The Genus of a Developable Surface

1935 ◽  
Vol 31 (2) ◽  
pp. 156-158 ◽  
Author(s):  
H. F. Baker
Keyword(s):  
Direct Proof ◽  
Ruled Surface ◽  
Developable Surface ◽  
Negative Number ◽  
Nodal Curve ◽  
Present Purpose ◽  
History Of ◽  
Triple Points

Cayley's remark that the formula by which the genus of a surface, according to Clebsch's definition, may presumably be computed leads to a negative number in the case of a cone, or a developable surface, or a ruled surface in general, has great importance in the history of the theory. But it would appear, from various indications, that, for a developable surface at least, it is more often quoted than read. I have thought therefore that the following simplifying remarks may have a use. Cayley uses formulae, due to Salmon and Cremona, without reference to the memoir where these are given in detail. Of two of these, for the number of tangents of a curve which meet it again, and for the number of triple points of the nodal curve, proofs by the theory of correspondence are extant; for the present purpose it is only necessary to have the sum of these two numbers. I do not know whether it has been remarked that there exists a remarkable formula for this sum, very similar to, and including the ordinary formula for the number of triple points of a general ruled surface (and like this probably capable of a direct proof by the theory of correspondence). For the genus of the nodal curve, deduced by Cayley from the Salmon-Cremona formulae, a proof by the theory of correspondence (in the general case, sufficient for the purpose in hand, in which i = τ = δ = δ′ = 0) is added here, which seems to have a certain interest.

Evaluation of Hypercholesterolemia in Childhood

1996 ◽  
Vol 17 (3) ◽  
pp. 94-97
Author(s):  
Thomas J. Starc ◽  
Richard J. Deckelbaum
Keyword(s):  
Risk Factors ◽  
At Risk ◽  
Heart Disease ◽  
Family History ◽  
Direct Proof ◽  
Children At Risk ◽  
History Of

For many adults, the risk of atherosclerosis can be reduced by intervention and treatment of known risk factors. Direct proof that similar intervention will be effective in children is not available. However, evidence suggests that prevention beginning in childhood will lead to a decrease in incidence of heart disease later in life. The majority of families are eager to take steps to prevent heart disease in their children, especially if there is a family history of early heart disease. It is the role of the pediatrician to identify those children at risk for early heart disease and to initiate advice on reducing risk factors.

scholarly journals The Hessian Fly and the Illinois Wheat Crop

1928 ◽  
Vol 17 (1-12) ◽  
pp. 363-385
Author(s):  
W. P. Flint ◽  
W. H. Larrimer
Keyword(s):  
Life History ◽  
Hessian Fly ◽  
Wheat Crop ◽  
Vast Amount ◽  
Present Purpose ◽  
History Of ◽  
Practical Recommendations

In order to fight the fly successfully, we had to learn just how it lives through the year, and justwhere it is to be found during each season. A vast amount of detailed information on these questions has been accumulated as a basis for practical recommendations, but a brief outline of the main facts in the life history of the insect will serve our present purpose and show why certain methods are here recommended.

A Summary of the Work on the Amphipod Gammarus Cheureuxi Sexton Carried out at the Plymouth Laboratory (1912–1936)

1936 ◽  
Vol 21 (1) ◽  
pp. 357-414 ◽  
Author(s):  
E. W. Sexton ◽  
A. R. Clark
Keyword(s):  
Direct Proof ◽  
Recessive Gene ◽  
Wide Distribution ◽  
The Body ◽  
Homogeneous Population ◽  
Laboratory Conditions ◽  
Recessive Genes ◽  
In The Wild ◽  
History Of ◽  
Series Of Experiments

The work began in June, 1912, simply as a study of the life-history of some of our common amphipods. The genus Gammarus was chosen, because of the number and the wide distribution of its species in the neighbourhood. Seven of these species, all black-eyed, from marine, estuarine, brackish and fresh waters, were kept in the laboratory for investigation until the first red-eyed specimens were discovered in one of the brackish species, later described as Gammarus chevreuxi (see p. 360). Since the manner in which these red-eyed individuals occurred raised points of considerable interest, it was decided to confine investigation to G. chevreuxi, and a series of experiments was started. The different variations involving both the structure and the pigmentation of the body and of the eyes appeared from time to time, some behaving as simple mendelian characters and attributable to the presence of a single recessive gene, others with a more problematical hereditary basis. These variations have been recorded as they occurred (see bibliography). For ten years, no second mutation appeared, although frequent dredgings were made and the animals thus obtained were kept for several generations in laboratory conditions. Because of this apparent stability of character the wild Gammarus was regarded as a homogeneous population until, in 1922, it became increasingly evident that the results showing in the laboratory cultures could only be explained on the supposition that many recessive factors must be present in the natural conditions.The evidence steadily accumulated, but direct proof was very difficult to obtain partly because (as we found in our experience with the cultures) the recessive types are often less viable than the normal, and therefore probably less able to withstand the competition in the wild, and partly perhaps because we had no criteria by which to assess the influence of the laboratory conditions (changes of temperature, food, salinity, pressure, etc.) on the constitution of the Gammarus, and so could not decide whether a variation was caused by the inherent action of the recessive genes, or by the untoward environment producing a change in the action of the normal genes.

scholarly journals Bridges: Their Historical and Literary Associations

1884 ◽  
Vol 1 (4) ◽  
pp. 364-375
Author(s):  
Cornelius Walford
Keyword(s):  
Historical Review ◽  
Present Purpose ◽  
History Of ◽  
The Subject

It will be seen by the above title that my present purpose is not to attempt a history of Bridges. That indeed would be an herculean task: for the materials lie scattered through the histories of nations, and no serious attempt has been made to bring them into a manageable compass. Still I assume it will be expected that I shall present such an historical review as may serve to make the subject intelligible to those who have not heretofore turned their attention to it.

Bentham on the Theory of Second Chambers

1928 ◽  
Vol 22 (3) ◽  
pp. 576-590 ◽  
Author(s):  
Lewis Rockow
Keyword(s):  
Political Science ◽  
Considerable Time ◽  
Political Ideas ◽  
Present Purpose ◽  
History Of ◽  
Almost All

When the problem of second chambers is discussed, we frequently find that interest is confined to the subsidiary question of technique, omitting the prior question, “Why have a second chamber?” It is in the main assumed that second chambers are universally valid, and therefore attention is centered on the varied methods of selection and the extent of functions. If the primary question is raised at all, it is invariably answered by an appeal to experience. It is claimed that almost all modern governments have for a considerable time had bicameral legislatures, and that it is hazardous to disregard a practice that is so nearly universal. Seldom is an attempt made to go beyond experience and to analyze critically this admittedly wide practice. In fact, a bicameral legislature is generally held to be an unassailable and eternal verity, one of the few axioms of political science.Nevertheless, among the more systematic writers on political science the validity of the bicameral theory is far from unanimously supported. Even a hasty reference to the history of political ideas shows recurrent dissent. Thus, during the period of democratic ferment inaugurated by the French and American revolutions we find unmistakable opposition. To mention some examples, Samuel Adams, Paine, Turgot, Sieyès, and Condorcet were in favor of the unicameral form. The basis of their hostility is well summarized in the famous dilemma of Sieyès. Sieyès has indeed indicated the broad outlines of the objections; and a succeeding century of bicameral experience shows how difficult it is to escape from his vexatious alternatives. To reconcile faith in democracy with the assumption of the value of an effective check is assuredly not an enviable task. At any rate, for our present purpose suffice it to say that bicameralism has frequently been rejected.

scholarly journals Bridging the gap between rectifying developables and tangent developables: a family of developable surfaces associated with a space curve

2021 ◽  
Vol 477 (2246) ◽  
pp. 20200617
Author(s):  
Brian Seguin ◽  
Yi-chao Chen ◽  
Eliot Fried
Keyword(s):  
Geodesic Curvature ◽  
Ruled Surface ◽  
Space Curve ◽  
Developable Surface ◽  
Absolute Value ◽  
Developable Surfaces ◽  
Alternative Construction ◽  
Tangent Developable ◽  
The Absolute

There are two familiar constructions of a developable surface from a space curve. The tangent developable is a ruled surface for which the rulings are tangent to the curve at each point and relative to this surface the absolute value of the geodesic curvature κ g of the curve equals the curvature κ . The alternative construction is the rectifying developable. The geodesic curvature of the curve relative to any such surface vanishes. We show that there is a family of developable surfaces that can be generated from a curve, one surface for each function k that is defined on the curve and satisfies | k | ≤  κ , and that the geodesic curvature of the curve relative to each such constructed surface satisfies κ g  =  k .

scholarly journals Logical and historical determination of the Arrow and Sen impossibility theorems

2007 ◽  
Vol 52 (172) ◽  
pp. 7-20 ◽  
Author(s):  
Branislav Boricic
Keyword(s):  
Social Choice ◽  
History Of Mathematics ◽  
Direct Proof ◽  
Mathematical Economics ◽  
General Classification ◽  
Logical Equivalence ◽  
History Of

General classification of mathematical statements divides them into universal, those of the form xA , and existential ?xA ones. Common formulations of impossibility theorems of K. J. Arrow and A. K. Sen are represented by the statements of the form "there is no x such that A". Bearing in mind logical equivalence of formulae ??xA and x?A, we come to the conclusion that the corpus of impossibility theorems, which appears in the theory of social choice, could make a specific and recognizable subclass of universal statements. In this paper, on the basis of the established logical and methodological criteria, we point to a sequence of extremely significant "impossibility theorems", reaching throughout the history of mathematics to the present days and the famous results of Arrow and Sen in field of mathematical economics. We close with specifying the context which makes it possible to formulate the results of Arrow and Sen accurately, presenting a new direct proof of Sen?s result, with no reliance on the notion of minimal liberalism. .

Planar threefolds in space of four dimensions

1933 ◽  
Vol 29 (1) ◽  
pp. 103-115
Author(s):  
W. G. Welchman
Keyword(s):  
Ruled Surface ◽  
Four Dimensions ◽  
Double Curve ◽  
Triple Points

1. It is known that, in [3], a ruled surface of order n and genus p has in general a double curve of order ½ (n − 1) (n − 2) − p and genus ½ (n − 5) (n + 2p − 2) + 1, 2(n + 2p − 2) torsal generators, 2(n − 2)(n − 3) − 2(n − 6)p generators which touch the double curve, and triple points.

scholarly journals Art. X.—Description of the Noble Sanctuary at Jerusalem in 1470 A.D., Kamâl (or Shams) ad Dîn as Suyûtî

1887 ◽  
Vol 19 (2) ◽  
pp. 247-305 ◽  
Author(s):  
Guy le Strange
Keyword(s):  
Great Britain ◽  
Point Of View ◽  
Present Purpose ◽  
Holy Places ◽  
Imperfect Knowledge ◽  
History Of ◽  
The Many ◽  
Vexed Question ◽  
The Temple

Among the many useful works that have appeared under the auspices of ‘The Oriental Translation Fund of Great Britain and Ireland,’ none is perhaps more palpably open to criticism than the Rev. J. Reynolds' History of the Temple of Jerusalem. To judge from the translation, Mr. Reynolds had, to begin with, but a very imperfect knowledge of Arabic, and, in the second place, from the extraordinary blunders he makes, he can have put himself to no pains whatever to become acquainted, by means of plans, and the descriptions of modern travellers, with the localities of which the Arab author speaks. It is not my present purpose to re-edit and correct Mr. Reynolds' work, for the book runs to some 550 pages, large 8vo., and it may safely be asserted that there is not a single one of his pages that would not require considerable alteration, to make it a tolerably exact rendering of his author's text. Moreover, the pages of the Royal Asiatic Society's Journal hardly afford room for so lengthy a work. I must therefore content myself with giving the headings of each of the seventeen chapters, and shall only translate such passages in the text as have seemed to me of most importance from an archæological or architectural point of view, and for throwing light on the vexed question of the sites of the Holy Places.

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