scholarly journals XII. On the theory of probabilities

1862 ◽  
Vol 152 ◽  
pp. 225-252 ◽  
Keyword(s):  
General Theory ◽  
Mathematical Analysis ◽  
Royal Society ◽  
General Character ◽  
Algebraic Equations ◽  
Functional Determinant ◽  
Complete Development ◽  
A Value ◽  
Peculiar Form

This paper has for its object the investigation of the general analytical conditions of a Method for the solution of Questions in the Theory of Probabilities, which was proposed by me in a work entitled “An Investigation of the Laws of Thought” (London, Walton and Maberly, 1854). The application of this method to particular problems has been illustrated in the work referred to, and yet more fully in a ‘Memoir on the Combination of Testimonies and of Judgments’ published in the Transactions of the Royal Society of Edinburgh (vol. xxi. Part 4). Some observations, too, on the general character of the solutions to which the method leads, founded upon induction from particular cases, were contained in the original treatise, and the outlines, still in some measure conjectural, of their general theory were given in an Appendix to the Memoir. But the complete development of that theory was attended with analytical difficulties which I have only lately succeeded in overcoming. It involves discussions relating to the properties of a certain functional determinant, and to the possible solutions of a system of algebraic equations of peculiar form—discussions which will, I trust, be thought to possess a value, as contributions to Mathematical Analysis, independent of their present application.

XXIX.—Boole's Unisignant

1912 ◽  
Vol 31 ◽  
pp. 448-455
Author(s):  
Thomas Muir
Keyword(s):  
Fourth Order ◽  
Mathematical Analysis ◽  
Functional Determinant ◽  
A Value ◽  
Peculiar Form

1. In two memoirs on the “Theory of Probabilities,” Boole was led to the consideration of a peculiarly interesting form of determinant which has only positive terms in its final form of development, and which in the case of the fourth order may be writtenV standing therein forIn the first of the two memoirs the determinant is not explicitly referred to, but in the second it receives considerable attention, Boole, indeed, there saying that the memoir “involves discussions relating to the properties of a certain functional determinant, and to the possible solutions of a system of algebraical equations of peculiar form, discussions which will, I trust, be thought to possess a value as contributions to mathematical analysis, independent of their present application.”

George Gabriel Stokes

2019 ◽  
Keyword(s):  
Fluid Dynamics ◽  
History Of Science ◽  
Mathematical Analysis ◽  
Royal Society ◽  
Science And Religion ◽  
Cambridge University ◽  
Public Servant ◽  
History Of ◽  
The Many ◽  
Natural Philosophers

George Gabriel Stokes was one of the most significant mathematicians and natural philosophers of the nineteenth century. Serving as Lucasian professor at Cambridge he made wide-ranging contributions to optics, fluid dynamics and mathematical analysis. As Secretary of the Royal Society he played a major role in the direction of British science acting as both a sounding board and a gatekeeper. Outside his own area he was a distinguished public servant and MP for Cambridge University. He was keenly interested in the relation between science and religion and wrote extensively on the matter. This edited collection of essays brings together experts in mathematics, physics and the history of science to cover the many facets of Stokes’s life in a scholarly but accessible way.

Al-Nawawī's Typology of Muftīs and its Significance for a General Theory of Islamic Law

1996 ◽  
Vol 3 (2) ◽  
pp. 137-164 ◽  
Author(s):  
Norman Calder
Keyword(s):  
General Theory ◽  
Islamic Law ◽  
The Other ◽  
Pivotal Role ◽  
General Character ◽  
Recent Debate ◽  
Closed Door

AbstractThis essay offers, in Section 2, a translation of al-Nawawī's presentation of the hierarchy of Muftīs. The context of the passage and its terminology and arguments are explored in the other Sections in order to assess their implications for the general character of Islamic juristic activities. Section 1 identifies two themes central to the text, namely loyalty to madhhab and differentiation of the task of the teaching jurist and the muftī. The first of these is elaborated in Section 3, which points to formal qualities of presentation and argument which assert the hermeneutical continuity of the school tradition; and in Section 4, which deals with the pivotal role of the founding imām in the legitimation of the school tradition. Section 5 takes up the terms taqlīd and ijtihād and shows that al-Nawawī's usage points towards a complex resolution of the recent debate about the open/closed door of ijtihād. The last Section returns to the original two themes to make two suggestions: (1) that taqlīd may be assessed as a principal of vitality within a hermeneutical tradition; (2) that the author-jurist (not the practising muftī) is the dominant creative agent within the ongoing juristic traditions.

scholarly journals A SÍNTESE DA TEORIA GERAL DO EMPREGO, DOS JUROS E DA MOEDA SEGUNDO ROY HARROD EM “MR. KEYNES AND TRADITIONAL THEORY”

1999 ◽  
Vol 23 ◽  
Author(s):  
Claudia Heller
Keyword(s):  
General Theory ◽  
Traditional Theory ◽  
Ongoing Research ◽  
Causal Relations ◽  
Complete Development ◽  
Space And Time

A hipótese discutida na pesquisa (ainda inconclusa) que dá origem a este texto é a de que as formalizações matemáticas da Teoria Geral do Emprego, dos Juros e da Moeda, elaboradas por Roy HARROD, John HICKS e James MEADE, além das de David CHAMPERNOWNE e de Brian REDDAWAY, ainda que semelhantes na forma final, foram alcançadas mediante diferentes raciocínios, justificativas e argumentos teóricos, e que a aceitação e o sucesso da versão matematizada se deu pelo fato dela permitir a incorporação – de modo implícito – das variadas relações de causalidade definidas por cada um destes autores. Por razões de tempo e de espaço, o texto explora esta hipótese de forma ainda preliminar e cinge-se apenas à contribuição de HARROD. Abstract The hypothesis behind the ongoing research that motivates this paper suggests that the mathematical formalizations of the General Theory of Employment, Interest and Money advanced by Roy HARROD, John HICKS and James MEADE, as well as the ones by David CHAMPERNOWNE and Brian REDDAWAY, although similar in their form, were constructed using different kinds of reasonings, justifications and theoretical arguments. Consequently, the acceptance and success of the mathematized version occurred because it allowed the – implicit – incorporation of the diverse causal relations proposed by each of these authors. Lack of space and time prevent a complete development of this hypothesis here, so this text focuses only on HARROD’s contribution.

III. On the theory of the electric telegraph

1856 ◽  
Vol 7 ◽  
pp. 382-399 ◽  
Keyword(s):  
Royal Society ◽  
Practical Applications ◽  
Complete Development ◽  
Incomplete Form

The following investigation was commenced in consequence of a letter received by the author from Prof. Stokes, dated Oct. 16, 1854. It is now communicated to the Royal Society, although only in an incomplete form, as it may serve to indicate some important practical applications of the theory, especially in estimating the dimensions of telegraph wires and cables required for long distances; and the author reserves a more complete development and illustration of the mathematical parts of the investigation for a paper on the conduction of Electricity and Heat through solids, which he intends to lay before the Royal Society on another occasion.

scholarly journals The general theory of relaxation methods applied to linear systems

1939 ◽  
Vol 169 (939) ◽  
pp. 476-500 ◽  
Keyword(s):  
General Theory ◽  
Sufficient Conditions ◽  
Formal Proof ◽  
Linear Operators ◽  
Successive Approximations ◽  
Continuous Systems ◽  
Algebraic Equations ◽  
Relaxation Methods ◽  
Linear Differential ◽  
Homogeneous Linear

During the last few years Southwell and his fellow-workers have developed a new method for the numerical solution of a very general type of problem in mathematical physics and engineering. The method was originally devised for the determination of stresses in frameworks, but it has proved to be directly applicable to any problem which is reducible to the solution of a system of non-homogeneous, linear, simultaneous algebraic equations in a finite number of unknown variables.* Southwell’s “ relaxation m ethod” is one of successive approximation and, in order to complete the previous investigations of this method, it is necessary to prove that the successive approximations do actually converge towards the exact solutions. This formal proof is given in § 4. Southwell’s “ relaxation” methods are not directly applicable to continuous systems, where the number of unknown variables is infinite, but it is shown here that simple extensions and modifications of the relaxation method render it suitable for application to either discrete or continuous systems (§ 5). The general theory of relaxation methods is then developed in terms of the theory of linear operators (§7) and sufficient conditions are prescribed for the convergence of the process of approximation (§ 8). These general methods are then applied to the solution of non-homogeneous, linear integral equations (§ 10) and to the solution of nonhomogeneous, linear differential equations (§§ 11, 12).

Reviews - A. E. Heath. Preface. Studies in logic and probability, by George Boole, Watts & Co., London1952, and the Open Court Publishing Company, LaSalle, Illinois, 1952, pp. 7–8. - R. Rhees. Note in editing. Studies in logic and probability, by George Boole, Watts & Co., London1952, and the Open Court Publishing Company, LaSalle, Illinois, 1952, pp. 9–43. - George Boole. The mathematical analysis of logic, being an essay towards a calculus of deductive reasoning. A reprint of 191. Studies in logic and probability, by George Boole, Watts & Co., London1952, and the Open Court Publishing Company, LaSalle, Illinois, 1952, pp. 45–119. - George Boole. Later notes (to the foregoing). Studies in logic and probability, by George Boole, Watts & Co., London1952, and the Open Court Publishing Company, LaSalle, Illinois, 1952, pp. 119–124. (Taken from manuscript in the Library of the Royal Society.) - George Boole. The calculus of logic. A reprint of 192. Studies in logic and probability, by George Boole, Watts & Co., London1952, and the Open Court Publishing Company, LaSalle, Illinois, 1952, pp. 125–140. - George Boole. Sketch of a theory and method of probabilities founded upon the calculus of logic. Studies in logic and probability, by George Boole, Watts & Co., London1952, and the Open Court Publishing Company, LaSalle, Illinois, 1952, pp. 141–166. (From manuscripts in the Royal Society Library, probably before 1851.) - George Boole. Of propositions numerically definite. A reprint of 194. Studies in logic and probability, by George Boole, Watts & Co., London1952, and the Open Court Publishing Company, LaSalle, Illinois, 1952, pp. 167–186. - George Boole. The claims of science, especially as founded in its relation to human nature. Studies in logic and probability, by George Boole, Watts & Co., London1952, and the Open Court Publishing Company, LaSalle, Illinois, 1952, pp. 187–210. (Lecture published in London, 1851.) - George Boole. Logic and reasoning. Studies in logic and probability, by George Boole, Watts & Co., London1952, and the Open Court Publishing Company, LaSalle, Illinois, 1952, pp. 211–229. (From Royal Society manuscripts, after 1855.) - George Boole. Extracts from a paper entitled “On the mathematical theory of logic and on the philosophical interpretation of its methods and processes.”Studies in logic and probability, by George Boole, Watts & Co., London1952, and the Open Court Publishing Company, LaSalle, Illinois, 1952, pp. 230–246. (From Royal Society manuscripts, later than 1855.)

1959 ◽  
Vol 24 (3) ◽  
pp. 203-209 ◽  
Author(s):  
Michael Dummett
Keyword(s):  
Mathematical Analysis ◽  
Royal Society ◽  
Mathematical Theory ◽  
Deductive Reasoning ◽  
Publishing Company ◽  
Philosophical Interpretation ◽  
Open Court ◽  
Court Publishing ◽  
George Boole ◽  
Nature Studies

scholarly journals Researches on the tides; sixth series. On the results of an extensive system of tide observations, made on the coasts of Europe and America, in June 1835

1837 ◽  
Vol 3 ◽  
pp. 399-399
Keyword(s):  
Royal Society ◽  
The Other ◽  
General Character ◽  
Extensive System ◽  
Total Range ◽  
Considerable Length ◽  
The Government

The author having, in several previous communications to the Royal Society, urged the importance of simultaneous tide observations made at distant places, here gives an account of the steps taken to carry this plan into effect, in consequence of his representations, both by the Government in England, and by the other maritime powers of Europe. He explains, in the present paper, the general character of the observations thus obtained, the mode employed in reducing them, and enters at considerable length into a discussion of the immense mass of information which they supply with respect to the phenomena of the tides. One of his principal objects was to fix with precision the form of the Cotidal lines by which the motion of the tide wave is exhibited. He devotes one section of the paper to an investigation of the general form of these lines; and another to a nearer approxima­tion to an accurate map of these lines, more especially as they exist in the German Ocean. The 4th section treats of the height of the tide in its total range from high to low water; the 5th relates to the diurnal inequality; the 6th to the semimenstrual inequality; and the 7th and last comprises general remarks on the tables which accom­pany the paper.

King Charles II, Fundator et Patronus (1630-1685)

1960 ◽  
Vol 15 (1) ◽  
pp. 39-45 ◽  
Keyword(s):  
Royal Society ◽  
General Character ◽  
James I ◽  
Interest In Science ◽  
Charles I ◽  
Charles Ii

Charles II ranks as founder of the Royal Society because he granted to it the charter which incorporated it and gave it its name. Its arms declare their origin; if not devised or proposed by him, at least they were consciously granted by him. The mace, which is placed before the President of the Society at all meetings of the Society and of Council, was also given to the Society by Charles as its founder. These (and other) benefactions were due not so much to any profound interest in science on Charles’s part as to his general character and to the tendencies of his time, and more especially to his friendship with some of the royalists among the founding members of the Society. He was born on 29 May 1630, the son of Charles I, King of England, Scotland, France, and Ireland, and of his French queen, Henrietta Maria; his grandparents were James I, ‘the wisest fool in Christendom’, Anne of Denmark, who was almost a nonentity, Henri IV, one of the most genial of men and the ablest of kings, and Marie de Medicis, at all times a source of trouble.

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