scholarly journals An Elementary Theorem on Gains from Virtual Trade

2020 ◽  
Author(s):  
Sugata Marjit ◽  
Lei Yang
Keyword(s):  
Elementary Theorem

scholarly journals II.—General Theorems on Determinants

1880 ◽  
Vol 29 (1) ◽  
pp. 47-54
Author(s):  
Thomas Muir
Keyword(s):  
The Other ◽  
Elementary Theorem ◽  
A Minor

The rows of a determinant of the nth order having been separated into two sets, one containing the first p rows and the other the rest, if each minor of the pth degree formed from the first set be multiplied by a minor, called its complementary, formed from the second set, and the result have its sign chosen in accordance with a certain law, it is well known as an elementary theorem that the aggregate of the products thus obtained is equal to the original determinant.

4. On Fermat's Theorem

1866 ◽  
Vol 5 ◽  
pp. 181-181
Author(s):  
Tait
Keyword(s):  
Elementary Processes ◽  
Prime Factors ◽  
Elementary Theorem

The author stated that in consequence of Legendre's work, the proof of Fermat's Theorem is reducible to showing the impossibility ofxm = ym+zm,when m is an odd prime, x, y, z being integers.Talbot has shown that in this case x, y, z are necessarily composite numbers.The author shows, among other results of very elementary processes, that if numbers can be found to satisfy the above equation, x and y leave the remainder 1 when divided by m; and that z has m as a factor. Many farther limitations are given on possible values of x, y, z—the process being based on the consideration of their prime factors, and on Fermat's Elementary Theorem Nm − N = Nm.

A theorem of M. L. Urquhart's and some consequences

2007 ◽  
Vol 91 (520) ◽  
pp. 39-50
Author(s):  
R. T. Leslie
Keyword(s):  
Euclidean Geometry ◽  
Straight Line ◽  
Elementary Theorem ◽  
Straight Lines

In an obituary of M. L. Urquhart in [1], David Elliott quotes him as claiming that Urquhart's theorem (below) is the most elementary theorem of Euclidean Geometry ‘since it involves only the concepts of straight line and distance’.Urquhart's theoremLet AC and AE be two straight lines.Let B be a point on AC, D a point on AE, and suppose that BE and CD intersect at F.If AB + BF = AD + DF then AC + CF = AE + EF. (1)

Integral Means and Zero Distributions of Blaschke Products

1972 ◽  
Vol 24 (5) ◽  
pp. 755-760 ◽  
Author(s):  
C. N. Linden
Keyword(s):  
Half Plane ◽  
Blaschke Product ◽  
Blaschke Products ◽  
Integral Means ◽  
Elementary Theorem ◽  
Image Position ◽  
Analogous Theorem

A sequence {zn} in D = {z: |z| < 1} is a Blaschke sequence if and only ifIf 0 appears m times in {zn} thenis the Blaschke product defined by {zn}. The set of all Blaschke products will be denoted by . If B ∊ it is well-known that B is regular in D, and |B(z, {zn})| < 1 when z ∊ D.For a given pair of values p in (0, ∞) and q in [0, ∞) we denote by ℐ(p, g) the class of all Blaschke products B(z, {zn}) such thatas r → 1 — 0. In the case q ≦ max(p — 1,0) the classes of functions B and ℐ(p, q) are identical: this is a particular case of an elementary theorem for functions subharmonic in a disc, the analogous theorem for functions subharmonic in a half-plane appearing in [1],

An Extension of an Elementary Theorem in Calculus

1969 ◽  
Vol 42 (5) ◽  
pp. 266-266
Author(s):  
Kennard W. Reed
Keyword(s):  
Elementary Theorem

59.17 An Elementary Theorem for Simple Polygons

1975 ◽  
Vol 59 (410) ◽  
pp. 266 ◽  
Author(s):  
A. S. Jones
Keyword(s):  
Simple Polygons ◽  
Elementary Theorem

scholarly journals Odd and Even Permutations

1960 ◽  
Vol 3 (2) ◽  
pp. 185-186 ◽  
Author(s):  
Israel Halperin
Keyword(s):  
Trans Position ◽  
Elementary Theorem

This note gives a proof for the familiar elementary theorem that if a permutation of the integers 1, …, n (with n ≥ 2) is expressed as a product π1 of N1 transpositions and also as a product π2 of N2 transpositions, then N1 and N2 are both even or both odd (equivalently: N1 + N2 is even).Here, a transposition means an interchange of two of the integers. If the interchange is between adjacent integers it is called an adjacent-trans position.

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