bluuebunny/crossref_metadata_2025_split huggingface dataset:
IX.—Possible Applications of Coincidence Counter Techniques in Optical Intensity Correlation Studies
Authors: Sillitto R. M. 
Published: July 2016

SynopsisMethods which are widely used in the mathematical analysis of random noise are used here to obtain expressions for the coincidence-counting rates which could be obtained in studies of the intensity correlations between plane-polarized, parallel beams of nearly monochromatic light. It is shown that, with presently available circuit techniques, delayed coincidence measurements could provide information about the breadths of lines radiated by atomic beam light sources, and in prompt coincidence experiments it should be possible to observe interference between beams of incoherent light from sources whose line widths are comparable with those of the Hg198 electrodeless discharge.
X.—Remarks on Coincidence Experiments with Visible Light
Authors: Bay Z. , Farago P. S. 
Published: July 2016

SynopsisAfter the detection of correlations in two coherent light beams by Hanbury Brown and Twiss, objections were raised by Brannen and Ferguson on the basis of the experiments of Adam, Janossy and Varga and their own experiments in which no correlations were detected. It is pointed out here that the different groups were looking for two entirely different effects, one being quadratic, the other one linear in the number of photons involved; the quadratic effect (discovered by Hanbury Brown and Twiss) is in agreement with quantum theory while the linear effect is not. It was shown by Purcell and by Hanbury Brown and Twiss that the choice of parameters in the experiments which gave negative results was inadequate to show the quadratic effect. It is shown in this paper that their experiments were also inadequate to decide between the existence or nonexistence of the linear effect.
XII.—Paraboloidal Co-ordinates and Laplace's Equation
Authors: Arscott F. M. 
Published: July 2016

SynopsisIn this paper we examine the general paraboloidal co-ordinate system, in which the normal surfaces are elliptic or hyperbolic paraboloids, including as special cases the “parabolic plate” and the “plate with a parabolic hole”. We then show that normal solutions of Laplace's equation in these co-ordinates are given as products of three Mathieu functions, and apply this to the solution of boundary-value problems for Laplace's equation in these co-ordinates. In a subsequent paper the corresponding treatment of the wave equation will be given.
XXIII.— Dual Series Relations. V. A Generalized Schlömilch Series and the Uniqueness of the Solution of Dual Equations involving Trigonometric Series
Authors: Srivastav R. P. 
Published: July 2016

SynopsisThe methods employed in papers I–IV of this series are modified to provide the solution of certain dual equations involving trigonometric series. It is necessary to introduce a modified form of the conventional operators of fractional integration and to discuss their relation with generalized Schlömilch series expansions of an arbitrary function. These general methods are illustrated by detailed reference to a particular special case.
VIII.—An Objective Criterion of the Limit of Useful Sophistication of the Semi-empirical Mass Equation
Authors: Feather N. 
Published: July 2016

SynopsisA “roughness parameter”, first used by the author in 1953 (Feather 1953 b) has been re-calculated for 348 points on the mass surface. Systematic features are identified in relation to the variation of this parameter with charge number (Z) and isotopie number (D). In the region of small Z these regularities provide evidence for the persistence of some degree of alpha-unit structure at least as far as Ca. In the region of greater Z (20 < Z < 50) they provide evidence for neutron-proton interactions among the last-added nucleons. Overall, they indicate that the “residuals” characterizing the various semi-empirical mass equations currently in use very probably arise in large part from sub-shell effects which it would be impracticable to attempt to include in the equations.
IX.—Orthogonal Boolean Matrices
Authors: Rutherford D. E. 
Published: July 2016

SynopsisMany results concerning real orthogonal matrices have their counterparts in the theory of orthogonal Boolean matrices. In particular, the analogues for Boolean matrices of certain theorems due to Kronecker are established. The structure of the group of orthogonal Boolean matrices of order n is determined in the case where the underlying Boolean algebra is finite.
X.—Nitrogen Dioxide Vapour and the Creation of Condensation Nuclei
Authors: Evans G. R. , Watson A. A. 
Published: July 2016

SynopsisAn investigation has been made of the condensation nuclei created by an electric field in a N2 – H2O mixture. These nuclei are distinguished by the fact that they induce condensation in a vapour which is only 4 per cent supersaturated.An explanation of these phenomena is found in the presence of nitrogen dioxide vapour, one of the products of reactions induced by the field, exerting a small pressure PNO2<1O−6 mm. Hg.The observations are consistent with the assumption that the nuclei are created in the reaction, 2NO2 + H2O ⇌ HNO2 + HNO3. It is believed that the reason for the requirement of a more than critically supersaturated vapour is that this must be the condition for the nuclei forming reaction to proceed.Once the nuclei have been created, any additional quantity of NO2 collected from the vapour forms acid molecules which promote condensation from a vapour which is not necessarily supersaturated.Drops formed by these nuclei contain a significant quantity of HNO2 + HNO3, so that, unlike drops of pure water, they are stable against reevaporation in a vapour, the relative humidity of which is <100 percent.
XIII.—The Generating Function of Solid Partitions
Authors: Wright E. M. 
Published: July 2016

SynopsisThe generating function for the number of linear partitions was found by Euler, the method being almost trivial. That for plane partitions is due to Macmahon, but, even in a simplified form found by Chaundy, the proof is far from trivial. The number of solid partitions of n, i.e. the number of solutions ofis denoted by r(n). It has often been conjectured that the generating function of r(n) is , but this is now known to be false. We write η(a, b, c) for the generating function of the number of solutions of (1) subject to the additional condition thatMacmahon 1916 found n(a, 1, 1) for general a. Here we find η(a, b, c) for general a, b. c.
XXI—The Whittaker-Hill Equation and the Wave Equation in Paraboloidal Co-ordinates
Authors: Arscott F. M. 
Published: July 2016

SynopsisThe problem considered is that of obtaining solutions of the Helmholz equation ∇2V + k2V = 0, suitable for use in connection with paraboloidal co-ordinates. In these co-ordinates the Helmholz equation is separable, and each of the separated equations is reducible to Hill's equation with three terms (the Whittaker-Hill equation). The properties of solutions of this equation are developed sufficiently to make possible the formal solution of simple boundary-value problems for paraboloidal surfaces, principally for the case k2 < 0.
XXII.—Tensor Fields and Connections on Cross-Sections in the tangent bundle of a differentiable manifold
Authors: Yano Kentaro 
Published: July 2016

SynopsisTensor fields and linear connections in an n-dimensional differentiable manifold M can be extended, in a natural way, to the tangent bundle T(M) of M to give tensor fields of the same type and linear connections in T(M) respectively. We call such extensions complete lifts to T(M) of tensor fields and linear connections in M.On the other hand, when a vector field V is given in M, V determines a cross-section which is an n-dimensional submanifold in the 2n-dimensional tangent bundle T(M).We study first the behaviour of complete lifts of tensor fields on such a cross-section. The complete lift of an almost complex structure being again an almost complex structure, we study especially properties of the cross-section as a submanifold in an almost complex manifold.We also study properties of cross-sections with respect to the linear connection which is the complete lift of a linear connection in M and with respect to the linear connection induced by the latter on the cross-section. To quote a typical result: A necessary and sufficient condition for a cross-section to be totally geodesic is that the vector field V in M defining the cross-section in T(M) be an affine Killing vector field in M.
A Sceptical Chemist in a Biological Wonderland
Authors: Davidson J. N. 
Published: July 2016

It is the custom of our Society that the President of the day should at some period in his term of office address the Fellows. The manner in which he interprets this charge will, of course, vary according to individual preference, but for obvious reasons, he usually elects to give his personal interpretation of that area of science in which he is himself most deeply concerned.Our Society was founded in the days before science was split into highly specialized sections and long before the advent of the specialist societies restricted to one scientific discipline, such as the Chemical Society, the Biochemical Society or the Society for Experimental Biology. This, in the opinion of many of our Fellows, is its main strength, since, as a general Society concerned with all aspects of science, it can exert an integrative function; in fact, it serves many of the purposes of the Academies which are so well known in other parts of Europe, as is made clear in the Letters Patent granting our Armorial Bearings.
XI.—On Unconditional Convergence in Topological Vector Spaces
Authors: Robertson A. P. 
Published: July 2016

SynopsisFor a series of elements of a topological vector space, necessary and sufficient conditions are found, in terms of the set of finite partial sums, for unconditional convergence and for the corresponding Cauchy condition. The extent to which these results remain valid for topological groups is investigated. A new and direct proof, for locally convex spaces, is given of the theorem of Orlicz.
XVI.—The Fission of Aromatic Ketones
Authors: Campbell Neil , Thomson Alexander 
Published: July 2016

SummaryThe acyl groups in aromatic ketones with hydroxyl or methoxyl groups in theorthoorparapositions are readily removed by hydrobromic acid in acetic acid. The results are correlated with the fine structure of the parent hydrocarbons. 5,8-Dimethoxy-I-tetralone and 1,3-dihydroxyxanthone fail to undergo ring-fission with the reagent. The mechanism is discussed and it seems probable that fission occurs by direct proton attack at nucleophilic carbon atoms bearing the acyl groups.
XVII.—The Tacnodal Form of Humbert's Sextic
Authors: Edge W. L. 
Published: July 2016

SynopsisHumbert's 5-nodal plane sextic first appeared in his 1894 paper. Its canonical curve C was identified in 1951, when it was shown that the sextic is the outcome of projecting C from one of its own chords on to a plane.In this present paper it is remarked that there are 60 chords of C such that the projection has two tacnodes, each a confluence of two of Humbert's 5 nodes, and an equation is found for this tacnodal curve.A certain specialization permits C to be invariant for a group of 32, not merely 16, projectivities. Further specializations, described in the proper place, permit groups of orders 64, 96, 160. The resulting tacnodal sextics have groups of birational self-transformations isomorphic to these.
XIX.—Asymptotic enumeration of connected graphs
Authors: Wright E. M. 
Published: July 2016

SynopsisThe number of different connected graphs (with some propertyP) onnlabelled nodes withqedges isfnq. AgainFnqis the number of graphs onnlabelled nodes withqedges, each of whose connected components has propertyP. We consider 8 types of graph for which. We use a known relation between the generating functions offnqandFnqto find an asymptotic expansion offnqin terms of binomial coefficients, valid if (q– ½nlogn)/n→∞ asn→∞. This condition is also necessary for the existence of an asymptotic expansion of this kind.
XII.—Quasi-residuated Mappings and Baer Assemblies
Authors: Blyth T. S. , Hardy W. C. 
Published: July 2016

SynopsisWe consider, for a given ordered set E with minimum element O, the semigroup Q of O-preserving isotone mappings on E and examine necessary and sufficient conditions under which an element fε Q is such that the left [resp. right] annihilator of f in Q is a principal left [resp. right] ideal of Q generated by a particular type of idempotent. The results obtained lead us to introduce the concept of a Baer assembly which we use to extend to the case of a semilattice the Baer semigroup co-ordinatization theory of lattices. We also derive a co-ordinatization of particular types of semilattice.
6.—Electron Diffraction and Electron Mobility in Non-polar Crystals
Authors: Cochran W. 
Published: July 2016

SynopsisIt is shown that the mobility of electrons in silicon or germanium can be estimated in a relatively simple manner. The scattering scross-section of a ’beam’ of electrons in the conduction band is evaluated in the same way as for a beam of X-rays or of slow neutrons which is scattered by phonons. It therefore involves the atomic scattering factor for electrons rather than the deformation potential introduced by Bardeen and Shockley. Predicted mobilities are in satisfactory agreement with observation.
11.—The Instability due to Acoustic Radiation striking a Vortex Sheet on a Supersonic Stream
Authors: Jones D. S. , Morgan J. D. 
Published: July 2016

SynopsisThe propagation of sound across a vortex sheet separating two fluids, with the same density and sound speed, which are in supersonic relative motion is examined for both harmonic and impulsive sources. It is found that instability waves are present when M < 2√2, M being the Mach number, and it is suggested that these may account for the phenomena observed in certain experiments. For M > 2 there are also neutral stability waves and these lie in regions in the supersonic stream which are otherwise silent when the excitation is an impulsive source.
13.—On Some Results of Everitt and Giertz
Authors: Atkinson F. V. 
Published: July 2016

SynopsisThe differential expression Mf = −f″+qf, on a half-line [a, ∞), is said to be ‘separated’ in L2(a, ∞) if the collection of all functions f ∈ L2(a, ∞) such that Mf is defined and also in L2(a, ∞), has the property that both the terms f″ and qf are separately in L2(a, ∞). When q is positive and differentiable on [a, ∞) this paper obtains sufficient conditions on the coefficient q for M to be separated; these take the form of bounds for q′q−3/2 on [a, ∞).
3.—A Note on Quadratic Systems
Authors: Hille Einar 
Published: July 2016

Synopsis‘Quadratic system’ is here used in the sense introduced by W. A. Coppel for a pair of simultaneous Riccati equations with constant coefficients. The problem is to study the occurrence of movable singularities for solutions of a systemunder suitable restrictions on the linesThe aim of the restrictions is to obtain systems where the trajectories have four finite and three infinite topological singularities which form specified configurations. For the movable (function theoretical) singularities the infinitary (topological) singularities are decisive. They are the endpoints of the coordinate axes and of the line F: L2–L1 = 0. A detailed qualitative discussion is given for the trajectories. The system forces various properties of monotony on the integral curves.The qualitative discussion is completed by quantitive data in the form of series expansions for the solutions. Here the value of the parameteris critical.If q is not an integer, then there is one and only one solution whose trajectory is associated with the upper end of the line F which has a simple pole at t = 0 (or any other preassigned value). All other trajectories in this family belong to solutions with expansions in terms of non-logarithmic psi-series of the formfor a singularity at t = 0. Here – 1 ≦ m, 0 ≦ n and c is an arbitrary constant.On the other hand, if q is a positive integer, then we have logarithmic psi-series of the formwhere Pn(s) and Qn(s) are polynomials in s of degree ≦ [n/q].Solutions associated with the ends of the axes have non-logarithmic psi-series. One coordinate becomes infinite like 1/t at zero, the other goes to zero like tλ where λ = –b1/a1 for the x-axis and –a2/b2 for the y-axis. The psi-series have exponents of the form j + Kλ, where j and k are integers, –1 ≦ j, 0 ≦ k.The results are used to construct new convergence proofs for the solutions of Emden's equation at a movable singularity.
18.—The Isotropic Turbulent Dynamics of a Maxwell Fluid
Authors: McComb W. D. 
Published: July 2016

SynopsisUsing the constitutive relationship for a Maxwell body, as an example of a viscoelastic fluid, the equations of motion are derived in the Fourier wavenumber-time domain, and specialised to the case of isotropic turbulence. It is shown that, for grid-generated turbulence, the model predicts increased spectral intensity levels, reduced decay rates and steepening of the spectrum in wavenumber, relative to the Newtonian case. These forms of behaviour have been observed in dilute solutions of drag reducing polymers. The key factor in this is found to be the presence of an ‘elastic’ non-linear term in the equations of motion: this term reverses the normal direction of turbulent energy transfer in wavenumber.
29.—Finiteness of the Order of Meromorphic Solutions of some Non-linear Ordinary Differential Equations
Authors: Hille Einar 
Published: July 2016

SynopsisIt is well known that the existence of transcendental meromorphic solutions of non-linear ordinary differential equations puts severe restrictions on the equation, the most striking example being the theorem of Malmquist [3]. The value distribution theory of R. Nevanlinna was applied to such questions by K. Yosida [8] who used it to prove Malmquist's theorem as well as important generalisations. An alternate approach was given by H. Wittich [4,5,6] and in his argument the finiteness of the order played an essential role. Wittich estimated the corresponding enumerative and proximity functions via the calculus of residues. In this note a geometric argument is proposed instead (closest packing of small discs in a bigger circle or on its rim). This method seems to generalise more readily to Yosida's extensions.
I.—On the Geometry of Metrisable Lie Algebras
Authors: Ruse H. S. 
Published: July 2016

SynopsisMetrisable Lie algebras have been defined by Tsou and Walker (1957). Their definition is adopted below in § I.The object of the present paper is to display something of the geometrical background of such algebras, particularly for those taken over the field of real numbers.§ I is introductory. In § 2 appears a statement, made as brief as possible because it is wholly classical, of the relationship between the vector-space of the Lie algebra L and the associated affine and projective spaces A and P. Some properties of metrisable Lie algebras are then examined in terms of the geometry of P, which provides an (n –I)-dimensional map of the n-dimensional algebra L. It is assumed throughout the paper that the Lie algebras under discussion are non-abelian, since the projective map of an abelian algebra presents nothing of interest.As the present work is intended as no more than a preliminary, it is confined, so far as its applications are concerned, to a discussion of metrisable algebras of dimensions 3 and 4 and to one example of an algebra of dimension 6.I have been privileged in preparing the paper to have access to the typescript of the paper by Tsou and Walker referred to above, and also to the doctoral thesis (1955) of the former. I am greatly indebted to them both, and also to Dr Paul Cohn and to a referee for suggestions regarding certain details of presentation.
XX.—On the Numerical Evaluation of a Class of Multivariate Normal Integrals
Authors: Ruben Harold 
Published: July 2016

SYNOPSISThe probability that each ofnequally correlated normal random variables shall not fall short of a given valuehis obtained as the product of the joint density function of the variables at the cut-off point (h, h,…, h) and an infinite power series inh. The coefficients in the latter series may be interpreted geometrically as the moments of a regular (n– l)-dimensional spherical simplex with common dihedral angles arc cos –prelative to a certain plane of symmetry. These moments may in their turn be expressed as linear functions of the measures of regular hyperspherical simplices of various dimensionalities, tables of which are available elsewhere.
XXVIII.—The Synthesis of 7-Substituted Fluoranthenes
Authors: Campbell Neil , Crombie Douglas A. 
Published: July 2016

SUMMARYThe synthesis of 7-bromo- and 7-chloro-fluoranthene from the readily accessible 1, 2, 3, 1ob-tetrahydro-3-oxofluoranthene is described. Oxidation of the chloro-compound yields 1-chlorofluorene-9-one-8-carboxylic acid and thus opens up a method for the preparation of 1, 8-disubstituted fluorenes and fluorenones.Thanks are expressed to the Department of Scientific and Industrial Research for the award of a Maintenance Grant to one of us (D. A. C).
A literature overview of knowledge sharing between Petri nets and ontologies
Authors: Cheng Haitao , Ma Zongmin 
Published: July 2016

AbstractKnowledge representation is a subarea of artificial intelligence concerned with using formal symbols to represent a set of facts within a knowledge domain. Two popular knowledge representation languages, namely Petri net and ontology, are promising knowledge sharing and reusing methods in knowledge engineering. The combination of Petri net and ontology can facilitate achieving complementary advantages. Currently, many efforts have been done on knowledge sharing between Petri nets and ontologies. To investigate these issues and more importantly serve as identifying the direction of knowledge sharing between Petri nets and ontologies, in this paper we give a comprehensive literature overview of knowledge sharing between Petri net models and ontology models to satisfy the obvious need. In detail, we discuss the knowledge sharing from two aspects: the different knowledge representation approaches of ontology to represent and reason Petri net and issues of constructing Petri net from ontology. In addition, other important issues on applications and directions for future research are discussed in detail.
Six unlikely intersection problems in search of effectivity
Authors: HABEGGER P. , JONES G. , MASSER D. 
Published: July 2016

AbstractWe investigate four properties related to an elliptic curveEtin Legendre form with parametert: the curveEthas complex multiplication,E−thas complex multiplication, a point onEtwith abscissa 2 is of finite order, andtis a root of unity. Combining all pairs of properties leads to six problems on unlikely intersections. Using a variety of techniques we solve these problems with varying degrees of effectivity (and for three of them we even present the list of all possiblet).
Bifurcation in the Duffing equation with independent parameters. I
Authors: Hale Jack K. , Rodriques Hildebrando M. 
Published: July 2016

SynopsisIn the standard treatment of the harmonic solutions of Duffing's equation with small non-linearities and small forcing, all small parameters are assumed to be common multiples of some small parameter. As a consequence, the parameters do not vary in a full neighbourhood of zero and the bifurcation surfaces are not obtained. It is the purpose of this paper to give a complete description of the number of harmonic solutions for the parameters varying in a full neighbourhood of the origin in the parameter space.
dg near rings on the infinite dihedral group
Authors: Malone J. J. 
Published: July 2016

SynopsisIt is shown that exactly six non-isomorphic distributively generated near rings can be defined on the infinite dihedral group. One has the null multiplication, two have trivial multiplications in which the group of left annihilators has index two, and three are distributive and have their product sets equal to a subgroup of order 2.