Pub Date : 1959-11-01DOI: 10.1017/S0950184300003207
G. N. Watson
Various improvements in the formula which was discovered by Wallis in 1669, were studied by D. K. Kazarinoff in No. 40 of these Notes (December 1956).
{"title":"A Note on Gamma Functions","authors":"G. N. Watson","doi":"10.1017/S0950184300003207","DOIUrl":"https://doi.org/10.1017/S0950184300003207","url":null,"abstract":"Various improvements in the formula which was discovered by Wallis in 1669, were studied by D. K. Kazarinoff in No. 40 of these Notes (December 1956).","PeriodicalId":417997,"journal":{"name":"Edinburgh Mathematical Notes","volume":"79 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1959-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122178263","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 : 1959-11-01DOI: 10.1017/S0950184300003189
L. Chambers
The use of the complex variable z ( = x + iy ) and the complex potential W (= U + iV ) for two-dimensional electrostatic systems is well known and the actual system in the ( x , y ) plane has an image system in the ( U , V ) plane. It does not seem to have been noticed previously that the electrostatic energy per unit length of the actual system is simply related to the area of the image domain in the ( U , V ) plane.
对于二维静电系统，复变量z (= x + iy)和复势W (= U + iV)的使用是众所周知的，(x, y)平面上的实际系统在(U, V)平面上有一个像系统。以前似乎没有注意到，实际系统的单位长度的静电能量仅仅与(U, V)平面的像域面积有关。
{"title":"The Electrostatic Energy of a Two-Dimensional System","authors":"L. Chambers","doi":"10.1017/S0950184300003189","DOIUrl":"https://doi.org/10.1017/S0950184300003189","url":null,"abstract":"The use of the complex variable z ( = x + iy ) and the complex potential W (= U + iV ) for two-dimensional electrostatic systems is well known and the actual system in the ( x , y ) plane has an image system in the ( U , V ) plane. It does not seem to have been noticed previously that the electrostatic energy per unit length of the actual system is simply related to the area of the image domain in the ( U , V ) plane.","PeriodicalId":417997,"journal":{"name":"Edinburgh Mathematical Notes","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1959-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127448856","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 : 1959-11-01DOI: 10.1017/S0950184300003219
N. Y. Wilson
A THEOREM ON POWER SUMS 161 We summarize these results in the following. Theorem. The solutions of (2) are as follows. If p = q, f(x) is a r b i-trary and g(x) = f(x). If p ^ q, the only monic solutions occur when p = 2 and q = 1, in which case f(x) and g(x) are defined by (12), where a is an arbitrary real constant Non-monic solutions for that case can be found using (13). As an example of these results suppose that p = 3 and q = 4. By (14) and (17) we have 13 (n , 4 (3x 2-3x + 1) J , (n = 1, 2, 3, • • •) x=l 1 x=l ' (4X 3-6x 2 + 4x-1) There are infinite many numbers with the property: if units digit of a positive integer, M, is 6 and this is taken from its place and put on the left of the remaining digits of M, then a new integer, N, will be formed, such that N = 6M. The smallest M for which this is possible is a number with 58 digits (1016949 • • • 677966). 1-4x-x 2 n=o with x = 0,1 we have 1,01016949 * • • 677966, where the period number (behind the first zero) is M.*
幂和的一个定理我们将这些结果总结如下。定理。式(2)的解如下:如果p = q, f(x)是ar b i- triv, g(x) = f(x)。如果p ^ q，在p = 2和q = 1时出现唯一的单元解，此时f(x)和g(x)由式(12)定义，其中a是任意实常数，这种情况的非单元解可以用式(13)找到。作为这些结果的一个例子，假设p = 3和q = 4。(14)和(17)我们有13 (n, 4(好几次3 x + 1) J (n = 1, 2, 3,•••)x = x = l l 1 “ (4 x 3-6x 2 + 4 x - 1)有无限多的数字财产:如果个位数的一个正整数,M,是6,这是来自它的位置,把剩下的数字的左边,然后一个新的整数,n,将形成,n = 6米。可能的最小M是58位数字(1016949•••677966)。1-4x-x 2 n= 0, x = 0,1，我们得到1,01016949 *••677966，其中周期数(在第一个零后面)是m *
{"title":"A Number Problem","authors":"N. Y. Wilson","doi":"10.1017/S0950184300003219","DOIUrl":"https://doi.org/10.1017/S0950184300003219","url":null,"abstract":"A THEOREM ON POWER SUMS 161 We summarize these results in the following. Theorem. The solutions of (2) are as follows. If p = q, f(x) is a r b i-trary and g(x) = f(x). If p ^ q, the only monic solutions occur when p = 2 and q = 1, in which case f(x) and g(x) are defined by (12), where a is an arbitrary real constant Non-monic solutions for that case can be found using (13). As an example of these results suppose that p = 3 and q = 4. By (14) and (17) we have 13 (n , 4 (3x 2-3x + 1) J , (n = 1, 2, 3, • • •) x=l 1 x=l ' (4X 3-6x 2 + 4x-1) There are infinite many numbers with the property: if units digit of a positive integer, M, is 6 and this is taken from its place and put on the left of the remaining digits of M, then a new integer, N, will be formed, such that N = 6M. The smallest M for which this is possible is a number with 58 digits (1016949 • • • 677966). 1-4x-x 2 n=o with x = 0,1 we have 1,01016949 * • • 677966, where the period number (behind the first zero) is M.*","PeriodicalId":417997,"journal":{"name":"Edinburgh Mathematical Notes","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1959-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117230114","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 : 1910-04-01DOI: 10.1017/S1757748900000591
R. Muirhead
Professor Chrystal remarks (Algebra, Chap. VII. §4) that “for tntative processes no general rule can be given.” The tentative processes consist in arranging the terms in groups in such a way as either to manifest a factor common to these groups or aggregates of terms, or to bring the expression under one of the Standard Forms of which the factors are already known, such as a 2 - b 2 , a 3 - b 3 , a 3 + b 3 .
{"title":"A Rule for Resolving Integral Algebraic Expressions into Factors","authors":"R. Muirhead","doi":"10.1017/S1757748900000591","DOIUrl":"https://doi.org/10.1017/S1757748900000591","url":null,"abstract":"Professor Chrystal remarks (Algebra, Chap. VII. §4) that “for tntative processes no general rule can be given.” The tentative processes consist in arranging the terms in groups in such a way as either to manifest a factor common to these groups or aggregates of terms, or to bring the expression under one of the Standard Forms of which the factors are already known, such as a 2 - b 2 , a 3 - b 3 , a 3 + b 3 .","PeriodicalId":417997,"journal":{"name":"Edinburgh Mathematical Notes","volume":"172 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1910-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121034432","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/S095018430000029X
D. K. Kazarinoff
In the course of mathematical progress new truths are discovered while older ones are sometimes more precisely articulated and often generalised. Because of their elegance and simplicity, however, some classical statements have been left unchanged. As an example, I have in mind the celebrated formula of John Wallis, which for more than a century has been quoted by writers of textbooks. Usually this formula is written as In this note it is shown that ¼
{"title":"On Wallis' formula","authors":"D. K. Kazarinoff","doi":"10.1017/S095018430000029X","DOIUrl":"https://doi.org/10.1017/S095018430000029X","url":null,"abstract":"In the course of mathematical progress new truths are discovered while older ones are sometimes more precisely articulated and often generalised. Because of their elegance and simplicity, however, some classical statements have been left unchanged. As an example, I have in mind the celebrated formula of John Wallis, which for more than a century has been quoted by writers of textbooks. Usually this formula is written as In this note it is shown that ¼","PeriodicalId":417997,"journal":{"name":"Edinburgh Mathematical Notes","volume":"49 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":"122773895","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/S0950184300003062
E. Primrose
{"title":"A property of quartic curves with two cusps and one node","authors":"E. Primrose","doi":"10.1017/S0950184300003062","DOIUrl":"https://doi.org/10.1017/S0950184300003062","url":null,"abstract":"","PeriodicalId":417997,"journal":{"name":"Edinburgh Mathematical Notes","volume":"75 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":"114853138","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/S095018430000269X
H. W. Turnbull
y1 = 0, y2 is negative o r 2/i = 2/2 = 2/3 = 0, 2/4 is negative o r 2/1=2/2 = 2/3 = 2/4 = 2/5 = °. Vo is negative, etc. Further the relation between the sign of dy/dx and the concavity of an arc is often obscurely presented. Take an x or time axis horizontally and a y axis vertically and consider an arc AB everywhere concave down. Let C be a point on the arc such that AC and CB have equal horizontal projections, and let their vertical projections be ac and cb. Then algebraically we have from a figure ac > cb, that is, heights gained in equal successive times are diminishing and therefore there is a retardation and d'-y/dx is negative. And we similarly associate concavity upwards with positive values of* d-y/dx.
{"title":"On certain modular determinants","authors":"H. W. Turnbull","doi":"10.1017/S095018430000269X","DOIUrl":"https://doi.org/10.1017/S095018430000269X","url":null,"abstract":"y1 = 0, y2 is negative o r 2/i = 2/2 = 2/3 = 0, 2/4 is negative o r 2/1=2/2 = 2/3 = 2/4 = 2/5 = °. Vo is negative, etc. Further the relation between the sign of dy/dx and the concavity of an arc is often obscurely presented. Take an x or time axis horizontally and a y axis vertically and consider an arc AB everywhere concave down. Let C be a point on the arc such that AC and CB have equal horizontal projections, and let their vertical projections be ac and cb. Then algebraically we have from a figure ac > cb, that is, heights gained in equal successive times are diminishing and therefore there is a retardation and d'-y/dx is negative. And we similarly associate concavity upwards with positive values of* d-y/dx.","PeriodicalId":417997,"journal":{"name":"Edinburgh Mathematical Notes","volume":"116 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":"132243525","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：