bluuebunny/crossref_metadata_2025 huggingface dataset:
Syntax and semantics in the acquisition of locative verbs
Authors: Gropen Jess , Pinker Steven , Hollander Michelle , Goldberg Richard
Published: February 2009

Children between the ages of three and seven occasionally make errors with locative verbs like pour and fill, such as * I filled water into the glass and * I poured the glass with water (Bowerman, 1982). To account for this pattern of errors, and for how they are eventually unlearned, we propose that children use a universal linking rule called OBJECT AFFECTEDNESS: the direct object corresponds to the argument that is specified as ‘affected’ in some particular way in the semantic representation of a verb. However, children must learn which verbs specify which of their arguments as being affected; specifically, whether it is the argument whose referent is undergoing a change of location, such as the content argument of pour, or the argument whose referent is undergoing a change of state, such as the container argument of fill. This predicts that syntactic errors should be associated with specific kinds of misinterpretations of verb meaning. Two experiments were performed on the ability of children and adults to understand and produce locative verbs. The results confirm that children tend to make syntactic errors with sentences containing fill and empty, encoding the content argument as direct object (e.g. fill the water). As predicted, children also misinterpreted the meanings of fill and empty as requiring not only that the container be brought into a full or empty state, but also that the content move in some specific manner (by pouring, or by dumping). Furthermore, children who misinterpreted the verbs' meanings were more likely to make syntactic errors with them. These findings support the hypothesis that verb meaning and syntax are linked in precise ways in the lexicons of language learners.
Non-dialogue speech during preschool interactions
Authors: Schober-Peterson Debra , Johnson Cynthia J.
Published: February 2009

Young children's skilfulness in conversational interaction is of great importance in understanding pragmatic aspects of language development. The purpose of this investigation was to describe the portion of preschool verbal interaction which could not be considered successful dialogue. Ten dyads of four-year-olds were videotaped during free play. Segments of talk were identified as dialogue or non-dialogue. Non-dialogue was coded when one child did not appear to direct his/her utterances to the other or when an attempted topic failed to capture the interest of the other child. Thirteen types of non-dialogue were identified. Results revealed that all dyads exhibited non-dialogue, but differences were noted in regard to amount and type. Dyads labelled as less co-operative displayed greater amounts of self-directed talk (monologue).
Strategies used to communicate route directions by telephone: a comparison of the performance of 7-year-olds, 10-year-olds and adults
Authors: Lloyd Peter
Published: February 2009

Standard outcome measures used in a referential communication (route finding) task showed that 7-year-olds were inferior to 10-year-olds and adults in terms of adequacy of messages provided (as speakers) and selection of referent (as listeners). Because the task involved negotiation of route directions by telephone, a richer dialogue resulted than is usual in referential communication studies. This made possible an analysis of the strategies used and revealed differences untapped by the standard measures. The types of strategies used (COMPONENTS, NUMBERING, DIRECTIONAL, MINIMAL) varied as a function of age, with the adults using much directional information and the children very little. Much of the younger children's description was either minimal or used inadequately specified mature strategies. Adults frequently used dual strategies (e.g. directional + numbering). Older children showed little evidence of these individually but achieved them, in practice, through dialogue with their partners. Age differences in quantity of communication (number of turns) were found to be linked to strategy use. The advantages of the telephone as an experimental medium of communication are discussed.
On the acquisition of syntax in Tamil: a comment on Garman (1974)
Authors: Lust Barbara , Eisele Julie
Published: February 2009

Garman (1974), reporting on twenty Tamil children aged three to five, postulated a linguistic strategy and two prelinguistic strategies to explain the results of a question-picture choice task involving sentences with embedded and subordinate clauses. In a reanalysis of his data, we identify four processing strategies and show that some of Garman's findings are better explained not as the outcome of prelinguistic strategies but as an artefact of the experimental design. In fact the data provide evidence of a grammatical sensitivity which is consonant with a sensitivity – demonstrated in recent language-acquisition studies – to the branching direction of the language being acquired.
Phonetic development in early infancy: a study of four Swedish children during the first eighteen months of life
Authors: Roug L. , Landberg I. , Lundberg L.-J.
Published: February 2009

The present paper presents data on the phonetic development of four normal Swedish infants, who were audiorecorded bi-weekly in their homes from 0;1 to 1;5. Our results show five distinct stages in the development of early vocalizations: the glottal stage, the velar/uvular stage, the vocalic stage, the reduplicated consonant babbling stage and the variegated consonant babbling stage. The results are based on auditory analysis of selected parts of the material. A comparison is made of this developmental pattern with studies of infants raised in other linguistic communities. The results of this comparison support the claim that babbling follows a universal developmental pattern.
Crossing boundaries: more evidence for phonological constraints on early multi-word utterances
Authors: Matthei Edward H.
Published: February 2009

A number of researchers have argued that phonological constraints may influence the emergence and form of combinatorial speech in children. Donahue (1986) presented evidence that one child's consonant harmony constraint operated across word boundaries. This paper presents further evidence for the operation of word-level phonological constraints in multi-word utterances. Selection and avoidance patterns as well as her modifications of adult forms indicate the presence of a syllable sequencing constraint in this child's grammar: an initial syllable must begin with a consonant whose sonority value is not less than that of the following syllable. The same constraint governs the form of her early word combinations. The existence of evidence for the operation of word-level constraints in word combinations, it is pointed out, has consequences for how we interpret two-lexicon models of phonological development.
A multiple form word production checklist for assessing early language
Authors: Reznick J. Steven , Goldsmith Lynn
Published: February 2009

We describe the development of a set of five equivalent checklists to assess word production of children in their second year. The words on each list do not overlap, but represent comparable levels of difficulty. Thus, individual lists may be used to estimate the child's production vocabulary, and the set of lists may be used serially in a longitudinal design.

A validation study on 25 infants suggests that the five lists produce comparable mean production scores, reflect differences in age, and preserve individual differences in total production and production of linguistic categories such as nouns, verbs, open class items, and closed class items. This finding provides further support for the reliability of parental report instruments in this developmental domain.
Acquisition of complementation
Authors: Bloom Lois , Rispoli Matthew , Gartner Barbara , Hafitz Jeremie
Published: February 2009

This study concerns the acquisition of complex sentences with perception and epistemic verbs that take a second verb in their complements. The acquisition of complementation began between two and three years of age in this longitudinal study of four children's spontaneous speech. The results of the study showed that (1) complement types and complementizer connectives and (2) the discourse contexts in which complementation occurred were specific to individual matrix verbs. The most frequent verbs acquired were the perception verbs see and look and the epistemic verbs think and know. Developments in both discourse and syntax indicated that these verbs expressed attitudes of certainty/uncertainty toward the content expressed in their complements. The results are discussed in terms of both linguistic and psychological factors in the acquisition of complex sentences with complementation.
Early bilingual development: one language or two?
Authors: Genesee Fred
Published: February 2009

It is commonly thought that children learning two languages simultaneously during infancy go through a stage when they cannot differentiate their two languages. Virtually all studies of infant bilingual development have found that bilingual children mix elements from their two languages. These results have been interpreted as evidence for a unitary, undifferentiated language system (the unitary language system hypothesis). The empirical basis for these claims is re-examined and it is argued that, contrary to most extant interpretations, bilingual children develop differentiated language systems from the beginning and are able to use their developing languages in contextually sensitive ways. A call for more serious attention to the possible role of parental input in the form of mixed utterances is made.
Rhyme and alliteration in poems elicited from young children
Authors: Dowker Ann
Published: February 2009

Attempts were made to elicit poems from 133 children between the ages of 2 and 6. Seventy-eight of the children produced 606 poems between them. Sixty per cent of the poems contained phonological devices; 42% contained rhyme and 26% contained alliteration. There was no obvious age trend as regards the use of rhyme but the frequency of alliteration declined with age. There were no significant age differences as regards the relative frequency with which different phonemes were manipulated in rhyme and alliteration. The possible functions of such sound-based language play in language development are discussed, with special reference both to children's sound play in crib speech, and to the development of phonological awareness and its importance in learning to read.
Children's over-regularization of nouns and verbs
Authors: Cox Maureen V.
Published: February 2009

The procedure used by Pratt, Tunmer & Bowey (1984) was employed in this study to investigate young children's abilities to correct over-regularized plural nouns and verbs in the past tense. Older children (mean age 6; 4) performed better than younger children (mean age 4; 11) and plural nouns were corrected significantly more than past-tense verb forms. As predicted, the younger children were better at correcting the nouns than the verbs; the two grammatical forms were corrected equally well by the older children.
Patterns in babbling: a cross-linguistic study
Authors: Blake Joanna , Boysson-Bardies Bénédicte De
Published: February 2009

Three Canadian–English infants and three Parisian–French infants were filmed bi-weekly for three to five months, from the age of 0;9 or 0;11 until 1;2, at home in naturalistic interaction with a parent. Their babbled utterances were transcribed phonetically and categorized according to consonant-type and vowel-type. The contexts for each utterance were described in terms of both specific and more general contextual categories. Observed frequencies of co-occurrences between phonetic and contextual categories were compared to expected frequencies, and deviations were considered to be patterns in babbling. Patterning increased after age 1;0 for most infants, and from 15% to 30% of each infant's babbled utterances recurred in particular contexts with a greater-than-expected frequency. Similarities in patterns were found both within and across language groups. These sound-meaning correspondences in babbling are viewed as continuous with early situation-bound meaning in words.
The relation of children's single word utterances to single word utterances in the input
Authors: Ninio Anat
Published: February 2009

The reported study investigated the relation between children's single-word utterances and maternal single-word utterances expressing similar communicative intents. Twenty-four Hebrew-speaking dyads (the children about 1;6) were videotaped for 30 min in an unstructured session. Single-word utterances were analysed for their communicative intent and the relationship of the expression to the underlying intent was defined in the form of realization rules. Of 17,471 child utterances, 97·0% were realizations that were also used by mothers for expressing the same communicative intent. The most frequently modelled rule for an intent had the highest chance of being adopted by children, and the probability sharply decreased for the relatively less frequently modelled rules. The results suggest that children's single-word utterances are similar to, and probably learned from, single-word utterances of caretakers expressing the same specific communicative intents.
The optional subject phenomenon in young children's English: a case study
Authors: Ingham Richard
Published: February 2009

Recent treatments of the optionality of sentence subjects in young-children's English have sought to link this phenomenon, and its eventual demise, to the development of the child's verb inflection system or to a parameter-resetting within the INFL (‘inflection’) constituent of the child's grammar. It is claimed that subject optionality disappears when these developments occur. The case-study reported here investigated the productive language of an English child between 2;5 and 3;0. It found that subjects were no longer optional at a stage when none of the reflexes of INFL claimed in the literature to be associated with the disappearance of subject optionality had yet been acquired. The possibility that subjects were present only when communicatively required was rejected. The frequency of subject realization of a Japanese child aged 3;0 was used to provide a measure of expected realization when subjects are not grammatically required. It is concluded that subject obligatoriness in English may be acquired as a characteristic of the language sui generis, independently of developments elsewhere in the child's emerging grammar.
Maternal speech to three-month-old infants in the United States and Japan
Authors: Toda Suero , Fogel Alan , Kawai Masatoshi
Published: February 2009

An American-Japanese comparison of maternal speech to 3-month-old infants is presented. Mother-infant dyads were videotaped in the laboratory, and the maternal speech was analysed by function and syntactic form. US mothers were more information-oriented than were Japanese mothers; they also used more question forms, especiallyyes/noquestions. Japanese mothers were affect-oriented, and they used more nonsense, onomatopoeic sounds, baby talk, and babies' names. The differences between countries in maternal speech addressed to 3-month-olds appear to reflect characteristic culture-specific communicative styles as well as beliefs and values related to childrearing.
The early development of perfect aspect: adverbial, verbal and contextual specification
Authors: Youssef Valerie
Published: February 2009

In a longitudinal study concerned to assess Verb Phrase (VP) development in three Trinidadian children, adverbials were found to be crucial in delineating specific areas of semantic intent, and to develop early (between ages 2;3 and 3;0). The children were studied over a two-year period, from the onset of morphological marking on the verb, and were recorded two to four hours per month, in their home environments, with a variety of addressees. Two of the children were exposed to, and acquired, both TC and SE verb categories and the third, TC, but the existence of TC past-completive zero 0 as a prominent verbal marker in all their systems made for reliance on adverbial and extralinguistic context in delineating meaning intentions at an early stage;the use which they made of adverbial specification, in particular for marking perfect aspect, indicates how useful these elements may be for precise specification of the development of tense-aspect categories. When they are considered alongside other VP features a clearer overall assessment of tense–aspect development may be made.
Syntactic distinctions in child language
Authors: Bloom Paul
Published: February 2009

This paper presents a study of young children's understanding of a constraint on English word order, which is that pronouns and proper names cannot be modified by prenominai adjectives. For adults, this is a syntactic constraint: adjectives can only precede nouns, and pronouns and proper names are lexical Noun Phrases (NPs). In two analyses, the spontaneous speech of 14 one- and two-year-old children was studied. These analyses show that even in children's very first word combinations, they almost never say things like big Fred or big he. Some non-syntactic theories of this phenomenon are discussed and found to have serious descriptive problems, supporting the claim that children understand knowledge of word order through rules that order abstract linguistic categories. A theory is proposed as to how children could use semantic information to draw the noun/NP distinction and to acquire this restriction on English word order.
On the pragmatics of contrast
Authors: Clark Eve V.
Published: February 2009

In this paper, I review properties and consequences of the PRINCIPLE OF CONTRAST. This principle, which I have argued from the beginning has a pragmatic basis, captures facts about the inferences speakers and addressees make for both conventional and novel words. Along with a PRINCIPLE OF CONVENTIONALITY, it accounts for the pre-emption of novel words by well-established ones. And it holds just as much for morphology as it does for words and larger expressions. In short, Contrast has the major properties Gathercole (1989) proposed as characteristic of her alternative to Contrast.
The Child Language Data Exchange System: an update
Authors: MacWhinney Brian , Snow Catherine
Published: February 2009

In a previous issue of thisJournal, MacWhinney & Snow (1985) laid out the basic sketch for an international system for exchanging and analysing child language transcript data. This system – the Child Language Data Exchange System (CHILDES) – has developed three major tools for child language research: (1) the CHILDES database of transcripts, (2) the CHAT system for transcribing and coding data, and (3) the CLAN programs for analysing CHAT files. Here we sketch out the current shape of these three major tools and the organizational form of the CHILDES system. A forthcoming book (MacWhinney, in press) documents these tools in detail.
The gliding motion of a bacterium: Flexibacter strain BH3
Authors: O'Brien R. W.
Published: February 2009

The flexibacters are a form of gliding bacteria which are often found on the surfaces of solid bodies in fresh and salt water. An individual organism lacks motility in the bulk aqueous phase but glides over a solid surface with its rod-like body aligned with and nearly touching the surface. It has been suggested that this gliding motion in Flexibacter strain BH3 may be caused by waves moving down the outer surface of the rod-shaped cell [2]. This paper is concerned with the fluid mechanical aspects of this form of propulsion.

Formulae for the velocity of the organism and for the power dissipation are obtained by using a lubrication theory analysis in the small gap between the bacterium and the wall. It is found that for any progressive waveform there is an optimum distance from the wall at which the flexibacter may maximize its speed for a given power output. Assuming that the flexibacter sits at this optimum distance and taking the waveform to be sinusoidal we calculate the power required for the flexibacter to move at the maximum observed speed. It is found that this power requirement represents only a small fraction of the power available to the cell.
Effects of iron on a toroidal conductor
Authors: Caldwell James
Published: February 2009

The effects of iron on the uniformity of the field produced by a current-carrying axisymmetric conductor are considered. Using a perturbation analysis a simple analytic expression is obtained which describes the field close to the axis of symmetry. A Fourier series approach is also used to provide an analytical solution to the problem and the accuracy of the perturbation method is estimated by comparing results.
Applications of the Lie theory of extended groups in Hamiltonian mechanics: the oscillator and the Kepler problem
Authors: Leach P. G. L.
Published: February 2009

The method of the Lie theory of extended groups has recently been formulated for Hamiltonian mechanics in a manner which is consistent with the results obtained using the Newtonian equation of motion. Here the method is applied to the three-dimensional time-independent harmonic oscillator and to the classical Kepler problem. The expected constants of motion are obtained. Previously unobserved relations between generators and invariants are also noticed.
Extended optima and equilibria for continuous games
Authors: Gates D. J. , Westcott M.
Published: February 2009

The new optima and equilibria discussed in the preceding two papers are compared with the results of bargaining experiments between two and three players performed by Fouraker and Siegel. Experiments where players have complete or incomplete information are considered. There is clear evidence that the new optima are operating, and that traditional optima–Cournot, Pareto and competitive (threat)–are less satisfactory in explaining the course of the whole bargaining process.
Extrapolation of sequences using a generalized epsilon-algorithm
Authors: Barber Michael N. , Hamer C. J.
Published: February 2009

The problem of estimating the limit f∞ of a sequence fn converging as fn − f∞ = O(n−λ) as n → ∞, where λ > 0, is discussed. Using the generalization of the ε-algorithm proposed recently by Vanden Broeck and Schwartz, an acceleration scheme is developed. The method is illustrated on several test sequences and compared to other acceleration procedures.
Linearized planing-surface theory with surface tension. Part I: Smooth detachment
Authors: Tuck E. O.
Published: February 2009

In the absence of surface tension, the problem of determining a travelling surface pressure distribution that displaces a portion of the free surface in a prescribed manner has been solved by several authors, and this “planing-surface” problem is reasonably well understood. The effect of inclusion of surface tension is to change, in a dramatic way, the singularity in the integral equation that describes the problem. It is now necessary in general to allow for isolated impulsive pressure, as well as a smooth distribution over the wetted length. Such pressure points generate jump discontinuities in free-surface slope. Numerical results are obtained here for a class of problems in which there is a single impulse located at the leading edge of the planing surface and detachment with continuous slope at the trailing edge. These results do not appear to approach the classical results in the limit as the surface tension approaches zero, a paradox that is resolved in Part II, which follows.
A generalization of Rapp's formula
Authors: Pearce C. E. M.
Published: February 2009

The Rapp formula of teletraffic dimensioning is generalized to admit an arbitrary renewal stream of offered traffic. The derivation proceeds from a heavy traffic approximation and provides also an estimate of the order of error involved in the Rapp formula. In principle, the method could be used to seek convenient higher order approximations.

Our equations give an incidental theoretical substantiation of an empirical result relating to marginal occupancy found recently by Potter.
Numerical integration on the sphere
Authors: Atkinson Kendall
Published: February 2009

This is a discussion of some numerical integration methods for surface integrals over the unit sphere in R3. Product Gaussian quadrature and finite-element type methods are considered. The paper concludes with a discussion of the evaluation of singular double layer integrals arising in potential theory.
Best difference equation approximation to Duffing's equation
Authors: Potts Renfrey B.
Published: February 2009

Duffing's differential equation in its simplest form can be approximated by a variety of difference equations. It is shown how to choose a ‘best’ difference equation in the sense that the solutions of this difference equation are successive discrete exact values of the solution of the differential equation.
A note on the impulse due to a vapour bubble near a boundary
Authors: Blake J. R. , Cerone P.
Published: February 2009

An expression for the impluse due to a vapour (cavitation) bubble is obtained in terms of an integral over a nearby boundary. Examples for a point source near a free surface, rigid boundary, inertial boundary and a fluid of different density are considered. It appears that the sign of the impluse determines the direction a cavitation bubble will migrate and the direction of the high speed liquid jet during the collapse phase. The theory may explain recent observations on buoyant bubbles near an interface between two fluids of different densities.
On the quantization of quadratic momenta
Authors: Vaisman Izu
Published: February 2009

Using geometric quantization, and accepting the quantum Hamiltonian of previous authors, we propose some candidate formulae for the quantum operator of an observable which is a quadratic form in the momenta.
The asymptotic behaviour due to a piecewise time dependent net maternity function
Authors: Cerone P. , Tognetti K. P.
Published: February 2009

The long term asymptotic behaviour of a population is evaluated where the age specific fertility behaviour is allowed to change with time. Thus in this article the behaviour of a population is determined with a time dependent net maternity function. It is shown that methods used when the net maternity function was independent of time are still applicable if the change with time is explicit only for the initial population. Further, using the fact that for realistic situations the net maternity function is non-zero over a finite interval α < x < β, it is shown that traditional methods can again be used if the time dependence is associated with ages less than α, the minimum age of childbearing. Recent extensions of Cerone and Keane to include exponential time dependence are utilized and models are presented which are piecewise defined, allowing general and exponential time dependence for the parent and new-born populations respectively. The Sharpe-Lotka single sex determinstic population model is used as the basis for the analysis.
Modelling the spread of grass fires
Authors: Anderson D. H. , Catchpole E. A. , De Mestre N. J. , Parkes T.
Published: February 2009

A simple elliptic model is developed for the spread of a fire front through grassland. This is used to predict theoretical fire fronts, which agree closely with those obtained in practice.
Welfare optimization and multinational monopolies
Authors: Russell A. M. , Martini C. A. , Rickard J. A.
Published: February 2009

This paper examines the role of import tariffs and consumption taxes when a product is supplied to a domestic market by a foreign monopoly via a subsidiary. It is assumed that there is no competition in the domestic market from internal suppliers. The home country is able to levy a profits tax on the subsidiary. The objective of our analysis is to determine the mix of tariff and consumption tax which simultaneously maximizes national welfare. We show that national welfare does not have an internal maximum, but attains its maximum on a boundary of the consumption tax–tariff parameter space. Furthermore, the optimal value of national welfare increases as the tariff decreases and the consumption tax increases. The results obtained generalize the results of an earlier paper in which national welfare was maximized with respect to either a tariff or consumption tax, but not both.
The construction of zonal models of dispersion in channels via matched centre manifolds
Authors: Watt S. D. , Roberts A. J.
Published: February 2009

Taylor's model of dispersion simply describes the long-term spread of material along a pipe, channel or river. However, often we need multi-mode models to resolve finer details in space and time. Here we construct zonal models of dispersion via the new principle of matching their long-term evolution with that of the original problem. Using centre manifold techniques this is done straightforwardly and systematically. Furthermore, this approach provides correct initial and boundary conditions for the zonal models. We expect the proposed principle of matched centre manifold evolution to be useful in a wide range of modelling problems.
A maximum principle for optimal control for a class of controlled systems
Authors: Xu Wensheng
Published: February 2009

Applying Ekeland's variational principle in this paper, we obtain a maximum principle for optimal control for a class of two-point boundary value controlled systems. The control domain need not be convex. For a special case, that is the so called LQ-type problem, we obtain the optimal control in the closed loop form and a corresponding Riccati type differential equation.
Optimal control computation to account for eccentric movement
Authors: Jennings L. S. , Wong K. H. , Teo K. L.
Published: February 2009

A class of optimal control models which involve different weightings in the integrand of the objective function is considered. The motivation for considering this class of problems is that this type of objective function is used to account for eccentric movement in biomechanical models. The computation of these optimal control problems using control parametrization directly is difficult, firstly because of ill-conditioning, and secondly because the objective function is not differentiable. A method for smoothing the integrand is presented with convergence results. An example is computed which shows favourable computational improvements.
A comparative study of smoothing approximations
Authors: Yang X. Q.
Published: February 2009

It is known that many optimization problems can be reformulated as composite optimization problems. In this paper error analyses are provided for two kinds of smoothing approximation methods of a unconstrained composite nondifferentiable optimization problem. Computational results are presented for nondifferentiable optimization problems by using these smoothing approximation methods. Comparisons are made among these methods.
Propagation relations for solutions of some higher order cauchy problems
Authors: Bragg L. R.
Published: February 2009

The Huygens' property is exploited to study propagation relations for solutions of certain types of linear higher order Cauchy problems. Motivated by the solution properties of the abstract wave problem, addition formulas are developed for the solution operators of these problems. The application of these alternative forms of the solution operators to data leads to connecting operator relations between distinct solutions of the problems at different times. We examine this solution behaviour for both analytic and abstract Cauchy problems. A basic algorithm for constructing addition formulas for solutions of ordinary differential equations is included.
Withdrawal of layered fluid through a line sink in a porous medium
Authors: Zhang H. , Hocking G. C.
Published: February 2009

The flow induced when fluid is withdrawn through a line sink from a layered fluid in a homogeneous, vertically confined porous medium is studied. A nonlinear integral equation is derived and solved numerically. For a given sink location, the shape of the interface can be determined for various values of the flow rate. The results are compared with exact solutions obtained using hodograph methods in a special case. It is found that the cusped and coning shapes of the interface can be accurately obtained for the sink situated at different depths in the fluid and the volume of flow into the sink per unit of time.
Small reynolds number flow between eccentric rotating cylinders with a permeable sleeve
Authors: Hird L. D. , Siew P. F.
Published: February 2009

Two eccentric rotating cylinders together with a permeable membrane surrounding the inner cylinder are used to model the flow around a modified viscometer. A perturbation method is used to solve for the flow between the membrane and the outer cylinder; the flow between the inner rotor and the membrane is assumed to be governed by Stoke's equation, and the two flow regimes are coupled by the through-flow across the membrane. For moderate values of Reynolds number and eccentricity, the permeability of the membrane plays a negligible role, and the flow through the membrane is found to be eccentricity dependent. High eccentricities result in the formation of eddies which, upon increasing the Reynolds number, move in a direction opposite to that of the rotation of the outer bowl.
Fast solvers for finite difference approximations for the stokes and navier-stokes equations
Authors: Shin Dongho , Strikwerda John C.
Published: February 2009

We consider several methods for solving the linear equations arising from finite difference discretizations of the Stokes equations. The two best methods, one presented here for the first time, apparently, and a second, presented by Bramble and Pasciak, are shown to have computational effort that grows slowly with the number of grid points. The methods work with second-order accurate discretizations. Computational results are shown for both the Stokes equations and incompressible Navier-Stokes equations at low Reynolds number.
Global strong solutions of equations of magnetohydrodynamic type
Authors: Rojas-Medar Marko A. , Boldrini José Luiz
Published: February 2009

By using the spectral Galerkin method, we prove a result on the global existence in time of strong solutions for a system of equations of magnetohydrodynamic type. Several estimates for the solution and their approximations are given. These estimates can be used in the derivation of error bounds for the approximate solutions.
Formation of singularities in a stratified fluid in the presence of a critical level
Authors: Dostovalova Anna S. , Simakov Sergey T.
Published: February 2009

The paper is concerned with formation of singularities in a density stratified fluid subject to a monochromatic point source of frequency σ. The frequency of the source is assumed to be such that the steady-oscillation equation is hyperbolic in the neighbourhood of the source and degenerates at a critical level. We obtain asymptotic formulae demonstrating how the solution diverges as t → ∞ on the characteristic surface emanating from the source. It is shown that, at points of the surface that belong to the critical level, the solution behaves as t⅔ exp {i(σt + π/2)} as t → ∞, whereas its large time behaviour at the other points of the surface is given by t½ exp {i(σt + π/2 ± π/4)}.
Optimal driving strategies for a train on a track with continuously varying gradient
Authors: Howlett P. G. , Cheng J.
Published: February 2009

This paper derives key equations for the determination of optimal control strategies in an important engineering application. A train travels from one station to the next along a track with continuously varying gradient. The journey must be completed within a given time and it is desirable to minimise fuel consumption. We assume that only certain discrete throttle settings are possible and that each setting determines a constant rate of fuel supply. This assumption is based on the control mechanism for a typical diesel-electric locomotive. For each setting the power developed by the locomotive is directly proportional to the rate of fuel supply. We assume a single level of braking acceleration. For each fixed finite sequence of control settings we show that fuel consumption is minimised only if the settings are changed when certain key equations are satisfied. The strategy determined by these equations is called a strategy of optimal type. We show that the equations can be derived using an intuitive limit procedure applied to corresponding equations obtained by Howlett [9, 10] in the case of a piecewise constant gradient. The equations will also be derived directly by extending the methods used by Howlett. We discuss a basic solution procedure for the key equations and apply the procedure to find a strategy of optimal type in appropriate specific examples.
Efficient multiple-term approximations for the generalised elliptic-type integrals
Authors: El-Gabali M.
Published: February 2009

The generalised elliptic-type integral Rμ(k, α, γ)

where 0 ≤ k < 1, Re(γ) > Re(α) > 0, Re(μ) ≥ −0.5, is represented in terms of the Gauss hypergeometric function by Kalla, Conde and Hubbell [8]. In 1987, Kalla, Lubner and Hubbell derived a simple-structured single-term approximation for this function in the neighbourhood of k2 = 1 in some range of the parameters α, γ and μ. Another formula which complements the parameter range was recently derived by the author. In this paper a novel technique is used in deriving multiple-term efficient approximations (in the neighbourhood of k2 = 1) which may be considered as a generalisation to the concept of the single-term approximations mentioned above. Two non-overlapping expressions which almost cover the entire range of parameters (α, γ, μ) are derived. Closed-form solutions are obtained for single- and double-term approximations (in the neighbourhood of k2 = 1). Results show that the proposed technique is superior to existing approximations for the same number of terms. Our formulation has potential application for a wide class of special functions.
On the quasi-stationary distribution for queueing networks with defective routing
Authors: Boucherie Richard J.
Published: February 2009

This note introduces quasi-local-balance for discrete-time Markov chains with absorbing states. From quasi-local-balance product-form quasi-stationary distributions are derived by analogy with product-form stationary distributions for Markov chains that satisfy local balance.
The allometric hypothesis when the size variable is uncertain: issues in the study of carcass composition by serial slaughter
Authors: Pleasants A. B. , Wake G. C. , Rae A. L.
Published: February 2009

The allometric hypothesis which relates the shape (y) of biological organs to the size of the plant or animal (x), as a function of the relative growth rates, is ubiquitous in biology. This concept has been especially useful in studies of carcass composition of farm animals, and is the basis for the definition of maintenance requirements in animal nutrition.

When the size variable is random the differential equation describing the relative growth rates of organs becomes a stochastic differential equation, with a solution different from that of the deterministic equation normally used to describe allometry. This is important in studies of carcass composition where animals are slaughtered in different sizes and ages, introducing variance between animals into the size variable.

This paper derives an equation that relates values of the shape variable to the expected values of the size variable at any point. This is the most easily interpreted relationship in many applications of the allometric hypothesis such as the study of the development of carcass composition in domestic animals by serial slaughter. The change in the estimates of the coefficients of the allometric equation found through the usual deterministc equation is demonstrated under additive and multiplicative errors. The inclusion of a factor based on the reciprocal of the size variable to the usual log - log regression equation is shown to produce unbiased estimates of the parameters when the errors can be assumed to be multiplicative.

The consequences of stochastic size variables in the study of carcass composition are discussed.
An integrable fourth-order nonlinear evolution equation applied to surface redistribution due to capillarity
Authors: Tritscher Peter
Published: February 2009

Members of an hierarchy of integrable nonlinear evolution equations, related to the well-known linearizable diffusion equation which has the diffusivity form as the reciprocal of the square of the concentration, are adapted to derive a new integrable nonlinear equation which models the surface evolution of an arbitrarily-oriented theoretical anisotropic material by the concomitant action of evaporation-condensation and surface diffusion. The constitutive relations are explicitly formulated and these show that the theoretical anisotropic material behaves like a liquid crystal. The integrable nonlinear equation may be used to advantage as test cases for numerical schemes. Its form has many attributes of the nonlinear governing equation for an isotropic material. Closed-form solutions are constructed for the evolution of a ramped surface by concomitant evaporation-condensation and surface diffusion.
Internal solitary waves with stratification in density
Authors: Sha Huyun , Vanden-Broeck J.-M.
Published: February 2009

Long periodic waves propagating in a closed channel are considered. The fluid consists of two layers of constant densities separated by a layer in which the density varies continuously. The numerical results of Vanden-Broeck and Turner [8] are extended. It is shown that their solutions are particular members of a family of solutions. Solutions are selected by requiring that the streamfunction takes values on the upper and lower walls which are consistent with a uniform stream far upstream. The new solutions are qualitatively similar to those of Vanden-Broeck and Turner [8]. In particular, there are periodic waves characterized by a train of ripples at their troughs. It is shown numerically that these waves approach solitary waves with oscillatory tails as their wavelength increases. Moreover special solutions for which the amplitude of the ripples is almost zero are identified. Such solutions without ripples were previously found for solitary waves with surface tension.
On a connection between the generalized incomplete gamma functions and their extensions
Authors: Chaudhry M. Aslam , Zubair S.M.
Published: February 2009

In this paper we have proved that the generalized incomplete gamma functions and their extensions are mutually related through integral and differential representations.
Some high-order zero-finding methods using almost orthogonal polynomials
Authors: Brent Richard P.
Published: February 2009

Some multipoint iterative methods without memory, for approximating simple zeros of functions of one variable, are described. For m > 0, n ≧ 0, and k satisfying m + 1 ≧ k > 0, there exist methods which, for each iteration, use one evaluation of f, f′, … f(m) followed by n evaluations of f(k), and have order of convergence m + 2n + 1. In particular, there are methods of order 2(n + 1) which use one function evaluation and n + 1 derivative evaluations per iteration. These methods naturally generalize the known cases n = 0 (Newton's method) and n = 1 (Jarratt's fourth-order method), and are useful if derivative evaluations are less expensive than function evaluations. To establish the order of convergence of the methods we prove some results, which may be of independent interest, on orthogonal and “almost orthogonal” polynomials. Explicit, nonlinear, Runge-Kutta methods for the solution of a special class of ordinary differential equations may be derived from the methods for finding zeros of functions. The theoretical results are illustrated by several numerical examples.
On air flow over free surfaces of stationary water
Authors: Tuck E. O.
Published: February 2009

A correspondence is established between flows of air above stationary water, and flows of water below air at atmospheric pressure. Flows in the latter category are well studied, and all such hydrodynamic flows can be “turned upside-down” to generate flows of air in which the free surface deforms under gravity, due to a balance between aerodynamic and hydrostatic pressures. Examples are given of some exact inverse solutions, and a general semi-inverse approach is outlined for numerical solutions via an integral formulation.
Analytic solution of the linearized shallow-water wave equations for certain continuous depth variations
Authors: Clements D. L. , Rogers C.
Published: February 2009

The linear long-wave equations with (and without) small ground motion are considered. The governing equations are represented in a matrix from and transformations are sought which reduce the system to (for example) a form associated with the conventional wave equation. Integration of the system is then immediate. It is shown that such a reduction may be acheived provided the variation in water depth is specified by certain multi-parameter forms.
Spectral resolution of the identity for matrices of elements of a lie algebra
Authors: Green H. S.
Published: February 2009

This is an application of the characteristic identity satisfied by matrices whose elements are also elements of a semi-simple Lie algebra. Generalized eigenvectors are determined for matrices consisting of generators of GL(n), O(n) and Sp(n), and it is shown how to resolve the identity into idempotents constructed from such eigenvectors. By this means rather general functions of the matrices may be defined. It is also shown how to determine traces of such functions, in terms of the invariants of the Lie algebra.
A note on integral representations in Stokes flow
Authors: Blake J. R.
Published: February 2009

An alternative method via generalised functions is used to obtain the surface integral representation for a finite body in an infinite fluid in Stokes flow. The problem is further generalised to a finite number of intersecting finite bodies in an infinite and semi-infinite fluid. Possible applications to line distributions for axi-symmetric bodies are discussed.
Fast local convergence with single and multistep methods for nonlinear equations
Authors: Abbott James P. , Brent Richard P.
Published: February 2009

Methods which make use of the differential equation ẋ(t) = −J(x)−1f(x), where J(x) is the Jacobian of f(x), have recently been proposed for solving the system of nonlinear equations f(x) = 0. These methods are important because of their improved convergence characteristics. Under general conditions the solution trajectory of the differential equation converges to a root of f and the problem becomes one of solving a differential equation. In this paper we note that the special form of the differential equation can be used to derive single and multistep methods which give improved rates of local convergence to a root.
Concentric circular misfit and a circular arc crack in an infinite isotropic elastic plate
Authors: Bhargava R. D. , Narayan Ram
Published: February 2009

A homogeneous isotropic infinite elastic plate contains a circular cavity and a circular arc crack symmetrically situated about thex-axis. The cavity and crack are concentric but are of different radii. A circular inhomogeneity of radius slightly larger than that of the cavity is inserted into the cavity; thus generating a system of stresses in the outer material as well as in the inhomogeneity. The elastic field in the inhomogeneity and in the outer material outside the inhomogeneity is evaluated in this paper.