8,967 results
Search Results
2. The fixed cycle traffic light problem: a note on a paper by Mcneil
- Author
-
Victor Siskind
- Subjects
Statistics and Probability ,Cycle time ,Traffic signal ,Operations research ,Intersection (set theory) ,General Mathematics ,Compound Poisson process ,Statistics, Probability and Uncertainty ,Constant (mathematics) ,Queue ,Mathematics - Abstract
Both paper and author (D. R. McNeil, (1968)) will be referred to below as DRM. The said paper deals with the following situation: an intersection is controlled by a traffic light with a fixed cycle time, T; the possibility of other delays, e.g., due to turning vehicles, is ignored; arrivals at the light form a compound Poisson process; if vehicles arrive to find the light green and the queue empty they are not delayed, while in the contrary case they depart when they reach the head of the queue, providing the light is green, each vehicle taking a constant time to move off. The length of the effective red period is R. For further details and discussion, DRM may be consulted.
- Published
- 1970
3. A supplement to the paper on exponential representations of analytic functions in the upper half-plane with positive imaginary part
- Author
-
N. Aronszajn and W. F. Donoghue
- Subjects
Combinatorics ,Pure mathematics ,Quasi-analytic function ,General Mathematics ,Analytic continuation ,Positive harmonic function ,Global analytic function ,Upper half-plane ,Non-analytic smooth function ,Analysis ,Symmetric derivative ,Mathematics ,Analytic function - Abstract
In a paper which appeared a few years ago the authors investigated the exponential representation of functions analytic in the upper half-plane with positive imaginary part there [1]. We refer to that paper in the sequel as A-D. One of the principal results of A-D, there called Theorem A, can be extended to a considerably more general result, the proof of which is perhaps simpler than that given in A-D. We give the extended version of Theorem A here. We will use the notations and results of A-D without further explanations. Before we present the extension and its proof we would like to add some information that by oversight was omitted from the list of fundamental properties of the functions in the class P given in Section 1 of A-D. In such a comprehensive review one should mention that the classical theorem on representation of a positive harmonic function in a circle by a Poisson-Stieltjes integral is due to G. Herglotz [2]. The following results of L. H. Loomis [3] were not given: XVII. For all ~ for which /t[~] = O, the limits lira Im[~b(~ + iq)] ~l~ O and lira hOg(A) exist and are f ini te simultaneously and are equal. Their ~ 0 common value is the symmetric derivative of #(A) at 2 = ~ multiplied by ~r. XVIII. I f for two values of 0 in the interval 0 < 0 < ~
- Published
- 1964
4. Addendum to the paper on partially stable algebras
- Author
-
A. Adrian Albert
- Subjects
Discrete mathematics ,Applied Mathematics ,General Mathematics ,Lemma (logic) ,Addendum ,Expression (computer science) ,Mathematics - Abstract
I regret to announce that there is a serious error in my paper in these Transactions, volume 84, pp. 430-443. The error was discovered by Louis Kokoris who found that on line 8 of page 434 the expression given as 4[g(bz)](az) should have been 4[g(az)](bz). As a consequence the computation of P(z, g, az, b) yields nothing, the proof of formula (30) is not valid, and the important Lemma 9 is not proved. Thus the paper does not give a proof of its major result stated as Theorem 1. Nevertheless, the theorems of the paper are all correct and we shall provide a revision of the proof here. This revised proof has been checked by Louis Kokoris to whom the author wishes to express his great thanks. We observe first that the equation
- Published
- 1958
5. Some remarks on a paper by R. H. Bruck
- Author
-
Trevor Evans
- Subjects
Loop (topology) ,Pure mathematics ,Rank (linear algebra) ,Subvariety ,Applied Mathematics ,General Mathematics ,Variety (universal algebra) ,Ring of integers ,Identity (music) ,Mathematics - Abstract
Introduction. In a recent paper [2] R. H. Bruck has introduced the concept of right neoring and discussed some properties of these systems. In particular, he has considered analogues of certain properties of the ring of integers. This paper is essentially a commentary on Bruck's paper and we generalize some of his results as follows. The construction of the universal right neoring in [2] is applied to the free monogenic $3-loop in any subvariety $3 of the variety of loops and a complete analogue of Theorem 4.1 of [2] is obtained for any one of these subvarieties. Then, using a result similar to those obtained in [5], it is shown that this construction yields uncountably many right neorings with an identity which generates the additive loop of the right neoring. Conversely, every right neoring with an identity which generates its additive loop can be obtained from a free monogenic $3-loop by the above construction. Each of these right neorings has some properties resembling those of the ring of integers. One possible answer is given to the question raised by Bruck concerning the existence of universal right neorings with free additive loop of arbitrary rank. A brief proof is given, using the results of [4; 5], of the cancellation properties of the monogenic universal right neoring. Finally, we discuss briefly the relationship between right neorings and the logarithmetics of Etherington.
- Published
- 1956
6. On Pearl's Paper 'A Decomposition Theorem for Matrices'*
- Author
-
Robert C. Thompson
- Subjects
Algebra ,General Mathematics ,engineering ,engineering.material ,Pearl ,Mathematics ,Decomposition theorem - Abstract
Let A be an m × n matrix of complex numbers. Let Aτ and A* denote the transpose and conjugate transpose, respectively, of A. We say A is diagonal if A contains only zeros in all positions (i, j) with i ≠ j. In a recently published paper [4], M.H. Pearl established the following fact: There exist real orthogonal matrices O1 and O2 (O1 m-square, O2 n-square) such that O1AO2 is diagonal, if and only if both AA* and A*A are real. It is the purpose of this paper to show that a theorem substantially stronger than this result of Pearl's is included in the real case of a theorem of N.A. Wiegmann [2]. (For other papers related to Wiegmann's, see [l; 3].)
- Published
- 1969
7. Direct product of division rings and a paper of Abian
- Author
-
M. Chacron
- Subjects
Subdirect product ,Nilpotent ,Ring (mathematics) ,Pure mathematics ,Noncommutative ring ,Applied Mathematics ,General Mathematics ,Order (ring theory) ,Von Neumann regular ring ,Commutative property ,Direct product ,Mathematics - Abstract
It is shown that the rings under the title admit an order-theoretical characterization as in the commutative case studied by Abian. Introduction. Let R be an associative ring equipped with the binary relation (^) defined by xay if and only if xy = x2 in R. In this paper, it is shown that ( ^ ) is an order relation on R if and only if, R has no nilpotent elements i9*0). Conditions on the binary relation (g) in order that R split into a direct product of division rings are then studied in the light of Abian's result (l, Theorem l). Using similar argumentation and using certain subdirect representation of rings with no nilpotent elements, one obtains a complete similarity with the commutative case (yet, no extra complication in the computa- tions). Conventions. R is an associative ring which is, unless otherwise stated, with no nilpotent elements (other than 0). As a result of (2), R can be embedded into a direct product of skewdomains, R—* YLiei £i (that is to say, rings R, having no one-sided divisors of zero). The former embedding is fixed throughout the paper. It is therefore legiti- mate to identify any element x in R with the family consisting of all its projections (xj.e/. Finally, all definitions in (l) are extended (verbatim) to the present case (of a noncommutative ring R) and are freely used throughout.
- Published
- 1971
8. Corrections and Supplementaries to My Paper concerning Krull-Remak-Schmidt’s Theorem
- Author
-
Gorô Azumaya
- Subjects
Pure mathematics ,General Mathematics ,Mathematics - Abstract
It has recently been found that my previous paper “On generalized semi-primary rings and Krull-Remak-Schmidt’s theorem” Jap. Journ. Math. 19 (1949) — referred to as S. K. — contained in its Theorems 19 and 20 some errors. Nevertheless the writer has been able to correct them in suitable forms so that most parts of both theorems hold, even under a weaker assumption, and also subsequent theorems remain valid. These will be, together with some supplementary remarks, shown in the present note.
- Published
- 1950
9. Remarks concerning the paper of W. L. Ayres on the regular points of a continuum
- Author
-
Karl Menger
- Subjects
Set (abstract data type) ,Discrete mathematics ,Kernel (set theory) ,Applied Mathematics ,General Mathematics ,Order (group theory) ,Point (geometry) ,Continuum (set theory) ,Mathematics - Abstract
The reading of Ayres' interesting paper suggested to me the following remarks: 1. The order of a subset of a set S in a point p4 cannot surpass the order of S in p. Hence if S2 denotes the set of all points of S of order 2, then S2 has in each point of S the order 2, the order 1, or the order 0, where the terms "order 0" and "0-dimensional" are used synonymously. SI(M), S2(1), S" may denote the set of all points of S in which S2 has the order 0, 1, 2, respectively. The points of order 2 of S are also called the ordinary points of S, and the set S2 of all ordinarv points of S may be called the ordinary part of S. The set S" of all ordinary points of the ordinary part of S may be designated the ordinary kernel of S. WVe have
- Published
- 1931
10. Corrections to My Paper 'On Krull’s Conjecture Concerning Valuation Rings'
- Author
-
Masayoshi Nagata
- Subjects
Valuation (logic) ,Algebra ,Conjecture ,General Mathematics ,Mathematics - Abstract
The proof of Theorem 1 in the paper “On Krull’s conjecture concerning valuation rings” (vol. 4 (1952) of this journal) is not correct. We want to give here a corrected proof of the theorem: From p. 30, l. 14 to p. 31, l. 7 should be changed as follows.
- Published
- 1955
11. An operator valued function space integral: A sequel to Cameron and Storvick’s paper
- Author
-
D. L. Skoug and G. W. Johnson
- Subjects
Pure mathematics ,Applied Mathematics ,General Mathematics ,Multiple integral ,Integral representation theorem for classical Wiener space ,Mathematical analysis ,Riemann integral ,Riemann–Stieltjes integral ,Singular integral ,Fourier integral operator ,Volume integral ,symbols.namesake ,symbols ,Daniell integral ,Mathematics - Abstract
Recently Cameron and Storvick introduced and studied an operator valued function space integral related to the Feynman integral. The main theorems of their study establish the existence of the function space integral as a weak operator limit of operators defined at the first stage by finite-dimensional integrals. This paper provides a substantial strengthening of their existence theorem giving the function space integrals as strong operator limits rather than as weak operator limits.
- Published
- 1971
12. Invariant means and fixed points: A sequel to Mitchell’s paper
- Author
-
L. N. Argabright
- Subjects
Discrete mathematics ,Combinatorics ,Uniform norm ,Invariant polynomial ,Applied Mathematics ,General Mathematics ,Banach space ,Convex set ,Fixed-point theorem ,Fixed point ,Fixed-point property ,Topological vector space ,Mathematics - Abstract
The purpose of this note is to present a new proof of a generalized form of Day's fixed point theorem. The proof we give is suggested by the work of T. Mitchell in his paper, Function algebras, means, and fixed points, [2]. The version of Day's theorem which we present here has not appeared explicitly in the literature before, and seems especially well suited for application to questions concerning fixed point properties of topological semigroups. 1. Preliminaries. We adopt the terminology and notation of [2] except where otherwise specified. New terminology will be introduced as needed. Let y be a convex compactum (compact convex set in a real locally convex linear topological space E), and let A( Y) denote the Banach space of all (real) continuous affine functions on Y under the supremum norm. Observe that A(Y) contains every function of the form h=f\Y + r where fe E* and r is real; thus A(Y) separates points of Y.
- Published
- 1968
13. Epidemics with carriers: A note on a paper of Dietz
- Author
-
F. Downton
- Subjects
Statistics and Probability ,Entire population ,education.field_of_study ,General Mathematics ,010102 general mathematics ,Population ,01 natural sciences ,Short interval ,010104 statistics & probability ,0101 mathematics ,Statistics, Probability and Uncertainty ,education ,Demography ,Mathematics - Abstract
In a recent paper Weiss (1965) has suggested a simple model for a carrier-borne epidemic such as typhoid. He considers a population (of size m) of susceptibles into which a number (k) of carriers is introduced. These carriers exhibit no overt symptoms and are only detectable by the discovery of infected persons. He supposed that after the initial introduction of the carriers, the population remains entirely closed and no new carriers arise. The epidemic then progresses until either all the carriers have been traced and isolated or until the entire population has succumbed to the disease.
- Published
- 1967
14. On a Paper by M. Iosifescu and S. Marcus
- Author
-
C. J. Neugebauer
- Subjects
General Mathematics ,Humanities ,Mathematics - Abstract
In this paper we will construct an example showing that the problem posed in [1] has a negative answer. Two more theorems on the subject treated in [1] will be included.Let Io = [0, 1], R the reals, and let, for A ⊂ R, Ao be the interior of A. Let {xn} be a sequence in [0, 1> such that 0 = x1 < x2 < … and lim xn = 1. For each n, let In be closed interval having x as its midpoint (except for n = 1 in which case x1 is the left endpoint of I1) such that In ∩ Im= ϕ, and the metric density relative to Io of at 1 is zero. Let Jn be a closed interval in In concentric with In (except for n = 1, where J1 has x1 as its left endpoint) whose length is half that of In
- Published
- 1963
15. A note on a paper by Atkin and Bastin
- Author
-
C. J. S. Clarke
- Subjects
Pure mathematics ,Physics and Astronomy (miscellaneous) ,Argument ,General Mathematics ,Context (language use) ,Type (model theory) ,Mathematical economics ,Quantum logic ,Mathematics - Abstract
The paper ‘A Homological Foundation for Scale Problems in Physics’ (Atkin & Bastin, 1970) is criticised on account of several inconsistencies in the argument. Possible applications of the general ideas used are then discussed in the context of a ‘quantum logic’ type of framework.
- Published
- 1972
16. A correction to a paper on the dimension of Cartesian product sets
- Author
-
H. G. Eggleston
- Subjects
Combinatorics ,Common point ,symbols.namesake ,Dimension (vector space) ,General Mathematics ,Product (mathematics) ,Euclidean geometry ,symbols ,Zero (complex analysis) ,Product measure ,Hausdorff measure ,Cartesian product ,Mathematics - Abstract
Let Em and En be orthogonal Euclidean spaces of dimensions m and n respectively and with the origin of each as their only common point. In a previous paper (3) I gave what was intended to be a proof of the relationwhere the dimension of A, dim A, is the Besicovitch dimension, i.e. the number s such that the Hausdorff measure in any dimension greater than s is zero whilst that in any dimension less than s is infinite, where A and B are subsets of En and Em respectively and where A × B is the Cartesian product of A with B.
- Published
- 1953
17. Addendum to a paper of Conner and Floyd
- Author
-
Charles Terence Clegg Wall
- Subjects
Pure mathematics ,Ring (mathematics) ,General Mathematics ,Multiplicative function ,Structure (category theory) ,Addendum ,Point (geometry) ,Cobordism ,Object (computer science) ,Mathematics - Abstract
In two recent papers of Conner and Floyd ((2)) and ((3)), the additive structure of the SU-cobordism (or bordism) ring was completely determined. The object of this note is to point out that their results can also be used to determine the somewhat complicated multiplicative structure.
- Published
- 1966
18. On extensions of Pascal's theorem (Second paper) Paul Serret's theorem
- Author
-
H. W. Richmond
- Subjects
Combinatorics ,Pure mathematics ,Regulus ,General Mathematics ,Degrees of freedom ,Fixed-point theorem ,Paragraph ,Brouwer fixed-point theorem ,Pascal's theorem ,Twisted cubic ,Carlson's theorem ,Mathematics - Abstract
The circumstances explained in the footnote on p. 61 of the former paper with this title might well have necessitated a re-writing of the whole. Fortunately it appears that only a few short comments are required. For example it may be noted that the first question in §4 can be answered by counting the degrees of freedom in the two configurations. Eight points of a twisted cubic have freedom 20; four pairs of planes drawn at random through four lines of a regulus have freedom 21; therefore the eight planes of the second paragraph of §4 cannot always lead back to the eight points of §2. This is corroborated by the corresponding numbers in [4], which are 31 and 34.
- Published
- 1938
19. Remark on a paper of C. H. Dowker
- Author
-
G. Fejes Tóth and L. Fejes Tóth
- Subjects
Pure mathematics ,General Mathematics ,Mathematics - Published
- 1973
20. Note on a paper of B. Grünbaum on acyclic colorings
- Author
-
Gerd Wegner
- Subjects
Discrete mathematics ,symbols.namesake ,General Mathematics ,symbols ,Algebra over a field ,Arithmetic ,Notation ,Group theory ,Planar graph ,Mathematics - Abstract
The aim of this short note is to improve some recent results of B. Grunbaum by some remarks. We use Grunbaum's notations.
- Published
- 1973
Discovery Service for Jio Institute Digital Library
For full access to our library's resources, please sign in.