, which led to the discovery of many new and useful properties. Mr. Jacobi proved, by a different method, that an elliptic function may be transformed in innumerable ways into another similar function, to which it bears constantly the same proportion. But his demonstrations require long and complicated calculations; and the train of deductions he pursues does not lead naturally to the truths which are proved, nor does it present in a connected view all the conclusions which the theory embraces. The author of the present paper gives a comprehensive view of the theory in its full extent, and deduces all the connected truths from the same principle. He finds that the sines or cosines of the amplitudes, used in the transformations, are analogous to the sines or cosines of two circular arcs, one of which is a multiple of the other; so that the former quantities are changed into the latter when the modulus is supposed to vanish in the algebraic expression. Hence he is enabled to transfer to the elliptic transcendents the same methods of investigation that succeed in the circle: a procedure which renders the demonstrations considerably shorter, and which removes most of the difficulties, in consequence of the close analogy that subsists between the two cases.

scholarly journals On electrostatics in a gravitational field

1928 ◽  
Vol 118 (779) ◽  
pp. 184-194 ◽  
Keyword(s):  
Differential Equation ◽  
Harmonic Functions ◽  
Gravitational Force ◽  
Algebraic Expression ◽  
Uniform Field ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Gravitational Fields ◽  
Limiting Case ◽  
General Method

In a recent paper, Prof. Whittaker has discussed the effect, according to the general theory of relativity, of gravitation on electromagnetic phenomena. In particular, he has discussed electrostatics in gravitational fields of two kinds, namely (i) the field due to a single gravitating mass, in which case space-time has the metric discovered by Schwarzschild, and (ii) a limiting case of this, called a quasi-uniform field, in which the gravitational force is, in the neighbourhood of the origin, uniform. Whittaker’s general method, so far as electrostatical problems were concerned, was to solve the partial differential equation satisfied by the electrostatic potential in terms of generalised harmonic functions, and then, from these, to build up other solutions. In this way, he succeeded in finding an algebraic expression which represents the potential of a single electron in the quasi-uniform field; he did not, however, obtain a corresponding algebraic expression for the potential of an electron in the Schwarzschild field.

scholarly journals XXV. A new method of investigating the sums of infinite series. By the Rev. S. Vince, A.M. of Cambridge, in a letter to Henry Maty, A.M. Secretary

1782 ◽  
Vol 72 ◽  
pp. 389-416
Keyword(s):  
Infinite Series ◽  
Royal Society ◽  
New Method ◽  
General Will ◽  
The Third ◽  
The Subject ◽  
General Method

Sir, Having lately discovered some very easy methods of investigating the sums of certain infinite series, I have taken the liberty of requesting the favour of you to present them to the Royal Society. I have divided the subject into three parts: the first contains a new and general method of finding the sum of those series which De Moivre has found in one or two particular cases; but whose method, although it be in appearance general, will, upon trial, be found to be absolutely impracticable. The second contains the summation of certain series, the last differences of whose numerators become equal to nothing. The third contains observations on a correction which is necessary in investigating the sums of certain series by collecting two terms into one, with its application to a variety of cases.

Transmission of a Lorentzian Spectral Line Through a Layer of Lorentzian Absorbers. Part I

1968 ◽  
Vol 23 (10) ◽  
pp. 1439-1446 ◽  
Author(s):  
Juergen Heberle ◽  
Sergio Franco
Keyword(s):  
Mössbauer Spectroscopy ◽  
Spectral Line ◽  
Numerical Integration ◽  
Infinite Series ◽  
Mossbauer Spectroscopy ◽  
Emission Lines ◽  
Algebraic Expression ◽  
Transmitted Intensity ◽  
Mößbauer Spectroscopy

This paper is concerned with the evaluation of the integral that represents the total transmitted intensity. We consider the general case in which the thin-absorber linewidth ΓA is allowed to be different from the linewidth ΓS of the source. The introduction of the parameter γ = ΓA/ΓS has made it possible to expand the integral in an infinite series, each term of which is a rational algebraic expression. Our formulation avoids the tedium of numerical integration and lends itself readily to programming in FORTRAN. The application to Mössbauer spectroscopy is discussed. The results are valid in the case of a split source even if the spacing between the emission lines is less than their linewidth.

A General Method for Spectrometer Design in the Scoff Approximation

1976 ◽  
Vol 34 ◽  
pp. 538-539
Author(s):  
J. R. Fields
Keyword(s):  
Electron Microscope ◽  
Transmission Electron Microscope ◽  
Energy Analysis ◽  
Incident Beam ◽  
Scanning Transmission Electron Microscope ◽  
Chemical Identification ◽  
Scanning Transmission Electron ◽  
Transmission Electron ◽  
Scanning Transmission ◽  
General Method

The energy analysis of electrons scattered by a specimen in a scanning transmission electron microscope can improve contrast as well as aid in chemical identification. In so far as energy analysis is useful, one would like to be able to design a spectrometer which is tailored to his particular needs. In our own case, we require a spectrometer which will accept a parallel incident beam and which will focus the electrons in both the median and perpendicular planes. In addition, since we intend to follow the spectrometer by a detector array rather than a single energy selecting slit, we need as great a dispersion as possible. Therefore, we would like to follow our spectrometer by a magnifying lens. Consequently, the line along which electrons of varying energy are dispersed must be normal to the direction of the central ray at the spectrometer exit.

Phase behavior of cationic and anionic surfactants at low concentrations

1992 ◽  
Vol 50 (1) ◽  
pp. 694-695
Author(s):  
E. Naranjo
Keyword(s):  
Phase Behavior ◽  
Structural Characterization ◽  
Dynamic Systems ◽  
Anionic Surfactants ◽  
Intermolecular Forces ◽  
Stable Form ◽  
Surfactant Mixtures ◽  
Low Concentrations ◽  
Cationic And Anionic Surfactants ◽  
General Method

Equilibrium vesicles, those which are the stable form of aggregation and form spontaneously on mixing surfactant with water, have never been demonstrated in single component bilayers and only rarely in lipid or surfactant mixtures. Designing a simple and general method for producing spontaneous and stable vesicles depends on a better understanding of the thermodynamics of aggregation, the interplay of intermolecular forces in surfactants, and an efficient way of doing structural characterization in dynamic systems.

Caricaturing as a general method to improve poor face recognition: Evidence from low-resolution images, other-race faces, and older adults.

2019 ◽  
Vol 25 (2) ◽  
pp. 256-279 ◽  
Author(s):  
Amy Dawel ◽  
Tsz Ying Wong ◽  
Jodie McMorrow ◽  
Callin Ivanovici ◽  
Xuming He ◽  
...  
Keyword(s):  
Older Adults ◽  
Face Recognition ◽  
Low Resolution ◽  
General Method ◽  
Low Resolution Images

Morphosemantic Analysis and Translation of Medical Compound Terms

1991 ◽  
Vol 30 (01) ◽  
pp. 30-35 ◽  
Author(s):  
P. Dujols ◽  
P. Aubas ◽  
C. Baylon ◽  
F. Grémy
Keyword(s):  
Medical Terms ◽  
General Method

This paper describes an automatic procedure for morphosemantic analysis and translation of compound medical terms. This analysis is of interest for the automatic indexation of medical discharge reports and summaries. Since words with the suffix -osis may have many different semantic interpretations, such -osis forms are taken as examples for a general method that avoids the difficulties in interpreting medical terms as reported in other studies.

Gold Catalyzed Hydroamination of Propargylic Alcohols: Controlling Divergent Reaction Pathways to Access 1,3-Aminoalcohols, 3-Hydroxyketones or 3-Aminoketones

2018 ◽  
Author(s):  
Victor Laserna ◽  
Tom Sheppard
Keyword(s):  
Gold Catalysis ◽  
Reaction Pathways ◽  
High Yield ◽  
Reaction Conditions ◽  
Propargylic Alcohols ◽  
Catalytic Quantity ◽  
Selective Formation ◽  
General Method

A versatile approach to the valorization of propargylic alcohols is reported, enabling controlled access to three different products from the same starting materials. Firstly, a general method for the hydroamination of propargylic alcohols with anilines is described using gold catalysis to give 3-hydroxy imines with complete regioselectivity. These 3-hydroxyimines can be reduced to give 1,3-aminoalcohols with high syn seletivity. Alternatively, by using a catalytic quantity of aniline, 3-hydroxyketones can be obtained in high yield directly from propargylic alcohols. Further manipulation of the reaction conditions enables the selective formation of 3-aminoketones via a rearrangement/hydroamination pathway.<br>

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