bluuebunny/crossref_metadata_2025_split huggingface dataset:
Equilibrium analysis of a stochastic model of traffic flow
Authors: Gordon W. J. , Newell G. F. 
Published: November 2008

AbstractA. J. Miller has proposed a stochastic model for the study of highway traffic in one direction along a two-lane road in which the desired speed of a vehicle is sampled from a continuous probability distribution and queues of vehicles are Poisson distributed on the highway. Miller has derived the equilibrium expression for the relation between the spacial densities of all vehicles and the spacial densities of those which are freely travelling. This relationship takes the form of a non-linear integral equation which is left unsolved. The present model differs from the original only in the assumption of a discrete distribution of desired speeds. Although the derivations of the equilibrium equations are based upon different arguments from those of Miller, these relations transform to the corresponding integral equations in the limit of a continuous speed distribution. The main body of the paper is devoted to a detailed investigation of the case of two speeds and asymptotic results are obtained for three speeds.
The exact Hausdorff measure of the sample path for planar Brownian motion
Authors: Taylor S. J. 
Published: November 2008

It has long been known (see Lévy (3), pp. 256, 260) that the sample paths of Brownian motion in the plane form an everywhere dense set of zero Lebesgue measure, with probability 1. In (7), a capacity argument was used to show that the Hausdorff measure with respect to tα is infinite for 0 < α < 2 with probability 1 so that the dimension of the path set is known to be 2. If one considers the initial part of the sample path Cω = C(1, ω) for 0 ≤ t ≤ 1, then it becomes interesting to ask if there is a measure function ψ(t) such that, with probability 1,for suitable positive constants c1, c2. The corresponding problem for paths in k-space (k ≥ 3) has been solved. In this case, if φ1(t) = t2 log log t−1, Lévy (4) obtained the upper bound and Ciesielski and Taylor (1) obtained the lower bound. For the planar case, the path is recurrent, and the intricate fine structure makes the measure function φ1(t) inappropriate. In (2), Erdő and Taylor showed that the measure is finite with probability 1 with respect to φ2(t) = t2 log t−1, and at that time we thought that (1) might be true with ψ(t) = φ2(t). Recently Ray (5) has obtained the lower bound in (1)withThe purpose of the present note is to obtain the upper bound in (1) for the same measure function, thus showing that (2) defines the correct measure function for measuring planar Brownian motion.
Differential inequalities and extension of Lyapunov's method
Authors: Lakshmikantham V. 
Published: November 2008

One of the most important techniques in the theory of non-linear differential equations is the direct method of Lyapunov and its extensions. It depends basically on the fact that a function satisfying the inequalityis majorized by the maximal solution of the equationUsing this comparison principle and the concept of Lyapunov's function various properties of solutions of differential equations have been considered (1–11).
On well-quasi-ordering transfinite sequences
Authors: Nash-Williams C. St. J. A. 
Published: November 2008

Abstract. Let Q be a well-quasi-ordered set, i.e. a set on which a reflexive and transitive relation ≤ is defined and such that, for every infinite sequence q1,q2,… of elements of Q, there exist i and j such that i < j and qi ≤ qi. A restricted transfinite sequence on Q is a function from a well-ordered set onto a finite subset of Q. If f, g are restricted transfinite sequences on Q with domains A, B respectively and there exists a one-to-one order-preserving mapping μ of A into B such that f(α) ≤ h(μ(α)) for every α ∈ A, we write f ≤ g. It is proved that this rule well-quasi-orders the set of restricted transfinite sequences on Q. The proof uses the following subsidiary theorem, which is a generalization of a classical theorem of Ramsey (4). Let P be the set of positive integers, and A(I) denote the set of ascending finite sequences of elements of a subset I of P. If s, t∈A(P), write s ≺ t if, for some m, the terms of s are the first m terms of t. Let T1,…,Tn be disjoint subsets of A(P) whose union T does not include two distinct sequences s, t such that s ≺ t. Then there exists an infinite subset I of P such that T ∩ A(I)is contained in a single Tj.
Feynman's kernel and the classical path
Authors: Clutton-Brock M. 
Published: November 2008

AbstractThe quantum mechanical kernel K(q″,t″; q′,t′) in Feynman's form of a sum over paths is evaluated by means of the canonical transformation to the system Q, P for which the Hamiltonian vanishes identically. The kernel is found to be completely determined by the classical paths, and is given byThe sum is over all classical paths leading from q′ at t′ to q″ at t′. S(q″, P, t′; q′, P, t′) is the classical action along the classical path characterized by the constant momentum P.
On semi-normal lattice rings
Authors: Bernau S. J. 
Published: November 2008

A lattice ring is a lattice group ((l), page 214) and a ring in which ab ≥ 0 whenever a ∧ b ≥ 0.In any lattice group (commutative or not) we define a+ = a ∨ 0, a− = (−a) ∨ 0 and |a| = a+ + a−. Itisknown((1). pages 219,220) that a+ ∧ a− = 0, a = a+ − a−, |a| = a+ ∨ a−, and that a ∧ (b ∨ c) = (a ∧ b) ∨ (a ∧ c), and a ∨ (b ∧ c) = (a ∨ b) ∧ (a ∨ c). For a non-empty subset M of a lattice group we define
On well-quasi-ordering infinite trees
Authors: Nash-Williams C. St. J. A. 
Published: November 2008

AbstractLet A be the set of all ascending finite sequences (with at least one term) of positive integers. Let s, t ∈ A. Write s ⊲ t if there exist m, n, x1, …, xn such that m < n and x1 < … < xn and s is x1, …, xm and t is x2, x3, …, xn. Call a subset S of A a P-block if, for every infinite ascending sequence x1, x2, … of positive integers, there exists an m such that x1, …, xm belongs to S. A quasi-ordered set Q (i.e. a set on which a reflexive and transitive relation ≤ is defined) is better-quasi-ordered if, for every P-block S and every function f:S → Q, there exist s, t ∈ S such that s ⊲ t and f(s) ≤ f(t). It is proved that any set of (finite or infinite) trees is better-quasi-ordered if T1 ≤ T2 means that the tree T1 is homeomorphic to a subtree of the tree T2. This establishes a conjecture of J. B.Kruskal that, if T1, T2, … is an infinite sequence of trees, then there exist i, j such that i < j and Ti ≤ Tj.
Linear equations with elements (l/m)k(n/m) + δnmand infinitely many variables
Authors: Wood W. W. 
Published: November 2008

Introduction.Infinite systemsare discussed in whichk(θ) andb(n) are differentiable. The aim is to determine the behaviour ofa(n) for largenand to reduce (1) to a finite system. This involves solvingfor the high ordera(n),n≥N, in terms of the precedinga(n), with a large enoughNto facilitate the iteration procedure employed. The desiredN− 1,N− 1 system follows on substitution for the high ordera(n) in the firstN− 1 equations (1).
Refractive index profiles based on the hypergeometric equation and the confluent hypergeometric equation
Authors: Heading John 
Published: November 2008

AbstractIsotropic ionospheric propagation of electromagnetic waves yields refractive index profiles via the standard transcendental equations. Some transformations of these equations have long been regarded as standard. Here, every possible transformation is derived by a systematic analysis, yielding all possible refractive index profiles satisfying certain stated criteria regarding the wave frequency.
The isotropic scattering of radiation from a point source in a finite spherical atmosphere
Authors: Smith M. G. 
Published: November 2008

AbstractThe investigation of the isotropic scattering of radiation in an infinite spherically symmetric atmosphere, which was carried out in a previous paper, is extended to a finite atmosphere bounded by a totally absorbing shell.It is shown that the solution may be expressed as a series which will certainly converge when the radius of the shell is large enough, and whose terms are found by iteration.Numerical investigation shows that even for quite modest values of the radius, the convergence is so fast that for most practical purposes all but the first term can be neglected. Except at the very ends of the range, a very simple expression then gives an excellent approximation.
On the forced torsional oscillations of an elastic cylinder
Authors: Shail R. 
Published: November 2008

AbstractThe forced torsional motion of a semi-infinite isotropic right-circular elastic cylinder is studied in this paper, the vibrations being excited by a harmonically oscillating rigid disc, securely attached to the plane face of the cylinder. Two distinctsituations are considered, namely, when the curved surface of the cylinder is clamped and when it is stress free. In both cases the problem is reduced to the solution of a Fredholm integral equation of the second kind which can be solved iteratively when the frequency of oscillation is small and the cylinder radius large. Using the iterative solutions, approximate expressions are deduced for the distribution of shear stress under the disc and the driving couple required. In an appendix a discussion is given of a mathematically similar problem in the theory of the swirling flow of a perfect fluid.
Polyhedral immersions
Authors: Irwin M. C. 
Published: November 2008

1. We work in the category of compact polyhedral spaces and polyhedral maps ((5)). Given spaces M and Q and a map f: M → Q, we define Ur(f) to be the set of points x ∈ M such that f−1f(x) contains at least r points. Sr(f) is the closure of Ur(f) in M. f is an embedding if it is a homeomorphism into, and an immersion if it is locally an embedding. We shall call f a simple immersion if S3(f) = ø and the connected components of S2(f) are individually embedded by f. Obviously a simple immersion is an immersion. If M and Q are manifolds (as they will be for the rest of the paper)f: M → Q is proper if it takes ∂M, the boundary of M, into ∂Q. In (2) the following result was proved:Theorem 1. Let Mmbe(2m−q)-connected and Qq be(2m−q + 1)-connected, m ≤ q−3. Then any proper map f: M → Q which embeds ∂M is homotopic rel ∂M to an embedding.
On the rigorous foundation of short-wave asymptotics
Authors: Ursell F. 
Published: November 2008

AbstractCertain physical theories are short-wave limits of more general theories. Thus ray optics is the short-wave limit of wave optics, and classical mechanics is the short-wave limit of wave mechanics. In principle it must be possible to deduce the former from the latter theories by a rigorous mathematical limiting process; in fact the arguments found in the literature are formal, plausible and non-rigorous. (We are here concerned with linear wave equations and time-periodic phenomena.) For some wave equations there are, however, a few explicit rigorous canonical solutions relating to simple geometrical configurations, e.g. to conics in two dimensions for the equations of acoustics, and for these the asymptotics can be found rigorously. For more general configurations the solution of a typical boundary-value problem can be reduced to the solution of a Fredholm integral equation of the second kind.
Some expansions in products of hypergeometric functions
Authors: Srivastava H. M. 
Published: November 2008

In the usual notation letwhere .Also, for the generalized hypergeometric function pFq(x) let us employ a contracted notation and writeThroughout the present paper i will run from 1 to p, I from 1 to P, and so on. Thus ((a) )m is to be interpreted as,and similar interpretations hold for ((A))m, etc.
On a non-linear integral equation occurring in diffraction theory
Authors: Millar R. F. 
Published: November 2008

AbstractThe problem of diffraction of a plane wave by a semi-infinite grating of iso-tropic scatterers leads to the consideration of a non-linear integral equation. This bears a resemblance to Chandrasekhar's integral equation which arises in the study of radiative transfer through a semi-infinite atmosphere. It is shown that methods which have been used with success to solve Chandrasekhar's equation are equally useful here. The solution to the non-linear equation satisfies a more simple functional equation which may be solved by factoring (in the Wiener-Hopf sense) a given function. Subject to certain additional conditions which are dictated by physical considerations, a solution is obtained which is the unique admissible solution of the non-linear integral equation. The factors and solution are found explicitly for the case which corresponds to closely spaced scatterers.
Solutions of unsteady compressible boundary-layer equations
Authors: Sarma G. N. 
Published: November 2008

AbstractThe unsteady two-dimensional compressible boundary layers have been studied by Sarma ((5)) assuming that the Prandtl number is unity and that the wall is in an arbitrary motion, the main stream being steady. In this paper the Prandtl number is taken to be an arbitrary parameter which need not be equal to unity, and it is assumed that the main stream velocity and temperature are perturbing about a steady mean, the wall being in an arbitrary motion. Solutions are obtained in two parts, one when the temperature gradient at the wall is perturbing about a zero mean and the other when the temperature of the wall is perturbing about a steady mean. Thus in this paper the theory given in Sarma ((5)) is made still more general. Following the work of Sarma ((4)–(6)) two types of solutions are developed in each part, one for large times and the other for small times.
The zeta function of a cubic surface over a finite field
Authors: Swinnerton-Dyer H. P. F. 
Published: November 2008

Introduction. The object of this paper is to obtain an explicit formula for the zeta function of an arbitrary non-singular cubic surface over a finite field. Let k denote the finite field of q elements, and kn the field of qn elements which is the unique algebraic extension of k of degree n. Let be a non-singular variety defined over k, and for each n > 0 let be the number of points defined over kn which lie on . The zeta function of is given byDwork has shown in (3) that for any this is a rational function of q−s; and in particular it follows from the results he proves in (4) that if is a non-singular cubic surface thenand hence alsoHere the numbers w o depend only on q and on .
Summability fields which span the bounded sequences
Authors: Baker J. W. , Petersen G. M. 
Published: November 2008

If A = (am, n) is a regular matrix, then for any sequence x = {xn}, Am(x) will denote the transform and A-lim x denotes if that limit exists. We shall denote by the set of bounded sequences which are summed by A. If B is another regular matrix with then we say that B is b-stronger than A. In that case B must be b-consistent with A (see (4) and (6)), i.e. if thenIf {μn} is a sequence of positive real numbers with we say that A and B are (μn)-consistent if every sequencer x = {xn} satisfying xn = 0(μn) which is summed by both A and B is summed to the same value by both matrices. A finite set of matrices A1, A2, …, AN is said to be simultaneously (μn)-inconsistent (b-consistent) if whenever is summed by Ai with (i = l, 2, …, N) then implies that The set of sequences, is denoted by
The isotropic scattering of radiation in a finite homogeneous two-dimensional atmosphere
Authors: Smith M. G. , Hunt G. E. 
Published: November 2008

AbstractThe integral equation for the isotropic scattering of radiation in a medium bounded laterally by planes ±y0 is solved as a series in powers of exp (−y0). This series is certainly convergent for y0 large enough, and rapidly convergent for most practical purposes.
M-structure in Banach spaces
Authors: Cunningham F. 
Published: November 2008

L-structure in a Banach space X was defined in (3) by L-projections, that is projections P satisfyingfor all x ∈ X. The significance of L-structure is shown by the following facts: (1) All L-projections on X commute and together form a complete Boolean algebra. (2) X can be isometrically represented as a vector-valued L1 on a measure space constructed from the Boolean algebra of its L-projections (2). (3) L1-spaces in the ordinary sense are characterized among Banach spaces by properties equivalent to having so many L-projections that the representation in (2) is everywhere one-dimensional.
Simultaneous rational approximations to certain algebraic numbers
Authors: Baker A. 
Published: November 2008

It is generally conjectured that if α1, α2 …, αk are algebraic numbers for which no equation of the formis satisfied with rational ri not all zero, and if K > 1 + l/k, then there are only finitely many sets of integers p1, p2, …, pkq, q > 0, such thatThis result would be best possible, for it is well known that (1) has infinitely many solutions when K = 1 + 1/k. † If α1, α2, …, αk are elements of an algebraic number field of degree k + 1 the result can be deduced easily (see Perron (11)). The famous theorem of Roth (13) asserts the truth of the conjecture in the case k = 1 and this implies that for any positive integer k, (1) certainly has only finitely many solutions if K > 2. Nothing further in this direction however has hitherto been proved.‡
Some computations for m-dimensional partitions
Authors: Atkin A. O. L. , Bratley P. , Macdonald I. G. , McKay J. K. S. 
Published: November 2008

1. It was known to Euler that p(n), the number of unrestricted partitions of n into non-increasing integral parts, is generated bywith the usual convention that p(0) = 1.
Finite extension inflation and torsion of a hollow cylindrical reinforced dielectric
Authors: Chaudhry H. R. 
Published: November 2008

AbstractEringen's theory(1) of homogeneous, isotropic, hyperelastic dielectric is applied to consider the effects of polarization on the surface tractions when a hollow cylindrical reinforced dielectric carrying a uniform surface charge at its inner surface is subjected to simultaneous large extension, inflation and torsion. New effects due to reinforcement and polarization have been observed separately. For vanishing charge, the results reduce to those of classical finite strain theory (2).
The fundamental group of the orbit space of a discontinuous group
Authors: Armstrong M. A. 
Published: November 2008

A group G of homeomorphisms of a topological space X will be called discontinuous if(1) the stabilizer of each point of X is finite, and(2) each point x ∈ X; has a neighbourhood U such that any element of G not in the stabilizer of x maps U outside itself (i.e. if gx ≠ x then U ∩ gU is empty). The purpose of this note is to prove the following result.
Steady electrically driven flows
Authors: Waechter R. T. 
Published: November 2008

AbstractCertain simple steady electrically driven flows under transverse applied magnetic fields, for which exact solutions are available, are considered. Electric potentials are prescribed on fixed perfectly conducting electrodes and the resulting Lorentz force j × B0 gives rise to a velocity field in the fluid. It is assumed that the magnetic Reynolds number of the flow is small (Rm ≪ 1) so that the induced magnetic field may be neglected. In particular, we examine in detail the simplest flat plate configuration which is correctly posed as a two-part mixed boundary value problem of the Wiener–Hopf type. At large Hartmann number, the fluid vorticity and the current flow transverse to the applied magnetic field are suppressed. Thin current transition layers, which emanate from an electrode edge and are aligned with the applied magnetic field, provide a smooth transition from one region of almost constant current to another. The thickness of these layers is found to be of the same order as the thickness of certain velocity transition layers occurring in other situations in magnetohydrodynamics.
On ideals of finite homoloǵical dimension in local rings
Authors: Burch Lindsay 
Published: November 2008

In this paper I shall demonstrate certain algebraic properties of ideals of finite homological dimension in local rings.In the first section, I show that no non-zero ideal of finite homological dimension in a local ring can be of zero grade (this is stated by Auslander and Buchsbaum in the appendix to (l), but I cannot find a proof in the literature). Using this result, together with the complex defined by a matrix, which is described by Eagon and Northcott in (2), I prove that an ideal of homological dimension one in a local ring Q may always, for some integer n, be described as the set of determinants of matrices obtained by adjoining to a certain (n–l)× n matrix with elements in the maximal ideal of Q another row with elements arbitrarily chosen in Q. (This result was established in (3), under the additional condition that Q should be a domain.)
On some results involving generalized hypergeometric polynomials
Authors: Shah Manilal 
Published: November 2008

The generalized hypergeometric polynomial ((7), equation (2·1)) has been defined bywhere the symbol Δ(δ, −n) represents the set of δ-parameters:and δ, n are positive integers. The polynomial is in a generalized form which yields many known polynomials on specializing the parameters.
On the method of matched asymptotic expansions
Authors: Fraenkel L. E. 
Published: November 2008

AbstractThe method of matched (or of ‘inner and outer’) asymptotic expansions is reviewed, with particular reference to two general techniques which have been proposed for ‘matching’; that is, for establishing a relationship between the inner and outer expansions, to finite numbers of terms, of an unknown function. It is shown that the first technique, which uses the idea of overlapping of the two expansions, can be difficult and laborious in some applications; while the second, which is the ‘asymptotic matching principle’ in the form stated by Van Dyke(13) can be incorrect. Two different sets of conditions sufficient for the validity of the asymptotic matching principle are then established, on the basis of assumptions about the structure of expressions which approximate to the desired function f(x,∈) for all relevant values of x. Finally, it is noted that in four classes of singular-perturbation problems for which complete and rigorous asymptotic theories exist, uniform approximations to the solutions have a structure which is a particular form of the general one assumed in this paper.
Some infinite integrals involving Whittaker functions and generalized hypergeometric polynomials, with their applications
Authors: Shah Manilal 
Published: November 2008

We have defined the generalized hypergeometric polynomial ((6), eqn. (2·1), p. 79) by means ofwhere δ and n are positive integers and the symbol Δ(δ, − n) represents the set of δ-parametersThe polynomial is in a generalized form which yields many known polynomials with proper choice of parameters and therefore the results are of general character.
On irreducible polynomials of certain types in finite fields
Authors: Cohen Stephen D. 
Published: November 2008

LetGF(q) be the finite field containingq=plelements, wherepis a prime andla positive integer. LetP(x)be a monic polynomial inGF[q, x] of degreem. In this paper we investigate the nature and distribution of monic irreducible polynomials of the following types:(I)P(xr), whereris a positive integer (r-polynomials).(II)xmP(x+x−1). (Reciprocal polynomials.) These have the form(III)xrmP(xr+x−r). (r-reciprocal polynomials.) These have the formQ(xr), whereq(x) satisfies (1·1).
On semi-Markov processes on arbitrary spaces
Authors: Çinlar Erhan 
Published: November 2008

Let E be an arbitrary set, a σ-algebra of subsets of the Borel sets of F. We write A × B for the product of the sets A and B, andfor the product σ-algebra of and (i.e. the σ-algebra generated by the rectangles A × B with A ∈ and B ∈ ).