scholarly journals XX. On the theory of the elliptic transcendents

1831 ◽  
Vol 121 ◽  
pp. 349-377 ◽  
Keyword(s):  
Algebraic Equation ◽  
Elliptic Function ◽  
Elliptic Integral ◽  
Elliptic Functions ◽  
The Other ◽  
Algebraic Equations ◽  
Integral Calculus ◽  
Circular Arc ◽  
Regular Theory ◽  
The Difference

The branch of the integral calculus which treats of elliptic transcendents originated in the researches of Fagnani, an Italian geometer of eminence. He discovered that two arcs of the periphery of a given ellipse may be determined in many ways, so that their difference shall be equal to an assignable straight line; and he proved that any arc of the lemniscata, like that of a circle, may be multiplied any number of times, or may be subdivided into any number of equal parts, by finite algebraic equations. These are particular results; and it was the discoveries of Euler that enabled geometers to advance to the investigation of the general properties of the elliptic functions. An integral in finite terms deduced by that geometer from an equation between the differentials of two similar transcendent quantities not separately integrable, led immediately to an algebraic equation between the amplitudes of three elliptic functions, of which one is the sum, or the difference, of the other two. This sort of integrals, therefore, could now be added or subtracted in a manner analogous to circular arcs, or logarithms; the amplitude of the sum, or of the difference, being expressed algebraically by means of the amplitudes of the quantities added or subtracted. What Fagnani had accomplished with respect to the arcs of the lemniscata, which are expressed by a particular elliptic integral, Euler extended to all transcendents of the same class. To multiply a function of this kind, or to subdivide it into equal parts, was reduced to solving an algebraic equation. In general, all the properties of the elliptic transcendents, in which the modulus remains unchanged, are deducible from the discoveries of Euler. Landen enlarged our knowledge of this kind of functions, and made a useful addition to analysis, by showing that the arcs of the hyperbola may be reduced, by a proper transformation, to those of the ellipse. Every part of analysis is indebted to Lagrange, who enriched this particular branch with a general method for changing an elliptic function into another having a different modulus, a process which greatly facilitates the numerical calculation of this class of integrals. An elliptic function lies between an arc of the circle on one hand, and a logarithm on the other, approaching indefinitely to the first when the modulus is diminished to zero, and to the second when the modulus is augmented to unit, its other limit. By repeatedly applying the transformation of Lagrange, we may compute either a scale of decreasing moduli reducing the integral to a circular arc, or a scale of increasing moduli bringing it continually nearer to a logarithm. The approximation is very elegant and simple, and attains the end proposed with great rapidity. The discoveries that have been mentioned occurred in the general cultivation of analysis; but Legendre has bestowed much of his attention and study upon this particular branch of the integral calculus. He distributed the elliptic functions in distinct classes, and reduced them to a regular theory. In a Mémoire sur les Transcendantes Elliptiques, published in 1793, and in his Exercices de Calcul Intégral, which appeared in 1817 he has developed many of their properties entirely new; investigated the easiest methods of approximating to their values; computed numerical tables to facilitate their application; and exemplified their use in some interesting problems of geometry and mechanics. In a publication so late as 1825, the author, returning to the same subject, has rendered his theory still more perfect, and made many additions to it which further researches had suggested. In particular we find a new method of making an elliptic function approach as near as we please to a circular arc, or to a logarithm, by a scale of reduction very different from that of which Lagrange is the author, the only one before known. This step in advance would unavoidably have conducted to a more extensive theory of this kind of integrals, which, nearly about the same time, was being discovered by the researches of other geometers.

scholarly journals On the theory of the elliptic transcendents

1837 ◽  
Vol 3 ◽  
pp. 60-60
Keyword(s):  
Elliptic Function ◽  
Elliptic Integral ◽  
Elliptic Functions ◽  
Algebraic Expression ◽  
Algebraic Equations ◽  
Similar Function ◽  
Circular Arcs ◽  
Straight Line ◽  
Regular Theory ◽  
General Method

Fagnani discovered that the two arcs of the periphery of a given ellipse may be determined in many ways, so that their difference shall be equal to an assignable straight line; and proved that any arc of a lemniscate, like that of a circle, may be multiplified any number of times, or may be subdivided into any number of equal parts, by finite algebraic equations. What he had accomplished with respect to the arcs of the lemniscates, which are expressed by a particular elliptic integral, Euler extended to all transcendents of the same class. Landen showed that the arcs of the hyperbola may be reduced, by a proper transformation, to those of an ellipse. Lagrange furnished us with a general method for changing an elliptic function into another having a different modulus; a process which greatly facilitates the numerical calculation of this class of integrals. Legendre distributed the elliptic functions into distinct classes, and reduced them to a regular theory, developing many of their properties which were before unknown, and introducing many important additions and improvements in the theory. Mr. Abel of Christiana happity conceived the idea of expressing the amplitude of an elliptic function in terms of the function itself, which led to the discovery of many new and useful properties. Mr. Jacobi proved, by a different method, that an elliptic function may be transformed in innumerable ways into another similar function, to which it bears constantly the same proportion. But his demonstrations require long and complicated calculations; and the train of deductions he pursues does not lead naturally to the truths which are proved, nor does it present in a connected view all the conclusions which the theory embraces. The author of the present paper gives a comprehensive view of the theory in its full extent, and deduces all the connected truths from the same principle. He finds that the sines or cosines of the amplitudes, used in the transformations, are analogous to the sines or cosines of two circular arcs, one of which is a multiple of the other; so that the former quantities are changed into the latter when the modulus is supposed to vanish in the algebraic expression. Hence he is enabled to transfer to the elliptic transcendents the same methods of investigation that succeed in the circle: a procedure which renders the demonstrations considerably shorter, and which removes most of the difficulties, in consequence of the close analogy that subsists between the two cases.

scholarly journals VII.—On the Motion of a Heavy Body along the Circumference of a Circle

1865 ◽  
Vol 24 (1) ◽  
pp. 59-71
Author(s):  
Edward Sang
Keyword(s):  
Royal Society ◽  
Elliptic Functions ◽  
The Other ◽  
Philosophical Magazine ◽  
Circular Arc ◽  
Heavy Body ◽  
Great Ease ◽  
Fourth Volume ◽  
The Common ◽  
The One

In the year 1861 I laid before the Royal Society of Edinburgh a theorem concerning the time of descent in a circular arc, by help of which that time can be computed with great ease and rapidity. A concise statement of it is printed in the fourth volume of the Society's Proceedings at page 419.The theorem in question was arrived at by the comparison of two formulæ, the one being the common series and the other an expression given in the “Edinburgh Philosophical Magazine” for November 1828, by a writer under the signature J. W. L. Each of these series is reached by a long train of transformations, developments, and integrations, which require great familiarity with the most advanced branches of the infinitesimal calculus; yet the theorem which results from their comparison has an aspect of extreme simplicity, and seems as if surely it might be attained to by a much shorter and less rugged road. For that reason I did not, at the time, give an account of the manner in which it was arrived at, intending to seek out a better proof. On comparing it with what is known in the theory of elliptic functions, its resemblance to the beautiful theorem of Halle became obvious; but then the coefficients in Halle's formulæ are necessarily less than unit, whereas for this theorem they are required to be greater than unit.

Enhancement of ADP-induced Platelet Aggregation by Adrenaline in Vivo and Its Prevention

1973 ◽  
Vol 29 (02) ◽  
pp. 490-498 ◽  
Author(s):  
Hiroh Yamazaki ◽  
Itsuro Kobayashi ◽  
Tadahiro Sano ◽  
Takio Shimamoto
Keyword(s):  
Platelet Count ◽  
Platelet Aggregation ◽  
Platelet Rich Plasma ◽  
The Other ◽  
Endothelial Surface ◽  
Important Interaction ◽  
Blood Coagulability ◽  
The Difference

SummaryThe authors previously reported a transient decrease in adhesive platelet count and an enhancement of blood coagulability after administration of a small amount of adrenaline (0.1-1 µg per Kg, i. v.) in man and rabbit. In such circumstances, the sensitivity of platelets to aggregation induced by ADP was studied by an optical density method. Five minutes after i. v. injection of 1 µg per Kg of adrenaline in 10 rabbits, intensity of platelet aggregation increased to 115.1 ± 4.9% (mean ± S. E.) by 10∼5 molar, 121.8 ± 7.8% by 3 × 10-6 molar and 129.4 ± 12.8% of the value before the injection by 10”6 molar ADP. The difference was statistically significant (P<0.01-0.05). The above change was not observed in each group of rabbits injected with saline, 1 µg per Kg of 1-noradrenaline or 0.1 and 10 µg per Kg of adrenaline. Also, it was prevented by oral administration of 10 mg per Kg of phenoxybenzamine or propranolol or aspirin or pyridinolcarbamate 3 hours before the challenge. On the other hand, the enhancement of ADP-induced platelet aggregation was not observed in vitro, when 10-5 or 3 × 10-6 molar and 129.4 ± 12.8% of the value before 10∼6 molar ADP was added to citrated platelet rich plasma (CPRP) of rabbit after incubation at 37°C for 30 second with 0.01, 0.1, 1, 10 or 100 µg per ml of adrenaline or noradrenaline. These results suggest an important interaction between endothelial surface and platelets in connection with the enhancement of ADP-induced platelet aggregation by adrenaline in vivo.

Energy Approximation

2017 ◽  
Author(s):  
Philip Isett
Keyword(s):  
Main Lemma ◽  
The Other ◽  
Coarse Scale ◽  
Continuous Solutions ◽  
Material Derivative ◽  
Energy Variation ◽  
Energy Approximation ◽  
The Difference ◽  
Derivatives Of

This chapter presents the equations and calculations for energy approximation. It establishes the estimates (261) and (262) of the Main Lemma (10.1) for continuous solutions; these estimates state that we are able to accurately prescribe the energy that the correction adds to the solution, as well as bound the difference between the time derivatives of these two quantities. The chapter also introduces the proposition for prescribing energy, followed by the relevant computations. Each integral contributing to the other term can be estimated. Another proposition for estimating control over the rate of energy variation is given. Finally, the coarse scale material derivative is considered.

Pengaruh Unsur Budaya Lokal dalam Ungkapan Berbahasa Perancis

Metahumaniora ◽  
2017 ◽  
Vol 7 (3) ◽  
pp. 378
Author(s):  
Vincentia Tri Handayani
Keyword(s):  
Mental Representation ◽  
Cultural Context ◽  
Oral Tradition ◽  
Minimal Element ◽  
The Other ◽  
Local Culture ◽  
Community Groups ◽  
Cultural Community ◽  
The Difference ◽  
Complex Words

AbstrakFolklor yang menghasilkan tradisi lisan merupakan perwujudan budaya yang lahirdari pengalaman kelompok masyarakat. Salah satu bentuk tradisi lisan adalah ungkapan yangmengandung unsur budaya lokal dalam konstruksinya yang tidak dimiliki budaya lainnya.Ungkapan idiomatis memberikan warna pada bahasa melalui penggambaran mental. Dalambahasa Perancis, ungkapan dapat berupa locution dan expression. Perbedaan motif acuansuatu ungkapan dapat terlihat dari pengaruh budaya masyarakat pengguna bahasa. Sebuahleksem tidak selalu didefinisikan melalui unsur minimal, tidak juga melalui kata-kata,baik kata dasar atau kata kompleks, namun dapat melalui kata-kata beku yang maknanyatetap. Hubungan analogis dari makna tambahan yang ada pada suatu leksem muncul dariidentifikasi semem yang sama. Semem tersebut mengarah pada term yang diasosiasikan danyang diperkaya melalui konteks (dalam ungkapan berhubungan dengan konteks budaya).Kata kunci: folklor, ungkapan, struktur, makna idiomatis, kebudayaanAbstractFolklore which produces the oral tradition is a cultural manifestation born out theexperience of community groups. One form of the oral tradition is a phrase that containsthe elements of local culture in its construction that is not owned the other culture. Theidiomatic phrase gives the color to the language through the mental representation. InFrench, the expression can consist of locution and expression. The difference motivesreference of an expression can be seen from the influence of the cultural community thelanguage users. A lexeme is not always defined through a minimal element, nor throughwords, either basic or complex words, but can be through the frost words whose meaningsare fixed. The analogical connection of the additional meanings is on a lexeme arises fromthe identification of the same meaning. The meaning ‘semem’ leads to the associated termsand which are enriched through the context (in idiom related to the cultural context).Keywords : folklore, idioms, structure, idiom meaning, cultureI PENDAHULUAN

Rhetoric and argumentation: the unity of the field

2017 ◽  
Author(s):  
Michel Meyer
Keyword(s):  
The Other ◽  
Classic Problem ◽  
False Dilemma ◽  
The Difference ◽  
As If

Rhetoric has always been torn between the rhetoric of figures and the rhetoric of conflicts or arguments, as if rhetoric were exclusively one or the other. This is a false dilemma. Both types of rhetoric hinge on the same structure. A common formula is provided in Chapter 3 which unifies rhetoric stricto sensu and rhetoric as argumentation as two distinct but related strategies adopted according to the level of problematicity of the questions at stake, thereby giving unity to the field called “Rhetoric.” Highly problematic questions require arguments to justify their answers; non-divisive ones can be treated rhetorically through their answers as if they were self-evident. Another classic problem is how to understand the difference between logic and rhetoric. The difference between the two is due to the presence of questions explicitly answered in the premises in logic and only suggested (or remaining indeterminate) in rhetoric.

scholarly journals The Respiration of some Planktonic copepods II. The Effect Of Temperature

1953 ◽  
Vol 31 (3) ◽  
pp. 447-460 ◽  
Author(s):  
D. T. Gauld ◽  
J. E. G. Raymont
Keyword(s):  
Respiratory Rate ◽  
The Body ◽  
The Other ◽  
Effect Of Temperature ◽  
Acartia Clausi ◽  
Temora Longicornis ◽  
Different Temperatures ◽  
Planktonic Copepods ◽  
The Difference ◽  
The Relationship

The respiratory rates of three species of planktonic copepods, Acartia clausi, Centropages hamatus and Temora longicornis, were measured at four different temperatures.The relationship between respiratory rate and temperature was found to be similar to that previously found for Calanus, although the slope of the curves differed in the different species.The observations on Centropages at 13 and 170 C. can be divided into two groups and it is suggested that the differences are due to the use of copepods from two different generations.The relationship between the respiratory rates and lengths of Acartia and Centropages agreed very well with that previously found for other species. That for Temora was rather different: the difference is probably due to the distinct difference in the shape of the body of Temora from those of the other species.The application of these measurements to estimates of the food requirements of the copepods is discussed.

scholarly journals Investigating the properties of a galaxy group at z = 0.6

2020 ◽  
Vol 15 (S359) ◽  
pp. 188-189
Author(s):  
Daniela Hiromi Okido ◽  
Cristina Furlanetto ◽  
Marina Trevisan ◽  
Mônica Tergolina
Keyword(s):  
Large Scale ◽  
The Other ◽  
Numerical Density ◽  
Spectroscopy Data ◽  
Stellar Kinematics ◽  
Galaxy Groups ◽  
The Galaxy ◽  
The Difference ◽  
The Impact ◽  
The Universe

AbstractGalaxy groups offer an important perspective on how the large-scale structure of the Universe has formed and evolved, being great laboratories to study the impact of the environment on the evolution of galaxies. We aim to investigate the properties of a galaxy group that is gravitationally lensing HELMS18, a submillimeter galaxy at z = 2.39. We obtained multi-object spectroscopy data using Gemini-GMOS to investigate the stellar kinematics of the central galaxies, determine its members and obtain the mass, radius and the numerical density profile of this group. Our final goal is to build a complete description of this galaxy group. In this work we present an analysis of its two central galaxies: one is an active galaxy with z = 0.59852 ± 0.00007, while the other is a passive galaxy with z = 0.6027 ± 0.0002. Furthermore, the difference between the redshifts obtained using emission and absorption lines indicates an outflow of gas with velocity v = 278.0 ± 34.3 km/s relative to the galaxy.

scholarly journals Characterization of Salmonella serotypes prevalent in asymptomatic people and patients

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Haiyan Xu ◽  
Weibing Zhang ◽  
Kai Zhang ◽  
Yue Zhang ◽  
Zhenyu Wang ◽  
...  
Keyword(s):  
Antimicrobial Resistance ◽  
Asymptomatic Infection ◽  
Resistance Rate ◽  
Human Infection ◽  
The Other ◽  
Resistance Testing ◽  
Multi Drug Resistance ◽  
Discriminative Ability ◽  
Source Of Infection ◽  
The Difference

Abstract Background Infection with Salmonella enterica usually results in diarrhea, fever, and abdominal cramps, but some people become asymptomatic or chronic carrier as a source of infection for others. This study aimed to analyze the difference in serotype, antimicrobial resistance, and genetic profiles between Salmonella strains isolated from patients and those from asymptomatic people in Nantong city, China. Methods A total of 88 Salmonella strains were collected from patients and asymptomatic people from 2017 to 2018. Serotyping, antimicrobial susceptibility testing, and PFGE analysis were performed to analyze the characteristics of these strains. Results Twenty serotypes belonging to 8 serogroups were identified in the 88 Salmonella strains. S. Typhimurium remained to be the predominant serotype in strains from both patients and asymptomatic people. Among the 27 strains from patients, S. Enteritidis and S. Rissen were shown as the other two major serotypes, while S. London, S. Derby, and S. Meleagridis were demonstrated as the other significant serotypes among the 61 strains from asymptomatic people. Antimicrobial resistance testing revealed that 84.1% of strains from both resources were multi-drug resistant. PFGE displayed a highly discriminative ability to differentiate strains belonging to S. Derby, S. Typhimurium, etc., but could not efficiently differentiate serotypes like S. Enteritidis. Conclusions This study’s results demonstrated that S. Typhimurium could cause human infection in both symptomatic and asymptomatic state; S. London, S. Derby, and S. Meleagridis usually cause asymptomatic infection, while S. Enteritidis infection mainly results in human diseases. The high multi-drug resistance rate detected in the antimicrobial resistance and diverse PFGE profiles of these strains implied that the strains were isolated from different sources, and the increased surveillance of Salmonella from both patients and asymptomatic people should be taken to control the disease.

scholarly journals Frequency–Amplitude Relationship of a Nonlinear Symmetric Panel Absorber Mounted on a Flexible Wall

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1188
Author(s):  
Yiu-Yin Lee
Keyword(s):  
Elliptic Integral ◽  
Algebraic Equations ◽  
Cavity Depth ◽  
Nonlinear Algebraic Equations ◽  
Flexible Panel ◽  
Flexible Wall ◽  
Elliptic Integral Method ◽  
Flexible Panels ◽  
Relationship Of ◽  
Panel Absorber

This study addresses the frequency–amplitude relationship of a nonlinear symmetric panel absorber mounted on a flexible wall. In many structural–acoustic works, only one flexible panel is considered in their models with symmetric configuration. There are very limited research investigations that focus on two flexible panels coupled with a cavity, particularly for nonlinear structural–acoustic problems. In practice, panel absorbers with symmetric configurations are common and usually mounted on a flexible wall. Thus, it should not be assumed that the wall is rigid. This study is the first work employing the weighted residual elliptic integral method for solving this problem, which involves the nonlinear multi-mode governing equations of two flexible panels coupled with a cavity. The reason for adopting the proposed solution method is that fewer nonlinear algebraic equations are generated. The results obtained from the proposed method and finite element method agree reasonably well with each other. The effects of some parameters such as vibration amplitude, cavity depth and thickness ratio, etc. are also investigated.

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