scholarly journals IV. On the determination of the terms in the disturbing function of the fourth order as regards the eccentricities and inclinations which give rise to secular inequali­ties

1835 ◽  
Vol 125 ◽  
pp. 57-81
Keyword(s):  
Fourth Order ◽  
A Priori ◽  
Disturbing Function ◽  
Left Hand ◽  
The Third ◽  
Hand Column ◽  
The Subject ◽  
Analytical Expressions

Hitherto in the theory of the secular inequalities the terms in the disturbing function of the fourth order as regards the inclinations have been neglected. As the magnitude of these terms depends, in great measure, upon certain numerical co­efficients, it is impossible to form any precise notion à priori with respect to their amount, and as to the error which may arise from neglecting them. I have therefore thought it desirable to ascertain their analytical expressions; and the details of this calculation form the subject of this paper. Some of the secular inequalities which result from these terms are far within the limits of accuracy which Laplace appears to have contemplated in the third volume of the Mécanique Céleste. The method which I have here adopted for developing the disturbing function rests upon principles which I have already explained. Very little trouble is requisite to obtain certain analytical expressions for the terms upon which the secular inequalities depend, or for any others, in the development of the disturbing function; but it is not so easy to put these expressions in the simplest form of which they are susceptible; and this is a point to which I think hitherto sufficient attention has not been paid. It will be found that I have obtained, finally, expressions of very remarkable sim­plicity; to accomplish this, however, I have been obliged to go through tedious pro­cesses of reduction, the details of which are here subjoined, in order that my results may be verified or corrected without difficulty. In order to give an additional example of the great facility with which terms in the disturbing function are arrived at by my method, I have calculated one of those given by Professor Airy, and which is required in the determination of his inequality of Venus; and I have arrived at the result which he has given. The same method, with certain modifications, is applicable to the de­velopment of the disturbing function in terms of the true longitudes. The terms in the disturbing function which give rise to the secular inequalities of the elliptic constants, when the terms of the order of the fourth powers of the eccentricities and inclinations are retained, and higher powers of those quantities are neglected, are as follows: and I propose, as they form, in fact, a system apart, to distinguish them by the indices given in the left-hand column.

scholarly journals On the determination of the terms in the disturbing function of the fourth order, as regards the eccentricities and inclinations which give rise to secular inequali­ties

1837 ◽  
Vol 3 ◽  
pp. 301-301
Keyword(s):  
Fourth Order ◽  
A Priori ◽  
Disturbing Function

The author observes, that the magnitude of the terms of the fourth order in the disturbing function, relating to the inclinations, in the theory of the secular inequalities of the planets, does not admit of being estimated à priori ; and consequently the amount of error which may arise from neglecting them cannot be appreciated. The object of the present investigation is to ascertain the analytical ex­pressions of these terms; and the method adopted for this purpose is derived from principles already explained by the author in a for­mer paper. He has bestowed great pains in putting these expressions into the simplest form of which they are susceptible; and has finally succeeded, after much labour of reduction, in obtaining ex­pressions of remarkable simplicity. He exemplifies their application by the calculation, on this method, of one of the terms given by Pro­fessor Airy as requisite for the determination of the inequality of Venus; and arrives, by this shorter process, at the same result. The same method, he remarks, is, with certain modifications, applicable to the developement of the disturbing function in terms of the true longitude.

Introduction

2018 ◽  
Author(s):  
Chakravarthi Ram-Prasad
Keyword(s):  
Philosophical Tradition ◽  
Phenomenological Tradition ◽  
The Third ◽  
Western Philosophical Tradition ◽  
The Subject ◽  
To Come

The Introduction outlines the various chapters. It then situates the question of ‘body’ in the modern Western philosophical tradition following Descartes, and argues that this leaves subsequent responses to come under one of three options: metaphysical dualism of body and subject; any anti-dualist reductionism; or the overcoming of the divide. Describing the Phenomenology of Merleau-Ponty as a potent example of the third strategy, the Introduction then suggests his philosophy will function as foil to the ecological phenomenology developed and presented in the book. Moreover, one approach within the Western Phenomenological tradition, of treating phenomenology as a methodology for the clarification of experience (rather than the means to the determination of an ontology of the subject) is compared to the approach in this book. Since classical India, while understanding dualism, did not confront the challenge of Descartes (for better or for worse), its treatment of body follows a different trajectory.

scholarly journals DETERMINATION OF THE OPTIMAL SCHEME FOR THE DEVELOPMENT OF A CUTTING AREA ACCORDING TO THE DEGREE OF UNDERGROWTH PRESERVATION

2021 ◽  
Author(s):  
Vitaliy Abramov ◽  
E. Shkardun ◽  
E. Sapova
Keyword(s):  
Optimal Scheme ◽  
The Third ◽  
Analytical Expressions

The article is devoted to the substantiation of the optimal scheme for the development of felling areas according to the degree of preservation of undergrowth. For this, three options were explored. The first method involves the laying of apiary trails, followed by the development of half-incisions with ribbons of a certain width, starting from the nearest to the apiary trail. In the second method of apiary development, the laying of apiary trails is not assumed and the felling of trees occurs inside the plantation on a belt of a certain width located perpendicular to the main trail. The third method of apiary development, proposed for comparison, involves the use of technological sighting devices at an angle to the main and apiary technological corridor. To compare the indicated methods of performing processing operations in apiaries, analytical expressions were obtained to determine technological areas and a calculation of all their components was performed.

Corrections

1978 ◽  
Vol 24 (5) ◽  
pp. 834-834
Keyword(s):  
Left Hand ◽  
Standard Curve ◽  
The Third ◽  
Glycocholic Acid ◽  
Hand Column

Abstract volume23 p 900: Insert decimal in figures in Table 1, to read: See Table in the pdf File p 2067, left-hand column, line 8: mp is 106-107.5 °C p 2108: The first equation in column two should read See equation in the pdf File p 2109: Under the section on Standard curve, the third sentence has a part missing; it should read "the midrange (Table 2) of the [U-3H]glycochenodeoxycholic acid (c - 20.6 ± 7) and of the [U-3H]glycocholic acid. ...". In the last paragraph of this paper, the correct references are (5-7, 9). p 2189: In this paper, Figures 3 and 4b should be interchanged. volume24 The addresses of the authors of the notes beginning on pages 149 and 150 were inadvertently interchanged.

An Efficient Algorithm for the Graphical Representation of the Three-Dimensional Workspace of Parallel Manipulators

1992 ◽  
Author(s):  
Clément M. Gosselin ◽  
Eric Lavoie ◽  
Pierre Toutant
Keyword(s):  
Graphical Representation ◽  
Three Dimensional ◽  
Parallel Manipulators ◽  
Dimensional Representation ◽  
Efficient Procedure ◽  
Three Dimensional Representation ◽  
The Subject ◽  
Six Degree Of Freedom ◽  
Analytical Expressions

Abstract This paper presents an algorithm for the graphical representation of the three-dimensional workspace of six-degree-of-freedom parallel manipulators. In fact, the algorithm introduced here follows from previous work on the subject (Gosselin 1990). In the latter reference, an algorithm was developed to obtain analytical expressions of the boundaries of the workspace. However, the method was applicable to two-dimensional sections of the workspace only. Therefore, a three-dimensional representation of the workspace, i.e., the set of positions attainable with a given orientation of the platform, could only be obtained by discretization. The algorithm introduced here involves the determination of analytical expressions of the boundaries of the three-dimensional workspace. Hence, it results in a very efficient procedure which can be performed interactively, in a context of CAD. The algorithm is described in detail in this paper. Examples of results that have been obtained with this algorithm are also presented.

scholarly journals The Light Curves of Double-Mode Cepheids: The CO Aur Case

1998 ◽  
Vol 185 ◽  
pp. 389-390
Author(s):  
E. Poretti ◽  
I. Pardo
Keyword(s):  
Frequency Analysis ◽  
Fourth Order ◽  
A Priori ◽  
Cross Coupling ◽  
Second Order ◽  
Light Curves ◽  
Third Order ◽  
The Third ◽  
Coupling Terms ◽  
Phase Differences

In two recent papers (Pardo & Poretti 1997; Poretti & Pardo 1997) we analyzed all the available photometry of galactic double-mode Cepheids (DMCs) with the aim of detecting in each case the importance of the harmonics and of the cross coupling terms. We found that no a priori fit can be reliably applied to the measurements of a DMC, but a careful frequency analysis must be done to evaluate the importance of each term. As a further application of this technique, we obtained very precise indications about the properties of the Fourier parameters. When discussing the generalized phase differences Gi,j we demonstrated that plotting them as a function of the order |i|+|j|, there are well-defined regions where they are confined: the second order terms have π < Gi,j < 3π/2; the third order terms have π/2 < Gi,j < π; the fourth order terms cluster around 2π.

scholarly journals Physicality as a possible key to understanding human nature

2021 ◽  
pp. 162-172
Author(s):  
Zulfiya Z. Ibragimova
Keyword(s):  
Human Nature ◽  
Human Body ◽  
A Priori ◽  
The Body ◽  
Human Existence ◽  
Ontological Status ◽  
Primitive Form ◽  
The Third ◽  
The Subject ◽  
Human Rationality

The statement about human nature is the subject of numerous discussions, which, however, does not negate the presence of the substrate of its origin, manifestations, specificity, and real dynamics in space and time. In the process of analysis, we find a lot of arguments that confirm this fact, as well as a decent number of counterarguments. In this article, a priori, we proceed from the validity of the existence of the term "human nature", recognizing its ambiguity. Of course, our stated physicality as an aspect of human nature does not exhaust the idea of his nature. The nominal division into soul, spirit, etc. gives us some methodological tools. No more than that. Physicality, in its turn, requires problematization. "Physicality "is a category that denotes what a given human body naturally becomes in the course of its social modifications, so this category can certainly not be considered outside of conjunction with another very important category - "spirituality". These concepts, as well as the phenomena they denote, are interrelated (MORGAN 2006). In our review, there are three main ways to interpret "Physicality". Firstly, it is the only factuality that initially claims the ontological status. Secondly, it is part of a harmonious whole that includes all non-corporeal things. I would like to focus on the third aspect, which includes at least three principles. Thirdly, physicality changes its seemingly simple "fate" dramatically, turning into a problem as a way of human existence. This can be interpreted "as a creative act of overcoming oneself". Only this overcoming of the present self presupposes a reliance on its relevance and reality. This ontologically conditioned event is always self-based. In this sense, the body as a creative phenomenon " never appears just by its own. Yet it is precisely overcoming that is the constitutive feature of human existence. A man is bigger than himself. We can say that the problem is a way of human existence. The problem in the most primitive form can be expressed as "I already want to, but I can't yet". Where does the desire come from if the object of desire (the desired situation) is not yet available? How can you want something that doesn't exist yet and never has? The man himself is a few steps ahead (BUBLIK, 2006). Human rationality is based not only on reflectivity, but also on the ability of a person to operate with ideas that do not have objective visibility (for example, the ultimate category of being). Thus, man proves his metaphysicality: "man's metaphysics expresses not only the presence of the supernatural dimension in man but also his ability to determine himself, to be his own creation". The main methods used in writing the article: the unity of historical and logical, the method of reflection.

scholarly journals The Third and Fourth Moments of the Local Stellar Velocity Distribution

1974 ◽  
Vol 3 ◽  
pp. 409-413
Author(s):  
R. H. Miller
Keyword(s):  
Velocity Distribution ◽  
Covariance Matrix ◽  
Fourth Order ◽  
Observational Error ◽  
The Third ◽  
Galactic Potential ◽  
The Galaxy ◽  
Stellar Velocity ◽  
Velocity Moments

AbstractThe velocity moments through the fourth order were calculated for a subset of 870 astrophysically selected stars from Gliese’s catalog. An essential part of this program was the determination of the covariances of estimates of the moments; both sampling and observational error contributions were taken into account in evaluating the total covariance matrix. In applications to the study of galactic structure, the Gliese stars are regarded as tracers of the galactic potential. The moments found are consistent with conventional assumptions about symmetries of the galaxy. Certain galactic parameters, such as the curvature in the law of rotation and the asymmetric drift, were studied with the help of the values obtained for the moments.

scholarly journals Electro–magneto-encephalography for a three-shell model: distributed current in arbitrary, spherical and ellipsoidal geometries

2008 ◽  
Vol 6 (34) ◽  
pp. 479-488 ◽  
Author(s):  
A.S Fokas
Keyword(s):  
Shell Model ◽  
A Priori ◽  
Arbitrary Geometry ◽  
The Third ◽  
Complete Determination ◽  
Simultaneous Use ◽  
Neuronal Current ◽  
The Brain ◽  
Three Components

The problem of determining a continuously distributed neuronal current inside the brain under the assumption of a three-shell model is analysed. It is shown that for an arbitrary geometry, electroencephalography (EEG) provides information about one of the three functions specifying the three components of the current, whereas magnetoencephalography (MEG) provides information about a combination of this function and of one of the remaining two functions. Hence, the simultaneous use of EEG and MEG yields information about two of the three functions needed for the reconstruction of the current. In particular, for spherical and ellipsoidal geometries, it is possible to determine the angular parts of these two functions as well as to obtain an explicit constraint satisfied by their radial parts. The complete determination of the radial parts, as well as the determination of the third function, requires some additional a priori assumption about the current. One such assumption involving harmonicity is briefly discussed.

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