bluuebunny/crossref_metadata_2025 huggingface dataset:
Enhancement of stability of growth, structural and NLO properties of KDP crystals due to additive along with seed rotation
Authors: Dhanaraj P. V. , Rajesh N. P. , Ramasamy P. , Jeyaprakasan M. , Mahadevan C. K. , Bhagavannarayana G.
Published: November 2008

Potassium Acetate (CH3COOK) and Potassium Citrate (K3C6H5O7) as new additives were added into the potassium dihydrogen phosphate (KDP) solutions in different molar ratios. The metastable zone width and induction period with and without these additives were determined and compared. Dielectric measurements on pure and doped KDP crystals at various temperatures ranging from 313 to 423 K were carried out by the conventional parallel plate capacitor method which results low dielectric constant value dielectrics in doped crystals. The high resolution XRD studies show that CH3COOK doped KDP crystal and K3C6H5O7 doped KDP crystal do not contain any internal structural grain boundaries and indicates that the crystalline perfection is very good. Moreover, the addition of these potassium additives improves the quality of the crystal and yields highly transparent crystals with well defined features. The effect of additives on the growth, nucleation kinetics, structural, NLO and optical properties has been investigated. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Strobilurin residue levels in greenhouse‐grown pepper and under cold‐storage conditions
Authors: Fenoll José , Ruiz Encarnación , Hellín Pilar , Lacasa Alfredo , Flores Pilar
Published: November 2008

BACKGROUND: Azoxystrobin and kresoxim‐methyl are strobilurin fungicides widely used in vegetable cultivation in southeastern Spain. The dissipation of these fungicides in peppers was evaluated in a study carried out in a greenhouse and under cold‐storage conditions. Pepper samples were collected during a 5‐week period in which two successive applications of these pesticides were performed. Gas chromatography (GC) with nitrogen–phosphorus detection (NPD) was used to study the disappearance of these compounds in peppers.

RESULTS: The disappearance rates of azoxystrobin and kresoxim‐methyl on peppers were described as pseudo‐first‐order kinetics (r between 0.950 and 0.992) and half‐life in the range of 10.28–15.21 days. These fungicides showed similar behaviour because they are structurally similar. After 21 days under cold and darkness storage conditions, dissipation of azoxystrobin and kresoxim‐methyl were not observed.

CONCLUSION: The pre‐harvest times established by Spanish law for these fungicides are correct since the residue levels were below the legal limit after two applications at the maximum recommended doses. Pepper storage or transport under refrigerated and darkness conditions do not contribute to dissipation of azoxystrobin or kresoxim‐methyl residues. Copyright © 2008 Society of Chemical Industry
Selecting variables in non‐parametric regression models for binary response. An application to the computerized detection of breast cancer
Authors: Roca‐Pardiñas Javier , Cadarso‐Suárez Carmen , Tahoces Pablo G. , Lado María J.
Published: November 2008

In many biomedical applications, interest lies in being able to distinguish between two possible states of a given response variable, depending on the values of certain continuous predictors. If the number of predictors, p, is high, or if there is redundancy among them, it then becomes important to decide on the selection of the best subset of predictors that will be able to obtain the models with greatest discrimination capacity. With this aim in mind, logistic generalized additive models were considered and receiver operating characteristic (ROC) curves were applied in order to determine and compare the discriminatory capacity of such models. This study sought to develop bootstrap‐based tests that allow for the following to be ascertained: (a) the optimal number q⩽p of predictors; and (b) the model or models including q predictors, which display the largest AUC (area under the ROC curve). A simulation study was conducted to verify the behaviour of these tests. Finally, the proposed method was applied to a computer‐aided diagnostic system dedicated to early detection of breast cancer. Copyright © 2008 John Wiley & Sons, Ltd.
Wages in Huating-Lou counties in the 1820s
Authors: Bozhong LI
Published: November 2008

The issue of wages has been ignored in previous studies of economic history in late imperial China. Focusing on Huating County and Lou County (today’s Songjiang County of Shanghai), this article explores the wages in agricultural, industrial, commercial, and service occupations of this area in the 1820s. The findings, though primary, are helpful to our understanding of incomes in early-nineteenth-century China.
The Mythical Man
Authors: Montgomery David
Published: November 2008

Jefferson Cowie and Nick Salvatore have offered us two distinct arguments, one persuasive, the other anything but. There is much to be said for their proposition that the political coalitions that instituted New Deal reforms, far from being the historic culmination of an inexorable march from laissez-faire to the welfare state, were fragile and limited from the start and crumbled beyond the possibility of retrieval after 1970. Much more dubious is their contention that the basic explanation of both the limits and the defeat of the New Deal is to be found in a political culture of individualism, which they claim has circumscribed the political life of the United States from the nation's founding to the present.
Lecture et linearite
Authors: Coste Daniel
Published: November 2008

Pour toute une tradition linguistique, la linéarité est considérée comme une des propriétés fondamentales du langage. “Tout le mécanisme de la langue en dépend” affirmait Saussure. La constitution de classes paradigmatiques, l'analyse distributionnelle supposent que les unités se suivent ou se remplacent mais ne sauraient être présentes simultanément en un même point de la chaîne.
The Acquisition and Use of Language System
Authors: Widdowson H. G.
Published: November 2008

I want to discuss two lines of enquiry in applied linguistic research which have come into prominence in recent years and which promise to have a bearing on a more learner-centred approach to language teaching pedagogy. These two lines have been pursued independently and at different points on the spectrum of applied linguistic studies. Furthermore, each one concentrates on a different aspect of natural language. I want to argue that we need to find ways of relating them if their pedagogic potential is to be effectively realized.
The Use of Verbal and Imagery Mnemonics in Second-Language Vocabulary Learning
Authors: Cohen Andrew D.
Published: November 2008

This paper provides a critical look at the use of mnemonic associations in vocabulary learning. The paper begins with a definition of mnemonic devices—that is, techniques for converting material to be learned into a form that makes it easier to learn and remember—and focuses on verbal and imagery mnemonics, whereby a word, a phrase, or a sentence and visual imagery serve as mediator between what is known and what is to be learned. Particular attention is given to the keyword approach, in which there is both an acoustic link between a native-language word and the second-language word, and an image of the keyword interacting with the native-language word or phrase. Contentions are discussed concerning both the learning of words through verbal and imagery mnemonics and their subsequent retrieval. Attention is also given to research issues in need of investigation.
Experiments in the Real world
Authors: Tomasello Michael , Herron Carol
Published: November 2008

Beck and Eubank (1991) criticize our recent SSLA article (Tomasello & Herron, 1989) on both theoretical and methodological grounds. While we appreciate their attempt to discuss and clarify important issues—and while they do make several sound and very interesting points—in a number of cases they seriously misrepresent our study. We will attempt to address the criticisms in roughly the order in which they were raised.
Nothing Does Not Equal Zero
Authors: Hudson Thom
Published: November 2008

During the past decade and a half, a great deal of research has posited a developmental sequence approach in second language acquisition. Much of this research has proposed that certain linguistic structures are acquired in a natural immutable order while other linguistic structures are acquired variably as a result of a learner's orientation (Clahsen, Meisel, & Pienemann, 1983; Meisel, Clahsen, & Pienemann, 1981; Pienemann, 1984, 1985, 1987; Pienemann & Johnston, 1987). Proposals have been made for extending the model into language assessment and pedagogy (Clahsen, 1985; Pienemann, 1984, 1992; Pienemann & Johnston, 1987). The present study reexamines the original social-psychological research upon which the multidimensional model is based and shows that it is incorrect due to faulty analyses. Further, it examines the limited applicability and generalizability of the developmental sequence approach for assessment and pedagogy.
Cognitive Foundations of Second Language Acquisition: Introduction
Authors: Tomlin Russell S. , Gernsbacher Morton A.
Published: November 2008

The growth of cognitive science as a field, or at least as a descriptive term, indicates an emerging scientific consensus that many fundamental human capacities require collaborative and interdisciplinary research to make further fundamental headway. Language, as central to our essential humanity as anything is, represents one area in which massive amounts of interdisciplinary research is underway at virtually every research institution in the world.
Elaborative Detail: Help or Hindrance to the NNS Listener?
Authors: Derwing Tracey M.
Published: November 2008

Three experiments were conducted to examine the effects of three types of elaboration—marked paraphrase, unmarked paraphrase, and unnecessary detail—on NNS listening comprehension. Participants (both NSs and NNSs) were asked to listen to instructions and then draw or alter drawings on a page in front of them. The instructions were heard in one of four conditions, the basic set or one of the three elaboration conditions. Subsequent analyses of the participants' comprehension indicated that all listeners had significantly more difficulty following instructions in the unnecessary detail condition than in any other. Marked paraphrase was found to facilitate comprehension in some cases. It was concluded that the quality of elaboration has implications for listening comprehension, in both the classroom and the workplace.
Morphological uniformity and the null subject parameter in adult SLA
Authors: Davies William D.
Published: November 2008

An area of keen interest in applying Chomsky's UG parameter-setting model to SLA has been the Pro-Drop or Null Subject Parameter (Cyrino, 1986; Hilles, 1986; Phinney, 1987; White, 1985, 1986). However, the nature of this parameter changes dramatically from the Jaeggli (1982) and Rizzi (1982) conception with Jaeggli and Safir's (1989) proposal linking uniform morphological agreement paradigms with null subjects. Data reported here show a number of L2 learners exhibit knowledge that English is morphologically nonuniform yet still accept English null subject sentences. This is inconsistent with the predictions of the Morphological Uniformity Hypothesis and renders uncertain its applicability to SLA. The results are considered in light of a number of possible positions that can be adopted when faced with data that disconfirm a hypothesis within the UG SLA research program; it is concluded that the Morphological Uniformity Hypothesis is disconfirmed and that any reformulation of the Null Subject Parameter must take these results into consideration.
Involutions on a Normal Quartic Curve in Space of Four Dimensions
Authors: James C. G. F.
Published: November 2008

The object of this note is to correct an error in my paper “Extensions of a theorem of Segre's…,” the notation used being the same. The curve C4 dealt with is regarded as given by its canonical representation

and at one point in the paper we sought the locus of the lines analogous to the line A2A4 of the figure of reference for each of the ∞2 representations of this type (p. 671, small print). In the space representation of the locus there is an additional principal curve

and the order of the locus must be reduced by that of the form corresponding to the points of this conic. The locus sought is in fact none other than the cubic form, locus of chords of C4, the present system of lines being the directrix systemt†. This follows at once from the following results, which can be shown immediately using the above representation:

(1) The space joining such a line g to any tangent cuts the curve again in coincident points, and thus contains a second tangent;

(2) The line joining the points of contact of these tangents meets g, and the points give the involution
On the real twisted cubic curves which are geodesic upon a quadric surface
Authors: Richmond H. W.
Published: November 2008

1. Geodesic curves, even of simple surfaces such as quadrics, are almost always transcendental: occasionally they are algebraic: still more rarely do they belong to simple and familiar types. The form of the differential equation referred to proves conclusively that even such integrals as are expressible by elementary functions must be quite exceptional.
On a modified electrostatic oscillograph
Authors: Crowther J. A.
Published: November 2008

The instrument to be described is a modification of an electrostatic oscillograph originally invented by Prof. Taylor Jones. In the original instrument a thin phosphor-bronze wire is stretched parallel to a flat metal plate towards which it is attracted when a difference of potential is established between them. A small mirror is fastened by one edge to the middle of the wire, and the other edge of the mirror is pivoted by bringing up to it a flat cork against which it presses. The motion of the wire is recorded by reflecting a beam of light from the mirror on to a rotating drum.
Spectral theory and Fuchsian groups
Authors: Patterson S. J.
Published: November 2008

In this paper we return to consider more fully some questions which were touched on in (6). This was the first of a series of papers dealing with the spectral theory of the Laplace–Beltrami operator on a Riemann surface. In the later parts of that series we dealt fully with the case when the fundamental group is finitely generated. In this paper we return to the study of more general questions. In many ways this work continues that of W. Roelcke (7). We shall develop in section 2 the spectral theory for the Laplace operator Δ operating on functions on G\D where D is the unit disc and G is an arbitrary Fuchsian group. The main object is to find generalized eigenfunction expansions which are valid in the sense of absolute convergence rather than L2 convergence. The most convenient form of spectral theory for our purposes appears to be a version due to Gårding for Carleman operators which is presented in ((4), Ch. xvii, §§ 8,9). As a first application we use the results in section 3 to solve a problem of W. K. Hayman. Then we turn to Fuchsian groups G with exponent of convergence δ(G) < ½. Using the results of (6) we first obtain sufficient information on the action of G on the principal circle of G (section 4) and finally determine the spectral resolution in section 5.
A combinatorial proof of a positivity result
Authors: Gillis J. , Kleeman J.
Published: November 2008

We shall be concerned with the Laguerre polynomials, defined by

Some time ago Szegö (8) showed that

for (a, b, c = 0, 1, …). It is easily deduced from this (cf. (5)) that

for all A λ ≥ 3.
Stochastic independence in non-commutative probability theory
Authors: Driessler Wulf , Wilde Ivan F.
Published: November 2008

For a family {Xα} of random variables over a probability space , stochastic independence can be formulated in terms of factorization properties of characteristic functions. This idea is reformulated for a family {Aα} of selfadjoint operators over a probability gage space and is shown to be inappropriate as a non-commutative generalization. Indeed, such factorization properties imply that the {Aα} mutually commute and are versions of independent random variables in the usual sense.
Borel and projective sets from the point of view of compact sets
Authors: Kunen Kenneth , Miller Arnold W.
Published: November 2008

In this paper we prove several results concerning the complexity of a set relative to compact sets. We prove that for any Polish space X and Borel set B ⊆ X, if B is not , then there exists a compact zero-dimensional P ⊆ X such that p ∩ X is not . We also show that it is consistent with ZFC that, for any A ⊆ ωω, if for all compact K ⊆ ωωA ∩ K is , then A is . This generalizes to in place of assuming the consistency of some hypotheses involving determinacy. We give an alternative proof of the following theorem of Saint-Raymond. Suppose X and Y are compact metric spaces and f is a continuous surjection of X onto Y. Then, for any A ⊆ Y, A is in Y iff f−1(A) is in X. The non-trivial part of this result is to show that taking pre-images cannot reduce the Borel complexity of a set. The techniques we use are the definability of forcing and Wadge games.
Limits of stable homotopy and cohomotopy groups
Authors: Jones J. D. S. , Wegmann S. A.
Published: November 2008

In this paper we formulate and prove generalizations of a theorem of Lin [7]. Let X be a CW complex with base point x0. Define a free involution T on S∞×(X Λ X) by T (w, xΛy) = (−w, yΛx). The quadratic construction on X is the complex

This construction can be applied to spectra. A complete and thorough account will appear in the work on equivariant stable homotopy theory in preparation by L. G. Lewis, J. P. May, J. McLure and M. Steinberger. Some of the results are announced in [8].
Special values of L-functions and height two formal groups
Authors: Yager Rodney I.
Published: November 2008

Let ψ be the Grossencharacter attached to an elliptic curve E defined over an imaginary quadratic field K ⊂ of discriminant −dK, and having complex multiplication by the maximal order of K. We denote the conductor of ψ by and fix a Weierstrass model for E with coefficients in ,

whose discriminant is divisible only by primes dividing 6. Let Kab be the abelian closure of K in and choose a fundamental period Ω ∈ for the above model of the curve.
Certain countably generated big Cohen-Macaulay modules are balanced
Authors: Sharp R. Y.
Published: November 2008

Throughout this note, A will denote a (commutative, Noetherian) local ring (with identity) having maximal ideal m and dimension d. Let x1, …, xd be a system of parameters (s.o.p.) for A. A (not necessarily finitely generated) A-module M is said to be a big Cohen–Macaulay A-module with respect to x1, …, xd, if x1, …, xd is an M-sequence. In the last ten or fifteen years there has been substantial interest in such modules, initially stemming from M. Hochster's discoveries that, if A contains a field as a subring, and x1, …,xd is any s.o.p. for A, then there exists a big Cohen-Macaulay A-module with respect to x1, …,xd, and that the existence of such modules has important consequences for the local homological conjectures in commutative algebra: see [6].
On a problem of Erdős concerning decompositions of the plane
Authors: Davies Roy O.
Published: November 2008

Sierpiński ((6), (7)) proved that the continuum hypothesis implies the following proposition:

Euclidean space E3 can be decomposed into three sets Si (i = 1, 2, 3) such that, for some three straight lines Di in E3, the intersection of each line parallel to Di with the corresponding set Si is finite.
Dispersion relations for a two-channel scattering process: residues of the scattering amplitudes
Authors: Underhill J.
Published: November 2008

1. This paper is a continuation of a previous one(1), in which dispersion relations satisfied by the scattering amplitudes for a non-relativistic two-channel scattering process were derived. It was shown that for the process described by the integral equations

with

the scattering amplitudes Mi(E, τ) (where E is the incident energy and τ is the momentum transfer), satisfy the relations
The thermal boundary layer in the flow between converging plane walls
Authors: Riley N.
Published: November 2008

The thermal boundary layer in the converging flow between non-parallel plane walls is studied. Analytical solutions of the boundary-layer equations are derived and the heat transfer across the wall is obtained from these solutions.
On Graeffe's Method for Complex Roots of Algebraic Equations
Authors: Brodetsky S. , Smeal G.
Published: November 2008

The only really useful practical method for solving numerical algebraic equations of higher orders, possessing complex roots, is that devised by C. H. Graeffe early in the nineteenth century. When an equation with real coefficients has only one or two pairs of complex roots, the Graeffe process leads to the evaluation of these roots without great labour. If, however, the equation has a number of pairs of complex roots there is considerable difficulty in completing the solution: the moduli of the roots are found easily, but the evaluation of the arguments often leads to long and wearisome calculations. The best method that has yet been suggested for overcoming this difficulty is that by C. Runge (Praxis der Gleichungen, Sammlung Schubert). It consists in making a change in the origin of the Argand diagram by shifting it to some other point on the real axis of the original Argand plane. The new moduli and the old moduli of the complex roots can then be used as bipolar coordinates for deducing the complex roots completely: this also checks the real roots.
Numerical evaluation of the integral
Authors: Catton Diana , Millis B. G.
Published: November 2008

Numerical values of the above integral are given for 3/2λ√3 = 0(0·1)1, to six decimals for |ω| = 0(0·l)2·0(0·2)4·8 and to seven decimals for |ω| = 5(0·5)10(1)15.

The integral satisfies a third-order differential equation; this equation is integrated numerically for ω ≥ 0 and ω ≤ 0, and in each case the method of isolating the solution which satisfies f(ω) → 0 as ω → ∞ is described.
The effect of selection in a haploid genetic population
Authors: Moran P. A. P.
Published: November 2008

In this paper, we consider the effect of selection in a finite population of haploid individuals in which mutation is occurring in both directions. Unlike Wright's models (2) where the members of each generation all die at the same time to be replaced by a new generation, we suppose that at each change in the state of the system only one individual dies and is replaced by a new individual. In a previous paper (1) we have represented the process by a Markov chain, but it is here more convenient to begin by considering a Markov process with a continuous time parameter. This enables us to introduce selection in a plausible manner.
Variational principles in high-frequency scattering
Authors: Kodis Ralph D.
Published: November 2008

A pair of variational principles are formulated for two-dimensional scattering by obstacles. The first of these is in terms of the obstacle boundary values, and it is shown that a simple ‘optical’ trial function leads to an incorrect frequency dependence for the scattering cross-section. In the second, the obstacle is viewed as the analogue of an aperture coupling two half spaces. The geometric optics part of the cross-section can then be made explicit and is split off to leave a stationary form for the frequency correction. The zero-order calculation for the cross-section of a circle, using corresponding ‘optical’ trial functions, is found to have the correct (Ka)−2/3 frequency dependence.
The structure of radiation
Authors: Stoner Edmund C.
Published: November 2008

It is shown that, assuming conservation of energy and momentum in individuai transitions, radiation must be regarded as propagated by linearly directed quanta. Evidence is brought forward in favour of the view that these quanta are spatially localised longitudinally as well as laterally. As these conclusions seem unavoidable, an attempt is made to see if there is any possibility of accounting for interference effects in terms of quants possessing periodic properties.

The idea that a single quantum can produce interference effects is untenable. The conception of the phase of a quant is introduced, and it is supposed that atoms may absorb a quant in a given phase provided they are in a “state” corresponding to that phase. Considering radiation emanating from a point, it is shown that a tentative explanation of interference may be obtained if the quants have a constant phase at emission, and if they give atoms at any point an impulse towards the state corresponding to their phase at the point. According as these impulses reinforce or oppose each other, bright or dark parts of a fringe System are obtained. Practically the whole nomenclature and method of the wave theory may be taken over and applied to the quant phase field surrounding an emitting source. Essentially, on this view, an explanation of interference is sought in terms of different quants, and the dark and bright parte of a fringe system are to be explained, not in terms of different numbers of quante arriving at them, but in different phase relations of quante which do arrive.

Quante are characterised by a magnetic and electric vector, whose magnitudes and directions define the state of polarisation and the phase. Electron orbite may also be regarded as characterised by two vectors in terms of which it seems as if the “state” may be specified.

The relation between transition character and type of radiation emitted is finally considered and it is shown that the evidence so far available renders plausible an explanation of interference of the kind put forward. Much further experimental work, particularly in connection with the Stark and Zeeman effects, is, however, necessary, before sufficient precision can be given to the views put forward to make them satisfying. On the other hand, it seems premature to suppose that only a formal treatment is possible of the physical phenomena involved.
Some expansions in products of hypergeometric functions
Authors: Dhawan G. K.
Published: November 2008

1. Making use of the familiar abbreviation

let us adopt a contracted notation for the generalized hypergeometric function AFB(x) and write

where (a) denotes the sequence of parameters a1, a2,…, aA. It will be assumed throughout the present paper that there are A of the ‘a’ parameters, A′ of the ‘a′’ parameters, and so on. Thus [(a)]m is to be interpreted as

with similar interpretations for [(a′)]m, etc.
On the Rayleigh assumption in scattering by a periodic surface
Authors: Millar R. F.
Published: November 2008

In treating plane wave scattering by a periodic surface, Lord Rayleigh (10) assumed that the discrete, outgoing and evanescent plane wave representation for the scattered field was valid on the surface itself. Recently, this Rayleigh assumption has been questioned and criticized. For the surface y = b cos kx on which the total field vanishes, Petit and Cadilhac(8) have demonstrated its invalidity when Kb > 0·448. The present paper discusses scattering of a wave, incident from y > 0, by an analytic periodic surface y = f(x) ( – ∞ < x < ∞), and shows that the Rayleigh assumption is valid if and only if the solution can be continued analytically across the boundary at least to the line y = minf(x). Conformal mapping and results relating to the analytic continuation of solutions to elliptic partial differential equations reduce the problem to one involving the location of singularities and critical points of a potential Green's function. Provided that the perturbation of the surface from a plane is sufficiently gentle, the validity of the Rayleigh assumption is established. For the surface y = b cos kx it is shown that the assumption is valid if Kb < γ, where γ is a positive number no greater than 0·448, the precise value of which is unknown. Possible extensions of the analysis to different or more general situations are suggested.
Inclusion of sets of regular summability matrices. II
Authors: Baker J. W. , Petersen G. M.
Published: November 2008

1. In a previous paper, ((1)), we have discussed problems which arise in finding a matrix which is in some sense stronger than each of a set of regular summability matrices. We intend in this paper to clear up other problems in this subject. We shall retain the notation and definitions of (1) throughout, but shall later modify one set of definitions in the light of some of our results. In this paper, the term matrix will be reserved for regular summability matrices. Also, u will be used to denote the unit sequence, u = {un} = {1} and h(A) will be used to denote the norm of the matrix A = (amn), i.e.
The generalization of Lagrange's expansion and the enumeration of trees
Authors: Good I. J.
Published: November 2008

In a previous paper ((8)), the joint probability generating function was written down for the sizes of the generations in a tree consisting of c distinct species or colours. It was pointed out in (12) that a generalization of Lagrange's expansion could be applied in order to obtain explicit formulae in some circumstances. The techniques have received new application, to polymer chemistry, in (16), (15), and (17). This application should not be confused with the application of the enumeration of trees to that of isomers ((4), (2), (26)). It was further pointed out in (12) that the technique could be applied to some problems concerning the enumeration of ‘ordered’ (planar) trees. This idea is here developed further, and is applied also to ‘labelled’ trees ‘ordered within colours’. One of our objectives is to specify some circumstances in which iterated generating functions, and consequently also the generalization of Lagrange's expansion, are applicable. The examples show how the techniques can be applied almost automatically in order to deduce results, both old and new. The number of labelled ‘chromatic’ trees with c colours is found: Scoins gave the result for c = 2.
The electromagnetic fields of moving dipoles
Authors: Ward G. N.
Published: November 2008

Recent papers by J. R. Ellis and the author contain formulae for the fields of moving dipoles which are expressed in rather different forms in the two papers, and it appears that the author's results are more general than Ellis's. Here, the results are re-derived from a consideration of the Hertzian six-vector potential for a distribution of moving dipoles, and a comparison is made with the previous forms. It is found that Ellis's results are essentially as general as the author's. The expressions for the potentials and the field tensors are treated as weak functions in Temple's sense, and very few restrictions have to be imposed on the dipole moments and velocities, which may be expressed either as functions of coordinate time or as functions of proper-time.
A note on the problem of the penny-shaped crack
Authors: Sneddon Ian N.
Published: November 2008

1. The problem of determining the distribution of stress in the neighbourhood of a penny-shaped crack defined in terms of cylindrical coordinates (ρ, φ, z) by 0 ≤ ρ ≤ α, z = 0, has been considered by Sneddon ((2)) and Sack ((1)). In the latter paper the solution is derived only in the case in which the stress field is due to the application of constant pressure to the faces of the crack. In the former paper the analysis given applies to an axisymmetric distribution of pressure p(ρ) applied to both the upper and lower face of the penny-shaped cavity, but the calculation of the stress intensity factor

and of the energy W required to open up the crack is a complicated matter even in the case in which p(ρ) is a constant.
A Theory of the Action of X-rays on living Cells
Authors: Crowther J. A.
Published: November 2008

The absorption by matter of energy from a beam of X-rays follows laws which are now well known. The first stage is the ejection from the absorbing atom of a high speed electron. This electron, in turn, produces pairs of ions from some of the molecules through which it passes until its energy is all spent. The process is essentially a discontinuous one in space, and the proportion of atoms affected at a given time is always exceedingly minute, even with an intense beam of radiation. With a beam of average intensity an individual atom would suffer ionisation, on an average, about once in a million years.
Some Relations between the Optical Spectra of Different Atoms of the same Electronic Structure. II. Aluminium-like and Copper-like Atoms
Authors: Hartree D. R.
Published: November 2008

The relevant results from the writer's previous paper on the relation between spectra of atoms of different atomic structure are summarised.

For non-penetrating orbits no new theoretical results are obtained, and there are few known spectra (other than those of lithium-like or sodium-like atoms already treated in the first paper) on which to test the relations previously obtained. Values of the polarisability for the A1+ and Si++ ions are calculated from terms of Al I and Si II respectively corresponding to non-penetrating orbits, and are shown to be very much greater than the values of the polarisability of the neon-like ions Al+++ and Si++++.

The main new results are those for penetrating orbits. Assuming a central field of force, it is shown that the quantum defect q for such an orbit can be expressed as the sum of contributions from the electrons in groups of core orbits of different principal quantum number n, and further that if for a given atom in different states of ionisation corresponding orbits of the series electron are compared, the contribution to q from a set of core orbits of given n is very nearly independent of the degree of ionisation so long as the number of electrons in core orbits in the group remains the same. It follows that, if q is the quantum defect for a term of the spectrum of an atom core charge C, the core of which contains SM orbits of principal quantum number M and none of higher quantum number, and q″ is the quantum defect for the corresponding term in the spectrum of the atom of the same element with core charge C + sM, which differs from the atom of core charge C only in lacking the core orbits of principal quantum number M, then q −; q″ is approximately the contribution from the core orbits of principal quantum number M to the quantum defect for the term of the atom core charge C.

Further, it is shown that if corresponding terms of different atoms of the same electronic structure are compared, then for large values of C the contribution to q from any group of core orbits should tend asymptotically to be proportional to the average time mean radius of these orbits, and its reciprocal should tend asymptotically to be linear in C.

Somewhat similar relations are obtained for the quantity Q = dq/d (ν/R) which measures the variation of quantum defect within a sequence.

These theoretical results, and in particular the result that l/(q − q″) should tend asymptotically to be proportional to C, are compared with the values of q deduced from the terms of such observed spectra of aluminium-like and copper-like atoms as are available, and it is found that though the theoretical relations are only established as asymptotically true for large C, there is a considerable measure of agreement with spectra for small values of C, which are the only ones which can be observed.
A note on wireless signal strength measurements made during the Solar Eclipse of 24 January, 1925
Authors: Appleton E. V. , Barnett M. A. F.
Published: November 2008

In the course of a series of signal intensity measurements made at Cambridge on the electric waves received from broadcasting stations a marked difference between day and night conditions has been observed. The day-time signals are sensibly constant but marked fluctuations of intensity become apparent about sunset and continue throughout the night. These variations are detectable at Cambridge on the signals from London, where they represent a change in strength of about 5 per cent.
An apparatus for the investigation of the effect of poisonous substances, and mixed vapours on catalytic activity
Authors: Constable F. H.
Published: November 2008

(1) An apparatus has been devised in which the composition of the vapour phase passing over the catalyst can be varied at will, or two vapours can be used alternately as reactants.

(2) By using ethyl alcohol, and amyl alcohol from fusel oil alternately as reactants, the poisoning of a very active copper gauze catalyst has been followed and the temperature coefficient of the dehydrogenation of ethyl alcohol by the copper has been measured during the poisoning.

(3) The activity of the catalyst, poisoned by amyl alcohol, fell in accordance with the simple logarithmic law

(4) Confirmation was obtained that the rates of dehydrogenation of ethyl and amyl alcohols were equal.

(5) The temperature coefficient of dehydrogenation on the catalyst was unchanged throughout the poisoning, though the reaction velocity was reduced 30 times.

(6) The temperature coefficient was also shown to be unchanged during sintering, the reaction-velocity having been reduced 10 times.

(7) Equations are derived for the rate of poisoning of an exponential distribution of centres of activity when the poison attacks the more active centres selectively.

(8) The relation deduced

cannot usually be distinguished (except with special relations between the constants) from the simple logarithmic law of poisoning.

(9) Thus the exponential distribution normally poisons like a surface composed of homogeneous centres, the temperature coefficient being unchanged by the poisoning.

(10) The equation

describes the reaction-velocity as a function of time, and temperature, and gives adequate explanation of previous experimental results on the forms of the heating and cooling curves with “poisonous” alcohols.

(11) Frenkel has shown , where τ0 is the vibration frequency of the molecule perpendicular to the surface, and μ0 is the heat of desorption of one gram molecule. Thus if the heat of desorption is not small compared with the energy necessary to cause chemical disruption of the molecule, the previous equation becomes

the form of the equation being unaltered.
The Action of Positive Ions of Caesium on a Hot Nickel Surface
Authors: Moon P. B.
Published: November 2008

Experiments on the emission of secondary electrons from hot nickel surfaces bombarded by Cs+ ions at normal incidence show that the emission is a function of bombarding voltage and target temperature. The emission is negligible below 300 volts and increases steadily with further increase of the bombarding voltage, rising to 4% at 4000 volts with the target at 950° C. Increase of temperature causes the secondary emission to diminish. If positive ions are allowed to evaporate from the hot target the number of Cs+ ions leaving the surface may, under certain conditions, be equal (with an accuracy greater than 1%) to the number arriving in the incident beam.

I much appreciate the kindness shown me in many ways by Lord Rutherford. The experiments were commenced at the instigation of Dr M. L. E. Oliphant and I gratefully acknowledge that this paper represents to a great extent the results of his advice and assistance. The work was made possible by a grant from the Department of Scientific and Industrial Research.
The Propagation of Radio Waves in an Ionised Atmosphere
Authors: Burnett D.
Published: November 2008

Larmor has shown that if the upper atmosphere contains electrons (charge ε, mass m, density ν) and if collisions between these electrons and molecules—and also the forces between the electrons themselves—are negligible, then electric waves are propagated as if the dielectric constant of the medium were reduced by , from which it appears that, so long as the approximations are valid, the velocity of propagation of the waves can be increased indefinitely by increasing either the electron density or the wave-length λ. Several later authors have attempted to take account of the collisions between electrons and molecules, assuming free paths or velocities according to Maxwell's laws for a uniform gas, and it appears that the above law holds only for short waves; but it is doubtful how far the properties of a uniform gas can be assumed when periodic forces are acting. In the first part of this paper an alternative method of solution is given by means of Boltzmann's integral equation for a non-uniform gas, the analysis being similar to that used by Lorentz in discussing the motion of free electrons in a metal. Only the case when ν is small is considered, i.e. the interactions of electrons with one another and with positive ions are neglected. How far it is possible to increase the velocity of propagation by increasing ν is a more difficult question, but it seems possible that the forces between the electrons and ions may impose a limit just as collisions with neutral molecules limit the effect of increasing the wave-length.
Some advances towards a purely geometrical justification of the use of unreal elements in projective geometry
Authors: Brahmachari I.
Published: November 2008

1. Considerable advantage has resulted from the postulation of unreal elements in projective geometry. In the first place these unreal elements were defined in terms of points represented by complex coordinates, and their use in purely geometrical reasoning had become well established before any serious attempt was made to justify this use, independently of algebraic considerations, by providing real representations of the unreal elements. The first successful attempt was that of von Staudt, who represented an unreal element by an elliptic involution associated with an order. In this system an ordered set of four real points is required to specify an unreal point. The system is comparatively simple to deal with in a single real plane, more complicated in a single real [3], and rapidly increases in complexity as the number of dimensions of the real field is increased.
Involutions of pairs of points in three dimensions determined by cubic surfaces
Authors: Babbage D. W.
Published: November 2008

1.1. In a linear space Sr, of r dimensions, we may consider involutory transformations determined by linear systems of primals whose freedom is r and whose grade, that is, the number of free intersections of r primals of the system, is two; we shall be concerned only with complete systems, systems of all the primals (of given order) satisfying certain fundamental linear conditions, for example, containing a point, or a curve, or touching a plane at a given point. The primals of such a system Φ that pass through a point P form a system ∞r−1; any r linearly independent primals of this subsidiary system will meet in one other point Q outside the base elements, and Q is common to every primal of Φ through P; further, all the primals of Φ that contain Q must contain P. We thus have an involutory transformation of the space Sr.
Absorption measurements and the continuous spectrum of β-rays
Authors: Chalmers J. A.
Published: November 2008

1. Many experiments have shown that the natural heterogeneous β-rays from any radioactive source are absorbed according to a law which is exponential for small thicknesses of absorber but which falls below the exponential for larger thicknesses, giving, finally, a quite definite ‘kink’. The positions of these kinks have been measured by the author(1), by Feather (2) and by others. Experiments on the continuous spectra of β-rays (e.g. Gurney(3)) seem to indicate a definite high-velocity limit to the continuous spectrum; and experiments on the absorption of homogeneous β-rays (e.g. Madgwick(4)) show a definite extrapolated range for the β-rays. So one might expect the ‘kinks’ found to represent the extrapolated ranges of the β-rays of highest velocity. The author (1), using the extrapolated ranges of Madgwick(4) and Varder(5), finds this interpretation of the kinks to give values of the end-points agreeing with the direct experimental values of Gurney(6). Feather(2), on the other hand, uses the results of the kinks in certain cases to give an empirical relationship between the kinks and the end-points. Feather's relationship is purely empirical and is independent of any interpretation given to the kinks; for the purpose of using the kinks to find the end-points, Feather's relationship is sufficient, but the actual interpretation of the kinks is of interest. Feather(7) has considered the matter from the theoretical standpoint, and he finds no reason to expect any abrupt discontinuity; he interprets the apparent kink as the limit of the measurable β-ray effect.
The Densities of the Regular Polytopes
Authors: Coxeter H. S. M.
Published: November 2008

In this paper it is shown how all the regular polytopes (including the Kepler-Poinsot polyhedra and Hess's analogous star polytopes in four dimensions) arise as rational solutions of trigonometrical equations.
Note on the operability of a synchronous motor at the end of a transmission line
Authors: Ingram W. H.
Published: November 2008

The problem of the transmission of power over a transmission line from an alternating current generator at one end to a synchronous motor at the other is easily solved when the line is uniform or made up of a small number of uniform line segments. The object of the present note is to apply the theory of integral equations to the general case of the non-uniform line. The solution obtained for the current at any point on the line in the form of a rational function of the frequency of the two alternators is of advantage when resonance effects are being considered; the latter effects are hard to trace in the case of the uniform line by the usual methods. It seems probable that numerical methods and computing devices can be developed for the solution of the integral equations given. The effect of armature inductance on the power limit of the system may then be more easily studied than at present.
Explicit formulae connecting Hölder's, Cesàro's and another mean value
Authors: Kienast A.
Published: November 2008

1. Having given the termssnof a sequence

then Hölder's meansare defined by

Cesàro's meansare defined by

and a third kind, σ, of mean which will be used in this paper is defined by
The application of quadratic forms in an infinity of variables to boundary problems in partial differential equations
Authors: Steen S. W. P.
Published: November 2008

The object of this paper is to find the characteristic functions and the characteristic numbers of the partial differential equation

valid in a domain G, and where on Γ, the boundary of G. The method employed is to transform two quadratic forms to their common self-conjugate “triangle“ of reference. The solution to the problem is given by this method in a simple manner, without the use of the integral equation theory, or the use of minimal sequences.
The tangent planes to a degenerate surface
Authors: Roth L.
Published: November 2008

1. In the Lehrbuch der abzählenden Methoden Zeuthen considers the problem of determining the nature and multiplicity of the tangent lines and planes to a degenerate surface in ordinary space. The surface φ in question consists of n arbitrary planes; these meet in pairs, forming double lines, and in threes, forming triple points. The tangent cone to φ from an arbitrary point consists of plane pencils, each counted twice, as follows from the known theory of degenerate plane curves. According to Zeuthen the tangent planes are of two types:

(i) those passing through one of the triple points; there are thus such systems, and each is to be counted six times;

(ii) those passing through certain points S lying on the double lines; these depend upon the passage to the limit, it being assumed that φ is obtained as the limiting form of some nondegenerate surface. Two such points lie on each double line, so that there are n(n−1) such systems of planes.