CREEP AND SHRINKAGE IN PLAIN, REINFORCED, AND PRE-STRESSED CONCRETE. A GENERAL METHOD OF CALCULATION.

1943 ◽  
Vol 21 (1) ◽  
pp. 38-57 ◽  
Author(s):  
A D ROSS
Keyword(s):  
Method Of Calculation ◽  
Creep And Shrinkage ◽  
General Method

Preflex Beams: A Method of Calculation of Creep and Shrinkage Effects

2006 ◽  
Vol 11 (1) ◽  
pp. 48-58 ◽  
Author(s):  
Salvatore Giacomo Morano ◽  
Claudio Mannini
Keyword(s):  
Method Of Calculation ◽  
Creep And Shrinkage

General method of calculation of any hadronic decay in the3 P 0 model

1992 ◽  
Vol 11 (4) ◽  
pp. 171-193 ◽  
Author(s):  
W. Roberts ◽  
B. Silvestre-Brac
Keyword(s):  
Hadronic Decay ◽  
Method Of Calculation ◽  
General Method

scholarly journals Projective method for spinorial techniques: Unifying calculational schemes of Dirac amplitudes

2019 ◽  
Vol 65 (6 Nov-Dec) ◽  
pp. 639
Author(s):  
E. Sanchez ◽  
M. Moreno
Keyword(s):  
Standard Method ◽  
Calculation Procedure ◽  
Closure Property ◽  
Projective Method ◽  
Method Of Calculation ◽  
Dirac Particles ◽  
Massless Spinor ◽  
Dirac Spinors ◽  
General Method

There have been numerous approaches to the calculation of spin dependent amplitudes for Dirac particles. All of them have their own advantages, particularly, the standard method of calculation, based on the multiplication by the unit, has a few shortcomings. In this work we use the closure property of the Dirac spinors to present a general method for the amplitude computation. It is shown that the massless spinor method and the helicity spinor method can be formulated through this method. Finally, we get an example of this calculation procedure computing the spin dependentamplitude for the Compton process.

scholarly journals Electronic wave functions - I. A general method of calculation for the stationary states of any molecular system

1950 ◽  
Vol 200 (1063) ◽  
pp. 542-554 ◽  
Keyword(s):  
Molecular System ◽  
Accurate Solution ◽  
Wave Functions ◽  
Orbital Method ◽  
Stationary States ◽  
Electronic Wave ◽  
Method Of Calculation ◽  
Electronic Wave Functions ◽  
Bond Method ◽  
General Method

This communication deals with the general theory of obtaining numerical electronic wave functions for the stationary states of atoms and molecules. It is shown that by taking Gaussian functions, and functions derived from these by differentiation with respect to the parameters, complete systems of functions can be constructed appropriate to any molecular problem, and that all the necessary integrals can be explicitly evaluated. These can be used in connexion with the molecular orbital method, or localized bond method, or the general method of treating linear combinations of many Slater determinants by the variational procedure. This general method of obtaining a sequence of solutions converging to the accurate solution is examined. It is shown that the only obstacle to the evaluation of wave functions of any required degree of accuracy is the labour of computation. A modification of the general method applicable to atoms is discussed and considered to be extremely practicable.

scholarly journals IV. On the summation of series

1865 ◽  
Vol 14 ◽  
pp. 332-336
Keyword(s):  
Method Of Calculation ◽  
Definite Integrals ◽  
Summation Of Series ◽  
Complicated Nature ◽  
General Method

In a Memoir published in the Philosophical Transactions for the year 1855, I applied the Theory of Definite Integrals to the summation of many intricate series. I have thought my researches on this subject might well be terminated by the following paper, in which I have pointed out methods for the summation of series of a far more complicated nature. I commence with some remarks intended to give clear conceptions of the general method of calculation.

Second essay on a general method in dynamics

1837 ◽  
Vol 3 ◽  
pp. 315-316 ◽  
Keyword(s):  
Characteristic Function ◽  
Differential Equations ◽  
Principal Function ◽  
General Transformation ◽  
Method Of Calculation ◽  
Present Essay ◽  
Separate Branch ◽  
The One ◽  
Gradual Variation ◽  
General Method

This essay is a sequel of the one which appeared in the last volume of the Philosophical Transactions, and which contained a general me­thod for reducing all the most important problems of dynamics to the study of one characteristic function, or one central or radical relation. It was there remarked that many eliminations required by this me­thod might be avoided by a general transformation, introducing the time explicitly into a part (S) of the whole characteristic function (V) ; and the first object of the present essay is to examine and develope the properties of this part (S), which the author designates by the term Principal Function . This function is applied by the author to problems of perturbation, in which he finds it dispenses with many laborious and circuitous processes, and furnishes accurate expressions of the disturbed configurations of a system by the rules of undisturbed motion, if only the initial components of velocities be changed in a suitable manner. Another manner of extending rigorously to dis­turbed, the rules of undisturbed motion, by the gradual variation of elements, in number double the number of the coordinates or other marks of position of the system, which was first invented by Lagrange, and was afterwards improved by Poisson, is considered in this second essay under a form rather more general; and the general method of calculation which has already been applied by the author to other analogous questions in optics and in dynamics, is now applied to the integration of the equations which determine these elements. This general method is founded chiefly on a combination of the principle of variations with those of partial differentials, and may furnish, when matured, a separate branch of analysis, which may be denominated the Calculus of Principal Functions . When applied to the integra­tion of the equations of varying elements, it suggests the consideration of a certain Function of Elements , capable of being variously trans­formed, and which may be either rigorously determined, or at least approached to, by a corollary of the general method. With a view to illustrate these new principles, and more especially those connected with problems of perturbation, they are applied, in this essay, first, to a very simple example, suggested by the motions of projectiles, the parabolic path being treated as the undisturbed; and secondly, to the problem of determining the motions of a ternary or multiple system, with any laws of attraction or repulsion, and with one pre­dominant mass. This latter problem, which was touched upon in the former essay, is here resumed in a new manner, by forming and in­tegrating the differential equations of a new set of varying elements, entirely distinct in theory (though little differing in practice) from the elements conceived by Lagrange; and having this advantage, that the differentials of all the new elements for both the disturbed and disturbing masses may be expressed by the coefficients of one disturbing function.

scholarly journals A General Method of Calculation in Kinetics

1906 ◽  
Vol 10 (6) ◽  
pp. 423-444 ◽  
Author(s):  
R. E. De Lury
Keyword(s):  
Method Of Calculation ◽  
General Method

VII. Second essay on a general method in dynamics

1835 ◽  
Vol 125 ◽  
pp. 95-144 ◽  
Keyword(s):  
Characteristic Function ◽  
Principal Function ◽  
Method Of Calculation ◽  
Present Essay ◽  
Separate Branch ◽  
Extensive Class ◽  
Gradual Variation ◽  
Disturbed Motion ◽  
General Method

The former Essay contained a general method for reducing all the most important problems of dynamics to the study of one characteristic function, one central or ra­dical relation. It was remarked at the close of that Essay, that many eliminations required by this method in its first conception, might be avoided by a general trans­formation, introducing the time explicitly into a part S of the whole characteristic function V; and it is now proposed to fix the attention chiefly on this part S, and to call it the Principal Function . The properties of this part or function S, which were noticed briefly in the former Essay, are now more fully set forth; and especially its uses in questions of perturbation, in which it dispenses with many laborious and cir­cuitous processes, and enables us to express accurately the disturbed configuration of a system by the rules of undisturbed motion, if only the initial components of veloci­ties be changed in a suitable manner. Another manner of extending rigorously to disturbed motion the rules of undisturbed, by the gradual variation of elements, in number double the number of the coordinates or other marks of position of the system, which was first invented by Lagrange, and was afterwards improved by Poisson, is considered in this Second Essay under a form perhaps a little more general; and the general method of calculation which has already been applied to other analogous questions in optics and in dynamics by the author of the present Essay, is now applied to the integration of the equations which determine these ele­ments. This general method is founded chiefly on a combination of the principles of variations with those of partial differentials, and may furnish, when it shall be ma­tured by the labours of other analysts, a separate branch of algebra, which may be called perhaps the Calculus of Principal Functions ; because, in all the chief applica­tions of algebra to physics, and in a very extensive class of purely mathematical questions, it reduces the determination of many mutually connected functions to the search and study of one principal or central relation. When applied to the integration of the equations of varying elements, it suggests, as is now shown, the consideration of a certain Function of Elements , which may be variously chosen, and may either be rigorously determined, or at least approached to, with an indefinite accuracy, by a corollary of the general method. And to illustrate all these new general processes, but especially those which are connected with problems of perturbation, they are applied in this Essay to a very simple example, suggested by the motions of projectiles, the parabolic path being treated as the undisturbed. As a more important example, the problem of determining the motions of a ternary or multiple system, with any laws of attraction or repulsion, and with one predominant mass, which was touched upon in the former Essay, is here resumed in a new way, by forming and inte­grating the differential equations of a new set of varying elements, entirely distinct in theory (though little differing in practice) from the elements conceived by Lagrange, and having this advantage, that the differentials of all the new elements for both the disturbed and disturbing masses may be expressed by the coefficients of one disturbing function.

scholarly journals CALCULATION OF THE SLEEVE PACKER ELEMENT WITH THE VARIABLE ANGLE OF LAYING OF THREADS OF THE CORD FOR CREATION OF EDGE PROTECTION (PART 1)

2020 ◽  
pp. 29-40
Author(s):  
N. Serdyukov ◽  
E. Ryzhenko ◽  
Yu. Smirnov ◽  
A. Mashkov
Keyword(s):  
Elastic Modulus ◽  
Packing Density ◽  
Calculation Procedure ◽  
Initial Angle ◽  
Technological Parameters ◽  
Method Of Calculation ◽  
Power Characteristics ◽  
Number Of Layers ◽  
Variable Angle ◽  
General Method

the method of calculation of influence of design and technological parameters of material of a cover of a packer element is developed: the initial angle of laying of threads of the reinforcing framework, the packing density of threads in the field of unions, number of layers of a framework, rubber elastic modulus on power characteristics of a cover, for the purpose of creation of edge protection of a packer element. In the first part of work the cover of a packer element with laying of threads with a constant corner on all length of a cover is investigated. The received results of calculation, allowed to evaluate and prove quantitatively the constructive and technological directions of reliability augmentation of edge protection of a packer element. The developed calculation procedure is a basis of development of more general method of calculation of power characteristics of a cover of a packer element with variable longwise covers the initial angle of laying of threads.

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