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Page 4171 of Mathematical Reviews Vol. , Issue 82j [page]

1982 Mathematical Reviews  
This paper presents the necessary and sufficient condiiions for an integer in R,, to be the sum of two squares of integers in R,,, for the following values of m: 5, 7, 8, 9, 10, 14, and 18.”  ...  There exist infinitely many real (respectively, imaginary) quadratic fields whose 2-rank is equal to a given nonnegative integer.  ... 

Real-valued and 2-rational group characters

R Gow
1979 Journal of Algebra  
of p can occur with multiplicity equal to twice an algebraic integer.  ...  Conversely, if B has a real-valued irreducible character x of height 0 and F-S invariant -~ I, x(h) + 0, since h belongs to a defect class for B. Theorem 4.3 shows that l!  ...  This number is the sum of half the number of weakly-real classes and the number of strongly-real classes, as required. ;2 similar result holds if G is '-nilpotent and its Sylow 2-subgroup is dihedral.  ... 
doi:10.1016/0021-8693(79)90288-6 fatcat:lq3xwfognbfc5k3r6gout3iufu

An invariant-sum characterization of Benford's law

Pieter C. Allaart
1997 Journal of Applied Probability  
The accountant Nigrini remarked that in tables of data distributed according to Benford's law, the sum of all elements with first digit d (d = 1, 2,· ··, 9) is approximately constant.  ...  In this note, a mathematical formulation of Nigrini's observation is given and it is shown that Benford's law is the unique probability distribution such that the expected sum of all elements with first  ...  Acknowledgement The author wishes to thank Prof. T.P. Hill for his extensive support and several useful conversations Prof. P.J. Holewijn for some useful suggestions and corrections Professors M.J.  ... 
doi:10.2307/3215195 fatcat:3limx6os5zgq5bwozbn3mpomfm

An invariant-sum characterization of Benford's law

Pieter C. Allaart
1997 Journal of Applied Probability  
The accountant Nigrini remarked that in tables of data distributed according to Benford's law, the sum of all elements with first digit d (d = 1, 2,· ··, 9) is approximately constant.  ...  In this note, a mathematical formulation of Nigrini's observation is given and it is shown that Benford's law is the unique probability distribution such that the expected sum of all elements with first  ...  Acknowledgement The author wishes to thank Prof. T.P. Hill for his extensive support and several useful conversations Prof. P.J. Holewijn for some useful suggestions and corrections Professors M.J.  ... 
doi:10.1017/s0021900200100907 fatcat:tqvvwda66fbtnbeyhwxklzpp3y

Symmetry of algebras over a number field

Saunders MacLane
1948 Bulletin of the American Mathematical Society  
Conversely, given an A which satisfies (i) and (ii), use (7) to define the invariants of a prospective algebra B. Such an algebra will exist, provided only that Z)(JB/p)=0 (mod 1).  ...  For each Q-normal algebra A, define Conversely, let t/s be a given rational number, where t is an integer.  ... 
doi:10.1090/s0002-9904-1948-08996-0 fatcat:dm5wyj6vwrfgxemsgdfyig6b34

Invariance of a Shift-Invariant Space

Akram Aldroubi, Carlos Cabrelli, Christopher Heil, Keri Kornelson, Ursula Molter
2009 Journal of Fourier Analysis and Applications  
A shift-invariant space is a space of functions that is invariant under integer translations.  ...  As a consequence, it is shown that principal shift-invariant spaces with a compactly supported generator cannot be invariant under any non-integer translations.  ...  In this case, if a is an arbitrary real number, then we can find numbers d j ∈ G that converge to a.  ... 
doi:10.1007/s00041-009-9068-y fatcat:h2cjghxeovgo5fxawi7d5f546m

Translation-invariant linear forms and a formula for the Dirac measure

Gary H. Meisters
1971 Bulletin of the American Mathematical Society  
If a and /3 are nonzero real numbers such that a/fi is irrational and not a Liouville transcendental, then there exist two {necessarily distinct) distributions S and T on R, both with compact A MS 1970  ...  According to Liouville (see [l, Theorem 191, p . 161]), if a/j8 is an algebraic real number of degree '^2, there exists a positive constant K such that, for all nonzero integers k,  ...  Furthermore, 5 and T can be chosen to have order 2 (at least when a//3 is a quadratic irrational) but can not have any lower order.  ... 
doi:10.1090/s0002-9904-1971-12627-7 fatcat:eznqrvpmpjg7zbndf4gxnxhyaa

Algebras and their arithmetics

L. E. Dickson
1924 Bulletin of the American Mathematical Society  
A complex number a • 1 + bi is said to have the real coordinates a and b and the basal units 1 and i. All complex numbers form an algebra of order 2 over the field of all real numbers.  ...  An algebra A is said to be the sum of two sub-algebras B and C if every element of A can be expressed as a sum of an element of B and an element of C.  ... 
doi:10.1090/s0002-9904-1924-03895-6 fatcat:kie4bqwwanfmxbygwrzrcforoy

Free rank n + 1 dense subgroups of Rn and their endomorphisms

David Handelman
1982 Journal of Functional Analysis  
ACKNOWLEDGMENT I would like to thank George Elliott for innumerable interesting conversations about the problems considered here.  ...  Thus Z2 decomposes into a direct sum of rank 1 A-invariant subgroups, but not into rank 1 B-invariant subgroups.  ...  Then 9 extends to an order-automorphism of R" (with respect to either the pointwise ordering or the strict ordering), and in the standard basis, this order-automorphism is a weighted permutation matrix  ... 
doi:10.1016/0022-1236(82)90041-6 fatcat:cpsfex56trgdxkndf7fir2jeyy

Page 233 of American Mathematical Society. Transactions of the American Mathematical Society Vol. 99, Issue 2 [page]

1961 American Mathematical Society. Transactions of the American Mathematical Society  
H is invariant with respect to the l-automorphisms of L.  ...  The converse is obvious. Example of an abelian |-group L with a basis such that L¥|D*|+[D].  ... 

NEW STRUCTURES IN PSEUDO MAGIC SQUARES

G.G. La Guardia
2019 International Journal of Applied Mathematics  
A pseudo magic square (PMS) of order n is an n × n square matrix whose entries are integers such that the sum of the numbers of any row and any column is the same number, the magic constant.  ...  We explore the group structure of PMS's to show that the quotient of the group of PMS's of order n by its subgroup with zero constant is isomorphic to the infinite additive group of integers, where theisomorphism  ...  To see that the converse is not true, it suffices to take the null PMS [0] n×n of order n.  ... 
doi:10.12732/ijam.v32i5.13 fatcat:f5hh6zr2b5hync56zacdazmb64

On a certain class of symmetric hypersurfaces

Darrell R. Shreve
1939 Bulletin of the American Mathematical Society  
Since there are no real points on 2 W = 0 if n is even, values of n will be restricted to odd positive integers throughout the remainder of this paper.  ...  Emch [l ] has shown that the equation of any surface of odd order in 5 3 , invariant under the symmetric öi 2 o on 5 x's whose sum is zero necessarily has the form Ap3+Bpz = 0, which is equivalent to X2  ...  Since there are no real points on 2 W = 0 if n is even, values of n will be restricted to odd positive integers throughout the remainder of this paper.  ... 
doi:10.1090/s0002-9904-1939-07123-1 fatcat:jxbvagh4zzc3xeua7kpudbjuhm

Page 263 of Mathematical Reviews Vol. 29, Issue 2 [page]

1965 Mathematical Reviews  
A fundamental result is *) Mig) s[oe-esae[ Re, p-8,p) ad) CY) [0,22) This result is available for proximate orders p(r) which converge to the order p which is not an integer.  ...  ., © restricted to be a sum of a finite number of non-overlapping intervals, arise.)  ... 

Page 483 of American Mathematical Society. Bulletin of the American Mathematical Society Vol. 53, Issue 5 [page]

1947 American Mathematical Society. Bulletin of the American Mathematical Society  
It is proved: (E) In order that A > E itis necessary and sufficient that an increasing sequence {v4} of positive integers exist for which lim )°_@a,=0. (Received March 18, 1947.) 195.  ...  It is shown that conversely the ergodic theorems imply that the measure is potentially invariant.  ... 

On the Core of a Cone-Preserving Map

Bit-Shun Tam, Hans Schneider
1994 Transactions of the American Mathematical Society  
This is the third of a sequence of papers in an attempt to study the Perron-Frobenius theory of a nonnegative matrix and its generalizations from the cone-theoretic viewpoint.  ...  Acknowledgment The first author is glad to acknowledge having fruitful discussions with D. Z. Djokovic on an earlier version of this paper.  ...  We denote by i>x(A) the index of X as an eigenvalue of A , that is, u(A-XI). Let A be an n x n real matrix. A" is said to be invariant under A, (or A leaves invariant K) if AK ç K.  ... 
doi:10.2307/2154729 fatcat:sq4bcdqvzfhdjmirw3hvkhqq6m
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