The double cusp has five minima

1978 ◽  
Vol 84 (3) ◽  
pp. 537-538 ◽  
Author(s):  
J. Callahan
Keyword(s):  
Critical Points ◽  
Standard Form ◽  
Singularity Theory ◽  
The Other ◽  
Universal Unfolding ◽  
The Real ◽  
Level Curves ◽  
Intersection Points ◽  
The One ◽  
Image Position

The double cusp is the real, compact, unimodal singularitysee (2), (4). Functions in a universal unfolding of the double cusp can have nine non-degenerate critical points near the origin, but no more. Index considerations show that precisely four of the nine are saddles, and it has long been part of the folklore of singularity theory that one of the other five must be a maximum. Indeed, a standard form of the unfolded double cusp (1), (3) is a function having a pair of intersecting ellipses as one of its level curves; see Fig. 1(a). There are saddles at the four intersection points, a maximum inside the central quadrilateral, and a minimum inside each of the other four finite regions bounded by the ellipses. The rest of Fig. 1 suggests, however, that a deformation of this function (in which one of the saddles drops below the level of the other three) might turn the maximum into a fifth minimum. The following proposition shows that a function similar to the one in Fig. 1(d) can be realized in an unfolding of the double cusp.

Hidden “holes” in the capital of banks and the supply of credit to the real sector of economy

2018 ◽  
pp. 49-68 ◽  
Author(s):  
M. E. Mamonov
Keyword(s):  
Credit Risk ◽  
The Other ◽  
Real Sector ◽  
Capital Management ◽  
Loan Loss ◽  
Short Term ◽  
The Real ◽  
Ex Post ◽  
The One

Our analysis documents that the existence of hidden “holes” in the capital of not yet failed banks - while creating intertemporal pressure on the actual level of capital - leads to changing of maturity of loans supplied rather than to contracting of their volume. Long-term loans decrease, whereas short-term loans rise - and, what is most remarkably, by approximately the same amounts. Standardly, the higher the maturity of loans the higher the credit risk and, thus, the more loan loss reserves (LLP) banks are forced to create, increasing the pressure on capital. Banks that already hide “holes” in the capital, but have not yet faced with license withdrawal, must possess strong incentives to shorten the maturity of supplied loans. On the one hand, it raises the turnovers of LLP and facilitates the flexibility of capital management; on the other hand, it allows increasing the speed of shifting of attracted deposits to loans to related parties in domestic or foreign jurisdictions. This enlarges the potential size of ex post revealed “hole” in the capital and, therefore, allows us to assume that not every loan might be viewed as a good for the economy: excessive short-term and insufficient long-term loans can produce the source for future losses.

On functional Nörlund methods

1970 ◽  
Vol 67 (1) ◽  
pp. 47-60 ◽  
Author(s):  
B. Choudhary
Keyword(s):  
The Other ◽  
Integral Transformations ◽  
Other Hand ◽  
Nörlund Means ◽  
The One ◽  
Image Position

Integral transformations analogous to the Nörlund means have been introduced and investigated by Kuttner, Knopp and Vanderburg(6), (5), (4). It is known that with any regular Nörlund mean (N, p) there is associated a functionregular for |z| < 1, and if we have two Nörlund means (N, p) and (N, r), where (N, pr is regular, while the function is regular for |z| ≤ 1 and different) from zero at z = 1, then q(z) = r(z)p(z) belongs to a regular Nörlund mean (N, q). Concerning Nörlund means Peyerimhoff(7) and Miesner (3) have recently obtained the relation between the convergence fields of the Nörlund means (N, p) and (N, r) on the one hand and the convergence field of the Nörlund mean (N, q) on the other hand.

scholarly journals Distribution of rational points on the real line

1973 ◽  
Vol 15 (2) ◽  
pp. 243-256 ◽  
Author(s):  
T. K. Sheng
Keyword(s):  
Algebraic Number ◽  
Rational Number ◽  
Real Line ◽  
Rational Points ◽  
The Other ◽  
Liouville Numbers ◽  
The Real ◽  
Other Hand ◽  
Image Position

It is well known that no rational number is approximable to order higher than 1. Roth [3] showed that an algebraic number is not approximable to order greater than 2. On the other hand it is easy to construct numbers, the Liouville numbers, which are approximable to any order (see [2], p. 162). We are led to the question, “Let Nn(α, β) denote the number of distinct rational points with denominators ≦ n contained in an interval (α, β). What is the behaviour of Nn(α, + 1/n) as α varies on the real line?” We shall prove that and that there are “compressions” and “rarefactions” of rational points on the real line.

TWO SYLLOGISMS IN THE MOZI: CHINESE LOGIC AND LANGUAGE

2018 ◽  
Vol 12 (3) ◽  
pp. 589-606 ◽  
Author(s):  
BYEONG-UK YI
Keyword(s):  
Standard Form ◽  
The Other ◽  
Valid Argument ◽  
Linguistic Differences ◽  
Argument Form ◽  
Chinese Counterpart ◽  
The One ◽  
Chinese And English ◽  
Chinese Logic

AbstractThis article examines two syllogistic arguments contrasted in an ancient Chinese book, the Mozi, which expounds doctrines of the Mohist school of philosophers. While the arguments seem to have the same form, one of them (the one-horse argument) is valid but the other (the two-horse argument) is not. To explain this difference, the article uses English plural constructions to formulate the arguments. Then it shows that the one-horse argument is valid because it has a valid argument form, the plural cousin of a standard form of valid categorical syllogisms (Plural Barbara), and argues that the two-horse argument involves equivocal uses of a key predicate (the Chinese counterpart of ‘have four feet’) that has the distributive/nondistributive ambiguity. In doing so, the article discusses linguistic differences between Chinese and English and explains why the logic of plural constructions is applicable to Chinese arguments that involve no plural constructions.

On indirect Methods of acquiring Knowledge - The Method of History. - The First Table of Mortality

1851 ◽  
Vol 1 (1) ◽  
pp. 40-46
Author(s):  
Edwin James Farren
Keyword(s):  
Real Line ◽  
English Language ◽  
The Other ◽  
Adult Student ◽  
Indirect Methods ◽  
The Real ◽  
Straight Line ◽  
Point To Point ◽  
The One

The term scholar, as current in the English language, has two extreme acceptations, tyro and proficient; or what the later Greeks fancifully termed the alpha and omega of acquirement. If we attempt to trace the steps by which even the adult student of any especial branch of professional or literary knowledge has fairly passed the boundary defined by the one meaning in passing on to that position denoted by the other, it will commonly be found, that in place of that lucid order, that straight line from point to point, which theory and resolve generally premise, the real order of acquirement has been desultory—the real line of progression, circuitous and uncertain.

scholarly journals The “Establishment”, the “Élites”, and the “People”

2017 ◽  
Vol 16 (4) ◽  
pp. 551-565 ◽  
Author(s):  
Ruth Wodak
Keyword(s):  
The Other ◽  
Right Wing ◽  
The Real ◽  
The People ◽  
Politics Of Fear ◽  
The One ◽  
Disenchantment With Politics

Abstract In this paper, I discuss the attempt by all right-wing populist parties to create, on the one hand, the ‘real’ and ‘true’ people; and on the other, the ‘élites’ or ‘the establishment’ who are excluded from the true demos. Such divisions, as will be elaborated in detail, have emerged in many societies over centuries and decades. A brief example of the arbitrary construction of opposing groups illustrates the intricacies of such populist reasoning. Furthermore, I pose the question why such divisions resonate so well in many countries? I argue that – apart from a politics of fear (Wodak 2015) – much resentment is evoked which could be viewed as both accompanying as well as a reaction to the disenchantment with politics and the growing inequalities in globalized capitalist societies.

scholarly journals MEMBANGUN SEMANGAT KERASULAN REMAJA KATOLIK DALAM KONTEKS MASYARAKAT PLURALIS DI INDONESIA

2017 ◽  
Vol 17 (9) ◽  
pp. 3-14
Author(s):  
Agustinus Supriyadi
Keyword(s):  
Logical Consequence ◽  
Cross Cultural ◽  
The Other ◽  
Real Form ◽  
Pluralistic Society ◽  
The Real ◽  
Self Discovery ◽  
The One ◽  
The Church

Catholic teens Indonesia is part of the Church in Indonesia and the Indonesian people. Indonesia consists of thousands of islands that stretched from Sabang to Merauke. This fact opens the possibility of a fairly wide occurrence of the encounter between cultures and simultaneous cross-cultural. This diversity is certainly a logical consequence to an enrichment of civilizations and diversity (plurality), although also contains elements of the loss. Plurality of Indonesian society on the one hand can make the Catholic teens swept away in the swift currents of the community to lose our identity or conflict. However Plurality can also awaken in the Catholic teen award nature between one race to the other races, between ethnic or tribal one with the other tribes, between groups with one another. In a pluralistic society such as this, the Catholic teens called to the apostolate. Through the act of self-discovery, live in love and have a sense of tolerance of differences is the real form of the apostolate.

scholarly journals Transformation of the Banking Sector of Ukraine: Reasons and Consequences

2017 ◽  
Vol 1 (13) ◽  
pp. 33-48
Author(s):  
Myroslava Khutorna
Keyword(s):  
Economic Development ◽  
Banking Sector ◽  
Financial System ◽  
Market Concentration ◽  
The Other ◽  
Real Economy ◽  
The Real ◽  
Other Hand ◽  
The One

This paper is devoted to the consideration of the preconditions and results of the banking sector of Ukraine transforming, its influence on the sector’s productivity, stability and significance for the real economy. It’s grounded that banking sector of Ukraine has seriously weakened its potential for the economic development stimulation. On the one hand, due to the banking sector clearance from the bad and unscrupulous banks the system has become much more sensitive to the monetary instruments and its state is going to be more predictable and better controlled. But on the other hand, massive banks’ liquidations have caused the worsening of the confidence in financial system and radical increasing of the market concentration the highest degree of which is observed in the householders’ deposit market.

French Impressions: The Transnational Afterlives of Verlaine’s ‘La lune blanche’ in Song

2021 ◽  
pp. 150-152
Author(s):  
David Evans
Keyword(s):  
Art Song ◽  
National Identities ◽  
The Other ◽  
Mode I ◽  
Source Text ◽  
The Real ◽  
Art Form ◽  
The One

In this chapter I compare settings of Verlaine’s ‘La Lune blanche’ (‘The White Moon’) by composers of different nationalities (Delius, Webern, Sorabji, Loomis, Nevin, Loeffler, Hennessy, Poldowski, McEwen, Szulc, Stravinsky) in order to show how different ideas of French song – and of art song itself – emerge through the multiple dialogues of its transnational crossings. Two opposing approaches become clear: on the one hand, songs which maintain a reverence towards the source text as a symbol of the cultural cachet which French mélodie has enjoyed since its 1880-1930 heyday; and on the other, songs which offer a curiously unplaceable musical material, staking a claim for music as an mode of articulation which functions independently from language and, indeed, from national identities which are always in danger of falling into repetition, cliché, and pastiche. This latter mode, I suggest, comes closest to the real heart of mélodie as understood by its foremost French purveyors, Fauré and Debussy, and which composers like Stravinsky draw out of Verlaine’s text: a conception of song as an art form uniquely placed to offer a critique of fixed national paradigms and stable interpretative systems, by constantly calling into question, through their formal complexities, the very processes by which meaning itself is produced.

Configuration of Quadrivalent Atoms

1929 ◽  
Vol 25 (2) ◽  
pp. 219-221
Author(s):  
T. M. Lowry
Keyword(s):  
The Other ◽  
Tetrahedral Configuration ◽  
X Ray ◽  
Metallic Atom ◽  
Other Hand ◽  
Function Change ◽  
The One ◽  
Image Position ◽  
Octahedral Configuration ◽  
As If

Two alternative views have been expressed in regard to the configuration of quadrivalent atoms. On the one hand le Bel and van't Hoff assigned to quadrivalent carbon a tetrahedral configuration, which has since been confirmed by the X-ray analysis of the diamond. On the other hand, Werner in 1893 adopted an octahedral configuration for radicals of the type MA6, e.g. inand then suggested that “the molecules [MA4]X2 are incomplete molecules [MA6]X2. The radicals [MA4] result from the octahedrally-conceived radicals [MA6] by loss of two groups A, but with no function-change of the acid residue…. They behave as if the bivalent metallic atom in the centre of the octahedron could no longer bind all six of the groups A and lost two of them leaving behind the fragment [MA4]” (p. 303).

Sign in / Sign up

Export Citation Format

Share Document