A correction to Lewis and Langford's Symbolic logic

1940 ◽  
Vol 5 (4) ◽  
pp. 149-149
Author(s):  
J. C. C. McKinsey
Keyword(s):  
The Other ◽  
Symbolic Logic ◽  
Minor Error ◽  
Counter Example ◽  
Other Hand ◽  
Image Position ◽  
A Minor

The purpose of this note is to call attention to a minor error in Lewis and Langford's Symbolic logic. On page 221, in discussing the Tarski-Łukasiewicz three-valued logic, the authors make the following assertion: “Let T(p) be any proposition, involving only one element, whose analogue holds in the two-valued system; if T(p) does not hold in the Three-valued Calculus, then pC.T(p) and Np.C.T(p) both hold.”I shall show, by means of a counter-example, that this assertion is not true. Let T(p) be the sentence:It is then easily verified that T(0) = T(1) = 1, and that T(½) = 0. Thus T(p) holds in the two-valued calculus, but not in the three-valued calculus. On the other hand, pC.T(p) does not hold, since ½.CT(½) = ½C0 = ½; similarly, Np.C.T(p) does not hold, since N½.C.T(½) = ½C0 = ½.

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.

A Medieval Open Work

POETICA ◽  
2021 ◽  
Vol 52 (3-4) ◽  
pp. 228-265
Author(s):  
Rafael Simian
Keyword(s):  
The Other ◽  
Specific Function ◽  
Umberto Eco ◽  
New Approach ◽  
Avant Garde ◽  
Other Hand ◽  
Open Work ◽  
New Perspective ◽  
A Minor

Abstract Guigo II is commonly known and praised among specialists of Western mysticism for his Scala claustralium, a work that presents a spiritual program for cloistered monks. His Meditations, on the other hand, have usually been relegated to the margin of attention. The First Meditation, in particular, is generally regarded as a minor piece. The paper argues, however, that a new approach can make better sense of the First Meditation, while also enabling us to recognize its specific function and value. Seen from this new perspective, Guigo’s purpose with the text is to train and exercise his readers’ minds according to the spiritual program laid out in the Scala. The paper shows that the First Meditation realizes that goal, surprisingly, by having the same essential features that Umberto Eco found in the ‘open works’ of the Western avant-garde.

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).

A System of Linear Equations with an Infinity of Unknowns

1924 ◽  
Vol 22 (3) ◽  
pp. 282-286
Author(s):  
E. C. Titchmarsh
Keyword(s):  
Present Note ◽  
Linear Equations ◽  
The Other ◽  
System Of Linear Equations ◽  
Other Hand ◽  
Image Position ◽  
Monotonic Character

I have collected in the present note some theorems regarding the solution of a certain system of linear equations with an infinity of unknowns. The general form of the equations isthe numbers a1, a2, … c1, c2, … being given. Equations of this type are of course well known; but in studying them it is generally assumed that the series depend for convergence on the convergence-exponent of the sequences involved, e.g. that and are convergent. No assumptions of this kind are made here, and in fact the series need not be absolutely convergent. On the other hand rather special assumptions are made with regard to the monotonic character of the sequences an and cn.

The extreme points of some classes of polynomials

1985 ◽  
Vol 101 (1-2) ◽  
pp. 99-110 ◽  
Author(s):  
D. A. Brannan ◽  
J. G. Clunie
Keyword(s):  
Extreme Points ◽  
The Other ◽  
Other Hand ◽  
Image Position

SynopsisWe study the extreme points of two classes of polynomials of degree at most n:It turns out that f ∈ Ext if and only if Re f(eiθ) has exactly 2n zeros in [0, 2π). On the other hand, if f∈Hn and 1−|f(eiθ)|2 has 2n zeros in [0, 2π), then either f ∈ Ext Hn or else f(z) = α + βzn where |α|+|β| = l and αβ≠0; if 1−|f(eiθ)|2 has 2m zeros, 2n, then f may or may not belong to Ext Hn.

The No-Three-In-Line Problem

1968 ◽  
Vol 11 (4) ◽  
pp. 527-531 ◽  
Author(s):  
Richard K. Guy ◽  
Patrick A. Kelly
Keyword(s):  
Finite Number ◽  
The Other ◽  
Probabilistic Argument ◽  
Number Of Solutions ◽  
Other Hand ◽  
Image Position

Let Sn be the set of n2 points with integer coordinates n (x, y), 1 ≤ x, y <n. Let fn be the maximum cardinal of a subset T of Sn such that no three points of T are collinear. Clearly fn < 2n.For 2 ≤ n ≤ 10 it is known ([2], [3] for n = 8, [ 1] for n = 10, also [4], [6]) that fn = 2n, and that this bound is attained in 1, 1, 4, 5, 11, 22, 57, 51 and 156 distinct configurations for these nine values of n. On the other hand, P. Erdös [7] has pointed out that if n is prime, fn ≥ n, since the n points (x, x2) reduced modulo n have no three collinear. We give a probabilistic argument to support the conjecture that there is only a finite number of solutions to the no-three-in-line problem. More specifically, we conjecture that

On the K-theory of the extended power construction

1982 ◽  
Vol 92 (2) ◽  
pp. 263-274 ◽  
Author(s):  
J. E. McClure ◽  
V. P. Snaith
Keyword(s):  
Minor Error ◽  
Ring Spectra ◽  
Power Construction ◽  
Complete Treatment ◽  
K Theory ◽  
Image Position ◽  
A Minor ◽  
Extended Power

The construction of Dyer-Lashof operations in K-theory outlined in (6) and refined in (12) depends in an essential way on the descriptions of the mod-p K-theory of EZp, ×ZpXp and EΣ ×σ p Xp given there. Unfortunately, these descriptions are incorrect when p is odd except in the case where the Bockstein β is identically zero in K*(X; Zp), and even in this case the methods of proof used in (6) and (12) are not strong enough to show that the answer given there is correct. In this paper we repair this difficulty, obtaining a complete corrected description of K*(EZp ×ZpXp; Zp) and K*(EΣp) (theorem 3·1 below, which should be compared with ((12); theorems 3·8 and 3·9) and ((6); theorem 3)). Because of the error, the method used in (6) and (12) to construct Dyer-Lashof operations fails to go through for odd primes when non-zero Bocksteins occur, and it is not clear that this method can be repaired. We shall not deal with the construction of Dyer-Lashof operations in this paper. Instead, the first author will give a complete treatment of these operations in (5), using our present results and the theory of H∞-ring spectra to obtain strengthened versions of the results originally claimed in ((12); theorem 5·1). There is also a minor error in the mod-2 results of (12) (namely, the second formula in (12), theorem 3·8 (a) (ii)) should readwhere B2 is the second mod-2 Bockstein, and a similar change is necessary in the second formula of ((12), theorem 3·8(b) (ii)). The correction of this error requires the methods of (5) and will not be dealt with here; fortunately, the mod-2 calculations of ((12), §6–9), (10) and (11) are unaffected and remain true as stated.

scholarly journals Murine B-cell subpopulations responsive to T-dependent and T-independent antigens.

1976 ◽  
Vol 144 (2) ◽  
pp. 382-397 ◽  
Author(s):  
G K Lewis ◽  
R Ranken ◽  
D E Nitecki ◽  
J W Goodman
Keyword(s):  
B Cells ◽  
B Cell ◽  
Minor Component ◽  
Memory Cell ◽  
Keyhole Limpet Hemocyanin ◽  
The Other ◽  
Other Hand ◽  
Cell Mitogen ◽  
A Minor

Strain A/J mice made secondary indirect plaque-forming cell (PFC) responses to azobenzenearsonate (ABA) conjugates of giant keyhole limpet hemocyanin (KLH), a thymic-dependent antigen, but not to conjugates of Ficoll, a T-independent antigen. ABA-Ficoll was also unable to elicit a response in animals primed with ABA-KLH, which have an expanded anti-ABA memory cell pool. On the other hand, ABA-Ficoll rendered mice unresponsive to ABA-KLH when administered before priming or boosting with the T-dependent immunogen. Hence, the T-independent antigen was able to tolerize but unable to trigger B-memory cells responsive to the T-dependent antigen. A/J mice immunized with dinitrophenyl conjugates of Ficoll or bovine IgG (BGG) made vigorous IgM and IgG PFC responses. PFC responses to ABA-KLH and 2,4-dinitrophenyl (DNP)-BGG were abrogated by depleting mice of C3 with cobra venom factor, whereas the IgM and IgG PFC responses to DNP-Ficoll were unaffected. B lymphocytes were fractionated on the basis of receptors for C3 and the subpopulations were assayed for in vitro PFC responses to DNP-Ficoll. Very little response was obtained from complement receptor lymphocyte [CRL(+)] B cells, whereas CRL(-) cells were more responsive than unfractionated B cells. Both populations responded to a polyclonal B-cell mitogen (lipopolysaccharide). On the other hand, the in vitro PFC response to a T-dependent antigen (sheep erythrocytes) correlated with the presence of CRL(+) B cells in the cultures. However, a minor component of this response, sensitive to anti-Thy-1 serum, was made by CRL(-) B cells, indicating the existence of subpopulations of T-dependent B cells with different signalling requirements. The results suggest that most B cells responsive to T-dependent antigens possess receptors for C3 and that C3 plays an obligatory role in the response of these cells. A distinct subpopulation of B cells which lack C3 receptors respond to T-independent antigens. The precursors of PFC for the ABA epitope reside largely or exclusively in the CRL(+) compartment in A/J mice, whereas precursors for the DNP determinant are found in both compartments.

scholarly journals La reivindicación cultural e identitaria a través de la autotraducción: el caso de la poesía autotraducida de Xuan Bello del asturiano al español

2018 ◽  
Vol 17 (17) ◽  
pp. 171
Author(s):  
Beatriz Flores Silva
Keyword(s):  
The Other ◽  
Other Hand ◽  
The One ◽  
A Minor ◽  
Sociocultural Systems ◽  
Sobre Todo

La autotraducción es un fenómeno que siempre ha estado presente, sobre todo, en aquellos sistemas socioculturales de gran riqueza lingüística y cultural. Este es el caso del sistema peninsular, donde cada vez más autores bilingües deciden escribir sus obras en una lengua minoritaria y, después, autotraducirlas al español. En este trabajo, se toma como objeto de análisis la poesía autotraducida del asturiano al español de Xuan Bello. Así, se observará si la autotraducción permite a este autor traductor, por un lado, trasladar sus reivindicaciones culturales a otro sistema ajeno al asturiano; y, por otro lado, definir su identidad individual.Palabras clave: autotraducción, poesía, asturiano, español, cultura, identidad.Self-translation is a phenomenon which has always been present, most of all in those sociocultural systems characterized by both their linguistic and cultural richness. One of those is the Spanish peninsular system where more and more bilingual authors tend to write their works in a minor language and subsequently translate them into Spanish. The aim of this paper is to research Xuan Bello’s self-translated poetry from Asturian into Spanish. That way it will be considered whether selftranslation helps this author-translator: on the one hand, to transfer his cultural demands; on the other hand, to define his individual identity.Keywords: self-translation, poetry, Asturian, Spanish, culture, identity.

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