bluuebunny/crossref_metadata_2025 huggingface dataset:
Discourse Worlds in the Classroom and in Foreign Language Learning
Authors: Edmondson Willis J.
Published: November 2008

The paper begins to explore the nature of the cognitive processing involved in foreign language learning. The notion of a “discourse world” as a set of elements against the background of which a unit of talk makes sense is introduced, and the claim is made that several such “discourse worlds” may be seen to coexist in classroom discourse, in part because of participants' “awareness” (on some level) of why they are there. The notion of a discourse world is then given a psychological interpretation in terms of frame-theory, and the view is argued that the simultaneous activation of several such frames is central to the business of understanding language, and to language learning. The classroom, it is argued, offers rich opportunities for the training of such multi-level perception of foreign language input, with consequent gains in learning. From this perspective Krashen's Monitor Theory is found implausible.
The Interaction Between Type of Contact and Type of Instruction: Some Effects on the L2 Proficiency of Adult Learners
Authors: Spada Nina
Published: November 2008

This paper reports the results of a study which investigated (a) the separate effects that differences in learners' contact can have on various aspects of proficiency, and (b) the combined effects that differences in informal contact and instructional variation can have on improvement in proficiency. Forty-eight adult learners from three intermediate-level ESL classes participated in the study.

To measure differences in learners' informal contact, a language contact questionnaire was administered. The results revealed both quantitative and qualitative differences in learners' out-of-class contact with the second language. When these differences were examined in relation to learners' performance on seven proficiency measures, correlational analysis revealed that while learners' performance on some measures was related to differences in amount of contact, it was related on other measures to differences in type of contact.

To determine whether differences in contact interacted with instructional variation to produce differences in improvement in proficiency, learners' pre-and post-test scores were examined in relation to contact and class in an analysis of co-variance. The results indicated that learners' informal contact interacted with differences in instruction to produce variation in improvement on two proficiency measures.

The findings are discussed in relation to the need for more class-room-centered research to investigate both the separate and combined effects of learner and instructional variables on second language proficiency.
Code-Switching in the Speech of Adolescents Born of Immigrant Parents
Authors: Dabène Louise , Billiez Jacqueline
Published: November 2008

In this article, the bilingual speech of members of Spanish, Portuguese, and Algerian communities in France is examined. After having conducted a systematic inventory of all the instances of code-switching in the corpus, the authors propose a model for their classification. This is followed by a quantitative analysis of a sample of interactions. Finally, a qualitative analysis is presented which aims to determine the different functions fulfilled by code-switching according to the speaker's intentions and the dynamics of the interaction.
Some Applications of Cognitive Theory to Second Language Acquisition
Authors: O'Malley J. Michael , Chamot Anna Uhl , Walker Carol
Published: November 2008

This paper describes recent theoretical developments in cognitive psychology that can be applied to second language acquisition and uses the theory to analyze phenomena discussed regularly in the second language literature. Some limitations of linguistic theories in addressing the role of mental processes in second language acquisition are identified, and current cognitive learning theory in general is outlined. The paper then examines the theoretical model developed by John Anderson (1983, 1985) as it applies to memory representation, learning, and language skill acquisition. The remainder of the paper describes possible applications of this model to issues in second language acquisition and suggests that the theory is useful both in explaining second language acquisition processes and in identifying areas in which research is needed.
The Primacy of Aspect
Authors: Robison Richard E.
Published: November 2008

Studies of first and second language acquisition have indicated that when verbal morphemes first appear, they tend to mark aspectual distinctions in non-native-like ways. This study tested the hypothesis that in L2 acquisition, verbal morphemes initially mark lexical aspect—the temporal features inherent in the semantics of a predicate, independent of the time line—regardless of their function in the target language. To reduce the subjectivity that has weakened previous studies, operational tests—which entailed inserting a base-form verb phrase into a frame and then judging whether the result is acceptable—were used to determine lexical aspect for each of over 550 verb tokens in the corpus, based on an interlanguage sample from a native speaker of Spanish. The results of a chi-square test allow rejection of the null hypothesis—that lexical aspect and morphology are independent—at the .001 confidence level. Past marking was found to correlate with punctual aspect, -ing with durative.
Pragmatic, Semantic, and Syntactic Constraints and Grammaticalization
Authors: Skiba Romuald , Dittmar Norbert
Published: November 2008

This contribution will compare the acquisition of German of three adult Poles over a period of 3 years. As background to the acquisition of grammatical features in German (e. g., morphology, auxiliary and modal verbs, constituency structure, temporality), an acquisition profile of the informants will be constructed. With the help of computer-aided corpus descriptions, the sequences in acquisition will be specified.
Instruction and the Development of Questions in L2 Classrooms
Authors: Spada Nina , Lightbown Patsy M.
Published: November 2008

This paper is a report on a quasi-experimental study designed to investigate contributions of form-focused instruction and corrective feedback to the development of interrogative constructions in the oral performance of English-as-a-second-language (ESL) learners. The subjects were young francophone learners of English (age 10–12) receiving intensive ESL instruction. Their accuracy and developmental progress in the use of interrogative structures was measured prior to a 2-week period of instructional treatment. Immediate and delayed posttests were administered after the instruction. The language produced by the instructors while teaching interrogative structures was examined in relation to the learners' oral performance. Similar analyses were carried out with a comparison group. The results support the hypothesis that form-focused instruction and corrective feedback provided within the context of communicative interaction can contribute positively to second language development in both the short and long term.
The Word Unit in Second Language Speech Production and Perception
Authors: Flege James Emil , Munro Murray J.
Published: November 2008

The purpose of this study, which focused on the wordtacoas spoken in Spanish and English, was to explore the word as a unit in second language (L2) speech acquisition. As expected, acoustic measurements revealed that Spanish and English monolinguals' renditions oftacodiffered systematically. It was also shown that the extent to which Spanish/English bilinguals approximated English phonetic norms for any one segment oftacowas correlated with their approximation for the other three segments, and that early learners differentiated Spanish versus Englishtacomore than did late learners. It also appeared that the bilinguals produced /t/ with less English-like voice onset time (VOT) values in Englishtacothan in other English words without a cognate in Spanish. In a perception experiment, listeners were able to identify the native language of Spanish and English monolinguals on the basis of their production oftaco. The listeners heard larger differences between Spanish and Englishtacotokens spoken by early than late learners of English L2. Two additional perception experiments assessed further the phonetic dimensions that listeners use to determine language identity and to gauge bilinguals' speech production accuracy. Listeners assigned to language identification and goodness rating tasks responded to acoustic information distributed over all four segments intaco, although the VOT of the word-initial /t/ appeared to be the single most important phonetic dimension. Taken together, the results of this study suggest that (a) bilinguals' accuracy in producing the various segments of a second language word may be interrelated and (b) in judging L2 speech, listeners respond to phonetic errors distributed over the entire word.
Specialist Knowledge and Interlanguage Development
Authors: Whyte Shona
Published: November 2008

This study investigates learner's construction of oral texts on topics of specialization. Using the framework of the discourse domain hypothesis, which holds that second language proficiency is acquired with reference to individual, specialized contexts of production, termed discourse domains, the study tests the prediction that learners will construct more independent and coherent texts on such topics. Data were elicited from advanced ESL learners at a U.S. university: Discourse domain talk on academic major topics by five invested subjects is compared with the performance of the same subjects on a general topic and with a control group who talked on two comparable general topics. Analysis focuses on discourse organization, including turntaking patterns and episode structure. Results suggest that text construction is facilitated by learners' expertise and investment in the topic of conversation. Invested subjects constructed more coherent episodes and, in some cases, more independent turns on their topics of specialization. In the absence of such expertise, however, recent rehearsal of topics by some control subjects appeared to permit similarly enhanced discourse organization. Thus, the study reveals a complex relationship between specialized knowledge and text construction that suggests new avenues for future research into topic-related interlanguage variation.
Zero Anaphora in Nonnative Texts
Authors: Hartford Beverly S.
Published: November 2008

This paper investigates the occurrence of null objects in a stable nonnative variety of English spoken in Nepal. Previous studies of zero anaphora with second language learners have assumed that advanced learners of English will acquire the native target norms, which highly constrain null object occurrences. This paper shows that in the construction of text speakers of Nepali English may omit both direct and indirect objects in contexts where native speakers may not. Pragmatic principles govern these occurrences although they differ for the two types of objects. Null direct objects are part of discourse topic chains and their referents are recoverable within the text, even across speakers. Null indirect objects, on the other hand, refer primarily to discourse participants and do not generally need textual coreferents. The resultant discourse organization for this variety of English is one that requires greater addressee participation than native English discourse. The paper shows that when learners are confronted with input from two typologically distinct discourse traditions they may develop a third framework that utilizes compatible features for each.
Child Second Language Acquisition of Syntax
Authors: Lakshmanan Usha
Published: November 2008

Recent advances in linguistic theory within the principles and parameters framework have exerted considerable influence on the field of second language acquisition. SLA researchers working within this framework of syntactic theory have investigated the extent to which developing second language grammars are constrained by principles of Universal Grammar (UG). Much of the UG-based SLA research in the 1980s focused on adult L2 acquisition, but the role of UG principles in child L2 acquisition remained largely unexplored. More recently, however, this state of affairs has begun to change as SLA researchers are becoming more and more interested in child second language syntactic development. In this paper, I review recent and current developments in UG-based child SLA research, and I argue that child SLA has a valuable role to play in enabling us to arrive at a better understanding of the role of biological factors in language acquisition and in strengthening the links between SLA and linguistic theory. Specifically, I discuss the findings of child SLA studies with respect to the following issues: the role of UG parameters in child SLA, the status of functional categories and their projections in child SLA, and the nature of the evidence available to and used by child L2 learners. The overall picture emerging from these studies suggests that child L2 developing grammars are indeed constrained by Universal Grammar. While it is not fully clear at the present time whether the child L2 learners& knowledge is a result of direct access to UG or indirect access to UG (i.e., through the mediation of the L1), the evidence indicates that L1 transfer (at least in certain syntactic domains) cannot be entirely ruled out.
On the Stability of the Periodic States of the Triode Oscillator
Authors: Greaves W. M. H.
Published: November 2008

1. Appleton and van der Pol have shown that in a simple Triode or Dynatron generating circuit the anode potential v is related to the time t by a differential equatior of the type

where f (v) is a power series in v, and may be written
Sluice-gate problems with gravity
Authors: Budden P. J. , Norbury J.
Published: November 2008

In this paper, a free-boundary problem of the steady plane flow of an ideal fluid through a slot is solved. The fluid flows under the effect of gravity between rigid boundaries, and then out of a slot as a jet which becomes horizontal at infinity downstream. A constructive proof of the existence of solutions to a non-linear integral equation is given for a parameter range 0 < ε < ε* ≃ 1·02 (where ε, the inverse Froude number, measures the effect of gravity). Approximations to the solution are then found for ε → 0.
The irrotational flow of a perfect fluid past two spheres
Authors: Sneddon I. N. , Fulton J.
Published: November 2008

1. The boundary value problem of Laplace's equation for two spheres is a classical one, and has been the subject of discussion by many mathematicians (1). The earliest attempt to solve a boundary value problem of this type is due to Poisson (2), but his analysis is applicable only to the electrostatic problem. The first of the methods which can be successfully applied to both electrostatic arid hydrodynamical problems was developed later by Lord Kelvin (3); this procedure, which is known as the ‘method of images’, was first applied to the problem of the motion of two spheres in a perfect fluid by Hicks (4). Another method of great generality, that of transforming Laplace's equation to bipolar coordinates and studying the solutions in these coordinates, was developed about the same time by Neumann (5) and much later by Jeffery (6). More recently a new method has been developed by Mitra (7) for the solution of the problem of two spheres in a potential field. It makes use of two sets of spherical polar coordinate systems; the solution is expressed in terms of infinite series whose coefficients satisfy an infinite set of linear algebraic equations. The chief interest of Mitra's method lies in the fact that he has found it possible to derive exact solutions of this infinite set of equations. All of these methods suffer from the disadvantage that the potential function is obtained in the form of an infinite series so that any numerical calculations are rendered cumbersome.
Loop transversals and the centralizer ring of a permutation group
Authors: Johnson K. W.
Published: November 2008

Many of the basic concepts in this paper are defined in (2), and it will be useful to the reader if he is familiar with that paper. In it the concept of a loop transversal to a subgroup S of a group G is defined and discussed, where if G is a transitive permutation group and no explicit S is mentioned it is assumed that S is a point stabilizer. In (3) there appeared the following problem (P):

Let G be a transitive permutation group which is 2-closed.

(i) Is there a fixed-point-free transversal in G (i.e. to a point stabilizer)?

(ii) Is there a loop transversal in G?

Unfortunately a note was added in which it was falsely stated that the answer to both (i) and (ii) is yes.
Representations of complex imprimitive reflection groups
Authors: Hughes M. C.
Published: November 2008

In his attempt to give the irreducible characters of the Weyl groups of type A, B and D, Mayer [3] found a unified theory using their common structure as reflection groups. In this paper, we give the characters of the complex imprimitive reflection groups. We are able to give an algorithm which allows us to calculate the irreducible components of the principal character of a ‘Weyl’ subgroup induced up to the whole group. This is a generalization of the algorithm given by Mayer.
The varieties of the mod p cohomology rings of extra special p-groups for an odd prime p
Authors: Tezuka Michishige , Yagita Nobuaki
Published: November 2008

In this paper we attempt to determine the mod p cohomology rings of the extra special p-groups for an odd prime p. Quillen has calculated the mod 2 case [8]. In our case, its structure seems to be very complicated [6]. It seems reasonable that we consider the variety defined by the cohomology ring of even degree according to Serre [11]. The main result of this paper (Theorem 5.3) gives a subalgebra of the cohomology ring such that the inclusion homomorphism induces a homeomorphism between the varieties.
Lattice Banach spaces, order-isomorphic to l1
Authors: Polyrakis Ioannis A.
Published: November 2008

It is known, (see [7], theorem 4 or [8], corollary II, 10.1), that a positive generated, ordered Banach space X is order-isomorphic to l1 iff X has a Schauder basis which generates its positive cone X+ and X+ has a bounded base.
Matrix transformations between some classes of sequences
Authors: Lascarides C. G. , Maddox I. J.
Published: November 2008

Let A = (ank) be an infinite matrix of complex numbers ank (n, k = 1, 2,…) and X, Y two subsets of the space s of complex sequences. We say that the matrix A defines a (matrix) transformation from X into Y, and we denote it by writing A: X → Y, if for every sequence x = (xk)∈X the sequence Ax = (An(x)) is in Y, where An(x) = Σankxk and the sum without limits is always taken from k = 1 to k = ∞. The sequence Ax is called the transformation of x by the matrix A. By (X, Y) we denote the class of matrices A such that A: X → Y.
Summability of Hermite polynomial expansions of generalized functions
Authors: Ditzian Z.
Published: November 2008

1. Introduction: The well-known result that every function f(x) ∈ L2(–∞, ∞) can be expanded in L2(– ∞,∞) by where and was recently followed by an expansion theorem for generalized functions. In papers by Wildlund(8), Giertz(4) and Zemanian(9) it was shown that a tempered distribution f∈S′ can be expanded by Hermite functions that is

for all ψ∈S (the space of rapidly decreasing test functions).
Zeros and poles of Artin L-series
Authors: Foote Richard , Murty V. Kumar
Published: November 2008

Let E/F be a finite normal extension of number fields with Galois group G. For each virtual character χ of G, denote by L(s, χ) = L(s, χ, F) the Artin L-series attached to χ. It is defined for Re (s) > 1 by an Euler product which is absolutely convergent, making it holomorphic in this half plane. Artin's holomorphy conjecture asserts that, if χ is a character, L(s, χ) has a continuation to the entire s-plane, analytic except possibly for-a pole at s = 1 of multiplicity equal to 〈χ, 1〉, where 1 denotes the trivial character. A well-known group-theoretic result of Brauer implies that L(s, χ) has a meromorphic continuation for all s.
Incompressible surfaces and Dehn surgery on 1-bridge knots in handlebodies
Authors: Wu Ying-Qing
Published: November 2008

Given a knot K in a 3-manifold M, we use N(K) to denote a regular neighbourhood of K. Suppose γ is a slope (i.e. an isotopy class of essential simple closed curves) on ∂N(K). The surgered manifold along γ is denoted by (H, K; γ), which by definition is the manifold obtained by gluing a solid torus to H – Int N(K) so that γ bounds a meridional disc. We say that M is ∂-reducible if ∂M is compressible in M, and we call γ a ∂-reducing slope of K if (H, K; γ) is ∂-reducible. Since incompressible surfaces play an important rôle in 3-manifold theory, it is important to know what slopes of a given knot are ∂-reducing. In the generic case there are at most three ∂-reducing slopes for a given knot [12], but there is no known algorithm to find these slopes. An exceptional case is when M is a solid torus, which has been well studied by Berge, Gabai and Scharlemann [1, 4, 5, 10]. It is now known that a knot in a solid torus has ∂-reducing slopes only if it is a 1-bridge braid. Moreover, all such knots and their corresponding ∂-reducing slopes are classified in [1]. For 1-bridge braids with small bridge width, a geometric method of detecting ∂-reducing slopes has also been given in [5]. It was conjectured that a similar result holds for handlebodies, i.e. if K is a knot in a handlebody with H – K ∂-irreducible, then K has ∂-reducing slopes only if K is a 1-bridge knot (see below for definitions). One is referred to [13] for some discussion of this conjecture and related problems.
On the Geometrical Genus of Certain Surfaces
Authors: Maxwell Edwin A.
Published: November 2008

In spite of a large amount of general theory, it remains a surprising fact that the number of known irregular surfaces in space of three dimensions is quite small. Moreover, although the evaluation of the arithmetical genus pα is comparatively direct, it is often a matter of considerable difficulty to calculate the geometrical genus pg. This paper deals with a number of surfaces for which the equations of the canonical system can be written down and their number counted. An extension to primals in higher space is also suggested for the simplest case.
On Order in Time
Authors: Russell Bertrand
Published: November 2008

It is generally agreed that instants are mathematical constructions, not physical entities. If, therefore, there are instants, they must be classes of events having certain properties. For reasons explained in Our Knowledge of the External World, pp. 116–20, an instant is most naturally defined as a group of events having the following two properties:

(1) Any two members of the group overlap in time, i.e. neither is wholly before the other.
The Polarizability of Molecular Hydrogen H2
Authors: Easthope C. E.
Published: November 2008

1. The problem of calculating the polarizability of molecular hydrogen has recently been considered by a number of investigators. Steensholt and Hirschfelder use the variational method developed by Hylleras and Hassé. For ψ0, the wave function of the unperturbed molecule when no external field is present, they take either the Rosent or the Wang wave function, while the wave functions of the perturbed molecule were considered in both the one-parameter form, ψ0 [1+A(q1 + q2)] and the two-parameter form, ψ0 [1+A(q1 + q2) + B(r1q1 + r2q2)], where A and B are parameters to be varied so as to give the system a minimum energy, q1 and q2 are the coordinates of the electrons 1 and 2 in the direction of the applied field as measured from the centre of the molecule, and r1 and r2 are their respective distances from the same point. Mrowka, on the other hand, employs a method based on the usual perturbation theory. Their numerical results are given in the following table.
The Intensity of the γ-Rays emitted by the Active Deposit of Thorium
Authors: Oppenheimer F.
Published: November 2008

1. Ellis(1) has proposed energy level systems for the bodies of the Thorium series, but the values of the γ-ray intensities forming the basis of this system fail to account satisfactorily for the total energy of the γ-rays emitted by Th C and its products. This is a serious discrepancy which needs examination. Since the publication of these level systems, we have obtained new values for the intensities of the γ-rays from Th C and Th Pb. The details of these measurements are given in the second part of this paper. These γ-ray intensities are, of course, deduced from the intensities of the discrete β-groups by dividing by the appropriate internal conversion coefficient. The changes which we have made in the γ-ray intensities are due first to revised values of the β-ray intensities from Th Pb and secondly to a revised set of values of the internal conversion coefficient (2). We have not however found it necessary to make any change in Ellis and Mott's (3) allocation of lines to dipole or quadripole type. The contributions of the two factors are made clear in Table I.
The Wiener–Pitt phenomenon on semi-groups
Authors: Davis T. A.
Published: November 2008

Let G be a locally compact Abelian group, written adoptively, with Haar measure m, L1(G) the group algebra of G, and M(G) the Banach algebra of all bounded, complex-valued, regular, countably additive measures on G. For a general account of L1(G) and M(G) see Rudin (7).
An inequality in Feynman integrands
Authors: Fairlie D. B.
Published: November 2008

A proof by means of graphical techniques is given of an inequality conjectured by Nakanishi concerning the Feynman integrand for any term in the perturbation expansion of the scattering amplitude.
On the Penetration of Waves and their Rays into a Medium of Gradually Varying Properties
Authors: Wilcken J. A.
Published: November 2008

The question has frequently been raised, whether the laws of ordinary Geometrical Optics, especially with regard to the reflexion and refraction at the confines of two media, are equally applicable when the transition is accomplished in a gradual manner. The problem has an important bearing on physical phenomena of a widely varying character, such as the propagation of sound and light in the atmosphere, with occurrence of mirage or zones of silence, the transmission of seismic disturbances through the earth, tidal waves in a canal of varying cross-section, and others.
On the Angle of Incidence in Soaring Flight
Authors: Hankin E. H. , North J. D.
Published: November 2008

Perhaps the most peculiar fact of observation yet recorded about the wing disposition of soaring birds is the apparent large negative angle of incidence shown by the wings of vultures when in fast horizontal flight.
Some enumerative formulae for algebraic curves
Authors: Macdonald I. G.
Published: November 2008

This paper is in two parts. In Part I we are concerned with one or more linear series on an algebraic curve; we consider a set of points on the curve which are contained with assigned multiplicities in a set of each of the linear series and, by persistent use of Severi's equivalence relation for the united points of an algebraic correspondence with valency, we derive formulae for the number of such sets of points when the constants involved are such as to make this number finite. All this is essentially a generalization of the formula for the number of points in the Jacobian set of a linear series of freedom 1, and the main result is Theorem 3.
Recurrence relations for oscillator-well radial integrals
Authors: Howell K. M.
Published: November 2008

The general radial integral between oscillator-well wave-functions with a Gauss interaction potential is expressed as a generalized hypergeometric function. A relation between contiguous functions is found and used to obtain a recurrence relation between these integrals.
Riemann surfaces of field extensions
Authors: Knight J. T.
Published: November 2008

Since Riemann's dissertation of 1851, Riemann surfaces have for the most part been considered as suitable domains of definition for analytic functions. Here, however, we view them as topological spaces associated with certain kinds of field extension, and consider how their topological properties are connected with algebraic properties of these field extensions. A specialization of these results gives us arithmetic properties of fields of algebraic functions of one real variable.
On Jacobi polynomials
Authors: Munot P. C.
Published: November 2008

1. The object of this paper is to prove some formulae of Jacobi polynomials including a generating function. The results (2·l)–(2·4), (2·6)–(2·9), (3·l)–(3·4), and (4·1) are believed to be new.
Some results on the H-function involving the generalized Laguerre polynomial
Authors: Shah Manilal
Published: November 2008

In this paper the integral involving the Fox H-function and the Laguerre polynomial has been evaluated and the expansion formula for the H-function has been established with the application of this integral. Many particular results have also been given.
Note on the reduction of dual and triple series equations to dual and triple integral equations
Authors: Williams W. E.
Published: November 2008

Dual integral equations involving Bessel functions occur in the solution of some boundary-value problems in potential theory with conditions prescribed on a circular disc and a considerable amount of attention has been given to the solution of such equations (cf. (1)). The method of solving these dual integral equations is very similar to that employed in the solution of certain dual series equations involving Legendre functions. Equations of this type occur in problems in potential theory with conditions prescribed on a spherical cap and their solution has been obtained by Collins (2). No definite mathematical connexion has, however, been established between these dual series and dual integral equations and the object of this note is to establish such a connexion.
Some results in spectral synthesis
Authors: Elliott Robert J.
Published: November 2008

For the group of real numbers R, an exponential monomial is defined as a function of the form xr(−ixz), for some non-negative integer r and some complex number z. Similarly, an exponential polynomial is a function P(x) exp (−ixz), for a polynomial P. In a now famous paper ((15)), Schwartz proved that every closed translation invariant subspace (variety) of the space of continuous functions on R is determined by the exponential monomials it contains. His techniques do not generalize to groups other than R as they use the theory of functions of one complex variable. A shorter proof of this result, using the Carleman transform of a function, was given by Kahane in his thesis ((9)). Ehrenpreis ((5)) proved results similar to those of Schwartz for certain varieties in the space of analytic functions of n complex variables, and Malgrange ((13)) proved the related result that any solution in ℰ(Rn) (for the notation see (16)) of the homogeneous convolution equation μ*f = 0, for some μ∈ℰ′, belongs to the closure of the exponential polynomial solutions of the equation.
Integral Invariants of the Affine Field
Authors: Newman M. H. A.
Published: November 2008

In this paper the method of infinitesimal transformations of coordinates, used by Weyl to determine conditions that a function of the tensors gik and φi, and certain of their derivatives, should be a scalar density, is applied (with certain modifications so as to give tensor relations) to functions of and . It is known that in order that such a function should be a scalar density it must be a homogeneous function, of degree ½n, of , and this must of course be deducible from the equations found by the infinitesimal transformations. In view of the part which these equations may play, as “equations of energy,” etc., in purely affine field theories, it seems desirable that the connection should be explicitly shown, and this is done in § 3.
The calculation of the van der Waal forces for hydrogen and helium at large inter-atomic distances
Authors: Hassé H. R.
Published: November 2008

This paper deals with the calculation of the inter-atomic force at large distances for the cases of hydrogen and helium, and is based on the method used in calculating the polarizability of helium.
On the Determination of Plane Curves by means of Assigned Singularities
Authors: Todd J. A.
Published: November 2008

The principal object of the present paper is to give a set of sufficient conditions, of considerable generality, under which a plane curve assigned to pass through certain points with given multiplicities shall be irreducible. The case considered is that in which the assigned multiple points of the curve are of such generality that the conditions presented to the curve at these points are independent. We shall shew that subject to certain explicit restrictions on the points, which ensure, for example, that no three points shall be collinear whose prescribed multiplicities in aggregate exceed the order of the curve, the curve determined by the points will be irreducible if its freedom is not negative, save in the case when it degenerates into a repeated elliptic curve. A familiar example of this last case arises in the problem of constructing a sextic with nine assigned nodes; in general the curve in question consists of the unique cubic through the nine points, counted twice.
On many-valued Riemann-Stieltjes integration
Authors: Young Rosalind Cecily
Published: November 2008

The considerations set forth in the present paper are valid for the most part in parallel form for integration in space of any number of dimensions, and in the widest measure for any modification of the process that may be devised naturally: integration of functions not necessarily one-valued, with respect to functions of sets, or functions of ∑, not necessarily unchanged by subdivision, in fields as wide or as restricted as may be convenient, as long as we maintain the possibility of forming subdivisions of arbitrarily small “norm,” and of splitting up such a subdivision arbitrarily into two parts, each of which may be subdivided independently in any manner, to give a subdivision of the whole. These conditions are essential for the proper working of the theory, and in particular for the validity in more dimensions of Hyslop's method referred to in 5.
The triatomic hydrogen ion
Authors: Massey H. S. W.
Published: November 2008

The advent of quantum mechanics has provided a means of treating the interaction of atoms and the formation of molecules and has had very many successes in this field. In particular the phenomenon of the saturation of valence forces appears as a natural consequence of the theory. Nevertheless there are very many difficulties still to be overcome.
Secondary electron emission from a nickel surface produced by positive ions of mercury
Authors: Chaudhri Rafi Mahommed
Published: November 2008

(1)A beam of positive ions of mercury produced from an arc in mercury vapour and fired upon a surface of nickel produces an emission of electrons.

(2)For a fresh untreated nickel target the electron emission is of the order of 1·5 per cent. for ion energies less than about 600 electron-volts, and rises to about 15–20 per cent. at 2000 electron-volts.

(3)After degassing thoroughly at a red heat the secondary electron emission is found to fall to about half the value observed with a dirty target. Continued bombardment with mercury ions leads to a progressive decrease in the emission, which approaches a final steady state after some hours. In this steady state the ratio is about 2·3 per cent. at 2000 electron-volts. After degassing afresh, the same process is repeated.

(4)Tests were made to assure that the emission is in reality one of electrons from the struck target, and that it is due to the impact of the positive ions.
The ‘relaxation’ term in Debye and Hückel's theory of ionic mobility
Authors: Paine H. H.
Published: November 2008

(1) The cataphoresis of ions and colloid particles is discussed in so far as it is affected by the ionic atmosphere.

(2) The ions in the atmosphere which carry a charge opposite in sign to that on the central particle are attracted to the central particle. However, when an electric field is applied to the liquid, they are able to drift away in virtue of their molecular energy, and the migration of the central particle is dependent on this fact. The relaxation force is the resultant of the forces between central particle and ions during this separation.

(3) Such a force draws the ions in the atmosphere after the central particle to some extent. From a consideration of the energy involved in the separation of particle and atmosphere, and of the molecular energies of the ions, we are able to calculate the number of ions which this relaxation force could draw through the liquid as though they were bound to the particle, and hence deduce the magnitude of the force in terms of the friction constant of the ions. The expression is the same as that given by Debye and Hückel.

(4) The cataphoresis equation usually employed for colloid particles takes no account of this relaxation force during migration. The corrected equation is given.
Note on a high-tension supply for Geiger counters operated from A.C. mains
Authors: Webster H. C.
Published: November 2008

A high-tension supply suitable for all types of Geiger counter must supply up to 5000 volts, free from A.C. ripple and other electrical disturbances, and it must be possible to rely on the voltage remaining constant to within one or two parts in a thousand over considerable intervals of time. With the apparatus here described these requirements have been fulfilled sufficiently well for satisfactory operation of Geiger-Müller tube-counters from ordinary A.C. mains, and since the method of keeping the voltage constant does not appear to have previously been used for this purpose, it seemed desirable to record it briefly.
Additional note on plane congruences and fifth incidence theorems
Authors: Welchman W. G.
Published: November 2008

In a recent paper I discussed plane congruences of order two in [4] and obtained congruences of types (2, 6)1, (2, 6)2, (2, 5), (2, 4) and (2, 3). The method employed was due to Segre, who showed that a plane congruence of order two in [4] has in general a curve locus of singular points which is met by each plane in five points. Then, if we can find a curve in [4], composite or not, with an ∞2 system of quadrisecant planes of which two pass through an arbitrary point, the planes must all meet a residual curve, and we shall have obtained a congruence of the second order and a fifth incidence theorem.
The sum of powers as canonical expression
Authors: Bronowski J.
Published: November 2008

1. In this paper I discuss the expression of the general form F of order n, homogeneous in r + 1 variables z0, z1,…, zl,…, zr, as the sum of the nth powers of h + H linear forms in these variables. I take h (> 0) of these linear forms to be undetermined, namely the forms

whose coefficients are undetermined; and I take the remaining H(≥0) linear forms to be assigned, namely the forms

whose coefficients are assigned.
On the stability of the three-phase synchronous motor
Authors: Ingram W. H.
Published: November 2008

A three-phase star-connected alternating-current motor of simplest type, connected to busbars maintained at sinusoidal potentials e1, e2 and e3 with respect to the star-point and connected to a shaft load which exerts a reactive torque f on the rotor, is dynamically specified by the following functions:

where the are the armature currents in the three phases, i is the current in the amortisseur circuit, Q the current in the field circuit, θ the rotor position angle, T the kinetic energy, V the potential energy, S the Rayleigh dissipation and U the activity of the external forces on the machine. The self-inductances of the armature circuits and the mutual inductances between them are assumed to be constant.
Note on the Effect of Alpha Particles on Paraffin
Authors: Richards William T.
Published: November 2008

1. It has been shown that the action of alpha particles on paraffin is independent of the state of aggregation of the substance.

2. Defects in the customary procedure for the decomposition liquids and solids by the emanation tube method are discussed.

3. A lecture demonstration of the chemical effect of alpha particles is described.
Some investigations of gas discharges by means of an exploring electrode
Authors: Emeléus K. G.
Published: November 2008

The glow discharge between cold aluminium electrodes in air, oxygen, nitrogen and hydrogen has been analyzed by Langmuir's method, for pressures between 0·1 and 0·4 mm. Hg, current densities of from 0·02 to 0·2 mA./sq.cm., and applied potentials between 300 and 700 volts. An annular exploring electrode has been used. It has been found that whilst practically the whole fall of potential is localized across the cathode dark space at the lower pressures, a fall of as much as 40 volts can exist across the remainder of the discharge at the higher pressures. Reversal of the electric field has been found in the negative glow, and in certain cases in the Faraday dark space, when conditions are favourable for passage of an electron current by diffusion against the field. In several instances the negative glow was at a higher potential than the anode. Two groups of electrons occur in the negative glow, together with a single fast group at the anode boundary of the cathode dark space, and a single slow group in the Faraday dark space.
The Specific Heat of Hydrogen at high temperatures
Authors: McCrea W. H.
Published: November 2008

T. Hori has recently carried out a careful study of the ultra-violet bands of the hydrogen molecule and deduced numerical values for the energy levels involved in their production. Mr R. H. Fowler pointed out to the writer the desirability of re-calculating the specific heat of H2 by using Hori's empirical values of the energy. The present note gives the result of the calculation, which is of course similar to the investigation of Kemble and van Vleck.
The stability of rotating masses of liquid; note to a former paper
Authors: Baker H. F.
Published: November 2008

In these Proceedings, Vol. xx (1920), pp. 198–204, the writer ventured (l.c. p. 203) on some remarks as to the reason why Sir G. Darwin and Mr Jeans had obtained discordant results for the stability of the pear-shaped figure of equilibrium, suggesting that this was due to a different mode of expansion of the functions involved. Sir G. Darwin used an infinite series of Lamé functions; Mr Jeans' method was equivalent to using the early parts from an expansion, of which every term, when expressed as an integral series of Lamé functions, would be an infinite series. At that time there was difficulty in obtaining Liapounoff's papers; since then, by the kindness of M. Belopolsky, of Pulkova, the whole of the four parts of Liapounoff's publication “Sur les figures d'équilibre peu différentes des ellipsoïdes d'une masse liquide homogène douèe d'un mouvement de rotation,” in all over 750 large folio pages, have become available; and these are now in the market. It is particularly interesting to see that the fourth part (1914) is devoted precisely to that change in the method of development which would arise in passing from Sir G. Darwin's expansion to the other expansion referred to above. And it is only by this change that Liapounoff is able to give the general proof of a form of expression of his results—in terms of polynomials and not infinite series—upon which his theorem of instability is made to depend. The careful consideration of the convergence of his expansions, which adds so greatly to the length of Liapounoff's papers, supplies materials for the proof that the expansion used in Mr Jeans' paper can be placed on a sure foundation, while Sir G. Darwin's expansion requires an estimation of the remainder.
On the substitution of Wallis's postulate of similarity for Euclid's postulate of parallels
Authors: Hill M. J. M.
Published: November 2008

The following is an alternative to Proposition II of the former paper. It does not assume the second of the initial assumptions in Art. 2, nor does it assume that the angles supplementary to equal angles are equal, which Hilbert regards as a proposition (Foundations of Geometry, p. 18 of the English translation).
Modern algebra and polynomial ideals
Authors: Macaulay F. S.
Published: November 2008

The aim of the following exposition is to give some idea of the scope of modern algebra in the light of the theory of ideals. It consists for the most part of definitions, examples, and the statement of theorems without proof; but the selection is severely restricted even in idealtheory. Thus no reference is made to the highly important matter of homomorphic, or multiply isomorphic, correspondence and its consequences.
On the regularity of surfaces, II
Authors: Roth L.
Published: November 2008

This paper is a sequel to one recently published, in which the regularity of surfaces was investigated by means of certain criteria suggested by Comessatti. We suppose throughout that the surface F under consideration is of general type in Sr, and that it has curve sections C of order n and genus π. It may be recalled that in the previous work the two most useful criteria were the following theorems:

If π < ½ (n + 2), then F is regular or referable. (I)

If πr (n) ≤ π ≤ n, where πr (n) is the maximum genus of a Cn in Sr, then F is regular or referable. (II)
The fundamental equations of electromagnetism, independent of metrical geometry
Authors: van Dantzig D.
Published: November 2008

It is trivial that the fundamental equations of electromagnetism are invariant under orthogonal transformations of space. This invariance can be brought into evidence by using the calculus adapted to the orthogonal group, viz. the vector-calculus. The equations can be written either in their integral form

or in their differential form
The effect of exchange on the polarisation of electrons by double scattering
Authors: Smith R. A.
Published: November 2008

The most outstanding discrepancy between experiment and Dirac's theory of the electron is at present that shown by Dymond's experiments on the polarisation of beams of electrons by double scattering. It has been shown by Mott, using Dirac's relativistic wave equation, that one would expect a 15% asymmetry of beams of 140 k.v. electrons scattered twice at 90° by gold. The experiments of Dymond referred to above show that there cannot be more than 1% asymmetry. Several attempts have been made to explain this discrepancy, but without success. (For an account of these see Dymond's paper II.) One possibility which has not yet been investigated is that of exchange between the incident electron and the electrons of the struck atom. It is evident that only elastic exchange need be considered, since the probability of excitation of any form is known to be small. Only exchange with theKandLshells may be expected to give any appreciable effect.
The Electric Moment of an Electron
Authors: Lees A.
Published: November 2008

It is well known that an electron possesses a magnetic moment. Frenkel has further deduced by relativistic arguments that the electron must also possess a real electric moment. Dirac has deduced, from his linear wave equation, a relation which indicates formally the existence of an imaginary electric moment as well as the real magnetic moment. It is shown that Frenkel's argument is not sound, since we now know that a relativistic state of affairs may not admit of tensorial representation, and that Dirac's reasoning is not sufficiently precise. When it is replaced by precise reasoning the magnetic moment remains as before, but the terms representing the electric moment disappear from the result. The electric moment therefore does not exist.