scholarly journals XI. A fourth memoir upon quantics

1859 ◽  
Vol 9 ◽  
pp. 165-165
Keyword(s):  
Canonical Form ◽  
The Other ◽  
The Subject ◽  
Further Development

The object of the present memoir is the further development of the theory of binary quantics; it should therefore have preceded so much of my third memoir, vol. cxlvii. (1857), p. 627, as relates to ternary quadrics and cubics. The paragraphs are numbered continuously with those of the former memoirs. The first three paragraphs, Nos. 62 to 64, relate to quantics of the general form (*≬ x, y ,..) m , and they are intended to complete the series of definitions and explanations given in Nos. 54 to 61 of my third memoir; Nos. 68 to 71, although introduced in reference to binary quantics, relate or may be considered as relating to quantics of the like general form. But with these exceptions the memoir relates to binary quantics of any order whatever: viz. Nos. 65 to 80 relate to the covariants and invailants of the degrees 2, 3, and 4; Nos. 81 and 82 (which are introduced somewhat parenthetically) contain the explanation of a process for the calculation of the invariant called the discriminant; Nos. 83 to 85 contain the definitions of the catalectieant, the lambdaic and the canonisant, which are functions occurring in Prof. Sylvester’s theory of the reduction of a binary quantic to its canonical form; and Nos. 86 to 91 contain the definitions of certain covariants or other derivatives connected with Bezout’s abbreviated method of elimination, due for the most part to Professor Sylvester, and which are called Bezoutiants, Cobezoutiants, &c. I have not in the present memoir in any wise considered the theories to which the catalecticant &c. and the other covariants and derivatives just referred to relate; the design is to point out and precisely define the different covariants or other derivatives which have hitherto presented themselves in theories relating to binary quantics, and so to complete, as far as may be, the explanation of the terminology of this part of the subject.

α-degrees of α-theories

1972 ◽  
Vol 37 (4) ◽  
pp. 677-682 ◽  
Author(s):  
George Metakides
Keyword(s):  
Initial Segment ◽  
Recursion Theory ◽  
The Other ◽  
Infinite Length ◽  
Infinitary Logic ◽  
Admissible Set ◽  
Recursively Enumerable ◽  
Limit Ordinal ◽  
The Subject ◽  
Further Development

Let α be a limit ordinal with the property that any “recursive” function whose domain is a proper initial segment of α has its range bounded by α. α is then called admissible (in a sense to be made precise later) and a recursion theory can be developed on it (α-recursion theory) by providing the generalized notions of α-recursively enumerable, α-recursive and α-finite. Takeuti [12] was the first to study recursive functions of ordinals, the subject owing its further development to Kripke [7], Platek [8], Kreisel [6], and Sacks [9].Infinitary logic on the other hand (i.e., the study of languages which allow expressions of infinite length) was quite extensively studied by Scott [11], Tarski, Kreisel, Karp [5] and others. Kreisel suggested in the late '50's that these languages (even which allows countable expressions but only finite quantification) were too large and that one should only allow expressions which are, in some generalized sense, finite. This made the application of generalized recursion theory to the logic of infinitary languages appear natural. In 1967 Barwise [1] was the first to present a complete formalization of the restriction of to an admissible fragment (A a countable admissible set) and to prove that completeness and compactness hold for it. [2] is an excellent reference for a detailed exposition of admissible languages.

Moving In-Frame

2022 ◽  
pp. 217-234
Author(s):  
Andi Johnson ◽  
Richard Lessey ◽  
Rebeca Ramos O'Reilly ◽  
Jessica Shi
Keyword(s):  
Active Learning ◽  
Reflective Practice ◽  
Subject Area ◽  
Lessons Learned ◽  
The Other ◽  
Learning Engagement ◽  
Digital Education ◽  
The Subject ◽  
Further Development

The researchers explored the dual experience of individuals who are both taking dance and movement classes digitally at the same time as they are also teaching dance and movement classes digitally. By focusing on this duality through a series of interviews with practitioners, the researchers explore how the learner/educators do or do not adapt one set of skills into the other area of work and the lessons learned from this reflective practice. The results are analyzed and broken down into five sections: glitches of the practice, reflective practice, active learning, engagement, and reframing communication. Through further analysis, the researchers explore possibilities for shifting the mindset around digital education methods. The researchers then offer suggestions for further development in the field and where further research can expand on the subject area.

scholarly journals XXII. A fourth memoir upon quantics

1858 ◽  
Vol 148 ◽  
pp. 415-427 ◽  
Keyword(s):  
Canonical Form ◽  
Linear Form ◽  
Covariant Operator ◽  
Complete Series ◽  
The Subject ◽  
The Given ◽  
Further Development

object of the present memoir is the further development of the theory of binary ntics; it should therefore have preceded so much of my third memoir, t. 147 (1857), 27, as relates to ternary quadrics and cubics. The paragraphs are numbered conously with those of the former memoirs. The first three paragraphs, Nos. 62 to 64, te to quantics of the general form (*)( x, y ,..) m , and they are intended to complete series of definitions and explanations given in Nos. 54 to 61 of my third memoir; 68 to 71, although introduced in reference to binary quantics, relate or may be dered as relating to quantics of the like general form. But with these exceptions memoir relates to binary quantics of any order whatever: viz. No. 65 to 80 relate he covariants and invariants of the degrees 2, 3 and 4; Nos. 81 and 82 (which are xluced somewhat parenthetically) contain the explanation of a process for the alation of the invariant called the Discriminant; Nos. 83 to 85 contain the definitions he Catalecticant, the Lambdaic and the Canonisant, which are functions occurring in ’essor Sylvester’s theory of the reduction of a binary quantic to its canonical form; Nos. 86 to 91 contain the definitions of certain co variants or other derivatives con­ed with Bezouts abbreviated method of elimination, due for the most part to Pro- Sylvester, and which are called Bezoutiants, Cobezoutiants, &c. I have not in present memoir in any wise considered the theories to which the catalecticant, &c. the last-mentioned other co variants and derivatives relate; the design is to point ind precisely define the different covariants or other derivatives which have hitherto ented themselves in theories relating to binary quantics, and so to complete, as far ay be, the explanation of the terminology of this part of the subject. If we consider a quantic ( a, b ,..)( x, y ,...) m an adjoint linear form, the operative quantic ( a, b ,..)(∂ e , ∂ n ,...) m ore generally the operative quantic obtained by replacing in any covariant of the quantic the facients ( x , y ,..) by the symbols of differentiation (∂ e , ∂ n ,...) ore generally the operative quantic obtained by replacing in any covariant of the quantic the facients ( x, y , ..) by the symbols of differentiation (∂ e , ∂ n ,...) (which ative quantic is, so to speak, a contravariant operator), may be termed the Pro - r; and the Provector operating upon any contravariant gives rise to a contravariant, h may of course be an invariant. Any such contravariant, or rather such con-iriant considered as so generated, may be termed a Provectant ; and in like manner operative quantic obtained by replacing in any contravariant of the given quantic the facients ( ξ , n ..) by the symbols of differentiation (∂ x , ∂ y ,...) (which opera quantic is a covariant operator), is termed the Contraprovector ; and the contraprove operating upon any covariant gives rise to a covariant, which may of course be an irriant. Any such covariant, or rather such covariant considered as so generated, may termed a Contraprovectant .

François Venant. Enige aanvullingen

1997 ◽  
Vol 111 (3) ◽  
pp. 163-176
Author(s):  
J. Bruyn
Keyword(s):  
The Other ◽  
Personal Style ◽  
Fresh Start ◽  
Untimely Death ◽  
The Subject ◽  
Further Development

AbstractSince J. G. van Gelder was able to identify a number of works by François Venant (1591/92-1636) in 1938 (note 2) and Kurt Bauch and Astrid Tümpel added to these one painting and a drawing (notes 14 and 3), the artist has been known as one of the so-called Pre-Rembrandtists. Together with his contemporaries Claes Cornelisz. Moeyaert (c. 1590/91-1655) and Jacob Pynas (1592/93-after 1650) he was one of the younger artists of this group. Its style was dominated by Pictcr Lastman (1583-1633) and Jan Pynas (1581/82-1633), both of whom underwent the influence of Adam Elsheimer during their stay in Rome. Venant married a younger sister of Lastman in 1625. The latter's influence on his work had however set in well before that year. Jacob's Dream, signed and dated 161(7?) (note 10, fig. 2) testifies to this, as well as showing traces of Elsheimer's influence, possibly transmitted by Jan Pynas (notes 12 and 13, fig. 3). A somewhat later signed work, David's parting from Jonathan (note 5, fig.1), closely follows Lastman's version of the subject of 1620 (note 6) though the grouping of the two figures may be taken as typical of Venant's personal style. In an unsigned picture of Gideon's Scacrifice, which may also be dated to the early 1620s (note 14, fig. 4), the artist once more makes use of motifs from various works by Lastman. Two undated drawings would seem to represent a slightly later stage in the artists's development. The Baptism of the Eunuch (notes 16 and 18, fig. 5) betrays the attempt to emulate Lastman's pictures on the subject, especially one of 1623 (note 17), by enhancing the dramatic actions in the scene, and so does Gideon's Sacrifice (note 20, figs. 6 and 8), which seems to be based on Lastman's Sacrifice of Monoah of 1627 (note 21, fig.7). To these works, spanning a period from 1617 (?) to the late '20s, may be added two more, another drawing and a painting. The drawing of Daniel at Belshazzar's Feast was formerly attributed to Lastman (notes 25-33, figs. and 10). While the technique, notably the use of wash, differs from that in the drawings mentioned above, the similarities to these in linear rhythm and conception are such that they may all be attributed to the same hand. The technical differences may be accounted for by assuming a slightly later date and, more particularly, a different purpose; whereas the other drawings were in all likelihood self-contained products, Belshazzar's Feast appears to be a sketch for a painting. The last phase of Venant's career seems to be represented by the largest painting known to us and the only one on canvas, Elisha Refusing Naäman's Gifts (note 34, fig. 11). It shows the artist disengaging himself from Lastman at last, possibly after the latter's death in 1633. While the composition is still reminiscent of his carlier work, here Venant seems to have made a fresh start by allowing study from life to play a more important role than before. The landscape differs radically from earlier backgrounds and may well have been influenced by Barholomeus Breenbergh, who returned from Italy around 1630 and whose influence may also be detected in the heavy wash that marks the Belshazzar drawing. The artist's further development was cut short by his untimely death, probably of the plague, in 1636.

scholarly journals On Legendre's functions P n ( θ ), when n is great and θ has any value

1916 ◽  
Vol 92 (642) ◽  
pp. 433-437
Keyword(s):  
Approximate Formula ◽  
The Other ◽  
Mathematical Methods ◽  
Other Hand ◽  
Great Generality ◽  
Associated Functions ◽  
Complete Series ◽  
The Subject ◽  
Comparison Of The Results ◽  
Further Development

As is well known, an approximate formula for Legendre's function P n (θ), when n , is very large, was given Laplace. The subject has been treated with great generality by Hobson, who has developed the complete series proceeding by descending powers of n , not only for P n but also for the "associated functions." The generality aimed at by Hobson requires the Use of advanced mathematical methods. I have thought that a simpler derivation, sufficient for practical purposes and more within the reach of physicists with a smaller mathematical equipment, may be useful. It had, indeed, been worked out independently. The series, of which Laplace's expression constitutes the first term, is arithmetically useful only when nθ is at least moderately large. On the other hand, when θ is small, p n tends to identity itself with the Bessel's function J 0 ( nθ ), is was first remarked by Mehler. A further development of this approximation is here proposed. Finally, a comparison of the results of the two methods of approximation with the numbers calculated by A. Lodge for n = 20 is exhibited.

scholarly journals Further researches on the extrusion of granules by trypanosomes and on their further development

1913 ◽  
Vol 86 (589) ◽  
pp. 377-389 ◽  
Keyword(s):  
Royal Society ◽  
The Other ◽  
Preliminary Note ◽  
The Subject ◽  
Further Development

In March, 1911, in the course of some work on trypanosomes carried out at the Wellcome Tropical Research Laboratories, Khartoum, the extrusion of certain granules from trypanosomes was observed by one of us (W. B. F.). The Director of the Laboratories, Dr. Andrew Balfour, was informed of these observations, and he himself shortly after observed a somewhat similar extrusion of granules from Spirochætes (spirochætosis of fowls), an account of which he published. In June, 1911, a preliminary note on the subject was communicated to the Royal Society by one of us (W. B. F.). Since then, a great deal of work has been done on the subject by us conjointly, but for the most part independently; by one of us (W. B. F.) at Khartoum and in London, by the other (H. S. R.) at Yei in the Lado Enclave.

Golgi Apparatus and Melanogenesis: Ultrastructural Study of a Human Cellular Blue Nevus (Melanocytoma)

1973 ◽  
Vol 31 ◽  
pp. 380-381
Author(s):  
S.R. Allegra
Keyword(s):  
Endoplasmic Reticulum ◽  
Golgi Apparatus ◽  
Ultrastructural Study ◽  
The Other ◽  
Blue Nevus ◽  
Normal Complement ◽  
Golgi Vesicles ◽  
Golgi System ◽  
The Subject ◽  
Cellular Blue Nevus

The respective roles of the ribo somes, endoplasmic reticulum, Golgi apparatus and perhaps nucleus in the synthesis and maturation of melanosomes is still the subject of some controversy. While the early melanosomes (premelanosomes) have been frequently demonstrated to originate as Golgi vesicles, it is undeniable that these structures can be formed in cells in which Golgi system is not found. This report was prompted by the findings in an essentially amelanotic human cellular blue nevus (melanocytoma) of two distinct lines of melanocytes one of which was devoid of any trace of Golgi apparatus while the other had normal complement of this organelle.

“Channeling” the powers of God’s Word

2010 ◽  
Vol 4 (2) ◽  
pp. 135-156 ◽  
Author(s):  
Dorothea E. Schulz
Keyword(s):  
The Other ◽  
Border Zone ◽  
Focus Attention ◽  
Spiritual Power ◽  
New Materials ◽  
God's Word ◽  
Audio Recordings ◽  
Heated Debate ◽  
The Subject ◽  
The One

Starting with the controversial esoteric employment of audio recordings by followers of the charismatic Muslim preacher Sharif Haidara in Mali, the article explores the dynamics emerging at the interface of different technologies and techniques employed by those engaging the realm of the Divine. I focus attention on the “border zone” between, on the one hand, techniques for appropriating scriptures based on long-standing religious conventions, and, on the other, audio recording technologies, whose adoption not yet established authoritative and standardized forms of practice, thereby generating insecurities and becoming the subject of heated debate. I argue that “recyclage” aptly describes the dynamics of this “border zone” because it captures the ways conventional techniques of accessing the Divine are reassessed and reemployed, by integrating new materials and rituals. Historically, appropriations of the Qur’an for esoteric purposes have been widespread in Muslim West Africa. These esoteric appropriations are at the basis of the considerable continuities, overlaps and crossovers, between scripture-related esoteric practices on one side, and the treatment by Sharif Haidara’s followers of audio taped sermons as vessels of his spiritual power, on the other.

The problem of woman’s emansipation in the feuilleton “Amazonia: a very inept story” by Mykola Chirsky

2020 ◽  
pp. 71-76
Author(s):  
Iryna Rusnak
Keyword(s):  
Scientific Understanding ◽  
The Other ◽  
Literary Studies ◽  
Ethical Guidelines ◽  
Compositional Structure ◽  
Urgent Task ◽  
The Subject ◽  
The One ◽  
Artistic Heritage

The author of the article analyses the problem of the female emancipation in the little-known feuilleton “Amazonia: A Very Inept Story” (1924) by Mykola Chirsky. The author determines the genre affiliation of the work and examines its compositional structure. Three parts are distinguished in the architectonics of associative feuilleton: associative conception; deployment of a “small” topic; conclusion. The author of the article clarifies the role of intertextual elements and the method of constantly switching the tone from serious to comic to reveal the thematic direction of the work. Mykola Chirsky’s interest in the problem of female emancipation is corresponded to the general mood of the era. The subject of ridicule in provocative feuilleton is the woman’s radical metamorphoses, since repulsive manifestations of emancipation becomes commonplace. At the same time, the writer shows respect for the woman, appreciates her femininity, internal and external beauty, personality. He associates the positive in women with the functions of a faithful wife, a caring mother, and a skilled housewife. In feuilleton, the writer does not bypass the problem of the modern man role in a family, but analyses the value and moral and ethical guidelines of his character. The husband’s bad habits receive a caricatured interpretation in the strange behaviour of relatives. On the one hand, the writer does not perceive the extremes brought by female emancipation, and on the other, he mercilessly criticises the male “virtues” of contemporaries far from the standard. The artistic heritage of Mykola Chirsky remains little studied. The urgent task of modern literary studies is the introduction of Mykola Chirsky’s unknown works into the scientific circulation and their thorough scientific understanding.

MUNDANE MIRACLES IN AWADH. ENCOUNTERS WITH THE REVEALED AND THE HIDDEN

2020 ◽  
pp. 130-140
Author(s):  
Maxim B. Demchenko ◽  
Keyword(s):  
The Other ◽  
Local People ◽  
Natural Phenomena ◽  
Mughal Empire ◽  
The Public ◽  
British Raj ◽  
The Subject ◽  
Other World ◽  
Better Than

The sphere of the unknown, supernatural and miraculous is one of the most popular subjects for everyday discussions in Ayodhya – the last of the provinces of the Mughal Empire, which entered the British Raj in 1859, and in the distant past – the space of many legendary and mythological events. Mostly they concern encounters with inhabitants of the “other world” – spirits, ghosts, jinns as well as miraculous healings following magic rituals or meetings with the so-called saints of different religions (Hindu sadhus, Sufi dervishes),with incomprehensible and frightening natural phenomena. According to the author’s observations ideas of the unknown in Avadh are codified and structured in Avadh better than in other parts of India. Local people can clearly define if they witness a bhut or a jinn and whether the disease is caused by some witchcraft or other reasons. Perhaps that is due to the presence in the holy town of a persistent tradition of katha, the public presentation of plots from the Ramayana epic in both the narrative and poetic as well as performative forms. But are the events and phenomena in question a miracle for the Avadhvasis, residents of Ayodhya and its environs, or are they so commonplace that they do not surprise or fascinate? That exactly is the subject of the essay, written on the basis of materials collected by the author in Ayodhya during the period of 2010 – 2019. The author would like to express his appreciation to Mr. Alok Sharma (Faizabad) for his advice and cooperation.

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