Pub Date : 1900-01-01DOI: 10.1017/S0950184300002846
A. C. Aitken
{"title":"A note on the “probleme des rencontres.”","authors":"A. C. Aitken","doi":"10.1017/S0950184300002846","DOIUrl":"https://doi.org/10.1017/S0950184300002846","url":null,"abstract":"","PeriodicalId":417997,"journal":{"name":"Edinburgh Mathematical Notes","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122079406","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.1017/S0950184300000240
G. N. Watson
The problem which I enunciate and solve in this paper seems to have originated in the study of properties of polyhedral functions. It is a problem of elementary analytical geometry of three dimensions, and the solution which I give, though somewhat tedious, is both elementary and direct. There are several comments which I have to make about current solutions, but I reserve these until the end of the paper since they will be more easily appreciated when it is possible to compare the current solutions with my solution.
{"title":"A bilinear transformation","authors":"G. N. Watson","doi":"10.1017/S0950184300000240","DOIUrl":"https://doi.org/10.1017/S0950184300000240","url":null,"abstract":"The problem which I enunciate and solve in this paper seems to have originated in the study of properties of polyhedral functions. It is a problem of elementary analytical geometry of three dimensions, and the solution which I give, though somewhat tedious, is both elementary and direct. There are several comments which I have to make about current solutions, but I reserve these until the end of the paper since they will be more easily appreciated when it is possible to compare the current solutions with my solution.","PeriodicalId":417997,"journal":{"name":"Edinburgh Mathematical Notes","volume":"146 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122134592","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.1017/S0950184300000033
A. Walker
Intermediaire des Mathematicians, 1894, pp. 70, 149 ; 1895, pp. 101, 169. Mathesis, 1895, p. 261 ; 1900, pp. 129 ff (Emmerich) ; 1901, p. 24 ; 1902, p. 43 ; 1902, pp. 112, 114 (Delahaye); 1925, pp. 316 ff. Bulletin des Sciences Math, et Phys. Elementaires, 1903-4, IX. p. 146; 1907-8, XII. p. 22 (Fontene). Neuberg, Bibliographic des Triangl-s Speciau.r, pp. 9 11. Crelle's Journal (Steiner), 1844, and Philosophical Magazine (J. J. Sylvester), 1853.
Intermediaire des Mathematicians》，1894 年，第 70、149 页；1895 年，第 101、169 页。Mathesis》，1895 年，第 261 页；1900 年，第 129 页及以下（Emmerich）；1901 年，第 24 页；1902 年，第 43 页；1902 年，第 112、114 页（Delahaye）；1925 年，第 316 页及以下。Bulletin des Sciences Math, et Phys. Elementaires, 1903-4, IX. p. 146; 1907-8, XII. p. 22 (Fontene).Neuberg, Bibliographic des Triangl-s Speciau.r, pp.Crelle's Journal (Steiner), 1844 年和 Philosophical Magazine (J. J. Sylvester), 1853 年。
{"title":"The inextensible string","authors":"A. Walker","doi":"10.1017/S0950184300000033","DOIUrl":"https://doi.org/10.1017/S0950184300000033","url":null,"abstract":"Intermediaire des Mathematicians, 1894, pp. 70, 149 ; 1895, pp. 101, 169. Mathesis, 1895, p. 261 ; 1900, pp. 129 ff (Emmerich) ; 1901, p. 24 ; 1902, p. 43 ; 1902, pp. 112, 114 (Delahaye); 1925, pp. 316 ff. Bulletin des Sciences Math, et Phys. Elementaires, 1903-4, IX. p. 146; 1907-8, XII. p. 22 (Fontene). Neuberg, Bibliographic des Triangl-s Speciau.r, pp. 9 11. Crelle's Journal (Steiner), 1844, and Philosophical Magazine (J. J. Sylvester), 1853.","PeriodicalId":417997,"journal":{"name":"Edinburgh Mathematical Notes","volume":"1400 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127440783","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.1017/S0950184300002871
C. Walsh
{"title":"Some series for π","authors":"C. Walsh","doi":"10.1017/S0950184300002871","DOIUrl":"https://doi.org/10.1017/S0950184300002871","url":null,"abstract":"","PeriodicalId":417997,"journal":{"name":"Edinburgh Mathematical Notes","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127788153","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.1017/S0950184300002639
A. Erdélyi, I. M. H. Etherington
The problems considered here are essentially algebraic; but it is convenient to begin with a picturesque formulation.
这里考虑的问题本质上是代数的;但从一个生动的表述开始是方便的。
{"title":"Some problems of non-associative combinations (2)","authors":"A. Erdélyi, I. M. H. Etherington","doi":"10.1017/S0950184300002639","DOIUrl":"https://doi.org/10.1017/S0950184300002639","url":null,"abstract":"The problems considered here are essentially algebraic; but it is convenient to begin with a picturesque formulation.","PeriodicalId":417997,"journal":{"name":"Edinburgh Mathematical Notes","volume":"93 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130853428","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.1017/S0950184300000318
R. A. Houstoun
{"title":"Horatio S. Carslaw","authors":"R. A. Houstoun","doi":"10.1017/S0950184300000318","DOIUrl":"https://doi.org/10.1017/S0950184300000318","url":null,"abstract":"","PeriodicalId":417997,"journal":{"name":"Edinburgh Mathematical Notes","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114077058","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.1017/S0950184300002603
S. Scott
Each share is 3a; — 2x — 5, the quantum being 3a;; each recipient of a quantum must return + 2a; + 5 to the fund-box. Out of the fund-box move 6a; pounds to A, and there distribute in 3a;-quanta to 2a; persons, who each return 2x + 5 and therefore a total of 4a; + 10a; to the box as shown. Next move 15a; out of the box to position B and there give.out in 3a; quanta to 5x persons who each return 2x + 5, that is, a total of 10x at C and 25a; at D. Next move out 27a; etc. until the fund is reduced to 45a; -f49 and further quantum distribution is impossible. The quotient is 2a; + 5a; + 9 people and the remainder 45a; + 49 pounds.
{"title":"Elementary methods in the theory of numbers","authors":"S. Scott","doi":"10.1017/S0950184300002603","DOIUrl":"https://doi.org/10.1017/S0950184300002603","url":null,"abstract":"Each share is 3a; — 2x — 5, the quantum being 3a;; each recipient of a quantum must return + 2a; + 5 to the fund-box. Out of the fund-box move 6a; pounds to A, and there distribute in 3a;-quanta to 2a; persons, who each return 2x + 5 and therefore a total of 4a; + 10a; to the box as shown. Next move 15a; out of the box to position B and there give.out in 3a; quanta to 5x persons who each return 2x + 5, that is, a total of 10x at C and 25a; at D. Next move out 27a; etc. until the fund is reduced to 45a; -f49 and further quantum distribution is impossible. The quotient is 2a; + 5a; + 9 people and the remainder 45a; + 49 pounds.","PeriodicalId":417997,"journal":{"name":"Edinburgh Mathematical Notes","volume":"65 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121898501","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.1017/S0950184300002949
A. Guinand
The object of this note is to give simpler proof* of two formulae involving the function ψ (z) which I have proved elsewhere by more complicated methods.
{"title":"A note on the logarithmic derivative of the gamma function","authors":"A. Guinand","doi":"10.1017/S0950184300002949","DOIUrl":"https://doi.org/10.1017/S0950184300002949","url":null,"abstract":"The object of this note is to give simpler proof* of two formulae involving the function ψ (z) which I have proved elsewhere by more complicated methods.","PeriodicalId":417997,"journal":{"name":"Edinburgh Mathematical Notes","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123579791","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.1017/S0950184300002706
C. Walsh
Let f(x) ≡ (1 – x) b + b a b-1 x o (x) ≡ x c – c Β c-1 x where b ≧ 1, c ≧ 1, 0 ≦ α ≦ 1, 0 ≦ β ≦ 1, and x is assumed to lie in the range (0, 1). By differentiation, or otherwise, it is easily shewn that f(x) and o ( x ) have minima when x = 1 – α and when x = β , respectively. Hence (1 – x) b + a b-1 x ≧ b a b-1 + (1 – b) a b x c β c-1 x ≧ (1 – c)β c .
让f (x)≡(1 - x) b + b b - 1 x o (x)≡x c - cΒ颈- 1 b≧1 x, c≧1,0≦α≦1 0≦β≦1,假设和x躺在(0,1)范围。通过分化,或否则,它很容易尚能f (x)和o (x)最小值时x = 1 -α和x =β,分别。因此(1 - x) b + a -1 x≧b a -1 + (1 - b) a b x c β c-1 x≧(1 - c)β c。
{"title":"Inequalities for Positive Series","authors":"C. Walsh","doi":"10.1017/S0950184300002706","DOIUrl":"https://doi.org/10.1017/S0950184300002706","url":null,"abstract":"Let f(x) ≡ (1 – x) b + b a b-1 x o (x) ≡ x c – c Β c-1 x where b ≧ 1, c ≧ 1, 0 ≦ α ≦ 1, 0 ≦ β ≦ 1, and x is assumed to lie in the range (0, 1). By differentiation, or otherwise, it is easily shewn that f(x) and o ( x ) have minima when x = 1 – α and when x = β , respectively. Hence (1 – x) b + a b-1 x ≧ b a b-1 + (1 – b) a b x c β c-1 x ≧ (1 – c)β c .","PeriodicalId":417997,"journal":{"name":"Edinburgh Mathematical Notes","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124667163","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.1017/S0950184300002573
D. Pedoe
In a recent paper, I showed how the properties of algebraic systems of circles in the (x, y) plane could be investigated by means of a representation in which to the circle x 2 + y 2 − 2 px − 2 qy + r = 0 there corresponds the point ( p, q, r ) in space of three dimensions. The plane of ( x, y ) may be considered to lie in the space ( x, y, z ), so that the centre of the mapped circle is the orthogonal projection of the representative point.
在最近的一篇论文中，我证明了在(x, y)平面上圆的代数系统的性质可以通过一个表示来研究，在这个表示中，圆x 2 + y 2−2 px−2 qy + r = 0对应于三维空间中的点(p, q, r)。(x, y)的平面可以认为位于空间(x, y, z)中，因此映射圆的中心是代表点的正交投影。
{"title":"Some properties of the paraboloid z = x 2 + y 2","authors":"D. Pedoe","doi":"10.1017/S0950184300002573","DOIUrl":"https://doi.org/10.1017/S0950184300002573","url":null,"abstract":"In a recent paper, I showed how the properties of algebraic systems of circles in the (x, y) plane could be investigated by means of a representation in which to the circle x 2 + y 2 − 2 px − 2 qy + r = 0 there corresponds the point ( p, q, r ) in space of three dimensions. The plane of ( x, y ) may be considered to lie in the space ( x, y, z ), so that the centre of the mapped circle is the orthogonal projection of the representative point.","PeriodicalId":417997,"journal":{"name":"Edinburgh Mathematical Notes","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125857716","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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