bluuebunny/crossref_metadata_2025_split huggingface dataset:
25.—Spectrum of a Third-order Differential Operator with Large Coefficients
Authors: Unsworth K. 
Published: July 2016

SynopsisThis paper sets out to study the spectrum of self-adjoint extensions of the minimal operator associated with the third-order formally symmetric differential expression. The technique employed is the method of singular sequences. Sufficient conditions are established on the coefficients of the differential expression in order that the spectrum should cover the entire real axis. Particular cases in which the coefficients behave roughly as powers of x as the magnitude of x becomes large are then considered, and certain conclusions are drawn regarding the spectra under different restrictions on these powers of x.
31.—Spectral Manifolds for Constant Coefficient Elliptic Operators in Lp(Rn)
Authors: Thompson M. 
Published: July 2016

SynopsisThe principal results of this paper concern the spectral properties of the maximal realisation Pp in Lp(Rn) of a formally self adjoint constant coefficient strongly elliptic partial differential operator P(D), assumed to be homogeneous of order 2m, for 1 ≦ p ≦ ∞ and n ≧ 2. If we assume that , for 2n/n + l ≦ p ≦ 2n/n−1, together with certain assumptions on the associated real zero surfaces P(ξ) = λ, λ > 0, then σ(Pp) = σc(Pp) = [0, ∞). We obtain an estimate on the norm of the resolvent of Pp for points near the real axis, which allows us to establish the existence of a generalised resolution of the identity in the sense of Kocan.
19.—Calculations relative to the Experimental Observation of the Products of Disintegration of 5He liberated as a Light Particle in Ternary Fission
Authors: Feather N. , Vass D. G. 
Published: July 2016

SynopsisThere is now strong evidence, from observations of directional correlation between the α-particles and neutrons of fission, for the release of 5He as a neutron-unstable light particle with a frequency of a few per 104 low-energy fission events (Cheifetz et al. 1972).Because the energy spectrum of the neutrons liberated in the disintegration of 5He particles travelling with a fixed kinetic energy is a rectangular spectrum (assuming isotropy of disintegration directions in the centre-of-mass space), it is in principle possible to deduce the kinetic energy spectrum characterising the 5He particles of ternary fission at the moment of disintegration from the energy spectrum of the liberated neutrons.Detailed calculations have been made in relation to the limitations of actual experimental arrangements with regard to this possibility. These limitations are shown to be severe—not least in respect of statistical accuracy. Indeed, it is shown that considerable difficulty attaches to the ‘simple’ evaluation of the 5He/4He ratio (which Cheifetz et al. estimate as 1 :(8 ± 2) for 252Cf, for α-particles of energy greater than 9 MeV).An instrumental cause is suggested for the maximum reported by Cheifetz et al. in the energy spectrum ascribed to the 5He disintegration neutrons.
27.—The Quantum Theory of the Klystron and the Modulation of Electron Beams at Optical Frequencies
Authors: Farago P. S. , Sillitto R. M. 
Published: July 2016

SynopsisThe relationship between the modulation of electron beams at optical frequencies (the Schwarz-Hora effect) and at microwave frequencies is discussed. At optical frequencies the interaction between the modulating field and the electron beam must be described quantum mechanically, although the field itself may be described classically; in the microwave case the process may be described entirely classically. The interaction modifies the state functions of the individual electrons, but the observable modulation of the total electron beam results from the coherence of the modulating field. The main features of the Schwarz-Hora effect result from ‘single photon’ processes, but the beam modulation in the klystron is a ‘multi-photon’ process.The exponential decay of the depth of modulation with distance from the interaction region, observable in the optical frequency case but not in the klystron, is not an inherently quantal effect. The periodic variation of the depth of modulation with distance along the beam, observed in the optical frequency case, is an essentially quantum mechanical effect, and is different, in its origins and in its dependence on the modulation frequency, from the space-charge waves which are observed on a klystron beam.
5.—Semi-bounded Dirichlet Integrals and the Invariance of the Essential Spectra of Self-adjoint Operators
Authors: Evans W. D. 
Published: July 2016

SynopsisIn the first part of the paper a criterion is given for two self-adjoint operators T, S in a Hilbert space to have the same essential spectrum, S being given in terms of T and a perturbation P. If P is a symmetric operator and the operator sum T+P is self-adjoint, then S = T+P. Otherwise, T is assumed to be semi-bounded and S is taken to be the form extension of T+P defined in terms of semi-bounded sesquilinear forms. In the case when S = T+P, the result obtained generalises the results of Schechter, and Gustafson and Weidmann for Tm- compact (m> 1) perturbations of T. In the second part of the paper a detailed study is made of the Dirichlet integralassociated with the general second-order (degenerate) elliptic differential expression in a domain Conditions under which t is closed and bounded below are established, the most significant feature of the results being that the restriction of q to suitable subsets of Ω can have large negative singularities on the boundary of Ω and at infinity. Lastly some examples are given to illustrate the abstract theory.
XIV.—On Analysing the Physical Evolution of Galaxies
Authors: Reddish V. C. 
Published: July 2016

SYNOPSISInvestigations based on gas masses, bright star counts, and luminosity-mass ratios of galaxies lead to one of two conclusions. If the galaxies are all of the same age, the faint ends of the initial luminosity functions of stars at formation differ greatly from one galaxy to another. On the other hand consistent results in the analysis are obtained with luminosity functions that are more nearly constant and ages which range from one to thirty thousand-million years. The various possibilities can be tested by observations on the Magellanic Clouds.Equations are set up which describe, as functions of time, the integrated properties of a galaxy as a system of stars and gas.
A generalisation of Niessen's limit-circle criterion
Authors: Bennewitz Christer 
Published: July 2016

SynopsisLet S and T be formally symmetric ordinary differential operators defined on a real interval I. It is assumed that the order of S is constant and everywhere strictly higher than the possibly varying order of T. The main result of this paper (Theorem 2.3) gives necessary and sufficient conditions for maximality of the deficiency indices of the differential relation Su = Tv considered in a Hilbert space with a scalar product which is a Dirichlet integral (see section 2) belonging to S. The conditions generalise those given in [5] for less general choices of operators S and T. For certain choices of Dirichlet integral they are explicit integrability conditions on the coefficients of the Dirichlet integral and the operator T.
22.—The Linear Transport Equation. The Degenerate Case c = 1. I. Full-range Theory
Authors: Lekkerkerker C. G. 
Published: July 2016

SynopsisThe aim of this paper is to give a functional analytic treatment of the homogeneous and inhomogeneous linear transport equation in the case that the parameter c occurring in that equation equals 1. The larger part of the paper is devoted to the study of a certain operator T−1 A in the space L2(– 1, 1). A peculiarity not arising in the case c < 1 (treated amongst others by Hangelbroek) is that, for c = 1, the operator T−1A has a double eigenvalue 0 and that it is no longer hermitian. The Spectral Theorem is used to diagonalise the operator as far as possible, and full-range and half-range formulae are derived. The results are applied inter alia to give a new treatment of the Milne problem concerning the propagation of light in a stellar atmosphere.
Iterative bounds for the stable solutions of convex non-linear boundary value problems
Authors: Mooney J. W. , Roach G. F. 
Published: July 2016

SynopsisWe consider a class of convex non-linear boundary value problems of the formwhere L is a linear, uniformly elliptic, self-adjoint differential expression, f is a given non-linear function, B is a boundary differential expression of either Dirichlet or Neumann type and D is a bounded open domain with boundary ∂D. Particular problems of this class arise in the process of thermal combustion [8].In this paper we show that stable solutions of this class can be bounded from below (above) by a monotonically increasing (decreasing) sequence of Newton (Picard) iterates. The possibility of using these schemes to construct unstable solutions is also considered.
13.—The Instability of Two Vortex Sheets enclosing a Subsonic Jet due to an Acoustic Point Source
Authors: Hardisty N. 
Published: July 2016

SynopsisThe propagation of sound from a point source placed in a subsonic jet separated by two plane 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.
16.—Square Integrable Solutions of Perturbed Linear Differential Equations
Authors: Wong James S. W. 
Published: July 2016

SynopsisThis paper is concerned with solutions of the ordinary differential equationwhere ℒ is a real formally self-adjoint, linear differential expression of order 2n, and the perturbed term f satisfiesfor some σ∈[0, 1]. Here λ(·) is locally integrable on [0,∞).In particular it is shown, under circumstances detailed in the text, that (*) possesses solutions in the Hilbert function space L2(0,∞).
22.—Analytic, Generalized, Hyperanalytic Function Theory and an Application to Elasticity
Authors: Gilbert Robert P. , Wendland Wolfgang L. 
Published: July 2016

SynopsisThough it is still an open problem for which class of first-order elliptic systems Carleman's theorem holds, this is proven here for a certain class of systems (with analytic coefficients) for which Douglis introduced the hypercomplex algebra and hyperanalytic functions. The proof is based on a representation formula generalising Vekua's approach with Volterra integral equations in C2 to more than two unknowns. The representation formula is of its own interest because it provides the generation of complete families of solutions. The equations of plane inhomogeneous elasticity problems lead to a system of the desired class.
20.—Inequalities for the Capacity of an Electrified Conducting Annular Disc
Authors: Love E. R. , Collins W. D. 
Published: July 2016

SynopsisThe simultaneous integral equations of Noble and Cooke, for inter alia the Dirichlet problem for an annular disc, are transformed into equations closely analogous to those recently given by Clements and Love for the corresponding Neumann problem. The transformed equations are relatively simple, and do not involve any artificial preliminary dissection of the known functions. They are also uncoupled, and admit iterative solution for virtually all radius ratios.In the case of the conducting annular disc, iteration of these equations isused to obtain two series for the capacity, an interim one with all terms positive, and a final one with all terms after the first negative. The final series is more rapidly convergent as well as neater. It is used to provide a family of inequalities which enclose the capacity and determine it to high accuracy with very few terms, failing only when the radius ratio is close to 1.
21.—On Expansive Free Interactions in Boundary Layers
Authors: Brown S. N. , Stewartson K. , Williams P. G. , Collins W. D. 
Published: July 2016

SynopsisWhen a Mach number dependent parameter σ ≠ 0 is accounted forin an expansive free interaction analogous to that of Stewartson [7], the solution terminates in a singularity with a finite pressure, but with a pressure gradient varying as the inverse three-fifths power of the distance from the singularity, apart from a subtle logarithmic modification.
23.—Oscillation Phenomena in the Hodgkin-Huxley Equations
Authors: Troy William C. , McLeod J. B. 
Published: July 2016

SynopsisA widely accepted model of nerve conduction in the squid axon is the systemof four non-linear partial differential equations developed by Hodgkin and Huxley. Under space clamp and current clamp conditions these equations are reduced to a system of ordinary differential equations.We find that under appropriate assumptions on the functions and parameters in the resulting fourth order Hodgkin-Huxley equations there occurs a bifurcation of periodic solutions from the steady state. This bifurcation takes place as the current parameter, I, passes through a critical value.
Embeddings of Sobolev spaces of fractional order
Authors: Martins J. S. 
Published: July 2016

SynopsisIf Ω is a bounded domain in Rn satisfying certain conditions, Ωk denotes its intersection with a k-dimensional hyperplane, 1 ≦ k ≦ n, it is shown that the embedding of the Sobolev space Ws,p(Ω), s>0, into Lq(Ωk) is of type lm if for q<p<∞. The same result is obtained for the space of Bessel potentials Ls,p(Ω). Piecewise polynomial and Fourier approximations of functions and interpolation theorems areused.
Transformations between second order linear differential equations and a reinterpretation of recurrence relations between Bessel functions with algebraic coefficients
Authors: Heading John 
Published: July 2016

SynopsisA scheme devised by Chandrasekhar for investigating the transformations between various differential equations of the second order governing perturbations of the Schwarzschild black hole demands further investigation. The transformation between two differential equations in normal form is considered, and a wide survey of the properties of the transformation is given. It is shown how Chandrasekhar's equations fit into the scheme, after which some examples with particular properties are considered. A detailed investigation of Bessel's equation is undertaken using various devices, in particular by employing asymptotic methods for products of Bessel functions, and employing matrix methods for dealing with large numbers of matrix equations which necessitates an interesting method of solution, the results being reinterpretations of the standard recurrence relations for Bessel functions.
Higher monotonicity properties of certain Sturm-Liouville functions. V
Authors: Muldoon M. E. 
Published: July 2016

SynopsisThe principal concern here is with conditions onfor on special solutions of the equationwhich ensure that the higher differences of the zeros and related quantities of solutions of (1) are regular in sign. In particular, by choosingf(x)= 2v−2x1/v−2, it is shown that if ⅓ ≦|v|<½, thenwherecvkdenotes thekth positive zero of a Bessel function of ordervand Δµk= Δk+1− µk. Lorch and Szego [15] conjectured that (2) should hold for the larger range |v| < ½ but the methods used here do not apply to the range |v<| ⅓.
Development of a laminar boundary layer under conditions of continuous incipient separation
Authors: Curle N. 
Published: July 2016

SynopsisThis paper, extending the work of Stratford [6] considers a boundary layer with uniform pressure when x < x0, and with the pressure in x > x0 so chosen that the layer is just on the point of separation for all x >x0. The required pressure distribution is shown to beThe displacement and momentum thicknesses are also derived as series in powers of ξ (and log ξ), and the shape parameter H then obtained as a similar series. The continuous change in H from the Blasius value (when ξ = 0) towards the Falkner-Skan [3] separation value is convincingly demonstrated, with the aid of the leading terms of an asymptomatic expansion for large ξ.
Dual extremum principles for the heat equation
Authors: Collins W. D. 
Published: July 2016

SynopsisDual extremum principles characterising the solution of initial value problems for the heat equation are obtained by imbedding the problem in a two-point boundary-value problem for a system in which the original equation is coupled with its adjoint. Bounds on quantities of interest in the original initial value problem are obtained. Such principles are examples of ones which can be obtained for a general class of linear operators on a Hilbert space.
Sex-Linked Hereditary Ataxic Diplegia, the Borderland Between Cerebral Palsy and Pelizaeus-Merzbacher Disease
Authors: Dunn H.G. , Thompson Margaret W. , Bandler Elizabeth , Andrews L.G. 
Published: July 2016

SUMMARY:After a review of the literature concerning hereditary cases of cerebral palsy, a family is reported in which ataxic diplegia appears to be inherited as a sex-linked and probably recessive condition occurring in 3 males in successive generations. This ataxic diplegia, occurring after an unremarkable perinatal course, is associated with mild to moderate mental retardation, congenital nystagmus and significantly small stature and prevents the acquisition of free walking. Associated extrapyramidal features may gradually become more marked, while the nystagmus may subside. The condition is similar to that described in three previous reports in the literature. No evidence of linkage with other sex-linked disorders has been found, Xga typing showed that recombination between the Xg locus and the locus for hereditary ataxic diplegia has occurred once out of three possible opportunities. In the absence of neuropathological findings or specific biochemical tests, the differential diagnosis from Pelizaeus-Merzbacher disease cannot be made with certainty. The differentiation from other progressive sex-linked neurological disorders is discussed.
Spinal Myoclonus in Association with Herpes Zoster Infection: Two Case Reports
Authors: Dhaliwal G.S. , McGreal D.A. 
Published: July 2016

SUMMARY:Two cases of segmental spinal myoclonus, attributed to herpes zoster infection, are presented. The findings support the suggestion made by Campbell and Garland (1956) that “subacute myoclonic spinal neuronitis” is of viral origin. Both patients were receiving immuno-suppressive treatment when the myoclonus developed. The value of carbamazepine in therapy is mentioned.
Metastatic Medulloblastoma
Authors: Parkinson Dwight , Ross R.T. , Shields Christopher B. 
Published: July 2016

SUMMARY:The incidence of metastatic medulloblastoma is probably greater than the thirteen documented patients. Case reports of metastatic medulloblastoma must be carefully analysed. We have added two cases which conform to Weiss’ criteria for metastatic disease. The direction and factors influencing spread have been discussed.
3H Leucine Incorporation Into Myofibrils of Normal and Dystrophic Mouse Skeletal Muscle
Authors: Monckton G. , Marusyk H. 
Published: July 2016

SUMMARY:The study of 3H leucine incorporation into skeletal muscle of mouse muscular dystrophy (129 ReJ/dy Bar Harbour strain) shows the uptake of isotope into myofibrils. The techniques employed were light and EM autoradiography before and after glycerination (Szent-Gyorgyi 1947). The results indicate a marked drop in uptake of the 3H-Leucine into myofibrils in the dystrophic animals, supporting the contention of Nihei et al (1971) that reduced myosin synthesis occurs in mouse muscular dystrophy.
Semiology Of Tremors
Authors: Molina-Negro P. , Hardy J. 
Published: July 2016

SUMMARY:Since the description by Galen in the 2nd Century, A.D., clinical neurology has acknowledged the existence of two types of tremor: that which occurs at rest and that occuring during the execution of movement. With the help of refined methods of analysis, E.M.G. and cinephotography, the authors have carried out a detailed clinical assessment in more than 400 patients.The basic criterion used to define a tremor was the classical definition of Dejerine: “An involuntary, rhythmical and symmetrical movement about an axis of equilibrium.”As a result of this study, the conclusion has been reached that there are two types of tremor: postural tremor and tremor of attitude. Both are present while the limb remains immobile, whether by wilful design or when at rest in a position of posture and subject only to the action of gravity.During voluntary movement, tremor is not present. Irregular, asymmetrical and non-rhythmic oscillations may appear however — as in so-called intention tremor, of cerebellar origin — but this abnormal movement can hardly be called a real tremor. It is merely a manifestation of ataxia.As a consequence of this study, it is suggested that further understanding of the basic mechanism of tremor can be reached by the investigation of the central neural structures which are involved in the physiology of posture and attitude.
Cellular Hypersensitivity to Basic Myelin (P2) Protein in the Guillain-Barré Syndrome
Authors: Sheremata William , Colby Susan , Karkhanis Y. , Eylar Edwin H. 
Published: July 2016

SUMMARY:Lymphocytes of 29 subjects were assayed for MIF production in response to P2 peripheral nerve protein, crude human peripheral nerve and human central nervous system Al basic myelin protein. Seven were performed in normal control subjects, 12 in Guillain-Barré patients (GB), 5 with other polyneuropathies and 5 in patients with multiple sclerosis (MS). Only GB patients with acute illness produced MIF in response to neuritogenic P2 protein and crude human nerve. Two MS patients in the acute phase of an exacerbation and one GB patient produced MIF in Response to Al protein. The results of this study demonstrate cellular hypersensitivity to a neuritogenic constituent in peripheral nervous tissue and support the concept that this may be important in the pathogenesis of GB.
Neurophysiological Changes Following Spinal Cord Lesions in Man
Authors: Ashby P. , Verrier M. 
Published: July 2016

SUMMARY:A study has been made of the neurophysiological changes that follow spinal cord lesions in man. The Achilles tendon reflex (ATR) is used to estimate transmission in the la monosynaptic pathway, and the tonic vibration reflex (TVR) to estimate transmission in the la polysynaptic pathway to motoneurons. The inhibition of the H reflex by vibration is used as an estimate of presynaptic inhibition of the la monosynaptic pathway. Immediately following a complete lesion of the spinal cord presynaptic inhibition of the la monosynaptic pathway appears to be greatly increased. This enhanced inhibition may last several months but it eventually declines and in some instances becomes less than normal. Transmission in the la polysynaptic pathway is permanently abolished by a complete spinal lesion. A hypothesis is developed from these findings to explain the evolution of some of the clinical features that follow complete spinal lesions in man. Distinct differences are observed when the spinal lesion is incomplete. Transmission in the la polysynaptic pathway may be preserved and there may be no increase in presynaptic inhibition. These differences may depend upon the integrity of certain spinal long tracts which cannot be tested clinically.
Meningo-Encephalomyelitis Due to the Saprophagous Nematode, Micronema Deletrix
Authors: Hoogstraten Jan , Young W. Gerard 
Published: July 2016

SUMMARY:A five-year-old boy succumbed 24 days following an unusual farm accident in which considerable manure was deposited in multiple lacerations.Death was due to an extensive meningo-encephalomyelitis caused by a nematode that is ordinarily saprophagous.
Fetal Cerebellar Tissue Associated with a Primitive Neuro-epithelial Tumor in an Ovarian Teratoma
Authors: Boor Paul J. , Schoene William C. 
Published: July 2016

SUMMARY:This is a single case report of an ovarian teratoma. It is a unique case of a primitive neuroepithelial tumor with many similarities to a medulloblastoma arising in an ovarian teratoma, and the second report of fetal cerebellum occurring in a teratoma of the ovary.