bluuebunny/crossref_metadata_2025_split huggingface dataset:
XXV.—On the Groups of Units of Ternary Quadratic Forms with Rational Coefficients
Authors: Mennicke J. 
Published: July 2016

SynopsisFuchsian groups that are unit groups of ternary quadratic forms with rational integer coefficients are studied. By means of the well-known Nielsen classification of finitely generated Fuchsian groups, a complete survey of the unit groups is given. For this, we have to use the arithmetical methods of B. W. Jones. In the second part, the relations between Fuchsian groups arising from different quadratic forms are studied. It turns out that, with a finite number of exceptions, all these Fuchsian groups are subgroups of a particular one.
II.—The Attempted Synthesis of Benzo[a]biphenylene
Authors: Campbell Neil , Morris Robert A. N. 
Published: July 2016

SummaryUnsuccessful efforts to synthesize benzo[a]biphenylene and dibenzo-biphenylenes by the dehydrohalogenation of suitable intermediates are described. 2-o-Chlorophenyl-2-phenylpropionitrile with potassamide in liquid ammonia failed to give 8-cyano-7-phenylbicyclo[4,2,o]octa-I,3,5-triene, while diethyl 2-bromobenzylphenylmalonate with sodium in dry ethanol yielded I-phenylisochroman-3-one after hydrolysis. Bromination of 3,3′,4,4′-tetrahydro-2,2′-binaphthyl was accompanied by spontaneous dehydrobromination to yield 2,2′-binaphthyl, and interaction of phenyl-o-chlorophenylbromomethane with phenyllithium followed by chloracetic acid gave 1,2-di-o-chlorophenylethane.
IV.—On the Integrals of Hua and James.
Authors: Jack Henry 
Published: July 2016

SynopsisRecently a power series representation of Hypergeometric functions with matrix argument has been established. This representation involves a special type of spherical function from the theory of semi-simple Lie groups, called the zonal polynomials. A general theory of these polynomials is well established; however an explicit representation of them is lacking. This paper considers two integrals which are related to this explicit representation. The final paragraph considers a third integral which gives an application of a result from a previous paper of the author.
XVIII.—A Theory to Predict the Transport and Relaxation Properties of a Turbulent Fluid
Authors: Tyldesley J. R. 
Published: July 2016

SynopsisA new approach to the analysis of transport processes in a turbulent fluid is presented In this approach a model is used to represent the detailed fluid behaviour and it is shown that the model has similarities with a Fourier integral representation of the flow field. The model assumes that the turbulent motions can be represented by fluid entities of random size, shape and velocity, and that the large-scale transport processes are the consequences of the creation, decay and mutual interaction of the individual entities. The effects of this are analysed and it is shown how the diffusivities for vector and scalar quantities can be determined in terms of properties of the turbulence. The theory is applied in both bounded and free turbulent flows and it is shown that the predicted diffusivity ratios compare favourably with experimental data. Relaxation phenomena are also investigated and the memory function for stress and thermal relaxation is determined. It is concluded that the model provides a most useful framework for the analysis of turbulence phenomena and that its diverse and accurate predictions make it a powerful research tool.
VI.—The Stress Intensity Factors for a Griffith Crack in an Elastic Body in which there is an Asymmetrical Distributtion of Body Forces
Authors: Sneddon I. N. , Tweed J. 
Published: July 2016

SynopsisFormulae for the calculation of the stress intensity factor at the tip of a Griffith crack and for the normal component of the surface displacement are derived for a stressfree crack in an elastic solid in which there is an asymmetrical distribution of body forces. Particular distributions of point forces are considered in detail.
13.—A Search for the Quark in Extensive Air Showers, using a Counter-controlled Cloud Chamber
Authors: Evans G. R. , Fancey N. E. , Muir J. , Watson A. A. 
Published: July 2016

SynopsisA search is reported for the relativistic e/3 quark among the cores of Extensive Air Showers initiated by primaries with energies greater than 1014 eV. The detector is a high-pressure cloud chamber filled with helium at 28 atmospheres, and is counter controlled. The experimental conditions avoid the criticisms levelled at the McCusker experiment and are such that the tracks of e/3 quarks cannot be simulated by singly charged shower particles either through statistical variations in primary ionisation or otherwise. The primary ionisation density, measured using a gap-counting technique on post-expansion electron and muon tracks, is compared with predictions from the theory of Budini et al. (1960). The agreement achieved shows that the theory is a reliable foundation for methods of identifying quark candidates, and measuring charges. The experiment has been running for 5000 hours. No quark candidates have been found. With an acceptance angle of 0·3 sr and an area of 140 cm2, this sets the upper limit of flux of e/3 quarks at 4 × 10−9 cm−2 sec−1 sr−1 with 95 per cent, confidence. The experiment is being continued.
22.—Organic Scintillators with Improved Timing Characteristics.
Authors: Birks J. B. , Pringle R. W. 
Published: July 2016

SynopsisTheoretical and experimental studies have been made of the scintillation pulse shapes of organic scintillators. In a unitary crystal the pulse shape is characterised by the scintillation decay timeτs. In solution scintillators additional parameters are required to describe the pulse shape: Δt, the pulse width (FWHM);tm, the time at which the intensity reaches a maximumpmax; andt½, the time at which the intensity reaches ½pmax. General relations are derived for τs, Δτ,τm,τ½, andpmaxfor binary liquid solutions in terms of molecular parameters, and the corresponding expression is given for the scintillation pulse shape of a binary plastic solution.The scintillation pulse shapes of 4 binary liquid solutions and 12 binary and 15 ternary plastic solutions were measured using a single-photon sampling fluorometer. The results confirm the theoretical analysis. A new plastic scintillator (NE 111) with improved timing characteristics has thus been developed, and some of its applications in nuclear physics are briefly discussed. The time association of nuclear events can be measured to within 130 ps with this scintillator, the limiting factor being the time jitter of the photomultiplier itself.
26.—Recent Light on Optical Interference
Authors: Sillitto R. M. 
Published: July 2016

SynopsisThe interpretation of optical interference experiments at low light intensities and with independent light sources is discussed. A new experiment on interference between modulated light beams is described briefly, and its significance is indicated. There are two appendices, one a fuller discussion of the conditions under which interference and intensity correlation may be produced, the other a comment on one aspect of Jánossy and Nagy's discussion (1956) of the feasibility of the alternating slit interference experiment.
3.—Some Structure Semigroup Results for Arens-Singer Semigroups
Authors: McKilligan Sheila A. 
Published: July 2016

SynopsisIn this paper we discuss the structure semigroup of the L1-algebra of an Arens-Singer semigroup. Arising from this study we provide a complete and rather unexpected description of a nontrivial structure semigroup. We then link the above ideas with that of the almost periodic compactification of the semigroup.
6—The Instability of Two Vortex Sheets Enclosing a Subsonic Jet due to Acoustic Radiation
Authors: Hardisty N. 
Published: July 2016

SummaryThe propagation of sound in a subsonic jet separated by two vortex sheets from two semi-infinite still media is considered and it is found that instability waves arise at particular points on the vortex sheets and that their effect is confined to certain regions.
15.—A Class of Focal Points for Non-self-adjoint Fourth-order Differential Equations
Authors: Kreith Kurt 
Published: July 2016

SynopsisConjugate points are defined in terms of solutions of a linear fourth-order differential equation satisfying two homogeneous boundary conditions at x = α and either u(β) = u′(β) = 0 or u′(γ) = u″(γ) = 0. The smallest β > α and γ > α such that these boundary conditions are satisfied by a non-trivial solution of the equation are denoted by η(α) and ῆ-(α), respectively. Upper bounds are established for min [η(α), ῆ(α)] relative to the conjugate points of a self-adjoint differential equation which is majorised by the more general equation under study.
V.—Bifurcation of a Parallel-Plate Waveguide by a Unidirectionally Conducting Screen
Authors: Arora R. K. 
Published: July 2016

SynopsisThe types of modes which may exist in an infinite parallel-plate waveguide with a centrally-placed unidirectionally conducting screen are studied. The effect of bifurcating an infinite parallel-plate waveguide by such a screen in the region x>O is investigated when a transverse electric mode is incident on the bifurcated region. The problem is solved by the Wiener-Hopf method, and expressions are derived for the amplitudes and phases of the reflected and transmitted modes. It is found that the transmitted field contains a hybrid wave and a slow wave, and the reflected field contains transverse electric and transverse magnetic waves.
VI.—Neumann-Series Solutions of the Ellipsoidal Wave Equation
Authors: Arscott F. M. 
Published: July 2016

SynopsisThe ellipsoidal wave equation is the name given to the ordinary differential equation which arises when the wave equation (Helmholtz equation) is separated in ellipsoidal co-ordinates. In this paper, solutions of the equation are expressed as Neumann series (series of Bessel functions of increasing order).
26.—The Strong Limit-2 Case of Fourth-order Differential Equations
Authors: Krishna Kumar V. 
Published: July 2016

SynopsisThe fourth-order equation considered isConditions are given on the coefficients r, p and q which ensure that this differential equation (*) is in the strong limit-2 case at ∞, i.e. is limit-2 at ∞. This implies that (*) has exactly two linearly independent solutions which are in the integrable-square space ℒ2(0, ∞) for all complex numbers λ with im [λ] ≠ 0. Additionally the conditions imply that self-adjoint operators generated by M[·] in ℒ2(0, ∞) are semi-bounded below. The results obtained are applied to the case when the coefficients r, p and q are powers of x ∈ [0, ∞).
1.—An Algorithm for the Construction of Limit Circle Expressions
Authors: Zettl Anton 
Published: July 2016

SynopsisConsider the differential expressionIt is shown here that givenpn> 0 withpn∈C2n(0, ∞) there exist coefficientssuch that all solutions of the equationRy= 0 are inL2(0,∞). Thepifori<ncan be explicitly obtained in terms ofpnand a parameter function.
2.—The Matrix Functional Differential Equation y′(x) = Ay(λx) + By(x)
Authors: Carr Jack , Dyson Janet 
Published: July 2016

SynopsisThe purpose of this work is to consider some analytic aspects of the matrix functional differential equation, y′(x) = Ay(λx) + By(x), (0 ≦ x < ∞), where λ is a constant with 0 < λ < 1 and A and B are constant matrices.
XXIV.—Sets of Integers Containing not more than a Given Number of Terms in Arithmetical Progression
Authors: Rankin R. A. 
Published: July 2016

SYNOPSISSets of integers are constructed having the property that n members are in arithmetical progression only if they are all equal; here n is any integer greater than or equal to 3. Previous results have been obtained only for n=3. The problem is generalized in various ways. The analysis can also be applied to construct sets for the analogous problem of geometrical progressions. These sets are of positive density, unlike those of the first kind, which have zero density.
Sir Charles Percy
Authors: Nicholls Mark 
Published: July 2016

IN THE CHANCEL of Dumbleton Church, Gloucestershire, there is a monument bearing the following inscription:Here lye the bodies of Sir Charles Percye Knight 3rd Sonne of the Earle of Northumberland and of Dame Dorathy his Wife the Daughter of Thomas Cocks of Cleeve Esquire and of Anne their daughter. Sir Charles was buried the 9 Day of Iuly Anno Domini 1628, Dame Dorathy the 28th of Iune 1646.
Non-linear boundary value problems for systems of differential equations†
Authors: Knobloch H. W. , Schmitt K. 
Published: July 2016

SynopsisThe paper deals with boundary value problems for second-order vector differential equations x″ = f (t, x, x′). Given a region Ω in (t, x)-space we ask whether there exists a solution x(t) of the problem satisfying (t, x(t)) ∊Ω. We arrive at a rather general type of conditions which are sufficient in order that Ω has the desired property. One of these conditions is geometric in nature and depends upon the boundary data only. The second condition can be expressed in terms of inequalities and depends upon the values of f on ∂Ω. These inequalities turn out to be the common background of a variety of conditions which can be found in the literature on boundary value problems and which in the case of a scalar equation reduce to the well-known properties of upper and lower solutions.
Sturm-Liouville operators with an indefinite weight function
Authors: Daho K. , Langer H. 
Published: July 2016

SynopsisSpectral properties of the singular Sturm-Liouville equation –(p−1y′)′ + qy = λry with an indefinite weight function r are studied in . The main tool is the theory of definitisable operators in spaces with an indefinite scalar product.
6.—Smooth Fronted Waves in the Shallow Water Approximation
Authors: Jeffrey Alan 
Published: July 2016

SynopsisThis paper examines the mathematical problem of the propagation of a smooth fronted wavein the context of shallow water theory. Here, a smooth fronted wave will be taken to be one in which the surface slope is continuous across a line in the free-surface, while the second derivative of the surface slope is discontinuous across that same line. This discontinuity line in the surface then plays the role of the wavefront. After establishing that such wavefronts propagate along the characteristics, and deriving the appropriate transport equations, the explicit form is found for the acceleration with respect to distance of the horizontal component of the water velocity of the surface immediately behind the wavefront as a function of position and seabed profile when the wave propagates into still water. The result is then used to prove that in this approximation such a wave cannever break immediately behind the wavefront before the shore line is reached.
8.—Bifurcation and Asymptotic Bifurcation for Non-compact Nonsymmetric Gradient Operators
Authors: Toland J. F. 
Published: July 2016

SynopsisThe first part of this paper is devoted to a study of the classical bifurcation problem in a Hilbert space, under the assumption that the operators involved are gradient operators, but not necessarily compact. Our approach to the problem was introduced by Krasnosel'skii, but here we show that his assumption about the compactness of the operators can be replaced by a much weaker Lipschitz type condition, without affecting the generality of his conclusions.The rest of the paper is concerned with the analogous problem when the operator is knownto be asymptotically linear rather than Fréchet differentiable. Indeed, we show that this question can always be reduced to the first case, after some manipulation. After this manipulation the new operator is found to be a Fréchet differentiable gradient operator, and so we can invoke the results of the first part. This manipulation is in the spirit of that of [11] but is necessarily different.
The existence of eigenvalues embedded in the continuous spectrum of ordinary differential operators
Authors: Eastham M. S. P. , McLeod J. B. 
Published: July 2016

SynopsisIn answer to two questions raised by W. N. Everitt, we show that, givenp> l and any countably infinite set of isolated points on the positive λ-axis, there is aq(x)inLp(0, ∞) for which the set of points constitutes the point-continuous spectrum associated with the equationy”(x) + {λ − q(x)}y(x) = 0 (0≦x<∞)and some homogeneous boundary condition atx= 0.
9.—Bivariational Bounds associated with Non-self-adjoint Linear Operators
Authors: Barnsley Michael F. , Robinson Peter D. 
Published: July 2016

SYNOPSISLet A be a closed linear transformation from a real Hilbert space ℋ, with symmetric inner product 〈, 〉, into itself; and let f ∈ ℋ be given such that the problem Aø = f has a solution ø ∈ D(A), the domain of A. Then bivariational upper and lower bounds on 〈g, ø〉 for any g ∈ ℋ are exhibited when there exists a positive constant a such that 〈AΦ, AΦ⊖ ≧ a2〈Φ, Φ〉 for all Φ ∈ D(A). The applicability of the theory both to Fredholm integral equations and also to time-dependent diffusion equations is demonstrated.
11.—Equations d'Evolution du Second Ordre Associées à des Operateurs Maximaux Monotones
Authors: Véron Laurent 
Published: July 2016

SYNOPSISThis paper extends some recent results of V. Barbu and H. Brézis. It is concerned with bounded solutions of the problem pu″+qu′ ∈ Au, u(0) = a, where A is a maximal monotone operator in a real Hilbert space H and p and q are real functions. Existence and uniqueness theorems are proved, with results on integrability of solutions in various measure spaces on R+. T(t) denotes the family of contractions of D(A) generated by the equation and we obtain a regularising effect on the initial data. Some properties of this family of contractions are studied.
14.—Global Non-existence of Solutions to Ladyzhenskaya's Variants of the Navier-Stokes Equations Backward in Time
Authors: Straughan Brian 
Published: July 2016

SYNOPSISIt is shown that classical solutions backward in time to the alternatives to the Navier-Stokes equations proposed by Ladyzhenskaya cannot exist for all time. Estimates are obtained for the maximum interval of existence.
17.—An Upper Bound for the Largest Zero of Hermite's Function with Applications to Subharmonic Functions
Authors: Hayman W. K , Ortiz E. L 
Published: July 2016

SYNOPSISLetbe Hermite's function of order λ and let h = h(λ) be the largest real zero of Hλ(t). SetIn this paper we establish the inequalitywhereEquality holds for S = ½. The result is also fairly accurate as S→0 and S→1. The proof is analytical except in the ranges −1·1 ≦ h ≦ −0·1 and where the argument is concluded by means of a computer.The following deduction is made elsewhere [2, Theorem A]. If u(x) is subharmonic in Rm(m ≧ 2) and the set E where u(x) > 0 has at least k components, where k ≧ 2, then the order ρ of u(x) is at least ϕ(1/k). In particular, if ρ < 1, E is connected. This result fails for ρ = 1.
21.—The Structure of certain Ordered Regular Semigroups
Authors: Blyth T. S. 
Published: July 2016

SYNOPSISIn a previous publication [1] we determined the structure of some new types of ordered inverse semigroup in which the ordering need not be the natural ordering. At the moment, very little is known about ordered regular semigroups and the purpose of this paper is to generalise the structure theorems in [1] to corresponding theorems on ordered regular semigroups. The results obtained provide an interesting bridge between the theory of semigroups and that of ordered semigroups, these theories currently having very little in common.
On mixed boundary value problems for the Helmholtz equation
Authors: Kress R. , Roach G. F. 
Published: July 2016

SynopsisExistence and uniqueness theorems are obtained for a class of mixed boundary value problems associated with the three-dimensional Helmholtz equation. In this context the boundary of the region of interest is assumed to consist of the union of a finite number of disjoint, closed, bounded Lyapunov surfaces on some of which are imposed Dirichlet conditions whilst Neumann conditions are imposed on the remainder. An integral equation method is adopted throughout. The required boundary integral equations are generated by a modified layer theoretic approach which extends the work of Brakhage and Werner [1] and Leis [2, 3].
Asymptotic stability and energy decay rates for solutions of hyperbolic equations with boundary damping
Authors: Quinn John P. , Russell David L. 
Published: July 2016

SynopsisThis report deals with the asymptotic behaviour of solutions of the wave equation in a domain Ω ⊆Rn. The boundary, Γof Ωft consists of two parts. One part reflects all energy while the other part absorbs energy to a degree. If the energy-absorbing part is non-empty we show that the energy tends to zero as t→∞. With stronger assumptions we are able to obtain decay rates for the energy. Certain relationships with controlability are discussed and used to advantage.
Bounded oscillations under the effect of retardations for differential equations of arbitrary order
Authors: Staikos V. A. , Stavroulakis I. P. 
Published: July 2016

SynopsisThis paper is concerned with the effect of the delays on the bounded solutions of the nth order n ≧ 1) differential equationSufficient conditions involving the retardations τJ(j = 1,2, …, m) which insure that every bounded solution of the considered equation is oscillatory are given. The results obtained generalise recent ones in [3 and 4].
Perturbation of non-linear partial differential variational inequalities, I
Authors: Stroescu Elena 
Published: July 2016

SynopsisThe present paper is devoted to the study of the weak respectively strong convergence of solutions of variational inequalities, with non-linear partial differential operators of the generalised divergence form and of monotone type, under a perturbation of the domain of the definition. In this study there are used convergence concepts defined according to [ 22] and abstract convergence theorems given in [15 and 16].
Asymptotic decay of the solution of a second-order elliptic equation in an unbounded domain. Applications to the spectral properties of a Hamiltonian
Authors: Bardos C. , Merigot M. 
Published: July 2016

SynopsisIn an unbounded domain Ω we study the asymptotic decay (for | x |→∞) of functions u ∊ L2(Ω) which are solutions of the following problem –Δu + cu = 0. c denotes a strictly positive function. Upper bounds are easily found via the maximum principle. When c is rotationally invariant lower bounds are obtained via asymptotic expansion. In the general case we use a method of ‘commutation’ of operators. In particular we consider the case where . Applications to the asymptotic decay of the bound states of a Hamiltonian are given.
On the regularity of solutions to quasi-linear variational inequalities of degenerate elliptic type
Authors: Cooper Frances 
Published: July 2016

SynopsisUsing the theory of the weighted Sobolev space H1,2(μ), on a bounded domain Ω, in Rn, the existence and regularity of solutions u in K to the variational inequalityis established for various convex subsets K of H1, 2(μ). The growth conditions imposed on the functions A and B give the differential inequality degenerate elliptic structure, extending the results on regularity for inequalities of elliptic type.
A theory of fractional integration for generalised functions II
Authors: McBride Adam C. 
Published: July 2016

SynopsisIn a previous paper [2], a theory of fractional integration was developed for certain spaces Fp,μ of generalised functions. In this paper we extend this theory by relaxing some of the restrictions on the various parameters involved. In particular we show how a generalised Erdelyi-Kober operator can be defined on Fʹp,μ for 1 ≦ p ≦ ∞ and for all complex numbers μ except for those lying on a countable number of lines of the form Re μ = constant in the complex μ-plane. Mapping properties of these generalised operators are obtained and several applications mentioned.