bluuebunny/crossref_metadata_2025_split huggingface dataset:
Harmonic tetrads and harmonic elliptic quartic curves
Authors: Dye R. H. 
Published: July 2016

SynopsisThe group of a harmonic elliptic quartic has exceptional action on the edges of the self-polar tetrahedron, singling out one pair of opposite edges. Geometrical explanations are given. One concerns the possession by each of these two edges of a certain harmonic tetrad constructible in three ways. The same constructions yield, for a general quartic, three distinct tetrads on each edge of its tetrahedron, with a related fourth. The cases of exceptional overlap of these tetrads are examined: they occur for quartics of moduli 0, ∞ and — 32/49.
26.—On Shapiro's Cyclic Inequality
Authors: Bushell P. J. , Craven A. H. 
Published: July 2016

SynopsisThe inequality, for suitable sets of non-negative numbers x1, x2, …, xn,is undecided in the cases n = 11, 12, 13, 15, 17, 19, 21 and 23. In this note we present the results of numerical analysis supporting the conjecture that the inequality is valid in these cases. A new counter–example for n = 25 and a new elementary proof when n = 7 are given.
On linear theory of heat conduction in materials with memory. Existence and uniqueness theorems for the final value problem
Authors: Grabmüller H. 
Published: July 2016

SynopsisAn improperly posed problem is studied for a linear partial integro-differential equation of convolution type on the semi-axis. The problem originates from a generalised process of heat conduction in materials with fading memory, where the temperature of the material has to be determined for prescribed homogeneous boundary conditions and for a given final temperature distribution. By using eigenfunctions of the n-dimensional Laplacian, the problem is reduced to a family of equivalent initial-value problems for ordinary integro-differential equations; the latter are treated by the method of factorisation in a suitable function algebra. Sufficient conditions for the existence and uniqueness of solutions to the original problem are obtained in terms of the solvability conditions of the reduced problems. The whole analysis is performed simultaneously in a broad variety of spaces consisting of functions with an exponential growth rate (in the time variable) at infinity. One of the main advantages in the present approach is that solutions, if they exist, can always be computed explicitly.
Marginal series in groups
Authors: Hulse J. A. , Lennox J. C. 
Published: July 2016

SynopsisWe consider the generalisation from central series to marginal series in groups and set up firstly various basic results. The main section of the paper is concerned with the study of which group theoretical properties may be transferred from a marginal factor in a group to the corresponding verbal subgroup and which properties may be transferred from one factor of a lower marginal series to successive factors of the series.
On a strong limit-point condition and an integral inequality associated with a symmetric matrix differential expression
Authors: Rigler D. A. R. 
Published: July 2016

SynopsisThis paper is concerned with some properties of an ordinary symmetric matrix differential expression M, denned on a certain class of vector-functions, each of which is defined on the real line. For such a vector-function F we have M[F] = −F“ + QF on R, where Q is an n × n matrix whose elements are reasonably behaved on R. M is classified in an equivalent of the limit-point condition at the singular points ± ∞, and conditions on the matrix coefficient Q are given which place M, when n> 1, in the equivalent of the strong limit-point for the case n = 1. It is also shown that the same condition on Q establishes the integral inequality for a certain class of vector-functions F.
1.—Perturbation Theory for Sobolev Spaces
Authors: Stummel Friedrich 
Published: July 2016

SynopsisThis paper studies Sobolev spaces under perturbation of domains of definition. It establishes the basic concepts, methods and results for the convergence of sequences of sets in ℝn, the strong and weak convergence of sequences of Sobolev spaces, the discrete compactness of natural embeddings and the continuous convergence of continuous linear functionals, boundary integrals and trace operators for sequences of Sobolev spaces.
3.—Uniqueness of Sturm-Liouville Coefficients
Authors: Wray S. D. 
Published: July 2016

SynopsisAn analogue of the Riemannian theory of uniqueness of Fourier coefficients is developed for Sturm Liouville series, using asymptotic formulae for the eigenfunctions and other quantities. This theory generalises earlier work by Haar in that the coefficient function in the differential equation is only assumed to be integrable.
7.—Convolution of Vector Measures
Authors: White A. J. 
Published: July 2016

SynopsisIn this paper we consider the problem of defining a convolution, analogous to the classical convolution of scalar measures, of measures defined on the Borel sets of a locally compact semi-groupSand having values in a Banach algebra. Using the bilinearintegral introduced by Bartle we show that the formalism of the scalar case persists in situations of considerable generality so that the formulasuitably interpreted, gives a Banach algebra structure to a large class ofvalued measures defined onS.Themethods exploit the connection between vector measures and operators and involve some results of independent interest.
19.—Improved Boundedness Conditions for Lowndes' Operators
Authors: Heywood Philip 
Published: July 2016

SynopsisThe operator Ik(η, α) and its adjoint Kk(η, α) have obvious boundedness properties for α ≧½ because of their resemblance to fractional integrals. By expressing Ik(0, α) as the product of two Hankel transformations and a translation Heywood and Rooney [1] have shown that if 0<α<½ then Ik(η, α) and Kk(η, α) can be extended to bounded operators from a weighted Lp space to itself provided that 2/(1+α) ≦ p ≦ 2/(1−α) and the weight is suitably restricted. Heywood and Rooney conjectured that this p range could be improved, andin the present paper it is extended towhich may be best possible.
20.—Deficiency Indices of Polynomials in Symmetric Differential Expressions, II
Authors: Zettl Anton 
Published: July 2016

SynopsisGiven a symmetric (formally self-adjoint) ordinary linear differential expression L which is regular on the interval [0, ∞) and has C∞ coefficients, we investigate the relationship between the deficiency indices of L and those of p(L), where p(x) is any real polynomial of degree k > 1. Previously we established the following inequalities: (a) For k even, say k = 2r, N+(p(L)), N−(p(L)) ≧ r[N+(L)+N−(L)] and (b) for k odd, say k = 2r+1where N+(M), N−(M) denote the deficiency indices of the symmetric expression M (or of the minimal operator associated with M in the Hilbert space L2(0, ∞)) corresponding to the upper and lower half-planes, respectively. Here we give a necessary and sufficient condition for equality to hold in the above inequalities.
7.—Elliptic Singular Perturbations of First-order Operators with Critical Points
Authors: de Groen P. P. N. 
Published: July 2016

SynopsisWe study the asymptotic behaviour for ɛ→+0 of the solution Φ of the elliptic boundary value problemis a bounded domain in ℝ2, 2 is asecond-order uniformly elliptic operator, 1 is a first-order operator, which has critical points in the interior of , i.e. points at which the coefficients of the first derivatives vanish, ɛ and μ are real parameters and h is a smooth function on . We construct firstorder approximations to Φ for all types of nondegenerate critical points of 1 and prove their validity under some restriction on the range of μ.In a number of cases we get internal layers of nonuniformity (which extend to the boundary in the saddle-point case) near the critical points; this depends on the position of the characteristics of 1 and their direction. At special values of the parameter μ outside the range in which we could prove validity we observe ‘resonance’, a sudden displacement of boundary layers; these points are connected with the spectrum of the operator ɛ2 + 1 subject to boundary conditions of Dirichlet type.
9.—Development and Separation of a Laminar Boundary Layer, under the Action of a Very Sharp Constant Adverse Pressure Gradient
Authors: Curle N. 
Published: July 2016

SynopsisThis paper, following Stratford [9], considers a boundary layer developing with uniform pressure when x < x0, and with large and constant when x > x0. The analysis improves or extends the work of Stratford as follows.(a) For large values of inner and outer asymptotic expansions are derived and matched—Stratford considered only the inner solution, his outer boundary condition being determined by physical arguments.(b) The skin-friction is determined as a series in powers of , whereas Stratford's, solution was obtained by approximate methods. In the limit as λ→∞ the predicted separation position, ξ = 0.09766, is probably correct to3 significant figures, at least, and differs little from Stratford's value.(c) This solution further shows that for finite λ, separation occurs whenξ = 0.09766-0.00014λ−3.Although the coefficient 0.00014 is not wholly reliable, clearly the position of separation varies little with λ unless λ−3 is very much greater than unity.(d) The present solution also yields the displacement and momentum thicknesses. When x > x0 the displacement thickness iswhere B1(ξ) is given as a slowly converging seriesin powers of ξ. It is shown how to improve convergence, using certain properties of the flow close to the separation position, and thus to sum the series.Likewiseso that when λ is large the momentum thickness changes even less than does the displacement thickness.
13.—The Functional Differential Equation y′(x) = ay(λx) + by(x)
Authors: Carr Jack , Dyson Janet 
Published: July 2016

SynopsisThe paper discusses the asymptotic behaviour of solutions of the functional differential equationwhere a is a complex constant, 0<λ<1, and b is a constant such that Re b = 0, but b ≠ 0.
The limit-4 case of fourth-order self-adjoint differential equations
Authors: Eastham M. S. P. 
Published: July 2016

SynopsisA new method is developed for identifying real-valued coefficientsr(x),p(x), andq(x)for which all solutions of the fourth-order differential equationareL2(0, ∞). The results are compared with those derived from the asymptotic theory of Devinatz, Walker, Kogan and Rofe-Beketov.
Qualitative properties of nonlinear ordinary differential equations
Authors: Onuchic Nelson , Táboas Plácido Z. 
Published: July 2016

SynopsisThe perturbed linear ordinary differential equationis considered. Adopting the same approach of Massera and Schäffer [6], Corduneanu states in [2] the existence of a set of solutions of (1) contained in a given Banach space. In this paper we investigate some topological aspects of the set and analyze some of the implications from a point of view ofstability theory.
8.—Constructive Methods for Solving the Exterior Neumann Problem for the Reduced Wave Equation in a Spherically Symmetric Medium
Authors: Colton David , Wendland Wolfgang 
Published: July 2016

SYNOPSISAn integral operator is constructed which maps solutions of the reduced wave equation defined in exterior domains onto solutions of ∆n u+λ2(l+B(r))u = 0 (*) defined in exterior domains, where B(r) is a continuously differentiable function of compact support. This operator is then used to construct a solution to the exterior Neumann problem for (*) satisfying the Sommerfeld radiation condition at infinity. Such problems arise in connection with the scattering of acoustic waves in a non-homogeneous medium, and this paper gives a method for solving these problems which is suitable for analytic and numerical approximations.
19.—Propagation of Weak Discontinuities in a Layered Hyperelastic Half-space
Authors: Suhubi Erdogan S. , Jeffrey Alan 
Published: July 2016

SYNOPSISThis paper investigates the one-dimensional propagation of weak discontinuities, that is acceleration waves, in a homogeneous and isotropic half-space composed of an arbitrary number of non-linearly hyperelastic layers. The transmission and reflection coefficients are evaluated in terms of the initial condition at the boundary, and the steepening of the waves to form a shock is discussed. The results are specialised to the case of periodic layering.
Finite bang-bang controllability for certain non-linear systems
Authors: Aronsson Gunnar 
Published: July 2016

SynopsisThis paper gives sufficient conditions ensuring that a non-linear control system of the formis controllable by means of control functions u(t), such that each ui(t) only takes two values, with a finite number of switches. It is assumed that the ‘unperturbed’ system ẋ = A(t)x + B(t)u is controllable in the usual sense, i.e. by measurable and bounded controls.
Cubic primals in [4] with polar heptahedra
Authors: Edge W. L. 
Published: July 2016

SynopsisThis note sets out from the observation that it is not, in general, possible to express a homogeneous cubic polynomial in five variables as a sum of cubes of seven linear forms. Some of the geometry, to which particular cubics which do happen to be so expressible give rise, is described. Further particularisations are mentioned, and one such cubic investigated in some detail.
Existence and stability of periodic solutions of a third-order non-linear autonomous system simulating immune response in animals
Authors: Hsü In-Ding , Kazarinoff Nicholas D. 
Published: July 2016

SynopsisA 3 × 3 autonomous, non-linear system of ordinary differential equations modelling the immune response in animals to invasion by active self-replicating antigens has been introduced by G. I. Bell and studied by G. H. Pimbley Jr. Using Hopf's theorem on bifurcating periodic solutions and a stability criterion of Hsu and Kazarinoff, we obtain existence of a family of unstable periodic solutions bifurcating from one steady state of a reduced 2×2 form of the 3×3 system. We show that no periodic solutions bifurcate from the other steady state. We also prove existence and exhibit a stability criterion for families of periodic solutions of the full 3×3 system. We provide two numerical examples. The second shows existence of orbitally stable families of periodic solutions of the 3×3 system.
Forced oscillations of the feedback control equation
Authors: Smith Russell A. 
Published: July 2016

SynopsisSchaefer's fixed-point theorem is used to obtain sufficient conditions for the existence of a periodic solution of the non-linear differential equation f(D)x+BMg(D)x = p. The most significant feature of these conditions is a geometrical restriction on the range of the matrix M which is the same as the elliptic ball criterion encountered in stability theory. The extension of the results to delay-differential equations with constant time lags is also discussed.
Disconjugacy and the limit-point condition for fourth-order operators
Authors: Kauffman Robert M. 
Published: July 2016

SynopsisLetLdenote the ordinary differential operator given byLf= (pf″)″ + (qf′)′ +rf, withp″,q′ andrcontinuous functions on [0,∞), and withp>0,q≦ 0, andr≧ 0. It is proved that if the equationLg= 0 possesses a non-oscillatory solution, then any non-trivial solutionftoLf= 0 such thatf(0) =f′(0) = 0 is eventually bounded away from zero.This theorem is used to prove that, for a general class of functionsqandrcontaining the polynomials as a very special case, the equationLg= 0 has at most two linearly independent square integrable solutions, whenpis identically one,q≦ 0 andr≧ 0.Finally, the main theorem is applied to show that certain sixth-order operators are limit-3.
Spectral theory for a class of pseudodifferential operators
Authors: Catchpole E. A. 
Published: July 2016

SynopsisWe investigate the spectral theory for a class of pseudodifferential operators which includes all constant coefficient differential operators, and also operators such as The operators considered are of the form Su(x) = Au(x)+q(x)u(x), where A is an operator which corresponds in the Fourier transform plane to a multiplication operator, and q(x) is a potential term. We prove an eigenfunction expansion theorem for S and derive some results concerning the spectrum of S.
The number of integrable-square solutions of products of differential expressions
Authors: Everitt W. N. , Zettl A. 
Published: July 2016

SynopsisGiven differential expressions τ1; τ2, …, τn— not necessarily symmetric—which are regular on [0,∞), we investigate the relationship between the number of linearly independentL2(0,∞) solutions of the equations τjy= 0 and of the product equation (τ1τ2… τn)y= 0. Our results extend those recently obtained in [15, 16, 17] for the special case τJ=τforj= 1, …,nand τ is symmetric. In particular they include the classification results of Everitt and Giertz [4,5,6] for this special case when τ is a real second-order symmetric expression.
On the Dirichlet problem for weakly non-linear elliptic partial differential equations
Authors: Dancer E. N. 
Published: July 2016

SynopsisWe study the existence of solutions of the Dirichlet problem for weakly nonlinear elliptic partial differential equations. We only consider cases where the nonlinearities do not depend on any partial derivatives. For these cases, we prove the existence of solutions for a wide variety of nonlinearities.
On a maximum principle for a class of fourth-order semilinear elliptic equations
Authors: Schaefer Philip W. 
Published: July 2016

SynopsisIt is shown that Ф = | grad u |2–uΔu, where u is a solution of Δ2u+pf(u) = 0 in D, assumes its maximum value on the boundary of D. This principle leads one to a lower bound on the first eigenvalue in the non-linear Dirichlet eigenvalue problem and to the non-existence of solutions to this non-linear partial differential equation subject to certain zero boundaryconditions.
The Anatomical Substratum of Pain Evidence Derived from Morphometric Studies on Peripheral Nerve
Authors: Thomas P.K. 
Published: July 2016

SUMMARYEarlier theories as to the anatomical basis of pain postulated a direct ‘pain pathway’ from specific receptors in the periphery. Anatomical studies linked this with small myelinated and unmyelinated fibers in the peripheral nerves. Subsequently, hypotheses were advanced which postulated that pain depended upon particular spatial and temporal patterns of sensory input into the nervous system rather than upon specific sets of fibers.More recent physiological studies have demonstrated the existence of peripheral receptors that respond exclusively to noxious stimuli and morphometric studies on peripheral neuropathies in man clearly implicate small myelinated and unmyelinated axons in the conduction of pain. Morphometric studies have also shown that spontaneous pain in neuropathies may be associated with a selective loss of small fibers. These observations therefore support the earlier concept of a specific nociceptive pathway involving small caliber fibers in the peripheral nerves. It is evident that this afferent pathway is capable of modification in the spinal cord both by peripheral inputs and by descending impulses. The notion of a ‘pain pathway’ as such is probably best avoided.
Cytoplasmic Tubular Aggregates and Nuclear Filamentous Bodies in Two Suspected Cases of Viral Encephalitis
Authors: Horoupian Dikran S. , Ross R.T. , Gurwith Mark J. , Hoogstraten Jan 
Published: July 2016

SUMMARYTwo suspected cases of viral encephalitis are presented. Viral nucleocapsids were not seen, but cytoplasmic paramyxovirus-like aggregates and nuclear filamentous bodies were frequently encountered. Both structures were seen in the same cell. Contrary to other reports, the cytoplasmic aggregates were mostly observed in hematogenous mononuclear cells, less frequently in neuronal cell elements and rarely in endothelial cells. The non-specific nature of these structures is emphasized.
Chronic Benign Congenital Myopathy: Fingerprint Body Type
Authors: Gordon A.S. , Rewcastle N.B. , Humphrey J.G. , Stewart B.M. 
Published: July 2016

SUMMARYThe term “benign congenital myopathy” describes a group of muscle disorders characterized by proximal or diffuse muscle weakness, a relatively non-progressive course, normal serum muscle enzyme assays and the presence of a distinctive morphological feature. We report here a 55 year old woman, with fingerprint body myopathy who exhibits all of the above features. She has been affected from birth, able to walk since the age of 12, and has not deteriorated in the past thirty years. Muscle biopsy reveals fatty infiltration, numerous small fibers undergoing structural change, good differentiation into type I and II fibers, and excessive intracellular lipid and lipochrome. Only on electron microscopic study is the distinctive feature of numerous subsarcolemmal round to ovoid fingerprint bodies observed. Many fibers also contain large collections of tubular aggregates, filamentous bodies, and autophagic vacuoles.The fingerprint bodies are similar to the ones described by A. Engel in a 5 year old girl. Thus, a rare opportunity is provided to study an individual who has had this disease for over fifty years.
Traumatic Infarction of the Spinal Cord
Authors: Keith W.S. 
Published: July 2016

SUMMARYInfarction of the spinal cord is an occasional complication of thoracic and aortic surgery and dissecting aneurysm. Only once has it been reported following injury. This paper recounts the histories of four children each of whom survived an automobile accident; each with permanent paraplegia due to infarction.
Relative Efficacy of Alcohol and Propranolol in Action Tremor
Authors: Rajput A.H. , Jamieson H. , Hirsh S. , Quraishi A. 
Published: July 2016

SUMMARY:Thirty-nine patients with a variety of diseases, including essential tremor, Parkinsonߣs Disease, olivopontocerebellar degeneration, ataxia telangiectasia, and cervical cord injury with action tremor, were evaluated for the effect of one ounce of absolute alcohol ingestion. Tremor significantly subsided in 61.9% of E.T.; 46.6% of P.D.; one patient with A.T.; and one patient with C6 lesion. The tremor became worse in one patient with O.P.C.D. Twenty of these patients were treated with propranolol, an average dose of 92 mgm. per day, and re-evaluated three to six months later. All those who improved on alcohol improved on propranolol and the one whose tremor accentuated with alcohol had a similar response to propranolol. It is concluded that the tremorilytic effect of alcohol is neither specific for, nor limited to, essential tremor and is of no value in differentiating various neurological disorders which manifest as action tremor. It is recommended that one ounce of absolute alcohol by mouth be used as an office procedure to predict the response of patientsߣ tremor to propranolol.
Skin Punch Biopsies and Lymphocytes in the Diagnosis of Lipidoses
Authors: Dolman C.L. , MacLeod P.M. , Chang E. 
Published: July 2016

SUMMARY:Skin punch biopsies and huffy coats of white blood cells were examined electron microscopically in patients suffering from a variety of storage diseases. No specific abnormalities could be detected in Gaucher’s disease and adrenoleucodystrophy. While characteristic deposits were found in cutaneous nerves in globoid and metachromatic leucodystrophy, this method was deemed inferior to sural nerve biopsy. In gangliosidoses, on the other hand, pathognomonic membranous cytoplasmic bodies were common in axons of cutaneous nerves, and in generalized gangliosidoses marked vacuolation of many other cells was prominent. Specific deposits were found in various cells in skin punch biopsies and in lymphocytes of children suffering from ceroid lipofuscinoses, and in lymphocytes of their parents. This constitutes the easiest diagnostic laboratory procedure in such cases.