scholarly journals III. On scalar and clinant algebraical coordinate geometry, introducing a new and more general theory of analytical geometry, including the received as a particular case, and explaining ‘imaginary points,’ ‘intersections,’ and ‘lines.’

1860 ◽  
Vol 10 ◽  
pp. 415-426 ◽  
Keyword(s):  
General Theory ◽  
Present Theory ◽  
Plane Geometry ◽  
Analytical Geometry ◽  
Abstract Equation ◽  
Unit Of Length ◽  
The Right ◽  
Coordinate Geometry

Scalar Plane Geometry .— With O as a centre describe a circle with a radius equal to the unit of length. Let OA, OB be any two of its unit radii, termed ‘coordinate axes.’ From any point P in the plane AOB draw PM parallel to BO, so as to cut OA, produced either way if necessary, in M. Then there will exist some ‘scalars’ (‘real’ or ‘possible quantities’) u, v such that OM = u . OA, and Mp = v . OB, all lines being considered in respect both to magnitude and direction. Hence OP, which is the ‘appense’ or ‘geometrical sum’ of OM and MP, or = OM + MP, will = u . OA + v . OB. By varying the values of the 'coordinate scalars’ u, v P may be made to assume any position whatever on the plane of AOB. The angle AOB may be taken at pleasure, but greater symmetry is secured by choosing OI and OJ as coordinate axes, where IOJ is a right angle described in the right-handed direction. If any number of lines OP, OQ, OR, &c., be thus represented, the lengths of the lines PQ, QR, &c., and the sines and cosines of the angles IOP, POQ, QOR, &c., can be immediately furnished in terms of the unit of length and the coordinate scalars. If OP = x . OI + y . OJ, and any relation be assigned between the values of x and y , such as y = fx or ϕ ( x, y ) = 0 , then the possible positions of P are limited to those in which for any scalar value of x there exists a corresponding scalar value of y . The ensemble of all such positions of P constitutes the ‘ locus ’ of the two equations, viz. the ‘concrete equation’ OP = x . Ol + y .OJ, and the ‘abstract equation’ y = f. x. The peculiarity of the present theory consists in the recognition of these two equations to a curve, of which the ordinary theory only furnishes the latter, and inefficiently replaces the former by some convention respecting the use of the letters, whereby the coordinates themselves are not made a part of the calculation.

Adversarial Medical and Scientific Testimony and Lay Jurors: A Proposal for Medical Malpractice Reform

1995 ◽  
Vol 21 (2-3) ◽  
pp. 281-300
Author(s):  
Jody Weisberg Menon
Keyword(s):  
General Theory ◽  
Legal System ◽  
Medical Malpractice ◽  
Common Knowledge ◽  
Common Law ◽  
Expert Witnesses ◽  
Malpractice Reform ◽  
The Right ◽  
Scholarly Attention ◽  
Scientific Testimony

Pleas for reform of the legal system are common. One area of the legal system which has drawn considerable scholarly attention is the jury system. Courts often employ juries as fact-finders in civil cases according to the Seventh Amendment of the Constitution: “In Suits at common law, where the value in controversy shall exceed twenty dollars, the right of trial by jury shall be preserved … .” The general theory behind the use of juries is that they are the most capable fact-finders and the bestsuited tribunal for arriving at the most accurate and just outcomes. This idea, however, has been under attack, particularly by those who claim that cases involving certain difficult issues or types of evidence are an inappropriate province for lay jurors who typically have no special background or experience from which to make informed, fair decisions.The legal system uses expert witnesses to assist triers of fact in understanding issues which are beyond their common knowledge or difficult to comprehend.

Fecundity of Resident and Anadromous Dolly Varden (Salvelinus malma) in Southeastern Alaska

1973 ◽  
Vol 30 (4) ◽  
pp. 543-548 ◽  
Author(s):  
R. F. Blackett
Keyword(s):  
Egg Size ◽  
Fish Length ◽  
Dolly Varden ◽  
Salvelinus Malma ◽  
Ovary Weight ◽  
Dolly Varden Salvelinus Malma ◽  
Egg Number ◽  
Unit Of Length ◽  
The Right ◽  
Linear Regressions

Fecundity of resident Dolly Varden (Salvelinus malma) in an isolated population of southeastern Alaska averaged 66 eggs per female in comparison with 1888 eggs for anadromous Dolly Varden from two nearby streams. A relatively large egg size, averaging 3.6 mm in diameter and overlapping the range for the anadromous char, has been retained by the females in the resident population. Curvilinear regressions between egg number and fish length and linear regressions between egg number and body and ovary weights show that resident females have fewer eggs per unit of length, approximately the same number of eggs per gram of body weight, and more eggs per gram of ovary weight than anadromous females. The resident char attain sexual maturity a year earlier in life and at a smaller size than the migratory char. Development of a larger left ovary containing more eggs than the right was a common occurrence for both resident and anadromous Dolly Varden.

scholarly journals III. On abstract geometry

1870 ◽  
Vol 18 (114-122) ◽  
pp. 122-123
Keyword(s):  
General Theory ◽  
Linear Function ◽  
Rational Functions ◽  
Plane Geometry ◽  
System Of Equations ◽  
Fundamental Notion ◽  
Solid Geometry

I submit to the Society the present exposition of some of the elementary principles of an Abstract m -dimensional geometry. The science presents itself in two ways,—as a legitimate extension of the ordinary two- and threedimensional geometries; and as a need in these geometries and in analysis generally. In fact whenever we are concerned with quantities connected together in any manner, and which are, or are considered as variable or determinable, then the nature of the relation between the quantities is frequently rendered more intelligible by regarding them (if only two or three in number) as the coordinates of a point in a plane or in space; for more than three quantities there is, from the greater complexity of the case, the greater need of such a representation; but this can only be obtained by means of the notion of a space of the proper dimensionality; and to use such representation, we require the geometry of such space. An important instance in plane geometry has actually presented itself in the question of the determination of the curves which satisfy given conditions: the conditions imply relations between the coefficients in the equation of the curve; and for the better understanding of these relations it was expedient to consider the coefficients as the coordinates of a point in a space of the proper dimensionality. A fundamental notion in the general theory presents itself, slightly in plane geometry, but already very prominently in solid geometry; viz. we have here the difficulty as to the form of the equations of a curve in space, or (to speak more accurately) as to the expression by means of equations of the twofold relation between the coordinates of a point of such curve. The notion in question is that of a k -fold relation,—as distinguished from any system of equations (or onefold relations) serving for the expression of it,—and giving rise to the problem how to express such relation by means of a system of equations (or onefold relations). Applying to the case of solid geometry my conclusion in the general theory, it may be mentioned that I regard the twofold relation of a curve in space as being completely and precisely expressed by means of a system of equations (P = 0, Q = 0, . . T = 0), when no one of the func ions P, Q, ... T, as a linear function, with constant or variable integral coefficients, of the others of them, and when every surface whatever which passes through the curve has its equation expressible in the form U = AP + BQ ... + KT., with constant or variable integral coefficients, A, B ... K. It is hardly necessary to remark that all the functions and coefficients are taken to be rational functions of the coordinates, and that the word integral has reference to the coordinates.

scholarly journals EL DERECHO A PROBAR EN EL PROCEDIMIENTO DE INVESTIGACIÓN Y SANCIÓN DEL HOSTIGAMIENTO SEXUAL: ¿UNA GARANTÍA RECORTADA?

2020 ◽  
pp. 91-102
Author(s):  
LUIS MARTÍN BRAVO SENMACHE
Keyword(s):  
Sexual Harassment ◽  
General Theory ◽  
Due Process ◽  
The Other ◽  
Legislative Reform ◽  
Due Process Of Law ◽  
The Right

Con base en la teoría general del proceso, la investigación determina que en el Procedimiento de Investigación y Sanción del Hostigamiento Sexual (PISHS)es identificable la estructura del contradictorio, por lo que su naturaleza es la de un proceso. Sin embargo, la revisión del tratamiento normativo que el PISHS ha dedicado al derecho a la prueba de la parte acusada pone en evidencia que, en la estructura de dicho proceso, el contradictorio no ha sido implementado más que parcialmente, dado que su dimensión sustancial (específicamente, el poder de influencia) no ha sido cabalmente asegurada a favor del presunto/a hostigador/a. Dos escenarios se erigen como posible solución al problema: uno a través de la vía de hecho (preferencia del principio del debido proceso) y otro mediante la reforma legislativa del art. 17.2 del reglamento. Based on the general theory of the process, the investigation determines that in the Investigation and Sanction Procedure for Sexual Harassment (PISHS) the structure of the contradictory is identifiable, so its nature is that of a process. However, the review of the normative treatment that the PISHS has dedicated to the right to proof of the accused party shows that, in the structure of said process, the contradictory has only been partially implemented, given that its substantial dimension (specifically, the power of influence) has not been fully secured in favor of the alleged harasser. Two scenariosare erected as a possible solution to the problem: one through the facto route (preference for the principle of due process of law) and the other through the legislative reform of the art. 17.2 of the reglament.

scholarly journals Sign in Elementary Analytical Geometry

1921 ◽  
Vol 10 (155) ◽  
pp. 363-368
Author(s):  
F. G. Brown
Keyword(s):  
Good Deal ◽  
Analytical Geometry ◽  
Absolute Value ◽  
Know How ◽  
The Third ◽  
Perpendicular Distance ◽  
The Absolute ◽  
Coordinate Geometry

The question of sign constitutes a real difficulty to the intelligent boy at the outset of his study of Coordinate Geometry. At the beginning of his Trigonometry he is told OP must be considered always positive, but later on he will find some authorities giving a point in the third quadrant as ( - r, θ), while others prefer (r, θ + π). The perpendicular distance of (h, k) from ax + by + c = 0 is given by ± (ah + bk +c)/(a2 + b2)½, and sign seems to matter, but usually the pupil is told that he only wants to know how far off (h, k) is, and he is advised to stick to the absolute value. But a little later on he wants the equations of the bisectors of the angles between two given lines, and then he is blamed for not remembering that signs matter a good deal.

On the Right Hamiltonian for Singular Perturbations: General Theory

1997 ◽  
Vol 09 (05) ◽  
pp. 609-633 ◽  
Author(s):  
Hagen Neidhardt ◽  
Valentin Zagrebnov
Keyword(s):  
General Theory ◽  
Symmetric Operator ◽  
Stability Domain ◽  
Bounded Operators ◽  
Friedrichs Extension ◽  
Abstract Problem ◽  
Dense Domain ◽  
Adjoint Extension ◽  
The Right ◽  
Adjoint Operators

Let the pair of self-adjoint operators {A≥0,W≤0} be such that: (a) there is a dense domain [Formula: see text] such that [Formula: see text] is semibounded from below (stability domain), (b) the symmetric operator [Formula: see text] is not essentially self-adjoint (singularity of the perturbation), (c) the Friedrichs extension [Formula: see text] of [Formula: see text] is maximal with respect to W, i.e., [Formula: see text]. [Formula: see text]. Let [Formula: see text] be a regularizing sequence of bounded operators which tends in the strong resolvent sense to W. The abstract problem of the right Hamiltonian is: (i) to give conditions such that the limit H of self-adjoint regularized Hamiltonians [Formula: see text] exists and is unique for any self-adjoint extension [Formula: see text] of [Formula: see text], (ii) to describe the limit H. We show that under the conditions (a)–(c) there is a regularizing sequence [Formula: see text] such that [Formula: see text] tends in the strong resolvent sense to unique (right Hamiltonian) [Formula: see text], otherwise the limit is not unique.

scholarly journals Congruences induced by transitive representations of inverse semigroups

1987 ◽  
Vol 29 (1) ◽  
pp. 21-40 ◽  
Author(s):  
Mario Petrich ◽  
Stuart Rankin
Keyword(s):  
General Theory ◽  
Inverse Semigroup ◽  
Symmetric Group ◽  
Transitive Group ◽  
Inverse Semigroups ◽  
Group Representations ◽  
Symmetric Inverse Semigroup ◽  
The Right ◽  
Special Case

Transitive group representations have their analogue for inverse semigroups as discovered by Schein [7]. The right cosets in the group case find their counterpart in the right ω-cosets and the symmetric inverse semigroup plays the role of the symmetric group. The general theory developed by Schein admits a special case discovered independently by Ponizovskiǐ [4] and Reilly [5]. For a discussion of this topic, see [1, §7.3] and [2, Chapter IV].

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