bluuebunny/crossref_metadata_2025 huggingface dataset:
Applying Accommodation Theory to Variable Performance Data in L2
Authors: Zuengler Jane
Published: November 2008

The pilot study reported here used Accommodation Theory in addressing this question: when L2 speakers are asked to reply to a statement which is ethnolinguistically threatening, will their speech diverge (i.e., become less TL-like) ? The study focused on phonological variants in the replies of 13 ESL speakers. Results indicated that the nature of reply was important: only those whose replies were personal and/or ethnically related showed a decrease in TL correctness.
Repair in Foreign Language Teaching
Authors: Kasper Gabriele
Published: November 2008

Repair, defined in this paper as modifications of trouble sources which have manifested themselves in the discourse, is an important activity in FL learning and communication, both in educational and non-educational contexts. It is argued that studies of repair in the FL classroom should include all repair activity rather than focus on one specific repair type, viz., the teacher's correction of learners' errors. In this study the four repair types suggested by Schegloff, Jefferson, and Sacks (1977) are analyzed, and a further distinction is made according to whether the trouble source is produced by the teacher or a learner. It is shown that different preferences for repair patterns vary with the type of classroom activity (language-centered vs. content-centered activities), and it is discussed how these preferences relate to repair in non-educational learner-native speaker discourse.
Second Language Acquisition by Adult Immigrants: Exemplified Methodology
Authors: Trévise Anne , Porquier Rémy
Published: November 2008

The description of second language acquisition by adult immigrants in a natural setting raises specific methodological questions. This paper attempts to clarify some of these problems using the European Project data (Perdue, 1982) in three different areas: (1) the acquisition and use of the over-generalized marker  (c'est in target French); (2) the acquisition of reference to time; and (3) the acquisition of reference to space by adult Spanish speakers in France.
Mother and Other Tongue Influence on Learner French
Authors: Singleton David
Published: November 2008

Recent perspectives on language transfer have highlighted the role of psychotypology and have given new life to Newmark's ignorance hypothesis. This paper examines such perspectives in the light of a body of data in French from a beginning learner of that language whose native language is English but who in addition has some knowledge of Irish, Latin, and Spanish. The fact that Spanish emerges as a privileged transfer source seems to point to a psychotypology factor, and certain distributional and contextual evidence appears to show that ignorance is in many cases triggering thè transfers. However, because ignorance does not seem to explain all cases, some speculation is entered into, on the basis of clues in the data, regarding the role of memory codes in transfer.
Testing Listening Comprehension in the Context of the ACTFL Proficiency Guidelines
Authors: Douglas Dan
Published: November 2008

This article discusses issues related to the testing of listening comprehension in the context of the 1986 ACTFL proficiency guidelines (American Council on the Teaching of Foreign Languages, 1987). After a review of current research on listening comprehension and development of listening tests, four issues are singled out for more detailed consideration: the meaning ofcontextin listening testing, the concept of criterion-referenced tests, the notion of specific purposes in testing, and the use of technology in listening tests. A number of research issues are also discussed.
The Writing of Anglo and Hispanic Elementary School Students in Bilingual, Submersion, and Regular Programs
Authors: Carlisle Robert S.
Published: November 2008

The purpose of this descriptive cross-sectional study was to describe and rate the writing of Hispanic students in a bilingual program and to compare their writing with that of Hispanic students in a submersion program and with native English speakers in a regular program. Five dependent variables were investigated: rhetorical effectiveness, overall quality of writing, productivity, syntactic maturity, and error frequency. Analyses of variance for both grade and program revealed that the sixth graders had significantly higher scores than did the fourth graders on all of the dependent variables except for error frequency. The students in the regular program had significantly higher scores on rhetorical effectiveness and overall quality of writing than did the submersion program students and the bilingual program students; they also made significantly fewer errors than did the bilingual program students. The bilingual program students had significantly higher scores on syntactic maturity and productivity than did the submersion program students. Results suggest that students who learn to write in their L1 before learning to write in their L2 will write just as effectively in their L2 as those students who learn to write only in their L2.
Integrative Motivation, Induced Anxiety, and Language Learning in a Controlled Environment
Authors: Gardner R. C. , Day J. B. , Maclntyre P. D.
Published: November 2008

The study examines the effects of both integrative motivation and anxiety on computerized vocabulary acquisition using a laboratory analog procedure as a microcosm of second language learning. An attempt was made to induce anxiety in one group of subjects by videotaping them while learning. Individual differences in integrative motivation were measured by aggregating relevant scales. Subjects higher in integrative motivation showed superior vocabulary acquisition and tended to initiate a translation more quickly than did those lower in integrative motivation. The anxiety manipulation did not appear to influence behavior during the learning trials. A second set of analyses revealed that subjects with more positive attitudes tended to respond more quickly and consistently to the attitude items. The results are discussed in terms of the operational definition of integrative motivation and its relation to anxiety.
The Role of Causal Reasoning and Language Competence in Narrative Comprehension
Authors: Horiba Yukie
Published: November 2008

The study investigates the role of causal reasoning in second language (L2) narrative comprehension. Subjects read and recalled texts that were either high or low in causal coherence. This read-and-recall procedure was repeated. Half of the subjects reported their thoughts during reading. The major finding was that first language (L1) readers recalled the high coherence texts better than the low coherence texts. Advanced L2 readers showed a similar advantage for thehigh coherence texts, but only in their second reading. Intermediate readers' recall was lower and showed no advantage for highly coherent texts. The verbal report data generally supported these patterns. These results indicate that L2 readers have difficulty detecting the higher order causal structure in texts. This structure is a central component of L1 readers' mental representation of the information in a text. As L2 readers' skills improve, their ability to detect causal relations increases, although even advanced L2 readers may need a second reading to do so.
Instance Theory and Second Language Rule Learning under Explicit Conditions
Authors: Robinson Peter J. , Ha Mee Aie
Published: November 2008

This study investigates the generalizability of claims by Logan (Klapp, Boches, Trabert, & Logan, 1991; Logan, 1985, 1988a, 1988b; Logan & Klapp, 1991) about the development of automaticity in the adult learning of alphabet arithmetic problems to the context of adult second language acquisition. Logan's proposal is that as individual solutions to problems accumulate in memory a transition in problem-solving procedures takes place. This transition involves the shift from an algorithm-based procedure for deducing correct solutions to direct retrieval of individual solutions or instances from memory. In the present study, second language learners of English were presented with a rule for understanding the morphological constraint on the dative alternation (Mazurkewich & White, 1984) and asked to judge the acceptability of 36 sentences presented in a training set. The sentences were controlled for frequency of presentation, one being presented eight times, one seven times, and so forth. When presented together with novel instances of the same type in a transfer set, reaction times to old instances were significantly faster. Reaction times to repetitions of the previously presented verbs in new frames and novel verbs in old frames were compared as a test of hypotheses about strategy switches in processing alternating and nonalternating verbs.
Where is Cognition?
Authors: Schumann John H.
Published: November 2008

This paper argues that the brain is the seat of cognition, that cognitive processes are neural processes, and that, in the brain, affect and cognition are distinguishable but inseparable. This perspective allows a reconceptualization of the affective filter in terms of the brain's stimulus appraisal system, which interacts with cognition to promote or inhibit second language acquisition. A research strategy is proposed for investigating these ideas.
Nonsegmental Factors in Foreign Accent
Authors: Munro Murray J.
Published: November 2008

Untrained native English listeners assigned foreign accent scores to sentence and narrative utterances that had been rendered unintelligible through low-pass filtering. Utterances produced by native English talkers were assigned consistently higher ratings than those produced by Mandarin-speaking learners of English, even when the listeners were unfamiliar with the content. Because these filtered speech stimuli contained very little of what could be considered segmental information, the results suggest that untrained listeners can identify foreign-accented speech on the basis of nonsegmental information alone, whether they are presented with material of known or of unknown content. Acoustical analyses of the stimuli suggested that differences in speaking rates, intonation patterns, and timing may have played a role in the listeners' assessments, although the cues to foreign-accentedness may have varied from talker to talker and from utterance to utterance. Surprisingly, no relationship was observed between the ratings of the filtered and unfiltered versions of the nonnative stimuli.
Ad Minorem Theoriae Gloriam
Authors: Schumann John H.
Published: November 2008

Eubank and Gregg (1995) claim that “Jacobs and Schumann wish to deny the existence of UG” (p. 42). This statement presupposes the existence of Universal Grammar (UG). However, Jacobs, Schumann, and Pulvermuller see the existence of UG and its possible neural substrate as an empirical issue and, therefore, are free to explore it, examine it, and question it. If it were demonstrated that there were, in fact, no UG, it would do great violence to Eubank and Gregg's theory. However, if it were demonstrated that UGdidexist, Jacobs, Schumann, and Pulvermüller could easily accommodate this fact in their positions. Jacobs (1988) and Jacobs and Schumann (1992) point out some neural arguments against UG; Pulvermuller and Schumann (1994) actually argue for a neural specialization for grammar but not specifically a UG, and Schumann (1993, 1994) examines differential success in second language acquisition by assuming a highly canalized, neural basis for grammar.
The Coconstruction of Cross-Cultural Miscommunication
Authors: Tyler Andrea
Published: November 2008

This paper examines the sources of miscommunication in a videotaped tutoring session involving a native speaker of Korean and a native speaker of U.S. English. Analysis revealed an initial nonmutual interpretation of participant role and status. These divergent interpretations appear to have resulted from the Korean tutor's transfer of a Korean conversational routine, which he defined as involving polite speaker modesty, to the U.S. English context. The initial conflicting interpretations are maintained and solidified by additional mismatches in discourse management strategies, schema, and contextualization cues. The cumulative effect of these mismatches was the judgment on the part of each of the interlocutors that the other was uncooperative.
Developing the Ability to Perform Speech Acts
Authors: Cohen Andrew D.
Published: November 2008

This paper calls attention to an increasingly prominent field of interest within second language acquisition research and pedagogy, namely, that of pragmatic ability. It focuses on an area within pragmatics, that of speech acts, considers the processes underlying the performance of such speech acts, and looks at the effects of explicit instruction in this area. The paper starts by asking what speech act ability entails. Several basic distinctions are made in the description of speech acts, such as that betweensocioculturalandsociolinguisticability. Second, directions of previous research describing speech acts are indicated and directions yet to be taken are pointed out. Difficulties in researching oral speech act performance are noted, and verbal report is recognized as one of a limited number of research tools available for investigating cognitive processes involved in speech act production. The paper then reviews four studies that utilize verbal report to gain at least some access to the underlying processes. Finally, the paper looks at previous research on the tutored and untutored acquisition of speech acts and provides suggestions for future research.
The Influence of Planning and Task Type on Second Language Performance
Authors: Foster Pauline , Skehan Peter
Published: November 2008

This study focuses on the impact of different variables on the nature of language performance in the context of task-based instruction. Characteristics of tasks are discussed, and then a framework is offered that can organize the nature of task-based instruction and relevant research. The framework is used to generate predictions regarding the effects of three different tasks (Personal Information Exchange, Narrative, and Decision-Making) and three different implementation conditions for each task (unplanned, planned but without detail, detailed planning) on the variables of fluency, complexity, and accuracy. The study reports strong effects of planning on fluency and clear effects also on complexity, with a linear relationship between degree of planning and degree of complexity. However, a more complex relationship was discovered between planning and accuracy, with the most accurate performance produced by the less detailed planners. In addition, interactions were found between task type and planning conditions, such that the effects of planning were greater with the Narrative and Decision-Making tasks than with the Personal Information Exchange task. The results are discussed in terms of an attentional model of learning and performance and highlight the importance of tradeoff effects between the goals of complexity and accuracy in the context of the use of limited capacity attentional resources. The study contributes to the development of cognitive models of second language performance and addresses a number of pedagogic issues.
Completeness and intertwined completeness of locally convex spaces
Authors: Bellenot Steven F. , Ostling Edward G.
Published: November 2008

Two collections of locally convex space topologies are shown to have the intertwined completeness property. This is done by relating their completions with sets of sequentially continuous functionals on the dual.
The solution of some transient differential equations by means of Green's functions
Authors: Walters A. G.
Published: November 2008

A method is given for the solution of transient differential equations of the type

where D is a differential operator in one or more dimensions. These equations arise in vibrational problems and problems on the conduction of heat. Some examples on the application of the method are given.
The change in strain energy caused by a dislocation
Authors: Dean W. R. , Mann E. H.
Published: November 2008

1. This paper and an earlier paper (l) were written at the suggestion of W. L. Bragg in connexion with his theory of yield in metal crystals (2).
Harmonic maps from surfaces into pseudo-Riemannian spheres and hyperbolic spaces
Authors: Erdem S.
Published: November 2008

In [2, 4, 5, 6, 7] Calabi, Barbosa and Chern showedthat there is a 2:1 correspondence between arbitrary pairs of full isotropic (terminology as in [8]) harmonic maps ±φ:M→S2mfrom a Riemann surface to a Euclidean sphere and full totally isotropic holomorphic maps f:M→2mfrom the surface to complex projective space. In this paper we show, very explicitly, how to construct a similar one-to-one correspondence whenS2mis replaced by some other space forms of positive and negative curvatures with their standard (indefinite) metrics obtained by restricting a standard (indefinite) bilinear form on Euclidean space to the tangent spaces. We get over a difficulty encountered by Barbosa of dealing with the zeros of a certain wedge product by a technique adapted from [8]. The case of complex projective space forms (indefinite complex projective and complex hyperbolic spaces) will be considered in a separate paper. Some further developments in classification theorems are given by Eells and Wood [8], Rawnsley[14], [15] and Erdem and Wood [10].
Complex Einstein hypersurfaces of indefinite complex space forms
Authors: Montiel S. , Romero A.
Published: November 2008

In [8], Fialkow classified Einstein hypersurfaces in indefinite space forms, when the Weingarten endomorphism is diagonalizable. Recently, [13]–[15], Magid completed this work when such endomorphism is not diagonalizable. On the other hand, Smyth [17], classified complex Einstein hypersurfaces in complex space forms. Since Barros & Romero, [1], have made a systematic study of indefinite Kāhlerian manifolds, in particular, indefinite complex space forms, we investigate here complex Einstein non-degenerate hypersurfaces in indefinite complex space forms. In our case, we cannot always diagonalize the Weingarten endomorphism Aassociated to a unit normal field because it is a self-adjoint endomorphism in an indefinite metric vector space, but we prove that, if A is not diagonalizable, one has either A2 = 0 and A ≠ 0 or A2 = −γ2I, γε. We obtain in Theorems 4.4 and 5.5 a full classification except in the case that the ambient space is flat and the Weingarten endomorphism A satisfies A2 = 0and A ≠0. Our classification is based on extending Smyth's results to show that, except in this last case, an Einstein hypersurface is locally symmetric. Using expressions for the curvature tensor to estimate the dimension of the isotropy group, together with Berger's list of symmetric spaces, [3], we then determine the possible Einstein hypersurfaces.
A new method for calculating eigenvalues with applications to gravity-capillary waves with edge constraints
Authors: Graham-Eagle James
Published: November 2008

The method to be described provides an alternative means of dealing with certain non-standard linear boundary-value problems. It is developed in several applications to the theory of gravity-capillary waves. The analysis is based on a variational formulation of the hydrodynamic problem, being motivated by and extending the original study by Benjamin and Scott [3].
On nilpotent wreath products
Authors: Meldrum J. D. P.
Published: November 2008

1. Introduction. The wreath product A wr B of a group A by a group B is nilpotent if and only if A is a nilpotent p-group of finite exponent and B is a finite p-group for the same prime p (Baumslag (1)). When A is an Abelian p-group of exponent pk, and B is the direct product of cyclic groups of orders pβ1, …, pβn and β1 ≥ β2 ≥ …, ≥ βn, then Liebeck has shown that the nilpotency class c of A wr B is
The diophantine equationAx4+By4+Cz4= 0
Authors: Mordell L. J.
Published: November 2008

In a paper (1) published in 1922 in theseProceedings, I conjectured that a curve of genus greater than one contained only a finite number of rational points, but this has never been proved. A particular case is given by the equation of genus three,

and so any results for such equations may be of interest.
Möbius transformations in stability theory
Authors: Smith Russell A.
Published: November 2008

1. Introduction: Consider the system of ordinary differential equations

where the unknown x(t) is a complex m-vector, t is a real variable, D is the operator d/dt and a0, …, an are complex m × m matrices whose elements are continuous functions of t, x, Dx, …, Dn−1x. Furthermore, det a0 ╪ 0. In the special case when a0, …, an are constant matrices the trivial solution x = 0 is asymptotically stable if and only if all the roots of the characteristic equation det f(ζ) = 0 have negative real parts, where
Fluid motion in a rotating sliced cylinder
Authors: Durance J. A.
Published: November 2008

Steady motion of a viscous incompressible fluid in a rotating circular cylinder with a sloping bottom is investigated at low Ekman number. The flow is driven by a lightly faster rotation of the top, and non-linear inertia terms are neglected.

A solution is found for a shallow container of small bottom slope. The side-wall boundary layer is shown to have an almost axi-symmetric component as well as the asymmetric layer found by Pedlosky and Greenspan (3). A further asymmetry in the interior flow is produced by the presence of the second component of the side-wall boundary layer.
Families of Jacobian manifolds and characteristic classes of surface bundles. II
Authors: Morita Shigeyuki
Published: November 2008

Let Σg be a closed orientable surface of genus g, which will be assumed to be greater than one throughout this paper. In our previous paper [11], we have associated to any oriented ∑g-bundle π: E → X with a cross-section s: X → E a flat T2g-bundle π: J → X and a fibre-preserving embedding j: E → J such that the restriction of j to any fibre Ep = π−1(p)(p ∈ X) is equivalent to the Jacobi mapping of Ep with respect to some conformal structure on it and relative to the base-point s(p) ∈ Ep. There is a canonical oriented S1-bundle over J and the main result of [11] is the identification of the Euler class of the pullback of this S1-bundle by the map j as an element of H2(E, ). In this paper we deal with the case of Σg-bundles without cross-sections. First of all we associate a flat T2g-bundle π′: J′ → X to any oriented Σg-bundle π: E → X and construct a fibre-preserving embedding j′: E → J′ such that the restriction of j′ to any fibre Ep is equivalent to some translation of the Jacobi mapping of it. Although our original motivation for the present work came from a different source, this should be considered as a topological version of Earle's embedding theorem [5] which states that any holomorphic family of compact Riemann surfaces over a complex manifold can be embedded in a certain associated family of the corresponding Jacobian varieties in an essentially unique way.
Geometrically finite groups, Khintchine-type theorems and Hausdorff dimension
Authors: Velani Sanju L.
Published: November 2008

1·1. Groups of the first kind. In [11], Patterson proved a hyperbolic space analogue of Khintchine's theorem on simultaneous Diophantine approximation. In order to state Patterson's theorem, some notation and terminology are needed. Let ‖x‖ denote the usual Euclidean norm of a vector x in k+1, k + 1-dimensional Euclidean space, and let

be the unit ball model of k + 1-dimensional hyperbolic space with Poincaré metric ρ. A non-elementary geometrically finite group G acting on Bk + 1 is a discrete subgroup of Möb (Bk+l), the group of orientation preserving Mobius transformations preserving Bk + 1, for which there exists some convex fundamental polyhedron with finitely many faces. Since G is non-elementary, the limit set L(G) of G – the set of limit points in the unit sphere Sk of any orbit of G in Bk+1 – is uncountable. The group G is said to be of the first kind if L(G) = Sk and of the second kind otherwise.
The system of inequalities ars > Xr—Xs
Authors: Afriat S. N.
Published: November 2008

In the investigation of preference orders which are explanations of expenditure data which associates a quantity vector xr with a price vector pr (r = 1, …, k), in respect to some n goods, there is considered the class of functions φ, with gradient g, which are increasing and convex in some convex region containing the points xr, such that gr = g(xr) has the direction of pr. † Let ur = pr/er, where so that
Hamiltonian approach to the method of summation over Feynman histories
Authors: Davies H.
Published: November 2008

The Feynman method of quantization by summation over q-histories is extended to a summation over q, p-histories, corresponding to the classical variational method of treating q and p as independent variables. The equivalence of this q-p summation to the usual quantization procedure is shown in the Heisenberg picture by choosing convenient canonical coordinates and in the Schrödinger picture by obtaining the usual representations of the q, p operators.
Diffraction by a wide slit and complementary strip. I
Authors: Millar R. F.
Published: November 2008

In recent years much attention has been directed towards the asymptotic solution of diffraction problems. In the present work, consideration is given to the relatively simple problem of the diffraction of an E-polarized plane wave by an infinite slit. The solution takes the form of a series in inverse powers of the ratio of slit-width to wavelength of the incident wave, and is based on the solution by successive substitutions of a pair of integral equations. The current densities induced on both halves of the screen are calculated, from which is deduced the electric field in the slit. The far-field is determined from the aperture distribution, and an asymptotic expression is found for the transmission coefficient as a function of the angle of incidence and the ratio of slit-width to wavelength.

While most previous work has been confined to near-normal incidence, the present theory is uniformly valid for all angles of incidence.
The decay constant of radium emanation
Authors: Bastings L.
Published: November 2008

(1) A method has been devised and applied for measuring the decay Constant of radium emanation, the method depending on careful comparisons with a simple electroscope under the most favourable conditions.

(2) A mean value for the Constant of radium emanation has been obtained, with an error unlikely to exceed 0·2 per cent.: λ = 0·1808 day−1, or half-period 3·833 days.
On the positive flash in vacuum discharge tubes
Authors: Whiddington R.
Published: November 2008

It has been known for a very long time that, under certain conditions rather difficult to specify, the discharge through an ordinary two-electrode vacuum tube containing gas at a low pressure, even when the potential is maintained by a battery of low resistance Storage cells, is intermittent.
The generalization of modal subspaces in the complex domain
Authors: Swann H. , Atkinson C. P. , Dhoopar B. L.
Published: November 2008

The purpose of this paper is to present the concept of ‘modal subspaces’ for systems of coupled non-linear autonomous homogeneous second-order differential equations of the complex variablesz1,z2. This development is an extension of the previous paper, entitled ‘Modal subspaces in the complex domain’, by Atkinson and Swann (6), which dealt with a pair of coupled non-linear autonomous homogeneous second-order differential equations of the form

Differentiation is with respect to a real variabletandajkandbjkare constants which may be complex:nis any positive integer:f1andf2are the real and imaginary parts respectively ofg1andg2are real and imaginary parts respectively ofandzj=xj+iyj(j= 1, 2).
Green function formulation of interactions of arbitrary fields
Authors: Islam Jamal N.
Published: November 2008

A Green function formulation of a system that describes the interaction of fields of arbitrary spin with the gravitational field andparticles is given. The Lagrangian considered is essentially the most general that admits of a description through Green functions.
Generators for certain normal subgroups of (2,3,7)
Authors: Leech John
Published: November 2008

The infinite group

is the group of direct symmetry operations of the tessellation {3,7} of the hyperbolic plane ((3), chapter 5). This has the smallest fundamental region of any such tessellation, and related to this property is the fact that the group (2, 3, 7) has a remarkable wealth of interesting finite factor groups, corresponding to the finite maps obtained by identifying the results of suitable translations in the hyperbolic plane. The simplest example of this is the group LF(2,7), which is Klein's simple group of order 168. I have studied this group in an earlier paper ((4)), showing inter alia that the group is obtained as a factor group of (2,3,7) by adjoining any one of the relations

each of which implies the others. The method used was to find a set of generators for the normal subgroup with quotient group LF(2,7) and, working entirely within this subgroup, to exhibit that any one of these relations implies its collapse. The technique of working with this subgroup had been developed earlier and applied in (6) to prove that the factor group

is finite and of order 10,752.
The H-function and its application to a problem in semi-circular electron focusing in metals
Authors: Hawkins F. M.
Published: November 2008

In this paper, a method is given for solving certain types of integral equations. It involves a technique of building up the solution of the given integral equation from that of a much simpler auxiliary equation and a consideration of this auxiliary equation forms a large section of the work. The method of solution is applied to a particular problem in semi-circular electron focusing in metals.
Note on Continuous Functionals
Authors: Verblunsky S.
Published: November 2008

1. Let ℱ be a family of functions X (t) defined in (0, 2π). The functionals to be considered are of a particular class, namely those which define a correspondence between each function X of ℱ and a number which we denote by F(X). It is convenient to refer to F(X) as the functional.
A theoretical study of the stopping power of hydrogen atoms for α-particles
Authors: Fowler R. H.
Published: November 2008

§ 1. Bohr's original (1913) theory of the stopping power of light atoms for α-particles seems to invite further study. It is well-known that in this theory, which exhibits a general agreement with experiment, the loss of energy by the α-particle is calculated on purely classical principles, as the energy transferred to electrons initially at rest; and elastically bound to atoms. A large part of the loss so calculated (about one-half) comes from transfers to electrons in distant atoms of amounts less than the energy required to transfer those atoms to their next higher stationary state. This has created a serious difficulty according to more recent views of the quantum theory in which it has been presumed that any effective interaction must always leave the atom in a stationary state, and has given rise to the investigations of Henderson, which however do-not agree with experiment. In some recent speculations Bohr has suggested a possible way of escape from this difficulty, of great theoretical interest, to which he has been led by somewhat similar difficulties in the theory of radiation. He suggests that there may be reason to expect that energy may be only statistically conserved in just such a type of interaction by the atomic switches, while the classical calculation for the α-particle ought to retain its validity.
Note on a Property of Continuous Arcs
Authors: Ayres W. L.
Published: November 2008

1. In a note in these Proceedings, Mr S. Verblunsky proves the following result:

Theorem A. Let C be a continuous arc joining the points (x1, y0) and (x2, y0), where x2 > x1. Suppose that C does not cross the line y = y0. Then, given any positive h < x2 − x1, there is α yh such that some two points (ξ1, yh), (ξ2, yh), in which y = yh cuts C, satisfy the relation ξ2 − ξ1 = h.
On many-valued Riemann-Stieltjes integration, II. Integration of bounded functions with respect to functions of bounded variation
Authors: Young Rosalind Cecily
Published: November 2008

The principles and general properties indicated in the first part of the present theory are those which belong most strictly to the province of the “algebra of many-valued quantities,” by their practically exclusive reliance on notions of equality, union, and passage to the limit in this domain.
Inverse probability and the use of Likelihood
Authors: Fisher R. A.
Published: November 2008

Logicians have long distinguished two modes of human reasoning, under the respective names of deductive and inductive reasoning. In deductive reasoning we attempt to argue from a hypothesis to its necessary consequences, which may be verifiable by observation; that is, to argue from the general to the particular. In inductive reasoning we attempt to argue from the particular, which is typically a body of observational material, to the general, which is typically a theory applicable to future experience. In statistical language we are attempting to argue from the sample to the population, from which it was drawn. Since recent statistical work has shown that this type of argument can be carried out with exactitude in a usefully large class of cases(2, 3), by means of conceptions somewhat different from those of the classical theory of probability, it may be useful briefly to restate the logical and mathematical distinctions which have to be drawn.
Plane congruences of the second order in space of four dimensions and fifth incidence theorems
Authors: Welchman W. G.
Published: November 2008

It is well known that the planes which meet four given lines in a space of four dimensions meet a fifth line, determined by the first four. Also the trisecant planes of a rational quartic curve in [4] which meet a line meet another rational quartic curve. These two theorems are of the same type and may conveniently be called “fifth incidence theorems”.
On Boole's operational solution of linear finite difference equations with rational coefficients
Authors: Milne-Thomson L. M.
Published: November 2008

The solution of linear differential equations by the method of Frobenius is a straightforward matter consisting merely in the substitution of a power series and obtaining the coefficients from a recurrence relation. The corresponding method when applied to difference equations is laborious and leads in general to divergent series from which convergent solutions can be obtained by a method due to Birkhoff(1). Actually a more appropriate method is to find a factorial series, but even here the direct substitution of such a series requires repeated transformations and throws little light on the structure of the equation. A method of symbolic operators was originated by Boole(2), but owing to the restricted definition of the operators it has a very limited scope. In the present paper a more general interpretation is given to the operators, and their application to a certain class of linear difference equations with rational coefficients is discussed.
On the possibility of a thermal effect accompanying sudden changes in the magneton-numbers in CuCl2 and NiSO47 H2O
Authors: Kothari D. S.
Published: November 2008

1. The temperature variation of the paramagnetic susceptibility of most of the solids follows the generalised Curie law

as found first by Kamerlingh Onnes and Weiss. This gives a linear relation between 1/ψ and T. The value of C is a measure of the atomic magnetic moment, and if this moment is expressed in terms of the Weiss magneton-number p, then

where CM is the value of C when ψ refers to a gram-molecule. The experimental results for a paramagnetic substance are usually expressed in terms of p and θ. Weiss (1), Foex (2), Cabrera and others have found that in some substances there are discontinuities in the slope of the 1/ψ, T curve. Thus Weiss (3) finds that magnetite above its Curie point shows several sudden changes in the 1/ψ, T curve, which he has interpreted as corresponding to the magneton-numbers p = 4, 5, 6, 8,10. Similarly, for cupric chloride (anhydride) Weiss (4) gives p= 9.2 and 10, for the temperature ranges — 140° to 20° and 20° to 500° respectively. Nickel sulphate (5) has also been found to possess a transition point at about — 113°, where the p value on cooling changes from 14.6 to 18.2.
The restriction to linearity of the Lorentz transformation
Authors: Narliker V. V.
Published: November 2008

The literature about the Lorentz transformation is already so wide that some justification is needed for presenting even a small paper on the subject. It is possible to deduce the transformation from essentially different sets of relevant assumptions. The standard text-books on relativity throw little light on this question, which is probably due to the circumstances in which the Lorentz transformation first came into the field. Probably the question is important enough for the following considerations to be worthy of notice.
Notes on the theory of series (III): On the summability of the Fourier series of a nearly continuous function
Authors: Hardy G. H. , Littlewood J. E.
Published: November 2008

The theorem which we prove here seems obvious enough when stated, but it appears to have been overlooked by the numerous writers who have discussed the subject, and the proof is less immediate than might be expected.
Some observations on the theory of interchange of vibrational and translational energy
Authors: Zener C.
Published: November 2008

The same perturbation method is found to be valid for a gentle mutual potential between free atom and vibrator as for an infinitely steep mutual potential, provided that the reduced mass of the system is sufficiently small.

A simplified method is discussed for the calculation of transition probabilities. This method is used to calculate the effect of a van der Waals' attractive field.
On the combination of subalgebras
Authors: Birkhoff Garrett
Published: November 2008

The purpose of this paper is to provide a point of vantage from which to attack combinatorial problems in what may be termed modern, synthetic, or abstract algebra. In this spirit, a research has been made into the consequences and applications of seven or eight axioms, only one [V] of which is itself new.
The normal rational septimic surface with two skew double lines in space of four dimensions
Authors: Bronowski J.
Published: November 2008

1. The surface here discussed arises most naturally in the study of a certain cubic primal in space of five dimensions. Let G be a cubic primal in five-dimensional space, containing two planes M1, M2 which do not intersect. From any point of G can be drawn one transversal to M1, M2; this does not meet G again, and meets a fixed prime p in one point. Thus G can be birationally projected upon p, and is rational.
Non-continuous interaction between hosts and parasites
Authors: Bailey V. A.
Published: November 2008

In a recent publication the problem of determining the abundance of two interacting species of animals was investigated, and the fundamental equations were established.
On the arc spectrum of antimony
Authors: Malurkar S. L.
Published: November 2008

An attempt is made in this paper to find the nature of terms that occur in the arc spectrum of antimony. The spectrum is analogous to those of the singly ionized elements of the sixth group. Prof. A. Fowler investigated the spectrum of ionized oxygen (O II). The classification was shown to be in exact accord with the “Hund-Heisenberg theory of complicated spectra” by R. H. Fowler and D. R. Hartree. Recently G. R. Toshniwal has classified the arc spectrum of bismuth.
The adiabatic hypothesis for magnetic fields
Authors: Dirac P. A. M.
Published: November 2008

The usual proof of the adiabatic invariance of the quantum integrals of a multiply periodic dynamical system rests on the assumption that the Hamiltonian equations remain valid for the adiabatically changing system, with the same Hamiltonian function H, or at any rate with a new Hamiltonian function differing from the old one only by terms that vanish with ȧ, (a) being the varying parameter.
On a group of 1440 birational transformations of four variables that arises in considering the projective equivalence of double sixes
Authors: Burnside W.
Published: November 2008

The lines of a double-six will here be represented by the usual notation

where two lines whose symbols are in the same line or same column of this scheme are non-intersectors and all other pairs of lines intersect. Any six of the lines, no two of whose symbols are in the same column, and just three are in the same row, are generators of a quadric, and the actual position in space of each of the other six is determined by the two points in which it intersects this quadric.
Insular Gravity and Oceanic Isostasy
Authors: Larmor Joseph
Published: November 2008

A century ago geodetic and gravitational universal surveys were mainly concerned with determining the effective (gravitational) ellipticity of the Earth, after due allowance had been made for local anomalies, with especial view to the exact purposes of physical astronomy. One of the chief of these anomalies was exhibited by a remark of Airy, after scrutiny of the available data in his treatise (1830) on “Figure of the Earth” in the Encyclopedia metropolitana, that the observations show gravity to be abnormally in excess on island stations. It appeared, for instance, that this cause might make the mass of the Moon uncertain up to 2 per cent. A very refined explanation of this anomaly of island stations (which will be seen presently to be only partially effective) was offered by Sir George Stokes, from whom this last remark is quoted, in the course of a memoir, fundamental for theoretical geodesy, in which he demonstrated that no outside survey could lead to any certain knowledge of the distribution of mass inside the Earth, even in its outer crust, except as a matter of probability when backed up by geological knowledge.
Some calculations on the range-velocity relation for alpha particles and protons
Authors: Duncanson W. E.
Published: November 2008

Recent experiments on α-particles and protons have demanded an accurate knowledge of the range-velocity relation of these particles, more particularly in the case of protons, since in most experimental work their energy can only be determined indirectly by measuring their range and by deducing the velocity from a range-velocity curve.
Some Generalizations of Montel's Theorem
Authors: Cartwright Mary L.
Published: November 2008

1. There are two well-known theorems on the limit of a bounded function at a point.

Montel's Theorem. Suppose that f (z) is regular for | arg z | ≤ α, | z | ≤ 1, except perhaps at z = 0, and that f(z) is bounded in that region. Suppose also that f(z) → l as z → 0 along arg z = β, where | β | < α. Then f(z) → l as z → 0 uniformly for | arg z | ≤ α − δ for every δ > 0.
On the Closure of and Integral Functions
Authors: Levinson Norman
Published: November 2008

1. A set of functions {øn (x)} is said to be closed L over an interval (a, b) if for an f (x) belonging to L

implies that f(x) = 0 almost everywhere. Here f(x) is a complex valued function of the real variable x.
The Refraction of a Wave Group
Authors: Stoneley R.
Published: November 2008

The considerations set out in this communication arose originally in the discussion of the refraction of surface elastic waves at the edge of a continent*. In view, however, of their general application, it is perhaps worth while to state them apart from their special context.
Cauchy's Problem in a Non-Linear Partial Differential Equation of Hyperbolic Type
Authors: Siddiqi M. Raziuddin
Published: November 2008

Let p (x) be an essentially positive function defined in the interval 0 ≤ x ≤ π. We consider the non-linear partial differential equation

for the boundary conditions u (x, t) = 0,

for x = 0 and x = π,
On the Virtual Grade of Curves on an Algebraic Surface
Authors: Pedoe D.
Published: November 2008

The theoretical method for computing the grade of a curve on an algebraic surface is well known. In practice difficulties arise which are not considered in the theory; so that it seems worth while to describe a practical method. This is done in § 1 of this paper. The method is then applied to some examples with the object of discovering whether Noether exceptional curves are necessarily exceptional curves†. In particular, a certain quintic surface with three tacnodes is studied, and our examination leads us to results which differ from those which have been accepted up till now. Another example illustrates the limitations of a practical method for computing grades, because of the possible presence of infinitesimal curves, and leads to the transformation of the quintic surface with two tacnodes into a double plane of order ten of a certain type, which has the singularity known as a (5, 5) point on its branch curve. Light is thrown on the Noether composition of this singularity by the transformation, which also shows the relation between two well-known types of surface for which the Noether relation p(2) = p(1) − 1 does not hold.
Pair Production by Magnetic Multipole Radiation
Authors: Jaeger J. C.
Published: November 2008

Taylor and Fisk have discussed the internal conversion of magnetic multipole radiation by K electrons and have found internal conversion coefficients which are much larger than those for electric multipoles, and which increase with the order of the multipole. The object of the present note is to determine whether this state of affairs holds also for pair production by internal conversion of magnetic multipole radiation.
The Second Mean Value Theorem in the Integral Calculus
Authors: Dixon A. C.
Published: November 2008

Hobson has given a proof of this theorem in its fullest generality. The present note gives an alternative for part of Hobson's argument. The theorem may be stated in two forms. If f(x) is a function of x, monotone when a ≤ x ≤ b, and φ(x) is integrable over the same range, then

where a ≤ X ≤ b,

(ii) the same holds with a < X < b except in some trivial cases where f(x) is constant in the open interval a < x < b. The form (ii) is not mentioned by Hobson.
A New Electroscope
Authors: Schonland B. F. J.
Published: November 2008

In the measurement of small ionisations it is usual and desirable to employ an ionisation-chamber whose central collecting electrode serves also as an electroscope, of the gold-leaf or the quartz-fibre type. As an instrument for the measurement of quantity of electricity even the most sensitive of these is inferior, by a factor of about 100, to the combination of an ionisation-chamber and a Compton electrometer. The new type of ionisation electroscope here described combines a high voltage-sensitivity with a small capacity and has a sensitivity for quantity of electricity of the same order as the combination mentioned.