bluuebunny/crossref_metadata_2025_split huggingface dataset:
X.—A Configuration of Points and Spheres in Four-dimensional Space
Authors: Brown L. M. 
Published: July 2016

SynopsisA theorem, due to Dr Grace, about a configuration of lines in [3], has been shown by him to be a rewording of a theorem about a configuration of points and spheres in [4]; in this six spheres pass through each point. The present paper discusses the analogous configuration in which seven spheres pass through each point.
XVI.—Two Hologram Methods in Diffraction Microscopy
Authors: Rogers G. L. 
Published: July 2016

SynopsisThe Bragg two-hologram method for eliminating the unwanted image in Diffraction Microscopy is here thoroughly examined. It is shown to be of general validity for objects containing both amplitude and phase-contrast terms.Other two-hologram methods are briefly discussed. In principle any two sufficiently distinct holograms may be used, but the Bragg 2:1 focal ratio is the simplest. The pair of holograms at ±f is also of interest, since it allows moderate degrees of phase-contrast and amplitude-contrast terms in the original object to be separated. A “three-wavelength” technique for obtaining the Bragg records is briefly outlined.
XV.—Dual Series Relations II. Dual Relations Involving Dini Series
Authors: Srivastav R. P. 
Published: July 2016

SynopsisThe problem discussed is that of determining the sequence {an} such thatwhere (λn) is the sequence of positive zeros of the function λJν(λ) + HJν(λ), arranged in order of increasing magnitude, þ, ν and H are real constants (−I <þ < I, ν > −½) and f1(ρ), f2(ρ) are prescribed. By expressing the sequence {cn} in terms of a sequence of integrals involving a function g(t) the problem is reduced to the solution of a non-singular Fredholm integral of the second kind for g(t).
XX.—Differential Geometry on Hypersurfaces in a Cayley Space
Authors: Yano K. , Sumitomo T. 
Published: July 2016

A seven-dimensional Euclidean space considered as the space of purely imaginary Cayley numbers is called a Cayley space. The six-dimensional sphere in a Cayley space admits an almost complex structure which is not integrable. Moreover the algebraic properties of the imaginary Cayley numbers induce an almost complex structure on any oriented differentiable hypersurface in the Cayley space. The Riemannian metric induced on the hypersurface from the metric of the Cayley space is Hermitian with respect to the almost complex structure.It is proved that the induced Hermitian structure of an oriented hypersurface in the Cayley space is almost Kaehlerian if and only if it is Kaehlerian, that a necessary and sufficient condition for a hypersurface in a Cayley space to be an almost Tachibana space is that the hypersurface be totally umbilical, and that a totally umbilical hypersurface in a Cayley space admits a complex structure when and only when it is totally geodesic.For a hypersurface in the Cayley space with the induced Hermitian structure which is an *O-space it is proved that all the principal curvatures of the hypersurface are constant, and from this is deduced a classification of such *O-spaces.
XXI.—A Mathematical Model of a Retinal Rod
Authors: Duxbury Anne 
Published: July 2016

SynopsisA study is undertaken of the field excited in a semi-infinite cylindrical dielectric rod having small conductivity when plane harmonic electromagnetic waves are incident obliquely upon its end. All back-scattering and the complicated edge effects due to the end of the rod are neglected. Expressions for the normalized power absorbed in the rod are obtained by an approximation technique from the corresponding results for a similar rod whose conductivity is zero, assuming that the radiation through the walls of the rod may be ignored. Selected numerical results are presented and the relevance of these to models of a retinal rod of the human eye is discussed.
XIV.—On Bounded Integral Operators in the Space of Integrable-Square Functions
Authors: Chisholm R. S. , Everitt W. N. 
Published: July 2016

§ 1. Let L2(0, ∞) denote the Hilbert space of Lebesgue measurable, integrable-square functions on the half-line [0, ∞).Integral operators of the formacting on the space L2 (0, ∞) occur in the theory of ordinary differential equations; see for example the book by E. C. Titchmarsh [4; § 2.6]. It is important to establish when operators of this kind are bounded; see the book by A. E. Taylor [3; § 4.1 and §§4.11, 4.12 and § 4.13].
XV.—A Uniform Asymptotic Expansion for a Certain Double Integral
Authors: Jones D. S. 
Published: July 2016

SynopsisThe effect of the presence of singularities on the method of stationary phase for a certain integral of two variables is examined. The singularities lie on two straight lines whose positions depend upon parameters. For certain values of the parameters the straight lines can pass through the point of stationary phase.The asymptotic development, which is uniform with respect to the parameters, is determined. It is found that it can be expressed in terms of a function which, in certain circumstances, reduces to a Fresnel integral. The main properties of this function are derived in an appendix.Explicit formulae are given for the dominant asymptotic terms in the cases when the point of stationary phase is approached by (i) neither line, (ii) only one of the lines, (iii) both lines.
XXI.—The Synthesis of Some Methyl- and Dimethylfluoranthenes
Authors: Andrew H. F. , Campbell Neil , Swan E. M. , Wilson N. H. 
Published: July 2016

3-Methylfluorene-9-propionic acid (1) with hydrofluoric acid undergoes ring-closure on the substituted ring to give 1,2,3,10b-tetrahydro-5-methylfluoranthen-3-one (II).Wolff-Kishner reduction of the ketone yielded l,2,3,10b-tetrahydro-5-methylfluoranthene which on dehydrogenation gave 2-methylfluoranthene (III, R=H) identical with a sample prepared according to the method of Tucker (1952) and differing from 8-methylfluoranthene. This proved that ring-closure of (I) had occurred as expected on the methyl-bearing benzene ring. In this instance ring-closure occurs in the position meta to the methyl group and is reminiscent of the similar ring-closure of 2-phenyl-2-p-tolylpropionic acid to give 6-methyl-3-phenylindanone (Pfeiffer and Roos 1941). It thus provided a further example of the limitations of von Braun's statement that Friedel-Crafts ring-closure occurs much less readily at the position meta to a methyl group than on a phenyl ring (von Braun, Manz and Reinsch 1928).
XXV.—A Surface Integral and Symmetric Functions.
Authors: Jack Henry 
Published: July 2016

SynopsisIn a previous paper (Jack 1970, § 5) the pre-zonal polynomials were defined by the surface integral (1) below. In that paper they were evaluated using a series of differential type operators acting on the sums of powers of the roots of a matrix.The present paper, although it is a continuation of Jack (1970), is self-contained and consists of three parts. The first part, §§ 3–7, shows how the pre-zonal polynomials may be calculated, certainly for low degree, using only the first of the differential operators. The next part, §§ 8–11, is devoted to establishing various recurrence relations between the pre-zonal polynomials and to conjecturing similar recurrence relations between the zonal polynomials (James 1964, p. 478). In the final part, §§ 12–14 the pre-zonal polynomials are evaluated directly from the integral (1) below, in terms of the augmented monomial symmetric functions.
2.—The Proportional Counter as a Position-Sensitive Device.
Authors: Braid T. H. 
Published: July 2016

SynopsisThe location of the trajectory of a charged nuclear particle can be determined by a number of devices whose operation depends on characteristics of gas counters operated in the region of proportional energy response. Such devices have advantages in precision, speed or available size over other types of position-sensitive counters. The events may be located by observing pulses on one of a set of closely spaced anode wires in a common gas volume, by measuring the drift time of primary electrons to a particular anode wire, or by determining the location of an electron avalanche along the length of a single anode. The operation of the different types of systems and the factors affecting their precision are described. Precision to less than 1 mm can be obtained in a number of ways,
4.—Search for Branching in the β+ Decay of the 42Sc Ground State
Authors: Burcham W. E. , Murray G. , Robinson D. C. , Freeman J. M. , Jenkin J. G. 
Published: July 2016

SynopsisA search was made for branching to the 1–84 MeV state of 42Ca in the 42Sc ground state decay. This was found to be less than 0·02 per cent. The branching has a negligible effect on the calculation of the vector coupling constant Gv for the weak interaction from the 42Sc decay.
8.—The Temperature Dependence of Localised Magnons
Authors: Cowley R. A. 
Published: July 2016

SynopsisThe temperature dependence of the properties of magnetic crystals containing defects is calculated with a simple linear chain model. The model enables the spin deviations caused by the impurity to be treated throughout the whole crystal instead of being restricted to the neighbourhood of the defect as in other recent theories. The results are in qualitative agreement with experimental results and suggest that stable spin clusters may be found surrounding each defect above Tc. The approximations used in other theories are shown to be suspect above 0·5 Tc.
14.—Ground State Rotational Bands in 158Dy, 160Dy and 162Dy
Authors: Ewan G. T. , Andersson G. I. 
Published: July 2016

SynopsisLevels in the ground state bands of 158Dy, 160Dy and 162Dy have been populated by (α, 2n) reactions on metallic targets of separated 156Gd, 158Gd and 160Gd isotopes. Two Ge(Li) detectors were used to study singles gamma-ray spectra, gamma-ray angular distributions, gamma-gamma coincidence spectra and relative yields of gamma-rays for bombarding energies from 20 to 27 MeV. Transitions from all levels in the ground state bands up to the 12+ member were identified and the following level energies in keV established: 158Dy: 0 (0+), 99·0 (2+), 317·4 (4+), 637·9 (6+), 1044·1 (8+), 1520·1 (10+) and 2049·4 (12+); 160Dy: 0 (0+), 86·7 (2+), 283·7 (4+), 581·4 (6+), 967·4 (8+), 1429·0 (10+), 1951·7 (12+); 162Dy: 0 (0+), 80·7 (2+), 265·7 (4+), 548·5 (6+), 921·1 (8+), 1374·8 (10+) and 1901·0 (12+). There is weak evidence for the 14+ levels in 158Dy and 160Dy. The level energies are compared with calculated values using the variable moment of inertia model.
19.—Classical Electromagnetism—How should One Teach It Today?
Authors: Kemmer N. 
Published: July 2016

SynopsisThe author maintains that a course in the classical theory of the electromagnetic field, with full exploitation of vector calculus methods, should be thought of as being as much of a basic essential in any physics honours course as is a course on classical mechanics. It is suggested that if the mathematical techniques are taught in a way that relates them directly to the central notions of field theory and avoids discussion of special techniques, the mathematical burden is sufficiently light to be borne by all physics students, not only those theoretically inclined. The course need not be of excessive length if it is understood as exclusively an introduction to field concepts and hence not to cover in any detail the electric and magnetic property of materials. A number of particular ideas arising from the author's teaching experience are discussed.
21.—Asymptotic Evaluation of Certain Integral Formulae for Ellipsoidal Wave Functions
Authors: Hargrave B. A. , Sleeman B. D. 
Published: July 2016

SynopsisAlthough integral equations and relations for ellipsoidal wave functions have been known for some time, it had previously been impossible to obtain asymptotic estimates for these integrals, with large wave parameter, as the available asymptotic expansions for the integrand were non-uniform. However, uniform asymptotic expansions have recently been calculated for the functions occurring in the integrand, and these expansions are now used to determine asymptotic expansions for ellipsoidal wave functions of the third kind. A different type of normalisation is proposed for ellipsoidal wave functions and this is compared with previous normalisations by evaluating asymptotically a double integral.
II.—The Effect of Concentration on the Terminal Fall Velocity of Particles in Suspension
Authors: Thorpe Hugh Rankin 
Published: July 2016

SynopsisThe paper describes an investigation of the terminal velocity of uniformly dispersed particles of various shapes, sizes and densities falling through water.It is concluded that for concentrations above 0–5 per cent by weight, the suspension as a whole behaves as though it were viscous even though the individual particles lie well outside the Stokes range. The shape of the particles has a significant effect only when the concentration is less than 0·5 per cent, and for concentrations between 0·5 and 7·0 per cent, the relative changes in velocity of descent are adequately described for a range of particle shapes from highly angular to spherical and for sizes at least up to 0·65 mm. nominal diameter, by the power seriesin which U is the velocity of the suspension, U0 that of a single particle, d the nominal diameter (i.e. that of a sphere having the same volume) and s the mean spacing of the particles.If the concentration is lower than 4 per cent, the equation may be assumed linear in (d/s) without serious error.
IV.—The Stress in the Vicinity of an Infinite Row of Collinear Cracks in an Elastic Body
Authors: Sneddon I. N. , Srivastav R. P. 
Published: July 2016

SynopsisThe distribution of stress in the neighbourhood of an infinite row of collinear cracks in an elastic body is calculated for general distributions of internal pressure. The case in which each of the cracks is opened out by the same constant pressure is considered in detail; the variation with the ratio of the width of the crack to the distance between two cracks of quantities of physical interest is shown in a series of diagrams.
29.—Fine-structure in the Mass-yield Curve for Binary Fission—A Possible Secondary Effect
Authors: Feather N. 
Published: July 2016

SynopsisThe recent suggestion (Feather 1974) that the short-range α-particles of fission are emitted predominantly from post-neutron-emission fragments in the mass-number range 140 to 145 is shown to have implications in relation to the fine-structure of the mass-yield curve. An examination of the mass-yield curves of Unik et al. (1973) discloses, in many of them, a fine-structure feature of the type predicted.
V.—On Certain Classes of Linear Algebras of Genus One
Authors: Patterson E. M. 
Published: July 2016

SynopsisA result proved elsewhere concerning the structure of linear algebras of genus one is used (i) to classify Jordan algebras of genus one, and (ii) to obtain necessary and sufficient conditions for an algebra of genus one to be simple. The class of simple Jordan algebras of genus one and dimension not less than 4 over an algebraically closed field is shown to coincide with the class of simple Jordan algebras of degree two.
4.—An Algorithm for the Construction of all Disconjugate Operators.
Authors: Zettl Anton 
Published: July 2016

SynopsisA differential operator (1) Ly = y(n) + an-1(t)y(n-1) +…+ao(t)y is said to be disconjugate on an interval I if every non-trivial solution of Ly = 0 has less than n zeros on I, multiple zeros being counted according to their multiplicity. An algorithm for the construction of disconjugate operators of type (1) is given here. All such operators are obtained at least in the case when the interval I is open or compact.
XVI.—The Synthesis of 1, 6-Naphthyridine
Authors: Ferrier B. M. , Campbell Neil 
Published: July 2016

SUMMARYThe synthesis of 1, 2, 3, 4-tetrahydro-1, 6-naphthyridine and 1, 6-naphthyridine is described and the ultra-violet spectra of these and related substances are discussed.
The evolution of general intelligence
Authors: Burkart Judith M. , Schubiger Michèle N. , van Schaik Carel P. 
Published: July 2016

AbstractThe presence of general intelligence poses a major evolutionary puzzle, which has led to increased interest in its presence in nonhuman animals. The aim of this review is to critically evaluate this question and to explore the implications for current theories about the evolution of cognition. We first review domain-general and domain-specific accounts of human cognition in order to situate attempts to identify general intelligence in nonhuman animals. Recent studies are consistent with the presence of general intelligence in mammals (rodents and primates). However, the interpretation of a psychometricgfactor as general intelligence needs to be validated, in particular in primates, and we propose a range of such tests. We then evaluate the implications of general intelligence in nonhuman animals for current theories about its evolution and find support for the cultural intelligence approach, which stresses the critical importance of social inputs during the ontogenetic construction of survival-relevant skills. The presence of general intelligence in nonhumans implies that modular abilities can arise in two ways, primarily through automatic development with fixed content and secondarily through learning and automatization with more variable content. The currently best-supported model, for humans and nonhuman vertebrates alike, thus construes the mind as a mix of skills based on primary and secondary modules. The relative importance of these two components is expected to vary widely among species, and we formulate tests to quantify their strength.
An estimate of harmonic measure in Ṟd, d ≧ 2
Authors: Essén Matts 
Published: July 2016

SynopsisLet D be an open connected subset of the open unit ball in Ṟd, d ≧ 2. We give an estimate of the harmonic measure of ∂D∩{|x| = 1} with respect to D. This estimate depends in a simple way on the geometry of D. An essential tool is a rearrangement theorem for differential inequalities. When d = 2, examples are given which illustrate the precision of the results.
14.—A Generalised Walsh-Lebesgue Theorem
Authors: O'Farrell A. G. 
Published: July 2016

SynopsisLet X be the boundary of a compact set which does not separate the plane, C. Let Φ and Ψ be homeomorphisms of C to C with opposite orientations. Then every continuous complex-valued function on X is the uniform limit on X of sums p(Φ)+q(ψ), where p and q are analytic polynomials.
10.—An Abstract Relation for Multiparameter Eigenvalue Problems
Authors: Källström A. , Sleeman B. D. 
Published: July 2016

SynopsisConsider the multiparameter systemwhere ut is an element of a separable Hilbert space Hi, i = 1, …, n. The operators Sij are assumed to be bounded symmetric operators in Hi and Ai is assumed self-adjoint. In addition consider the operator equationwhere B is densely defined and closed in a separable Hilbert space H and Tj, j = 1, …, n is a bounded operator in H. The problem treated in this paper is to seek an expression for a solution v of (**) in terms of the eigenfunctions of the system (*).
17.—A New Class of Bessel Function Inequality useful for investigating the Roots of a Class of Transcendental Equation involving Bessel Functions
Authors: Rawlins A. D. , Jones D. S. 
Published: July 2016

SynopsisThe paper derives some new Bessel function inequalities These are used to determine conditions for the absence of roots of the transcendental equation F(z)Zv(z)+Zv′(z) = 0, where Zv(z) is a Bessel function, in certain regions of the v and z-plane
22.—A Critical Class of Examples concerning the Integrable-square Classification of Ordinary Differential Equations
Authors: Everitt W. N. , Giertz M. 
Published: July 2016

SynopsisLet the coefficient q be real-valued on the half-line [0, ∞) and let q′ be locally absolutely continuous on [0, ∞). The ordinary symmetric differential expressions M and M2 are determined byIt has been shown in a previous paper by the authors that if for non-negative numbers k and X the coefficient q satisfies the conditionthen M is limit-point and M2 is limit–2 at ∞.This paper is concerned with showing that for powers of the independent variable x the condition (*) is best possible in order that both M and M2 should have the classification at ∞ given above.
Non-existence of eigenvalues of Schrödinger operators
Authors: Kalf H. 
Published: July 2016

SynopsisThe paper provides conditions which enstlre that the Schrödinger operatordefined on an exterior domain has no eigenvalues on a certain half-ray. These conditions are in terms of weak local assumptions onThe proof uses Kato's ideas [16] in conjunction with the physicists' “commutator proof” of the quantum mechanical virial theorem.
The scattering of acoustic waves by a spherically stratified inhomogeneous medium
Authors: Colton David 
Published: July 2016

SynopsisIntegral operators are used to solve the direct and inverse problems of the scattering of acoustic waves by a spherically stratified inhomogeneous medium of compact support. The results are valid for all values of the wave number and an arbitrarily large index of refraction. In the limiting case of small wave number or small inhomogeneities the results are in agreement with those of Rorres and Born.
On two integral inequalities
Authors: Copson E. T. 
Published: July 2016

SynopsisIn 1932, Hardy and Littlewood [1] proved the inequalityThe constant 4 is best possible; equality occurs when f(x) = A Y(Bx), wherey(x) = e−½x sin (x sin y−y) (y = ⅓π), (x ≧ o)and A and B (>0) are constants. In [2], three proofs are given. The inequality has also been discussed in [3, 4]. A very elementary proof in which the function Y(x) emerges naturally is given in this paper.
Large Electroencephalographic Responses and Their Relationship to Cleido-Cranial Dysplasia
Authors: Upton Adrian , Bundey Sarah , Sanders Susan 
Published: July 2016

SUMMARY:We have reported six individuals (five certain heterozygotes for cleido-cranial-dysostosis and one possible heterozygote) who have unusual EEG findings, consisting of very large responses to photic flash stimulation at very low stimulus rates.Such visual responses are extremely rare and have not been seen before in the experience of an EEG department over 12 years and they were not seen in 98 control subjects. It is likely that these responses are an irregular mani-festation of the gene for cleido-cranial-dysplasia, and that the responses are independent of skull deformity. One importance of these responses is their demonstration in neurologically normal individuals for previously such large responses have only been reported in association with neurolipidosis. They may have neurophysiological significance in that they may reflect an unusual balance between inhibitory and excitatory mechanisms in the nervous system.
Giant Intracranial Dermoid Cyst: Case Report and Review of the Literature on Intracranial Dermoids and Epidermoids
Authors: Miller Neil R. , Epstein Melvin H. 
Published: July 2016

SUMMARY:A 45-year old man was referred to the Johns Hopkins Hospital with a seven-year history of repeated episodes of light-headedness, increasing irritability and forgetfulness. Examinations revealed a right superior, incongruous quadrantanopsia. EEG showed an abnormality in the left temporal lobe, and a cerebral angiogram outlined an avascular mass in the left cerebral hemisphere. At operation, the patient was found to have a giant dermoid cyst involving the left frontal, temporal and parietal lobes. Over the last 30 years we have encountered only 6 cases of intracranial epidermoids and 3 cases of intracranial dermoids. These cases are cited, and a discussion of the embryology, histology, clinical characteristics, and treatment of these lesions with a review of the literature is undertaken.
Compression of the Cauda Equina due to a Necrobiotic Granuloma of Ligamentum Flavum
Authors: Bilbao Juan M. , Horsey William , Gonsalves Charles , Chalvardjian Ara 
Published: July 2016

SUMMARY:A 56 year old woman developed symptoms of lumbar nerve root compression caused by a granuloma arising in the ligamentum flavum. The histological features of the lesion are discussed and the clinical and radiological findings of the patient are described.