scholarly journals XV. On systems of circles and spheres

1886 ◽  
Vol 177 ◽  
pp. 481-625 ◽  
Keyword(s):  
General Relation ◽  
General Theorem ◽  
London Mathematical Society ◽  
Quarterly Journal ◽  
The Other ◽  
Radius Of Curvature ◽  
Coordinate Systems ◽  
Definition Of ◽  
First Time

This Memoir is divided into three Parts: Part I. treats of systems of circles in one plane; Part II. treats of systems of circles on the surface of a sphere; and Part III. of systems of spheres; the method of treatment being that indicated in two papers among Clifford’s ‘Mathematical Papers,ʼ viz., “On Power-Coordinates” (pp. 546—555) and “On the Powers of Spheres” (pp. 332-336). These two papers probably contain the notes of a paper which was read by Clifford to the London Mathematical Society, Feb. 27, 1868, “On Circles and Spheres,” which was not published (‘Lond. Math. Soc. Proc.,ʼ vol. 2, p. 61). The method of treatment indicated in these papers of Clifford’s was successfully applied by the author to prove some theorems given by him in a paper “On the Properties of a Triangle formed by Coplanar Circles” (1885) (‘Quarterly Journal of Mathematics,ʼ vol. 21), and then to the extension of those theorems to the case of spheres. But as Clifford’s papers contained some suggestions as to the application of the same method to the treatment of Bi-circular Quartics, he was induced to develop these ideas and extend the results to the case of the analogous curves on spheres—called by Professor Cayley Spheri-quadrics—and also of cyclides. It is impossible to say whether, if at all, Clifford was indebted to Darboux for any of the ideas contained in the two papers cited above; but it is noticeable that they coincide in a great measure with those expressed by Darboux in several papers published during the years 1869‒1872. In Part I. (§§ 1—124) of this Memoir a general relation is first shown to subsist between the powers of any two groups of five circles; the definition of the power of two circles, as the extension of Steiner’s “power of a point and a circle,” being due to Darboux, but the definition is here slightly modified so as to include the case when the radius of either (or each) circle is infinite. In Chapter II. an extension of the definition so as to apply to a certain system of conics is given; this is practically adapted from Chapter II. in Professor Casey’s Memoir “On Bicircular Quartics” (1867) (‘Irish Acad. Trans.,’ vol. 24). In Chapter III. the general theorem is applied to several interesting cases of circles; some of the results of this chapter are believed to be new. In Chapter IV. the problem of drawing a circle to cut three given circles at given angles is considered, and the circles connected with a triangle formed by three circles, which are analogous to the circumcircle, the inscribed and escribed, and the nine-points circle of an ordinary triangle are discussed. The results are the same, with one or two exceptions which may be new, as arrived at, but in a different manner, in the paper by the author in the ‘Quarterly Journal’ (vol. 21). In Chapter V. the power-coordinates of a point (or circle) are defined, and the equations of circles, &c., discussed; and it is shown that there are two simple coordinate systems of reference; one consisting of four orthogonal circles, mentioned by Clifford (Casey and Darboux consider five orthogonal spheres), the other consisting of two orthogonal circles and their two points of intersection, which seems to have been indicated for the first time by Mr. Homersham Cox in a paper “On Systems of Circles and Bicircular Quartics” (‘Quarterly Journal,’ vol. 19, 1883). In Chapter VI. the general equation of the second degree in power-coordinates is discussed, and in Chapter VII. Bi-circular Quartics are classified according to the number of principal circles which they possess. In Chapter VIII. the connexion between Bi-circular Quartics and their focal conics is briefly indicated, the circle of curvature is found, and an expression for the radius of curvature at any point of a bi-circular quartic is investigated. In these last three chapters the results are probably all old, but as the method employed is different from any previously used to discuss these curves in detail, it may not be without interest.

Vladimir Titov’s Letter to Vladimir Odoevsky as a Well-Known Response to Ivan Turgenev’s Article “Hamlet and Don Quixote” (Contemporaries’ Reception of Turgenev’s Interpretation of the Image of Hamlet)

2021 ◽  
pp. 104-116
Author(s):  
Ivan O. Volkov ◽  
Keyword(s):  
German Idealism ◽  
Don Quixote ◽  
The Other ◽  
National Library ◽  
Other Hand ◽  
The One ◽  
Definition Of ◽  
First Time

For the first time, in the article, Vladimir Titov’s letter (dated 12/24 February 1869) is published and commented. In the 1820s, in Russia, Titov was well-known as a writer and literature theorist, the author of a romantic novella The Remote House on Vasilyevsky Island (1829) close to Society of Lyubomudriye. The letter extracted from the archives of the National Library of Russia is addressed to Duke Vladimir Odoevsky whose relationship with Titov was friendly from the very beginning of their acquaintance. The letter focuses on Ivan Turgenev’s speech published in the first issue of Sovremennik and titled “Hamlet and Don Quixote”. Reacting to Turgenev’s article, Titov shortly and critically accesses the comparison concentrating mainly on the image of Hamlet and thoroughly expresses his opinion on the essence of his tragic state. Titov’s opinion is just the opposite of Turgenev’s complex and multidimensional interpretation. Having experienced the great impact of the philosophy of German idealism at the beginning of his career, Titov to a great extent idealizes Shakespeare’s character whom he long knows and whom he is clearly eager to vindicate. Meanwhile, Titov does not pursue the aim to absolutely advocate the romantic halo of Hamlet as a Titanic personality (grandiose intellect and scale of feeling) and to enact the tragic pathos of the inner fight only. Developing Goethe’s definition of the essence of the character’s inner conflict, Titov, on the one hand, approaches its real understanding underlying the prince’s necessity to stay in a derogatory position of a “pitiful semiclown, indecisive grouch and shred”. On the other hand, the assessment can not be absolutely objective because Titov wants to see Hamlet as a victim of the fatal fortune which turns him into a character of an almost classical tragedy of fate. Titov’s bright and developed reaction (in the document of private nature) to Turgenev’s article is attractive and important first of all for its vividly demonstrated novelty and creativity of the writer’s view, wideness and multimodality of the author’s perception of Hamlet’s image. For the first time, Turgenev gave a developed interpretation of Shakespeare’s image in the tale “Hamlet of Shchigrovsky Province” (1848). Continuing his searches in the area of “Russian” (or “steppe”) Hamlet, Turgenev creates moral and philosophical problems of the English tragedy in the crisis socio-historical and cultural atmosphere of Russia of the 1840s. However, the principles of the artistic generalization and the peculiarities of the new reading, not mentioned and not fully comprehended by his contemporaries, were surprising and rejected when the speech “Hamlet and Don Quixote” appeared, in which Shakespeare’s character is presented ultimately vividly and lively in the then current interpretation.

Supra-constitutional norms in constitutional law

2021 ◽  
Vol 30 (1) ◽  
pp. 100-127
Author(s):  
Dmitry Shustrov
Keyword(s):  
International Law ◽  
20Th Century ◽  
Natural Law ◽  
Constitutional Law ◽  
The Other ◽  
Constitutional Court ◽  
Definition Of ◽  
First Time ◽  
Positive Character ◽  
Constitutional Changes

The idea of supra-constitutionality was formulated in the science of constitutional law in the second quarter of the 20th century and associated with the names of M.Hauriou and K.Schmitt, who for the first time noticed the possibility of the existence of norms that are higher than the constitution. This article is an attempt to give the doctrine of supra-constitutionality an actual theoretical and dogmatic meaning in the context of the study of the material limits of constitutional changes. The doctrine of supra-constitutionality claims to play an important role in explaining that unchangeable norms can exist in constitutional law and that they cannot be excluded, changed, limited, overcome, affected by the other sources of constitutional law, including the constitution itself. Supra-constitutionality is viewed as a characteristic of unchangeable constitutional norms that constitute the material limits of constitutional changes. Supra-constitutionality presupposes the existence of norms that surpass the rest of the constitutional norms and predetermine their content through the definition of what can, should and should not be included in the constitution or excluded from it. The basis of constitutional supra-constitutionality is the argument of hierarchical differentiation. In addition to recognizing unchangeable constitutional norms as supra-constitutional, the article raises the question of the existence of natural law and international law supra-constitutional norms. Natural law supra-constitutional norms have an external and non-positive character. They are not enshrined in the constitution, but stem from a reasonably understood concept of what is due in the most civilized societies, which is determined by the constitutional court. International law supra-constitutionality is understood as the superiority of the norms of international law over the constitution. It has an external and positive character. International law supra-constitutionality can cause political objections from opponents of the absolute rule of international law. Supra-constitutional constitutional, natural and international law norms can come into conflict with each other. The paradox of the doctrine of supra-constitutionality lies in the fact that it creates a hierarchy of norms within the constitution itself, distinguishing between simple and supra-constitutional constitutional norms, or distinguishes certain non-positive norms that are outside the constitution, as having priority over the constitution, or puts some norms of international law over all norms of national law, including the constitution. The purpose of the doctrine of supra-constitutionality is to preserve the inviolable fundamental (natural or generally recognized) values, which justifies its logical flaws and paradoxicality.

Phylogeny and re-definition of the genus Melanophora (Diptera: Rhinophoridae), with description of a new species from Sardinia

Zootaxa ◽  
2009 ◽  
Vol 2318 (1) ◽  
pp. 552-565 ◽  
Author(s):  
PIERFILIPPO CERRETTI ◽  
THOMAS PAPE
Keyword(s):  
New Species ◽  
Type Species ◽  
Cladistic Analysis ◽  
The Other ◽  
New Combinations ◽  
Generic Delimitation ◽  
Definition Of ◽  
First Time ◽  
A New Species

A cladistic analysis of the genus Melanophora Meigen, 1803 (type-species: Musca grossificationis Linnaeus, 1758 [= Musca roralis Linnaeus, 1758]) is presented and the generic delimitation is critically redefined. The nominal genus-group taxon Bequaertiana Curran, 1929 (type-species: Bequaertiana argyriventris Curran, 1929) is synonymised with Melanophora Meigen syn. nov. The following new combinations are proposed: Melanophora argyriventris (Curran, 1929) comb. nov. and Melanophora basilewskyi (Peris, 1957) comb. nov. Melanophora chia sp. nov. from SW Sardinia is described, illustrated and compared with the other known species of the genus. The male of Melanophora asetosa Kugler, 1978 is described for the first time. Melanophora basilewskyi (Peris, 1957) is recorded from Kenya for the first time.

‘Disability’ and ‘Discrimination’ in the Context of Disability Discrimination Legislation: The UK and Australian Acts Compared

2000 ◽  
Vol 4 (3) ◽  
pp. 203-245 ◽  
Author(s):  
Jennifer Hamilton
Keyword(s):  
Functional Limitations ◽  
Public Life ◽  
The Other ◽  
Disability Discrimination ◽  
Other Hand ◽  
Positive Feature ◽  
The Government ◽  
Definition Of ◽  
The Uk ◽  
First Time

Both the Commonwealth of Australia and the UK now have in place anti-disability discrimination legislation. In the example of the Commonwealth, that legislation reflected a positive desire by the community and the government to eliminate disability discrimination in public life. In the UK on the other hand, the legislation introduced represented something of a compromise between activists, who wanted stronger legislation, and the government who up until that point had wanted none. Historically anti-discrimination legislation in both jurisdictions has been similarly structured; containing similar grounds of discrimination and also a similar conceptualisation of discrimination. However, partly no doubt as a result of government antipathy, the UK model of legislation departs from the model used in earlier antidiscrimination legislation in a number of key respects: the legislation contains a new conceptualisation of discrimination; and, it introduces for the first time in antidiscrimination legislation a general ‘defence’ of justification for all forms of discrimination. Additionally, the definition of ‘disability’ employed in the Act is very narrow, concentrating upon a person's functional limitations in relation to ‘normal’ activities. The purpose of this article is to contrast the concepts of ‘disability’ employed in the Acts, and to consider the effectiveness of both the ‘traditional’ and the new conceptualization of discrimination contained in the Commonwealth and UK Acts respectively. While disability under the UK Act is reflective of the government's antipathy to the new legislation, the reconceptualization of discrimination is, on the whole, a positive feature, moving away from the principle that equality equals ‘sameness’, to one which gives recognition to disadvantage and places an explicit, positive, obligation on employers to redress that disadvantage. Other areas of difference between the two Acts — such as in the area of ‘defenses’, the development of enforceable Standards (under the Commonwealth Act), and methods of enforcement will be covered in a subsequent article.

scholarly journals The Concept of subject in the philosophy of E. Husserl

2021 ◽  
pp. 35-44
Author(s):  
Sergei Sergeevich Rusakov
Keyword(s):  
Edmund Husserl ◽  
Early Period ◽  
The Other ◽  
Other Hand ◽  
German Philosopher ◽  
The Subject ◽  
The One ◽  
Definition Of ◽  
First Time

This article analyzes the elements of the concept of  subject traced in the philosophy of Edmund Husserl throughout all his works. The author follows the transformation of the views of German philosopher on the idea of subject. As well as their implementation in the context of phenomenological thought. Special attention is given to correlation between the works of Husserl of the early period and the later period.  It is noted that unlike the Cartesian or Kantian model of subjectivity, the egological subject for the first time conceptualizes intersubjectivity as the foundation for the development of the fundamentally new concept of understanding a human as a subject endowed with self-consciousness. The main conclusions consist in the following theses: despite the fact that the key role in the egological concept of subject belongs to the definition of evidence, intentionality, and reduction, the problem of cognition, considered in this article, is developed by Husserl as further complication of the Kantian approach; the egological concept of subject implements the concept of intersubjectivity, which demarcates the ideas of E. Husserl among other approaches towards the concept of subject. understanding the subject. On the one hand, intersubjectivity weakens the position of the idea of absolute autonomy of the subject’ while on the other hand, it is the new mechanism for legitimizing the subjective process of cognition and the truth itself, due to recognition of ego behind the figure of the Other.

2.2. Working Group 2: Conceptual Definitions of Reference Coordinate Systems for Earth Dynamics

1975 ◽  
Vol 26 ◽  
pp. 21-26
Keyword(s):  
Coordinate System ◽  
Working Group ◽  
General Character ◽  
Coordinate Systems ◽  
Reference Coordinate System ◽  
Group 2 ◽  
Definition Of ◽  
Earth Dynamics

An ideal definition of a reference coordinate system should meet the following general requirements:1. It should be as conceptually simple as possible, so its philosophy is well understood by the users.2. It should imply as few physical assumptions as possible. Wherever they are necessary, such assumptions should be of a very general character and, in particular, they should not be dependent upon astronomical and geophysical detailed theories.3. It should suggest a materialization that is dynamically stable and is accessible to observations with the required accuracy.

Note on Selection of Coordinate Systems for Geodynamics

1975 ◽  
Vol 26 ◽  
pp. 395-407
Author(s):  
S. Henriksen
Keyword(s):  
Sea Level ◽  
The Other ◽  
Coordinate Systems ◽  
Mean Sea Level ◽  
The Earth ◽  
The One ◽  
Static Systems ◽  
Selection Of

The first question to be answered, in seeking coordinate systems for geodynamics, is: what is geodynamics? The answer is, of course, that geodynamics is that part of geophysics which is concerned with movements of the Earth, as opposed to geostatics which is the physics of the stationary Earth. But as far as we know, there is no stationary Earth – epur sic monere. So geodynamics is actually coextensive with geophysics, and coordinate systems suitable for the one should be suitable for the other. At the present time, there are not many coordinate systems, if any, that can be identified with a static Earth. Certainly the only coordinate of aeronomic (atmospheric) interest is the height, and this is usually either as geodynamic height or as pressure. In oceanology, the most important coordinate is depth, and this, like heights in the atmosphere, is expressed as metric depth from mean sea level, as geodynamic depth, or as pressure. Only for the earth do we find “static” systems in use, ana even here there is real question as to whether the systems are dynamic or static. So it would seem that our answer to the question, of what kind, of coordinate systems are we seeking, must be that we are looking for the same systems as are used in geophysics, and these systems are dynamic in nature already – that is, their definition involvestime.

Immunoferritin localization of intracellular antigens in positively stained frozen sections

1978 ◽  
Vol 36 (2) ◽  
pp. 168-169
Author(s):  
K. T. Tokuyasu
Keyword(s):  
Surface Tension ◽  
Water Surface ◽  
Thin Layers ◽  
The Other ◽  
Positive Staining ◽  
Frozen Sections ◽  
The Past ◽  
Ultrathin Frozen Sections ◽  
Definition Of

During the past investigations of immunoferritin localization of intracellular antigens in ultrathin frozen sections, we found that the degree of negative staining required to delineate u1trastructural details was often too dense for the recognition of ferritin particles. The quality of positive staining of ultrathin frozen sections, on the other hand, has generally been far inferior to that attainable in conventional plastic embedded sections, particularly in the definition of membranes. As we discussed before, a main cause of this difficulty seemed to be the vulnerability of frozen sections to the damaging effects of air-water surface tension at the time of drying of the sections.Indeed, we found that the quality of positive staining is greatly improved when positively stained frozen sections are protected against the effects of surface tension by embedding them in thin layers of mechanically stable materials at the time of drying (unpublished).

Darwin's two competing phylogenetic trees: marsupials as ancestors or sister taxa?

2012 ◽  
Vol 39 (2) ◽  
pp. 217-233 ◽  
Author(s):  
J. David Archibald
Keyword(s):  
Fossil Record ◽  
Evolutionary Biology ◽  
Phylogenetic Trees ◽  
Charles Darwin ◽  
The Other ◽  
Charles Lyell ◽  
Single Origin ◽  
Molecular Studies ◽  
Richard Owen ◽  
First Time

Studies of the origin and diversification of major groups of plants and animals are contentious topics in current evolutionary biology. This includes the study of the timing and relationships of the two major clades of extant mammals – marsupials and placentals. Molecular studies concerned with marsupial and placental origin and diversification can be at odds with the fossil record. Such studies are, however, not a recent phenomenon. Over 150 years ago Charles Darwin weighed two alternative views on the origin of marsupials and placentals. Less than a year after the publication of On the origin of species, Darwin outlined these in a letter to Charles Lyell dated 23 September 1860. The letter concluded with two competing phylogenetic diagrams. One showed marsupials as ancestral to both living marsupials and placentals, whereas the other showed a non-marsupial, non-placental as being ancestral to both living marsupials and placentals. These two diagrams are published here for the first time. These are the only such competing phylogenetic diagrams that Darwin is known to have produced. In addition to examining the question of mammalian origins in this letter and in other manuscript notes discussed here, Darwin confronted the broader issue as to whether major groups of animals had a single origin (monophyly) or were the result of “continuous creation” as advocated for some groups by Richard Owen. Charles Lyell had held similar views to those of Owen, but it is clear from correspondence with Darwin that he was beginning to accept the idea of monophyly of major groups.

Sphagnum mosses (Sphagnaceae, Bryophyta) of mires Chefandzar and Masota in North Ossetia (Caucasus)

2018 ◽  
Vol 52 (2) ◽  
pp. 455-462 ◽  
Author(s):  
G. Ya. Doroshina ◽  
I. A. Nikolajev
Keyword(s):  
Plant Communities ◽  
The Other ◽  
North Caucasus ◽  
Sphagnum Mosses ◽  
Greater Caucasus ◽  
The North ◽  
First Time ◽  
North Ossetia

Sphagnum mires on the Greater Caucasus are rare, characterized by the presence of relict plant communities of glacial age and are in a stage of degradation. The study of Sphagnum of Chefandzar and Masota mires is carried out for the first time. Seven species of Sphagnum are recorded. Their distribution and frequency within the North Caucasus are analyzed. Sphagnum contortum, S. platyphyllum, S. russowii, S. squarrosum are recorded for the first time for the study area and for the flora of North Ossetia. The other mosses found in the study area are listed.

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