Reconstruction of Quadratic Cremona Transformation

2017 ◽  
Vol 5 (2) ◽  
pp. 59-68
Author(s):  
Короткий ◽  
Viktor Korotkiy
Keyword(s):  
Geometric Modeling ◽  
The Other ◽  
Practical Implementation ◽  
Cremona Transformation ◽  
Quadratic Transformation ◽  
Modern Computer ◽  
Set Up ◽  
The One ◽  
Straight Lines ◽  
Base Data

The geometric correspondence between the points of two planes can be considered well defined only when base data for its establishing is available, and a construction method by which its possible on the basis of these data for each point in one plane to find the corresponding points in the other one. Quadratic Cremona transformation can be specified by pointing out in the combined plane seven pairs of corresponding points. Naturally there is a need to establish a method for constructing any number of corresponding points. An outstanding Russian geometer K.A. Andreev indicated the linear construction based on the consideration of two correlations by which for each eighth point in the one plane is found the corresponding point of the other one. But in his work was not set up a problem to construct excluded (fundamental) points of quadratic Cremona transformation specified by seven pairs of points. There are many constructive ways to obtain the quadratic transformation in the plane. For example, it can be obtained by using two pairs of projective pencils of straight lines with vertices at the fundamental points (F-points). K.A. Andreev noted that this method for establishing of quadratic correspondence spread only to those cases when all F-points are the real ones. This statement is true for the 19th century’s level of geometric science, but today it’s too categorical. The theory of imaginary elements in geometry allows to develop a universal algorithm for construction of corresponding points in a quadratic transformation, given both by real and imaginary F-points. Summarizing the K.A. Andreev task, we come to the problem of finding the fundamental points (F-points) for a quadratic transformation specified by seven pairs of corresponding points. Almost one and half century the K.A. Andreev generalized task remained unsolved. The formation of this task’s constructive solution algorithm and its practical implementation has become possible by means of modern computer geometric modeling. According to proposed algorithm, the construction of F-points is reduced to the construction of second order auxiliary curves, on which intersection are marked the required F-points. The result received in this paper is used for development of the Cremona transformations’ theory, and for further application of this theory in the practice of geometric modeling.

scholarly journals Haurtzaroko sexu abusuak: prebentzio programa baten eraginkortasuna frogatzen

2019 ◽  
pp. 94-114
Author(s):  
Ane Díez ◽  
Zuriñe Gaintza
Keyword(s):  
Sexual Abuse ◽  
The Other ◽  
Educational Project ◽  
Other Hand ◽  
Post Test ◽  
Set Up ◽  
The One ◽  
Protective Behaviours

This study assesses how knowledge about protective behaviours against sexual abuse changes among 6 to 7 year-olds 22 girls and boys, after implementing the programme “Grita muy fuerte" (Shout out loud). The program is developed over 5 weeks in sessions of 60 minutes per week. In order to determine the effect of it, an evaluation is carried out with pre-test and post-test measures included in the program itself. According to the results, on the one hand, all students improve their knowledge of protective behaviours against sexual abuse and, on the other hand, in terms of gender, girls have greater knowledge than boys. It is concluded that the programme is effective in increasing awareness of protective behaviours against sexual abuse and that it is therefore advisable to set up this type of experience as part of the schools' educational project.

Group Insolvencies

2016 ◽  
Author(s):  
Reinhard Bork ◽  
Renato Mangano
Keyword(s):  
The Other ◽  
Limited Extent ◽  
Specific Policy ◽  
Policy Choices ◽  
Cross Border ◽  
Other Hand ◽  
The World ◽  
Set Up ◽  
The Many ◽  
The One

This chapter deals with European cross-border issues concerning groups of companies. This chapter, after outlining the difficulties encountered throughout the world in defining and regulating the group, focuses on the specific policy choices endorsed by the EIR, which clearly does not lay down any form of substantive consolidation. Instead, the EIR, on the one hand, seems to permit the ‘one group—one COMI’ rule, even to a limited extent, and, on the other hand, provides for two different regulatory devices of procedural consolidation, one based on the duties of ‘cooperation and communication’ and the other on a system of ‘coordination’ to be set up between the many proceedings affecting companies belonging to the same group.

scholarly journals Equations with powers of singular moduli

2019 ◽  
Vol 15 (03) ◽  
pp. 445-468 ◽  
Author(s):  
Antonin Riffaut
Keyword(s):  
Rational Number ◽  
The Other ◽  
Other Hand ◽  
Singular Moduli ◽  
Cm Points ◽  
The One ◽  
Straight Lines ◽  
Positive Integers

We treat two different equations involving powers of singular moduli. On the one hand, we show that, with two possible (explicitly specified) exceptions, two distinct singular moduli [Formula: see text] such that the numbers [Formula: see text], [Formula: see text] and [Formula: see text] are linearly dependent over [Formula: see text] for some positive integers [Formula: see text], must be of degree at most [Formula: see text]. This partially generalizes a result of Allombert, Bilu and Pizarro-Madariaga, who studied CM-points belonging to straight lines in [Formula: see text] defined over [Formula: see text]. On the other hand, we show that, with obvious exceptions, the product of any two powers of singular moduli cannot be a non-zero rational number. This generalizes a result of Bilu, Luca and Pizarro-Madariaga, who studied CM-points belonging to a hyperbola [Formula: see text], where [Formula: see text].

Towards a General Theory of Reduction. Part III: Cross-Categorical Reduction

Dialogue ◽  
1981 ◽  
Vol 20 (3) ◽  
pp. 496-529 ◽  
Author(s):  
C.A. Hooker
Keyword(s):  
Nervous System ◽  
Prima Facie ◽  
The Other ◽  
Mental Function ◽  
Physical Processes ◽  
Monetary System ◽  
State Association ◽  
Set Up ◽  
The One ◽  
Different Parts

Any theory of reduction that goes only so far as carried in Parts I and II ([165], [166]) does only half the job. Prima facie at least, there are cases of would-be reduction which seem torn between two conflicting intuitions. On the one side there is a strong intuition that reduction is involved, and a strongly retentive reduction at that. On the other side it seems that the concepts at one level cross-classify those at the other level, so that there is no way to identify properties at one level with those at the other. There is evidence to suggest that there will be no unique mental state/neural state association that can be set up, because, e.g., many different parts of the nervous system are all capable of taking over ‘control’ of the one mental function. And it is alleged that infinitely many, worse: indefinitely many, different bio-chemo-physical states could correspond to the economic property ‘has a monetary system of economic exchange’; and similarly for the property ‘has just won a game of tennis’. Yet one doesn't want an economic system or a game of tennis to be some ghostly addition to the actual bio-chemo-physical processes and events involved (cf. Rudner [188]). Similarly one hopes that neurophysiology allied with the rest of natural science will render human experience and behaviour explicable.

Arithmetic in The Junior High School

1925 ◽  
Vol 18 (2) ◽  
pp. 111-118
Author(s):  
Lewis W. Colwell
Keyword(s):  
High School ◽  
Junior High School ◽  
Junior High ◽  
The Other ◽  
Social Nature ◽  
Other Hand ◽  
Good For ◽  
Set Up ◽  
The One

The curriculum of the junior high school must be determined on the one hand by the needs of a developing civilization and on the other by the nature and capacities of developing youth. These two criteria of worth are by no means opposed to each other. They constitute no bifurcated demand. They set up no dilemmas. For every child is born into organized society on the one hand and becomes a duly constituted member thereof, while on the other hand he possesses a social nature that fits him into the world's work just in the measure that he finds himself. It is perhaps not far afield to say that all friction due to anti-socialistic tendencies is a maladjustment of individuals who have not discovered what they are good for.

scholarly journals XIX. —Consideration of the objections raised against the geometrical representation of the square roots of negative quantities

1829 ◽  
Vol 119 ◽  
pp. 241-254 ◽  
Keyword(s):  
The Other ◽  
Square Root ◽  
Square Roots ◽  
The Third ◽  
Oblique Direction ◽  
Real Nature ◽  
Positive Quantity ◽  
Algebraic Operations ◽  
The One ◽  
Straight Lines

Some years ago my attention was drawn to those algebraic quantities, which are commonly called impossible roots or imaginary quantities: it appeared extraordinary, that mathematicians should be able by means of these quan­tities to pursue their investigations, both in pure and mixed mathematics, and to arrive at results which agree with the results obtained by other independent processes; and yet that the real nature of these quantities should be entirely unknown, and even their real existence denied. One thing was evident re­specting them; that they were quantities capable of undergoing algebraic operations analogous to the operations performed on what are called possible quantities, and of producing correct results: thus it was manifest, that the operations of algebra were more comprehensive than the definitions and funda­mental principles; that is, that they extended to a class of quantities, viz. those commonly called impossible roots, to which the definitions and funda­mental principles were inapplicable. It seemed probable, therefore, that there was a deficiency in the definitions and fundamental principles of algebra ; and that other definitions and fundamental principles might be discovered of a more comprehensive nature, which would extend to every class of quantities to which the operations of algebra were applicable; that is, both to possible and impossible quantities, as they are called. I was induced therefore to examine into the nature of algebraic operations, with a view, if possible, of arriving at these general definitions and fundamental principles: and I found, that, by considering algebra merely as applied to geometry, such principles and definitions might be obtained. The fundamental principles and definitions which I arrived at were these: that all straight lines drawn in a given plane from a given point, in any direction whatever, are capable of being algebra­ically represented, both in length and direction; that the addition of such lines (when estimated both in length and direction) must be performed in the same manner as composition of motion in dynamics; and that four such lines are proportionals, -both in length and direction, when they are proportionals in length, and the fourth is inclined to the third at the same angle that the second is to the first. From these principles I deduced, that, if a line drawn in any given direction be assumed as a positive quantity, and consequently its oppo­site, a negative quantity, a line drawn at right angles to the positive or nega­tive direction will be the square root of a negative quantity, and a line drawn in an oblique direction will be the sum of two quantities, the one either posi­tive or negative, and the other, the square root of a negative quantity.

The Formation of the ‘Crusade Idea’

1970 ◽  
Vol 21 (1) ◽  
pp. 11-31 ◽  
Author(s):  
E. O. Blake
Keyword(s):  
The Other ◽  
Christian Tradition ◽  
Relative Importance ◽  
First Crusade ◽  
Holy Places ◽  
Unique Experience ◽  
The Subject ◽  
Set Up ◽  
The One ◽  
A Minor

In order to understand the crusading movement it has always been necessary to define what was understood by the ‘crusade’ as a religious exercise within the Christian tradition. This attempt to identify the ‘crusade idea’ goes back to the earliest commentators on the First Crusade, but has gained increasing vitality during the last thirty years. It is not a matter of weighing the relative importance of, on the one hand, the religious and, on the other, the secular or political motives, but of describing the content of the nova religio as such. In this sense Erdmann, who first set up the subject as capable of disciplined study, traced the antecedents in socio-religious forms of behaviour without which the Kreuzzugsidee could not have been conceived, regarding it as in its essentials formulated at the launching of the First Crusade, with Jerusalem as only a minor and ancillary target. Alphandéry, to single out another notable contributor to this type of study, diagnosed the dramatic emergence of a distinctive idée de croisade during the very course of the First Crusade, concentrated on the deliverance of the Holy Places, a unique experience never to be wholly repeated. Another notion of the ‘crusade’ was developed by Rousset—an institution de salut with its characteristic ideology, entertained generally during the first half of the twelfth century.5 There are studies also of the ideas associated with crusading in the crusade appeals, preaching, justification and criticism of the twelfth and thirteenth centuries, in the forms of procedure, and in Latin and vernacular poetry.

Africa — Latin America — Asia and Pacific — Middle East

1986 ◽  
Vol 26 (251) ◽  
pp. 115-124
Keyword(s):  
Latin America ◽  
Middle East ◽  
Large Scale ◽  
The Other ◽  
Displaced Persons ◽  
Assistance Programme ◽  
Medical Teams ◽  
Set Up ◽  
The One ◽  
Voluntary Agencies

In January and February, the ICRC reduced, as planned, the level of its relief activities in Ethiopia. This reduction was made possible, on the one hand, by an increase in food supplies for the population in the northern provinces of that country affected by conflict and drought and, on the other, by more intensive activity on the part of other voluntary agencies in the area. While leaving in place the structures which would enable it rapidly to set up a large-scale assistance programme if the need were to appear in a given region, the ICRC has lowered the volume of its general relief distributions. In December 1985, 10,700 tonnes were distributed to 830,000 persons. This was reduced to 5,000 tonnes for 424,300 persons in January, and further to 2,800 tonnes for 181,000 persons in February in the provinces of Eritrea, Tigray, Wollo, Gondar and Hararge. The last three therapeutic feeding centres were closed on 16 January (Wukro), and on 16 and 27 February (Idaga Hamus and Adwa). However, ICRC medical teams continued to monitor the health of the populations living in provinces which were receiving assistance, concentrating their activities on groups of displaced persons in Eritrea (in the region between Keren and Barentu), Tigray (in the region between Aksum and Adwa and the region of Mehony), Wollo (in the region of Sekota) and Hararge (Wobera Woreda; Habro Woreda), all areas with major security problems.

scholarly journals Automation of the inner design of the aircraft

2019 ◽  
Vol 11 (S) ◽  
pp. 135-141
Author(s):  
Mikhail Yu. KUPRIKOV ◽  
Leonid V. MARKIN
Keyword(s):  
Design Automation ◽  
Geometric Modeling ◽  
Virtual Prototyping ◽  
Practical Implementation ◽  
Cad Systems ◽  
Geometric Models ◽  
Modern Computer ◽  
Modeling Systems ◽  
Swept Surface ◽  
Blind Search

The task of forming the wind-swept surface according to the results of the aircraft’s inner design is described. The approach of the integration of natural and virtual prototyping in the design of equipment compartments is substantiated. Such approaches open up new possibilities for creating intelligent composition algorithms that eliminate the "blind search". For the practical implementation of these approaches, it is necessary to link the appropriate software to standard geometric modeling systems in the form of additional computational modules. Preparing the aircraft for design automation complicates the mathematical description of geometric models of placed objects, increases the complexity of their visualization in modern computer graphics systems and the need to create an additional interface between new geometric models and common CAD systems (SolidWorks, AutoCAD, COMPAS, etc.).

scholarly journals Tax treatment of dividends and alternative for shareholders. Tax treatment of dividends and alternative for shareholders

2020 ◽  
pp. 9-20
Author(s):  
José Luis Bárcenas-Puente ◽  
Miguel Ángel Andrade-Oseguera
Keyword(s):  
At Risk ◽  
Income Tax ◽  
Business Practice ◽  
The Other ◽  
General Law ◽  
Financial Consequences ◽  
The Law ◽  
Set Up ◽  
Compliance With The Law ◽  
The One

In simple terms, a shareholder is a person who puts their money at risk by providing it to a business, what we call investment, which, if it generates profits, these are distributed in proportional parts to each partner, called dividends. In this way, the payment of dividends to shareholders represents the fair remuneration to the risk assumed. Dividend income is regulated in the Law on Income Tax and its correlation with the General Law of Commercial Companies, through precise guidelines. However, average business practice does not follow these provisions. Indeed, shareholders have money during the year in amounts on considerable amounts, without following any legal formality; thus facing fiscal and financial consequences. On the one hand, then, there is a reasonable right to remuneration and, on the other hand, compliance with the law. That is why alternatives to the old problem, of the checks without verification, set up as fictitious dividends.

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