bluuebunny/crossref_metadata_2025_split huggingface dataset:
Teaching-induced aspects of interlanguage discourse
Authors: Kasper Gabriele 
Published: November 2008

The paper examines the influence of the formal classroom as a learning environment on the discourse behaviour of advanced German students of English in conversations with English native speakers. It is proposed that FL teaching as a causal factor in the formation of IL-specific rules can operate either directly, in presenting the learner with FL material which deviates from target norms, or indirectly, by triggering off psycholinguistic processes which in turn lead to IL-specific rule formation. These are referred to as primary and secondary teaching induction, respectively. On a more concrete level, the impact of two constituents of FL teaching on IL discourse is discussed:(1) the textbook and other teaching materials;(2) classroom specific discourse norms.The influence of the first factor type manifests itself primarily in (a) the use of an inappropriately formal register, (b) an inappropriate use of modal verbs. The second factor type is found to result in (a) rising intonation with non-interrogative function, (b) inappropriate propositional explicitness of speech act realizations and discourse functions, (c) “complete sentence” responses, (d) a lack of marking for expressive and relational functions (“speech act modality”).In conclusion of the data analysis, a classroom specific pidgin will be hypothesized which, when transferred to non-classroom settings, leads to pragmatically inappropriate communicative behaviour.On a more general level, it will be postulated that second language acquisition hypotheses should be formulated with reference to specific types of acquisition/learning contexts.
Nature, Nurture, and Age in Language Acquisition
Authors: Wode Henning 
Published: November 2008

The purpose of this paper is twofold: first, to draw attention to the research on speech perception and, second, to use the results for a reassessment of the contribution of innate capacities versus external stimulation in conjunction with age in first and second language acquisition. The theoretical framework is the universal theory of language acquisition. The focus is on the functional potential of the biological substrate rather than its anatomy.Neonates are innately capable of two major modes of auditory perception, namely, categorical and continuous perception. The interaction of these two modes allows infants to develop the perceptual categories of their ambient language(s). The continuous mode functions as a monitoring device in shaping the categories of the target(s). Various kinds of evidence are reviewed that suggest that these original sensory abilities remain unchanged throughout an individual's lifespan, but they become difficult to access during later stages of life, such as in adult L2 acquisition, because of the way perceptual-phonological information is stored in memory and/or activated in language processing. There are no biologically based restrictions as to the number of languages that can be learned, or the age ranges during which this can happen.
An early formulation by Stokes of the theories of the rotatory polarizations of light
Authors: Larmor Joseph 
Published: November 2008

AbstractThe two letters now communicated are from G. G. Stokes to W. Thomson, of dates Dec. 12–13, 1848, three years after Faraday's great magneto-optic discovery. They formulated already the permissible types for general equations of propagation, virtually on the basis of the very modern criterion of covariance,—relative to all changes of the spatial frame of reference in the case of active fluids, but having regard to the fixed direction of the extraneous magnetic field in the Faraday case. Their form was elucidated in each case by correlation with a remarkable and significant type of rotational stress in a propagating medium.
The remainder in a gap Tauberian theorem for Abel summability
Authors: Luther Wolfram 
Published: November 2008

Using Pitt's Tauberian classes and a theorem of Pitt (3), Krishnan(2) has recently obtained a gap Tauberian theorem for (Aα) summability. We recall briefly the notation introduced in (2). Letand assume that the series a(t) and A(t) converge for all t > 0.
Innovation projections of a jump process and local martingales
Authors: Elliott Robert J. 
Published: November 2008

AbstractSquare integrable and local martingales on a family of σ-fields generated by a basic jump process are shown to have representations as stochastic integrals with respect to a family of martingales associated with the jump process by using the idea of an innovation projection and the associated Lévy system, which is a local characterization of the jumps.
The asymptotic nature of the analytic spread
Authors: Brodmann M. 
Published: November 2008

In (3), corollary, p. 373) Burch gives the following inequality for the analytic spread l(I) of an ideal I of a noetherian local ring (R, m):In this paper we shall improve this by showing that the number min depth (R/In) may be replaced by the asymptotic value of depth (R/In) for large n (which exists) (see Section (2)). By its definition (see (6), def. 3)) the analytic spread is of asymptotic nature, i.e. depends on the modules In/mIn = Un only for large n. We shall prove a stronger result, Section (4), which also shows the asymptotic nature of l(I). This result might be interesting for itself, particularly as it is not of local nature. Once Section (4) is proved and once we know that depth (R/In) is asymptotically constant (which turns out to be an easy consequence of (1), (1)), our improved inequality is easily established: Indeed, replacing R by R/xR where x is regular with respect to almost all modules (R/In), we perform a change which affects only finitely many of the modules Un (see Section (8)).
On multi-dimensional annealing problems
Authors: Chan Terence 
Published: November 2008

In [1] Chan and Williams considered a one-dimensional diffusion of the formwhere F is a strictly increasing continuous function with F(0) = 0 and ε is a decreasing deterministic function such that ε(0) is finite and ε(t) ↓ 0 as t↑ ∞, and gave necessary and sufficient conditions for Yt →0 a.s. as t→∞.
The Electrical Resistance of Dilute Solid Solutions
Authors: Mott N. F. 
Published: November 2008

1. As is well known, the electrical resistance of a metal is very greatly in-creased by the addition of a second metal with which it forms a solid solution. The increase Δρ in the resistivity due to the addition of a small percentage of the second metal is in general independent of the temperature (Matthiessen's rule), though there are oertain exceptions (e.g. Cr in Au). The quaritum-mechanical explanation of both these facts was first given by Nordheim, and may be expressed as follows: the electrical conductivity of any metal may be written in the formwhere τ is the “time of relaxation”, equal to half the time between collisions, and N is the effective number of free electrons per unit volume: hence, for the resistivity, we have
Uniform approximate solutions of certain nth-order differential equations. I
Authors: Heading J. 
Published: November 2008

Exact analytical solutions of certain second-order linear differential equations are often employed as approximate solutions of other second-order differential equations when the solutions of this latter equation cannot be expressed in terms of the standard transcendental functions. The classical exposition of this method has been given by Jeffreys (6); approximate solutions of the equation (using Jeffreys's notation)are given in terms of solutions either of the equationor of the equationwhere h is a large parameter. A complete history of this technique is given in the author's recent text An introduction to phase-integral methods (Heading (5)).
On a problem of Littlewood concerning Riccati's equation
Authors: Swinnerton-Dyer H. P. F. 
Published: November 2008

The study of the Riccati equationplays an essential part in the ‘large parameter’ theory of the inhomogeneous van der Pol equation; see for example Littlewood(1), (2). The crucial result is Lemma B of (1), restated and proved as Lemma 5 of (2); for the present paper the relevant parts of it are as follows:Lemma 1. Let z = z(x) be the solution of (1·1) which satisfies the initial condition z = 0 at x = 0, and assume α > 0. Then there is a unique β0 = β0(α) with the property that(i) if β > β0 then z → − ∞ as x → + ∞;(ii) if β < β0 then z → + ∞ at a vertical asymptote x = x0(α,β);(iii) if β = β0 then z ≥ 0 in 0 ≤ x < + ∞ and z = x + β0 + o(1) as x → + ∞.Moreover, β0(α) is a continuous monotone increasing function of α.
The average number of maxima of a random algebraic curve
Authors: Das Minaketan 
Published: November 2008

AbstractLet g0, gl, g2,…be a sequence of mutually independent, normally distributed random variables with mathematical expectation zero and variance unity. In this work, we obtain the average number of maxima (minima) of the random algebraic curves with the equationsThis average is (½(3½ + 1)) log N + O((log N)⅔ (log log N)½), when N is large.
Statistical processes of aggregation and polymerization
Authors: Whittle P. 
Published: November 2008

AbstractWe study processes in which units (particles) associate into clusters, which are then also capable of dissociation. Such processes are discussed generally in section 2, where a stochastic kinetic equation (10) is proposed which bridges the gap between the conventional kinetic equations (8) and the statistical equilibrium concept of the Gibbs distribution.In section 4 we consider the equilibrium behaviour of a process for which the association rate of two units which are already bound tojandkother units respectively has the form (21). This is very much more general than the equi-reactive bond model usually discussed. The principal results are given in Theorem 1; from a single pair of equations (28) and (29) based on theHjof (21) one can determine critical points, expected number of bonds, the distribution and moments of cluster size, and most other quantities of interest. This is without reference to any other consideration, such as kinetic or stoichiometric relations.Some particular cases are worked through in section 5. The classic Flory-Stockmayer results for units withfequi-reactive sites are obtained systematically and economically, with all parameters in terms of physically given quantities. Another type of example seems to indicate the existence of a second critical point.Corresponding results for the case of several types of unit are stated and illustrated in section 6.
Statistical electrodynamics
Authors: Marshall T. W. 
Published: November 2008

AbstractThe random pure radiation field postulated in an earlier paper is set up in a relativistically invariant manner. The requirement that this field be isotropic in three dimensions makes much of the formalism identical with the theory of isotropic turbulence, as has been noted by a previous author. It is found, however, that the more stringent requirement of invariance under the Lorentz group, together with the fact that the field components satisfy Maxwell's equations, mean that, to within a multiplicative constant, the entire random process is uniquely specified.In accordance with results obtained previously, the constant is effectively identified as Planck's constant. There then results a striking resemblance between the formalism of the present theory, and that of the quantized pure radiation field, with random variables taking the place of operators, and correlations between these random variables taking the place of commutator brackets.The infinite field energy, which arises also in quantum field theory, where, however, it is usually considered to be purely formal, remains a central difficulty of the random theory. It can be shown to be a natural consequence of assuming Maxwell's equations, and it therefore becomes necessary to consider non-linear modifications of these.The connexion between the present results and the inconsistencies of classical and quantum electrodynamics is discussed. Also some new information is obtained concerning the behaviour of thermodynamic quantities under a Lorentz transformation.
Unsteady heat transfer in compressible boundary layers
Authors: Riley N. 
Published: November 2008

AbstractThe flow following a sudden change in the wall temperature in a laminar boundary layer, which was originally incompressible and steady, is studied. The temperature to which the wall is raised is supposed large enough to bring about density changes in the boundary layer. The details of the flow immediately after the change in wall temperature are analysed for a general boundary layer. Two specific examples are considered and for these the manner in which the new steady state is achieved is also investigated.
On simplexes doubly incident with a quadric
Authors: Thaswamy R. Vaidyana 
Published: November 2008

(1) The simplex in a space Sn of order n (or n − 1 dimensions) is a set of n points a1 a2 …an which do not all lie in a subspace of Sn.The elements of the simplex a1 a2 …an are the n points a1 a2 …an whieh are elements of order one, the lines ar as which are elements or faces of order two, etc., etc., and finally the n primesa1 a2 … ar−1 ar+1 … an which are elements or faces of order n – 1.
Note on the Gibbs Phenomenon, II
Authors: Verblunsky S. 
Published: November 2008

1. This note is a sequel to a previous one. Our first object is to rectify some mistakes in I. For these corrections I am indebted to the kindness of Prof. J. R. Wilton. In the enunciation of Theorem A (I, p. 159) the equationshould be altered toThe mistake occurs at the end of I (p.169) where it is erroneously assumed thatthe correct being
Note on the instability of a surface of discontinuity
Authors: Rosenhead L. 
Published: November 2008

In a paper recently published I found it necessary to extend those investigations of Lord Rayleigh which deal with the instability of the surface common to two streams of fluid. The Rayleigh investigation is equivalent to a first order approximation to the flow and concludes that the initial form of the disturbance of the common surface is maintained but that its amplitude increases exponentially with the time, the form of the surface at time t being, with particular values inserted,where a is the initial amplitude, 2π/k the wave-length, U the velocity of the upper stream, – U the velocity of the lower stream, and ρ the density of both fluids. A second order approximation to the flow for the above particular case shows that the original disturbance does not grow symmetrically, the ordinate of the common surface being given by(A slightly amended form of this solution is given byequation III(8).) The solution suggests the initial stages in the formation of vortices. The problem was further discussed by a numerical step-by-step method and showed the formation of vortices quite clearly.
The interval between the departure of the disintegration particle and the emission of the gamma radiation
Authors: Wright P. 
Published: November 2008

Previous work on the existence and period of radium C′ is discussed with reference to an experiment of Jacobsen which provides evidence that a γ ray transformation of period comparable with that of radium C′ precedes the expulsion of α particles. It is shown that, from Jacobsen's results, part of the γ radiation from a source of recoil atoms should originate in the space surrounding the source.A rough calculation is made which shows that the γ rays above the source should be detectable by ordinary methods, and a description is given of an ionisation method capable of detecting the effect. The γ rays predicted by Jacobsen's experiment were tested for by using specially prepared sources of radium C. Phenomena associated with α recoil were also investigated for sources of radium (B + C) and thorium (B + C).No evidence of a γ ray emission from the space above any of the sources was obtained. The negative result indicates that the interval between the departure of the disintegration particle and the emission of the γ ray quantum is considerably less than 10−5second.
Energy distribution curves of the disintegration electrons
Authors: Sargent B. W. 
Published: November 2008

With the aid of experimental results on the absorption of homogeneous β-rays in aluminium, a method is developed for calculating the absorption curve of β-rays forming a continuous spectrum. When applied to certain known spectral distributions reasonable agreement is obtained with the experimental absorption curves of these heterogeneous β-rays. Distribution curves with momentum of the β-rays from actinium C″, uranium X2, thorium C and thorium C″ are found, which lead to similar agreement.The distribution curves with energy and with momentum for eight β-ray bodies and a table of average energies emitted in thése spectra are shown.
Note on the trisecants and quadrisecants of a space curve
Authors: Welchman W. G. 
Published: November 2008

1. Formulae obtained by enumerative methods are always liable to break down owing to the appearance of an infinity of degenerate solutions, and when this happens it is usually necessary to make a fresh start. Enumerative arguments have been used to prove the two following results for a curve of order n and genus p in space of three dimensions:(i) The order of the ruled surface formed by trisecant lines of the curve is(ii) The number of quadrisecant lines is
Rational normal octavic surfaces with a double line, in space of five dimensions
Authors: Babbage D. W. 
Published: November 2008

The following paper arises from a remark in a recent paper by Professor Baker. In that paper he gives a simple rule, under which a rational surface has a multiple line, expressed in terms of the system of plane curves which represent the prime sections of the surface. The rule is that, if one system of representing curves is given by an equation of the formthe surface being given, in space (x0, x1,…, xr), by the equationsthen the surface contains the linecorresponding to the curve φ = 0; and if the curve φ = 0 has genus q, this line is of multiplicity q + 1.
The upper limit of energy in the β-ray spectrum of actinium B
Authors: Sargent B. W. 
Published: November 2008

Using a thin-walled electroscope, absorption curves in paper and aluminium were obtained for the β-rays of actinium (B + C) and actinium C″. From these curves the range of the β-rays of actinium B was found to be 0·08 ± ·02 gm./cm.2 The energy required for this range is 300,000 ± 50,000 volts, which must be the end-point of the continuous spectrum.On account of the overlapping of the β-ray spectra of actinium B and actinium C″ the range method can never yield an accurate value of the end-point of the former. Magnetic analysis appears to be the best means of finding this accurately, but the weakness and rapid decay of sources are formidable difficulties.
A general canonical expression
Authors: Bronowski J. 
Published: November 2008

1. In a recent paper I established new conditions for a form φ of order n, homogeneous in r + 1 variables, to be expressible as the sum of nth powers of linear forms in these variables; and for this expression, if it exists, to be unique. These conditions, I further showed, may be stated as general theorems regarding the secant spaces of manifolds Mr in higher space, namely:Necessary and sufficient conditions that through a general point of a space N, of h (r + 1) − 1 dimensions, there passes (i) no, (ii) a unique (h − 1)-dimensional space containing h points of a manifold Mr lying in N are that(i) the space projecting a general point of Mr from the join of h − 1 general r-dimensional tangent spaces of Mr meets Mr in a curve, so that Mr cannot be so projected upon a linear space of r dimensions;(ii) the space projecting a general point of Mr from the join of h − 1 general r-dimensional tangent spaces of Mr does not meet Mr again, so that Mr can be so projected, birationally, upon a linear space of r dimensions..
A figure in space of seven dimensions, and its sections
Authors: Edge W. L. 
Published: November 2008

Several papers have recently been published which include proofs of the following:Theorem 1. Those trisecant planes of a rational normal quartic curve Cu which meet a second rational normal quartic curve Cv having six points in common with Cu also meet a third rational normal quartic curve Cw through these same six points. The three suffixes may be permuted in any way, the three curves forming a symmetrical set.
Ramanujan's Continued Fraction
Authors: Watson G. N. 
Published: November 2008

The best of the theorems on continued fractions, to be found in Ramanujan's manuscript note-book may be stated as follows:where there are eight gamma-functions in each product and the ambiguous signs are so chosen that the argument of each gamma-function contains one of the specified numbers of minus signs. Thenprovided that one of the numbers β, γ δ, ε is equal to ± n, where n is a positive integer; and the products and sums on the right range over the numbers α β, γ δ, ε.
Summation of the integral conjugate to the Fourier integral of finite type
Authors: Grimshaw Margaret Eleanor 
Published: November 2008

1. The complete Denjoy-Fourier integral is of the formwherethe generating function ƒ(t) being integrable in the general Denjoy sense in every finite interval, and the integrals (1·2) being interpreted as principal values or in some other suitable way.
Some Applications and Implications of Duane's Quantum Theory of Diffraction
Authors: Williams E. J. 
Published: November 2008

Duane's quantum theory of diffraction is applied to the reflexion of electrons by crystals and to the spatial distribution of photoelectrons and fluorescent radiation from a crystal.Two alternative criteria for coherence are given. According to the second of these there is coherence provided that the momentum imparted to the components of a system during the process concerned is insufficient, owing to quantum restrictions to their motion, to change their energy. Calculations made on this supposition show that in the case of the scattering of radiation by a crystal there is complete coherence for the lower orders, while for higher orders this ceases to be the case and the reflected intensity is reduced as the result of incoherent scattering. The specular reflexion by gases is also considered.Duane's theory of diffraction has not been placed on a rigorous basis and the solutions which have been proposed here for various problems may be incorrect. Even so the theory has at least served to bring to light several points of theoretical and experimental interest which deserve consideration.
Investigations on condensation phenomena in mercury vapour
Authors: Ho P. C. 
Published: November 2008

Owing to its physical and chemical properties being greatly different from those of any of the liquids which have hitherto been used in the Wilson cloud chamber, mercury has been used in the experiments described in this paper and the condensation phenomena of its vapour at different temperatures observed. Before constructing the apparatus it was considered necessary to get from theoretical considerations some idea about the magnitude of the critical supersaturation for mercury vapour in equilibrium with a drop carrying unit charge. Assuming that J. J. Thomson's formula.where s is the supersaturation of mercury vapour in equilibrium with a drop of mercury of radius a, charge e, density σ and surface tension T, the value of which is assumed here to be independent of the radius of the drop, K the specific inductive capacity of the dielectric surrounding the drop, and R the gas constant for one gramme of weight, all at temperature θ, can be applied to the present problem, this critical supersaturation sm is given by the formula