Equality in

1973 ◽  
Vol 38 (4) ◽  
pp. 571-575 ◽  
Author(s):  
Jonathan P. Seldin
Keyword(s):  
Axiom Scheme ◽  
Image Position ◽  
Made In

In [CLg. II, §15B6], the problem of representing equality in the system by means of an ob Q is discussed; it is shown there that if Q is taken to be a canonical atom of degree 2 and if the axiom schemeis postulated, then it follows by Rule Eq thatand, if no other properties are postulated for Q, then the converse of (1), Q-consistency, also holds. However, it is also desirable to have, in addition, the propertyat least for some obs Z, and the statement is made in [CLg. II, §15B6] that no known way of incorporating this principle existed (at the time this statement was written) in such a way that there was a proof of Q-consistency. In this paper it is shown that if Z is restricted to be a basic canob of degree 1, i.e., if Z is restricted to be a predicate of one argument, then a system in which (2) is postulated can be proved Q-consistent.The notations and conventions of [CLg. II] especially §15B, will be used throughout the paper.

scholarly journals Slaves to Rome: The Rhetoric of Mastery in Titus' Speech to the Jews (Bellum Judaicum 6.328-50)

Ramus ◽  
2007 ◽  
Vol 36 (1) ◽  
pp. 25-38 ◽  
Author(s):  
Myles Lavan
Keyword(s):  
Historical Account ◽  
Self Presentation ◽  
Image Position ◽  
Relationship Of ◽  
The Relationship ◽  
Made In

(BJ6.350)Those who discard their weapons and surrender their persons, I will let live. Like a lenient master in a household, I will punish the incorrigible but preserve the rest for myself.So ends Titus' address to the embattled defenders of Jerusalem in the sixth book of Josephus'Jewish War(6.328-50). It is the most substantial instance of communication between Romans and Jews in the work. Titus compares himself to the master of a household and the Jewish rebels to his slaves. Is this how we expect a Roman to describe empire? If not, what does it mean for our understanding of the politics of Josephus' history? The question is particularly acute given that this is not just any Roman but Titus himself: heir apparent and, if we believe Josephus, the man who read and approved this historical account. It is thus surprising that, while the speeches of Jewish advocates of submission to Rome such as Agrippa II (2.345-401) and Josephus himself (5.362-419) have long fascinated readers, Titus' speech has received little or no attention. Remarkably, it is not mentioned in any of three recent collections of essays on Josephus. This paper aims to highlight the rhetorical choices that Josephus has made in constructing this voice for Titus—particularly his self-presentation as master—and the interpretive questions these raise for his readers. It should go without saying that the relationship of this text to anything that Titus may have said during the siege is highly problematic. (Potentially more significant, but unfortunately no less speculative, is the question of how it might relate to any speech recorded in the commentaries of Vespasian and Titus that Josephus appears to have used as a source.) What we have is a Josephan composition that is embedded in the broader narrative of theJewish War.

St. Mark 4.1–34

1952 ◽  
Vol 5 (1) ◽  
pp. 49-66
Author(s):  
C.E.B. Cranfield
Keyword(s):  
The Other ◽  
General Question ◽  
Composite Section ◽  
Image Position ◽  
Made In

The structure of this section, which is one of the two large blocks of teaching in Mark (the other being chapter 13), may be indicated as follows: That this is a composite section is fairly obvious. In v. 1 Jesus is sitting in a boat and in v. 36 he is apparently still in the boat, but vv. 10–20 presuppose a different scene. As things stand it is not clear to whom the teaching in vv. 21–32 was addressed. Are we to conclude from its relation to vv. 10–20 that it was addressed to the disciples alone, or are we to conclude from its relation to vv. 33 f. that it was addressed to the multitude? It seems likely that we have to do here with a number of originally independent pieces of tradition which have been brought together in several stages to form an artificial unity. Vv. 10–20 disturb the unity of scene of a grouping of parables and sayings which is probably itself artificial. But vv. 10–20 themselves are not originally a unit. Vv. 11–20 give a double answer to the disciples' question in v. 10. V. 13 (with the singular ‘this parable’) presupposes a question about the meaning of the particular parable and would follow on v. 10 quite smoothly. It is true that the plural ‘the parables’ in v. 10 might suggest a more general question, but it need not; and one wonders whether it represents a correction made in order to make the insertion of vv. 11 f. easier.

Conjoined Twins — A Genealogical Study

1970 ◽  
Vol 19 (1-2) ◽  
pp. 213-216 ◽  
Author(s):  
George B. Callahan ◽  
Roy C. Mitchell
Keyword(s):  
North Carolina ◽  
Medical Schools ◽  
Conjoined Twins ◽  
The State ◽  
Family Tree ◽  
Genetic Studies ◽  
Court Records ◽  
Siamese Twins ◽  
Image Position ◽  
Made In

Beautiful and brilliant, content and capable, skillful and successful, these and multiple other adjectives may be used to describe persons on a family tree of Eng-Chang, the original Siamese twins (Fig. 1). These men chose the State of North Carolina for homes, and are considered among its most renowned citizens. They had some of the above characteristics and their descendants shared others.Data upon six generations of Eng-Chang families — some verified by their 1836 pamphlets, others as recent as 1969 court records in their county residence — are shown in the following table:Fig. 2 shows second and third generations in family groups made in the summer of 1865. Nine of Eng's 11 children are shown; 2 had died young. Likewise, 9 of Chang's 10 children are seen; one was born in 1868, as certified by Edinburgh's famous Prof. James Y. Simpson (1869). Two sets of twins, not joined, are recorded in their descendants. Though some members on this family tree are difficult to certify, the data available in these six generations are by far the most comprehensive found. Chromosome and other genetic studies are being initiated and pursued in anatomy departments of American and Thai Medical Schools.

A Compact Imbedding Theorem for Functions without Compact Support

1971 ◽  
Vol 14 (3) ◽  
pp. 305-309 ◽  
Author(s):  
R. A. Adams ◽  
John Fournier
Keyword(s):  
Sobolev Space ◽  
Compact Support ◽  
Unbounded Domains ◽  
Bounded Domains ◽  
Complete Continuity ◽  
Compact Imbedding ◽  
Compactness Theorems ◽  
Image Position ◽  
Necessary And Sufficient ◽  
Made In

The extension of the Rellich-Kondrachov theorem on the complete continuity of Sobolev space imbeddings of the sort1to unbounded domains G has recently been under study [1–5] and this study has yielded [4] a condition on G which is necessary and sufficient for the compactness of (1). Similar compactness theorems for the imbeddings2are well known for bounded domains G with suitably regular boundaries, and the question naturally arises whether any extensions to unbounded domains can be made in this case.

scholarly journals Polar analogues of two theorems by Minkowski

1974 ◽  
Vol 11 (1) ◽  
pp. 121-129 ◽  
Author(s):  
Kurt Mahler
Keyword(s):  
Classical Theory ◽  
Distance Function ◽  
Convex Bodies ◽  
Classical Concept ◽  
Geometry Of Numbers ◽  
Basic Theorem ◽  
The Real ◽  
Unit Hypersphere ◽  
Image Position ◽  
Made In

Since Minkowski's time, much progress has been made in the geometry of numbers, even as far as the geometry of numbers of convex bodies is concerned. But, surprisingly, one rather obvious interpretation of classical theorems in this theory has so far escaped notice.Minkowski's basic theorem establishes an upper estimate for the smallest positive value of a convex distance function F(x) on the lattice of all points x with integral coordinates. By contrast, we shall establish a lower estimate for F(x) at all the real points X on a suitable hyperplanewith integral coefficients u1, …, un not all zero. We arrive at this estimate by means of applying to Minkowski's Theorem the classical concept of polarity relative to the unit hypersphereThis concept of polarity allows generally to associate with known theorems on point lattices analogous theorems on what we call hyperplane lattices. These new theorems, although implicit in the old ones, seem to have some interest and perhaps further work on hyperplane lattices may lead to useful results.In the first sections of this note a number of notations and results from the classical theory will be collected. The later sections deal then with the consequences of polarity.

Some Observations on Industrial Assurance

1898 ◽  
Vol 34 (2) ◽  
pp. 105-144
Author(s):  
C. H. E. Rea
Keyword(s):  
Industrial Companies ◽  
National Importance ◽  
Friendly Societies ◽  
Image Position ◽  
Made In ◽  
Assurance Contracts

The almost phenomenal advances that have recently been made in the business of industrial assurance have brought this branch of our provident system into a position of national importance. Ten years ago, the business of our industrial companies was, roughly speaking, as under:—whereas to-day it is, approximately,Beyond the business of these companies, a very large number of industrial assurance contracts exist in the societies, clubs, and various orders registered under the Friendly Societies Act of 1875.

Prehistoric Macedonia

Antiquity ◽  
1929 ◽  
Vol 3 (11) ◽  
pp. 318-323
Author(s):  
W. A. Heurtley
Keyword(s):  
British School ◽  
Image Position ◽  
Made In

The excavations so far made in Macedonia are as follows:—In the valleys of the Vardar (Axiós) and Galliko (Echédoros)In the neighbourhood of SalonicaIn the valley of the HaliakmonBoubústi, by the British School at Athens, 1927.In the Lankadá valleySarátsi, by the British School at Athens, 1929.In Chalcidice

scholarly journals On the smallest number of entries necessary in a table of logarithms to seven decimal places

1891 ◽  
Vol 10 ◽  
pp. 35-37 ◽  
Author(s):  
J.E.A. Steggall
Keyword(s):  
Image Position ◽  
Made In

Taking seven figure logarithms it is required to find at what interval from n, a number of five figures, the next entry need be made, in order that any intermediate logarithm may be calculated by the method of proportional parts.We have

The Athenian Code of Laws, 410–399 B.C.

1991 ◽  
Vol 111 ◽  
pp. 87-100 ◽  
Author(s):  
P. J. Rhodes
Keyword(s):  
Know How ◽  
Image Position ◽  
The City ◽  
Made In

Discussion of the problems must begin with the allegations made in Lysias' speech XXX) Against Nicomachus:When he became writer-up (anagrapheus) of the laws (nomoi), who does not know how he defiled the city? His instructions were to write up the laws of Solon in four months, but he set himself up as a lawgiver (nomothetes) in the place of Solon, instead of four months he made his office last six years, and every day he was taking money to insert some laws and wipe out others. (3) We were brought to this point, that the laws were doled out to us by his hand, and opposing litigants in the courts would produce conflicting laws, each claiming to have received them from Nicomachus. When the archons tried to impose fines on him and to bring him to court, he refused to hand over the laws: the city was brought to the direst disaster before he could be removed from his office and made to submit to examination (euthynai) for what he had done. (4) And yet, gentlemen, after failing to pay the penalty for those offences, he has done the same thing with his present office. First, he has been writing up for four years, when he could have had done with it in thirty days.

scholarly journals The Vibrations of a Particle about a Position of Equilibrium—Part III

1922 ◽  
Vol 41 ◽  
pp. 128-140
Author(s):  
Bevan B. Baker
Keyword(s):  
Dynamical System ◽  
Series Solution ◽  
Elliptic Functions ◽  
The Other ◽  
Real Solution ◽  
Present Part ◽  
Image Position ◽  
Region Of Convergence ◽  
Range Of Values ◽  
Made In

In the two parts of this investigation previously published it has been shown that the solution in terms of elliptic functions represents the motion of the particular dynamical system under consideration throughout the whole range of values of s and g for which a real solution exists, except for those values for which s = 2g and k = 1, but that, on the other hand, the series solution is convergent and represents the motion only so long asfor values of s and g for which the sign of this inequality is reversed the trigonometric series representing the solution are divergent. It is of importance to investigate what discontinuities, if any, of the system correspond to values of s and g which lie on the boundary of the region of convergence; the present part is concerned primarily with showing that under such circumstances no discontinuity of the system exists, thus confirming the suggestions made in Part I., § 12.

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