bluuebunny/crossref_metadata_2025_split huggingface dataset:
The concept of order
Authors: Bastin E. W. , Kilmister C. W. 
Published: November 2008

ABSTRACTFrom the idea of the continuous development of an investigation, as expressed in the use of indefinitely continuing sequences of procedures, the concept of a measurement together with its result is formulated. The resulting theory is initially very general, but it is possible to restrict it in such a way as to make the construction of a consistent world possible. The physical condition providing the restrictions that make this construction possible is found in the use of the general idea of a test-particle in all fundamental investigations, which is shown to be a case of the use of the theory-languages of the previous paper (1). Finally, the theory is applied to the solution of the problem of preferred inertial frames.
The electron-phonon interaction, according to the adiabatic approximation
Authors: Ziman J. M. 
Published: November 2008

ABSTRACTThe behaviour of the conduction electrons in a vibrating metallic lattice is treated by the Born-Oppenheimer method. Non-adiabatic processes, due to certain terms usually neglected, are shown to correspond to scattering of electrons by the lattice vibrations, as in Bloch's theory of electrical resistivity, but the matrix elements are not the same as Bloch's except when energy is conserved in the process. This may have important consequences in Fröhlich's theory of superconductivity.
Simultaneous linear differential equations with constant coefficients
Authors: Afriat S. N. , Eggleston H. G. 
Published: November 2008

The equations to be considered are of the formwhere Xk is to be determined as a function of t, is its ith derivative with respect to t, Fj is a given analytic function of t, a given constant, and i = 0, 1, …, n; j, k = 1,…, m, and they represent a system of simultaneous linear differential equations of order n in m functions Xk (k = 1,…, m).
On clumps formed when convex laminae or bodies are placed at random in two or three dimensions
Authors: Mack C. , Bartlett M. S. 
Published: November 2008

ABSTRACTA correction is made to a previous paper(2) on clumps formed by random placing of laminae, a useful property of such placings is deduced and formulae are found for clumps formed when convex bodies are randomly placed in space and for clumps formed by the orthogonal projections of such placings.
The image system of a vortex element in a rigid sphere
Authors: Lighthill M. J. 
Published: November 2008

It will be shown that a vortex element has the following image system in a rigid sphere immersed in incompressible fluid:(i) A transverse vortex element at the inverse point, equal in strength to minus the transverse resultant of the given vortex element, divided by the ratio of its distance from the centre to the radius of the sphere.(ii) A radial vortex element at the inverse point, equal in strength to plus the radial resultant of the given vortex element, divided by the same ratio.(iii) A uniform line vortex stretching from the inverse point to the centre of the sphere, equal and opposite in total strength to the radial vortex element at the inverse point.
Diffraction by a cylinder of finite length
Authors: Williams W. E. , Lighthill M. J. 
Published: November 2008

ABSTRACTThe diffraction of a plane harmonic sound wave by a hollow circular cylinder of finite length is considered. The problem is treated by using Laplace transforms and is reduced to the solution of two complex integral equations. An approximate solution is obtained for these equations when the product of the wave number (k) and the cylinder length (l) is large. The resonance of the system is considered and an equation derived for the resonant lengths which is then solved approximately for kl large. An explicit expression is obtained for the end correction of an. r–resonant system (i.e. kl ≈ rπ), and also comparison is made with experimental results.
FC-nilpotent and FC-soluble groups
Authors: Duguid A. M. , McLain D. H. 
Published: November 2008

Let an element of a group be called an FC element if it has only a finite number of conjugates in the group. Baer(1) and Neumann (8) have discussed groups in which every element is FC, and called them FC-groups. Both Abelian and finite groups are trivially FC-groups; Neumann has studied the properties common to FC-groups and Abelian groups, and Baer the properties common to FC-groups and finite groups. Baer has also shown that, for an arbitrary group G, the set H1 of all FC elements is a characteristic subgroup. Haimo (3) has defined the FC-chain of a group G byHi/Hi−1 is the subgroup of all FC elements in G/Hi−1.
The electron-phonon interaction, according to the adiabatic approximation
Authors: Taylor J. C. 
Published: November 2008

ABSTRACTThe interaction of conduction electrons with a vibrating metallic lattice has been considered by Ziman in terms of non-adiabatic perturbations to the adiabatic approximation of the Born-Oppenheimer theory. This programme is continued to calculate the self-energy of the electrons. When account is taken of the dependence of the energy levels of the adiabatic Hamiltonian itself upon the electron configuration, the final result is the same as the standard one.
A theorem on infinite groups
Authors: Baumslag Gilbert 
Published: November 2008

It is well known ((1), pp. 120–1) that if G is a finite p–group then the factor group G/G′ is cyclic if and only if G is itself cyclic. A trivial consequence of this fact is that, in such a case, the factor group G′/G″ is the unit group. (As usual, G(r) denotes the rth derived group of the group G.)We prove the following theorem.
Percolation processes
Authors: Broadbent S. R. , Hammersley J. M. 
Published: November 2008

ABSTRACTThe paper studies, in a general way, how the random properties of a ‘medium’ influence the percolation of a ‘fluid’ through it. The treatment diifers from conventional diffusion theory, in which it is the random properties of the fluid that matter. Fluid and medium bear general interpretations: for example, solute diffusing through solvent, electrons migrating over an atomic lattice, molecules penetrating a porous solid, disease infecting a community, etc.
Wave functions for the normal states of Ne+3 and Ne+4
Authors: Froese Charlotte , Hartree D. R. 
Published: November 2008

ABSTRACTSolutions of Fock's equations for the self-consistent field with exchange have been carried out for Ne+4, using the EDSAC at the Mathematical Laboratory, Cambridge. The initial estimates for the calculation were made by a simplified version of a method previously suggested for interpolating atomic wave functions with respect to atomic number. This gave good estimates for Ne+4, and it is probable that estimates for Ne+3, obtained similarly, are already accurate enough for practical use. Such wave functions for Ne+3 are given. The results have application in astrophysical contexts.
A statistical method for analysing observations of faint radio stars
Authors: Scheuer P. A. G. 
Published: November 2008

ABSTRACTThe observation of faint radio sources is often limited by the angular resolving power of the radio telescope, and not by its sensitivity. Continuous recording of the output from the receiving apparatus then produces a trace which always shows the sum of the effects of a number of sources in the reception pattern, instead of showing sources passing through the reception pattern one at a time. The apparent intensities of sources found on the records are affected by the presence of several other, fainter, sources in the reception pattern, and even the existence of many of the faint sources is doubtful. Counts of numbers of sources at given intensity levels are therefore unreliable.Any assumed number-intensity law for radio sources can, however, be tested by a method free from the uncertainties due to confusion between adjacent sources, using a direct relation between the number-intensity law and the frequency distribution of deflexions of various sizes on the observed records. The present paper shows the derivation of the relation between M (I) dI, the mean number of radio sources per steradian in the intensity interval dI, and P(D)dD, the probability that the deflexion D recorded at an arbitrary instant lies in the interval dD. Expressions for P(D) are worked out for some specific models of M (I); a comparison with observation has been given in an earlier paper (6).
On a non-symmetric theory of the pure gravitational field
Authors: Sciama D. W. 
Published: November 2008

ABSTRACTIt is suggested, on heuristic grounds, that the energy-momentum tensor of a material field with non-zero spin and non-zero rest-mass should be non-symmetric. The usual relationship between energy-momentum tensor and gravitational potential then implies that the latter should also be a non-symmetric tensor. This suggestion has nothing to do with unified field theory; it is concerned with the pure gravitational field.A theory of gravitation based on a non-symmetric potential is developed. Field equations are derived, and a study is made of Rosenfeld identities, Bianchi identities, angular momentum and the equations of motion of test particles. These latter equations represent the geodesics of a Riemannian space whose contravariant metric tensor is gij–, in agreement with a result of Lichnerowicz(9) on the bicharacteristics of the Einstein–Schrödinger field equations.
Oscillations of a system of disk dynamos
Authors: Rikitake Tsuneji 
Published: November 2008

ABSTRACTThe behaviour of two disk dynamos coupled to one another is examined in relation to the earth's magnetic field. It is found that reversals of electric current and magnetic field occur, unlike the case of a single disk dynamo.On assuming a simple engine that drives a disk dynamo, the coupling between electro-magnetism, motion and heat is discussed. A possible range of temperature fluctuation associated with a dynamo action is also estimated very roughly.
Weak ergodicity in non-homogeneous Markov chains
Authors: Hajnal J. , Bartlett M. S. 
Published: November 2008

ABSTRACTThe paper deals with weak ergodicity, i.e. the tendency for a chain to ‘forget’ the distant past. This may occur in non-homogeneous chains even if the probabilities of being in a given state do not tend to a limit as the number of trials increases.Investigation of the general conditions of weak ergodicity leads to the definition of a special subclass of regular matrices. Conditions for chains involving regular matrices are also given (§§2,3).Section 4 discusses similarities in asymptotic behaviour between chains whose transition matrices differ only by small amounts.
Single-space axioms for homology theory
Authors: Kelly G. M. 
Published: November 2008

Eilenberg and Steenrod(1) give a set of axioms for the homology theory of pairs of spaces and their maps, and prove that these axioms are categorical on triangulable pairs.Here we give a set of axioms for the homology theory of single spaces and their maps, that is, for absolute rather than relative homology. This axiomatization is shown to be essentially equivalent to that of Eilenberg and Steenrod, the relative homology groups being suitably denned in terms of the absolute groups.
Random walk and electric currents in networks
Authors: Nash-Williams C. St J. A. 
Published: November 2008

ABSTRACTLet G be a locally finite connected graph and c be a positive real-valued function defined on its edges. Let D(ξ) denote the sum of the values of c on the edges incident with a vertex ξ. A particle starts at some vertex α and performs an infinite random walkin which (i) the ξj are vertices of G, (ii), λj. is an edge joining ξj–1 to ξj (j = 1, 2, 3, …), (iii) if λ is any edge incident with ξj, thenLet υ be a set of vertices of G such that the complementary set of vertices is finite and includes α. A geometrical characterization is given of the probability (τ, say) that the particle will visit some element of υ without first returning to α. An essentially equivalent problem is obtained by regarding G as an electrical network and c(λ) as the conductance of an edge λ; the current flowing through the network from α to υ when an external agency maintains α at potential I and all elements of υ at potential 0 is found to be τD(α).A necessary and sufficient condition (of a geometrical character) for the particle to be certain to return to α. is obtained; and, as an application, a new proof is given of a conjecture of Gillis (3) regarding centrally biased random walk on an n–dimensional lattice.
On Lie groups and their homotopy groups
Authors: James I. M. 
Published: November 2008

We prove a theorem which facilitates homotopy classification of maps into a topological group G. Some information about homotopy groups of G is obtained, including the following two results. Consider the Samelson product, as defined in (7), which constitutes a bilinear pairing of πp(G) with πq(G) to πp+q(G). The product of a α ∈ πp(G) with β ∈ πq(G) is written in the form 〈α, β〉. There exist groups having Samelson products of infinite order. Homotopy-commutative groups have zero Samelson products. We shall proveTheorem (1·1). If G is a connected Lie group then there exists a positive integer n such that n〈α, β〉 = 0 for every pair α, β of elements in the homotopy groups of G.
The shortest path through many points
Authors: Beardwood Jillian , Halton J. H. , Hammersley J. M. 
Published: November 2008

ABSTRACTWe prove that the length of the shortest closed path throughnpoints in a bounded plane region of areavis ‘almost always’ asymptotically proportional to √(nv) for largen; and we extend this result to bounded Lebesgue sets ink–dimensional Euclidean space. The constants of proportionality depend only upon the dimensionality of the space, and are independent of the shape of the region. We give numerical bounds for these constants for various values ofk; and we estimate the constant in the particular casek= 2. The results are relevant to the travelling-salesman problem, Steiner's street network problem, and the Loberman—Weinberger wiring problem. They have possible generalizations in the direction of Plateau's problem and Douglas' problem.
New (Regge) symmetry relations for the Wigner 6j-symbol
Authors: Jahn H. A. , Howell K. M. , Mott N. F. 
Published: November 2008

ABSTRACTThe Wigner 6j–symbol, written in the formis shown to be invariant under separate permutations of A, B, C alone, separate permutations of α, β, γ alone and separate change in sign of any pair of α, β, γ; results equivalent to the new symmetry relations of Regge. Alternatively, written in the formwith J0 + J1 + J2 + J3 = K1 + K2 + K3, Jr(r = 0, 1, 2, 3) and K3 (s = 1, 2, 3) integral, it is invariant for separate permutations of the Jr and of the Ks. If Jm = max (J0, J1, J2, J3), then each 6j-symbol with distinct value may be associated with an ordered partition of Jm into 6 integral parts: Jm = n1 + n2 + n3 + p1 + p2 + p3, n1 ≥ n2 ≥ n3; p1 ≥ p2 ≥ n3. The 6j-symbol is proportional to the Saalschützianof unit argument.
Generalizations to several variables of Lagrange's expansion, with applications to stochastic processes
Authors: Good I. J. 
Published: November 2008

ABSTRACTA generalization to two independent variables of Lagrange's expansion of an inverse function was given by Stieltjes and proved rigorously by Poincaré. A new method of proof is given here that also provides a new and sometimes more convenient form of the generalization. The results are given for an arbitrary number of independent variables. Applications are pointed out to random branching processes, to queues with various types of customers, and to some enumeration problems.
Construction of orders in Abelian groups
Authors: Teh H.-H. 
Published: November 2008

Let G be an Abelian group. A binary relation ≥ denned in G is called an order of G if for each x, y, z ε G,(i) x ≥ y or y ≥ x (and hence x ≥ x);(ii) x ≥ y and y ≥ x ⇒ x = y,(if x ≥ y and x ≠ y, we write x > y);(iii) x ≥ y and y ≥ z ⇒ x = z;(iv) z ≥ y ⇒ x + z ≥ y + z.
A problem on tangents to a sphere
Authors: Croft H. T. 
Published: November 2008

The problem is no. 226, Colloq. Math. 5 (1958), a problem of Steinhaus. If T is a closed set of tangent lines to a sphere S, are conditions (1) and (2) compatible:(1) Every great circle of S has at least one tangent belonging to T.(2) No great circle of S has two parallel tangents belonging to T?
The number of real zeros of the solution of a linear homogeneous differential equation
Authors: Brearley M. N. 
Published: November 2008

The following theorem will be established:Provided the roots of the associated characteristic equation are all real, any solution of a linear homogeneous differential equation with constant coefficients has at most n − 1 zeros for real finite values of the independent variable, where n is the order of the equation.The theorem applies to equations with a complex independent variable, but since the conclusion concerns only real values of the variable there is no loss of generality in considering an equation of order n in the formwith y = y(x), where x is real. The constant coefficients ar may be complex.
Note on the Hopf-James invariants
Authors: Hardie K. A. 
Published: November 2008

The Hopf-James invariants are a series of homomorphisms(see (3) or (13)). I. M. James (7) and H. Toda (13), have shown effectively that in the case n even and r a prime p the restrictions to the p-primary components may be embedded in exact sequencesIn this note we show that there are similar exact sequences if n is even and r = pq or if n is odd and r = 2pq, and we establish connexions in certain cases between the homomorphisms Hmn and the composite homomorphisms HmHn. We are able to compute the action of the invariants on the groups of the r-stem for r ≤ 9 with the partial exception of π6(S2) and π7(S2). The exact sequences yield useful criteria for determining the reduced product filtrations (see (9)) of elements.
A method for the numerical integration of the one-dimensional heat equation using chebyshev series
Authors: Elliott David 
Published: November 2008

ABSTRACTA numerical solution ofwith general linear boundary conditions alongx= ±1, is described where at any timetthe Chebyshev expansion of θ(x,t) in –1 ≤x≤ 1 is computed directly. Compared with the more usual finite difference methods, this method requires much less computation and there are no stability problems. Two cases are considered in detail.
Relativistic magnetohydrodynamics and irreversible thermodynamics
Authors: Hughes W. F. 
Published: November 2008

ABSTRACTThe basic equations of non-relativistic magnetohydrodynamics are briefly reviewed. Beginning with the energy-momentum tensor for the coupled electromagnetic and fluid fields relativistic energy and momentum equations are formulated. The effect of heat conduction is included and relativistic constitutive equations are discussed. A relativistic first law of thermodynamics is developed in terms of internal energy and entropy. Finally, the second law and entropy production rate are derived in a covariant fashion.
A family of exact solutions of one-dimensional anisentropic flow
Authors: Weir D. G. 
Published: November 2008

Martin(1) has shown that if the pressure p and the Lagrange variable ψ (ψ = constant on a trajectory) are taken as independent variables, then problems in one-dimensional unsteady flow of an ideal gas reduce to the question of finding solutions of the Monge-Ampère equationwhere τ = 1/ρ, ρ being the density, and S = S(ψ) is the specific entropy. Thus the right-hand term is a function of p and ψ depending upon the equation of state and the function S(ψ).
A note on time-varying gravitational potentials
Authors: Surdin M. 
Published: November 2008

ABSTRACTUsing Newtonian theory of gravitation and postulating the existence of informational waves of gravitation, a time-varying gravitational potential is obtained. When a point mass is submitted to such a potential a precession of its orbit, of the right order of magnitude, is obtained. The correct value of the angle of deflexion of light by massive bodies can also be calculated.
On some inequalities of H. Kober
Authors: Diananda P. H. 
Published: November 2008

Throughout this paper q1,q2,… are positive and x1,x2,… non-negative real numbers. When q1+…+ qn = 1, we define Δn, Sn and Σn as follows:andWe use the term ‘comparable’ in Kober's(2) sense. Two functions f(x1, …, xn) and g(x1, …, xn) are comparable if and only if αg ≤ f ≤ βg for some positive constants α and β.
Some two-dimensional punch and crack problems in classical elasticity
Authors: England A. H. , Green A. E. 
Published: November 2008

AbstractGeneral methods for solving two-dimensional punch and crack problems in classical elasticity have been developed by Muskhelishvili and others. An alternative method for solving such problems is presented here. Use is made of suitable integral representations of the complex potentials and each problem is reduced to the solution of an Abel or Fredholm type of integral equation.
The motion of a non-conducting sphere through a conducting fluid in a magnetic cross-field
Authors: Ludford G. S. S. , Singh M. P. 
Published: November 2008

AbstractThe title problem for a perfectly conducting sphere was considered by Stewartson(6). Here we use a different method and a more realistic assumption concerning the sphere. Although the flow is still ultimately cylindrical, there is no longer a column of fluid which moves with the sphere as if solid. There is no reason to expect that in practice the flow will break away into eddies. In fact the same is true in Stewartson's case, once his results are corrected.
h2- and h4-extrapolation in eigenvalue problems
Authors: Dennis S. C. R. 
Published: November 2008

Two recent papers have discussed eigenvalue problems relating to second-order, self-adjoint differential equations from the point of view of the deferred approach to the limit in the finite-difference treatment of the problem. In both cases the problem is made definite by considering the differential equationprimes denoting differentiation with respect to x, with two-point boundary conditionsand given at the ends of the interval (0, 1). The usual finite-difference approach is to divide the range (0, 1) into N equal strips of length h = 1/N, giving a set of N + 1 pivotal values φn as the analogue of a solution of (1), φn denoting the pivotal value at x = nh. In terms of central differences we then haveand retaining only second differences yields a finite-difference approximation φn = Un to (1), where the pivotal U-values satisfy the equationsdefined at all internal points, together with two equations holding at the end-points and approximately satisfying the end conditions (2). Here Λ is the corresponding approximation to the eigenvalue λ. A possible finite-difference treatment of the end conditions (2) would be to replace (1) at x = 0 by the central-difference formulaand use the corresponding result for the first derivative of φ, i.e.whereq(x) = λρ(x) – σ(x). Eliminating the external value φ–1 between these two and making use of (1) and (2) we obtain the equationwhere for convenience we write k0 = B0/A0. Similarly at x = 1 we obtainwithkN = B1/A1. If we neglect terms in h3 in these two they become what are usually taken to be the first approximation to the end conditions (2) to be used in conjunction with the set (4) (with the appropriate change φ = U, λ = Λ). This, however, results in a loss of accuracy at the end-points over the general level of accuracy of the set (4), which is O(h4), so there is some justification for retaining the terms in h3, e.g. if a difference correction method were being used they would subsequently be added as a correction term.
Coulomb wave functions for low energies
Authors: Meligy A. S. 
Published: November 2008

AbstractThe irregular radial Coulomb wave function is expanded in a convergent series of Bessel functions in which the coefficients are expressed in powers of the energy and the argument of the Bessel functions depends on the radius only and not on the energy. This formulation is suitable for low-energy particles. The corresponding expansion for the regular Coulomb function can be deduced from previous work by Tricomi.