{"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}
{"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}
{"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}
{"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}
{"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}
{"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}
{"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}
{"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}
{"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}
{"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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