bluuebunny/crossref_metadata_2025 huggingface dataset:
The range of narrative forms conversationally produced by young children
Authors: Preece Alison
Published: February 2009

The productive narrative competence of three young children as revealed in their spontaneously occurring conversations recorded over an 18-month period during their kindergarten and grade one years was investigated. Almost 90 hours of the children's conversations, produced as they were being driven to and from school, were audiotaped and analysed in order to determine whether children between the ages of five and seven include narrative accounts in their conversations with each other and, if so, the nature of the narrative language produced. The subjects were found routinely and regularly to produce a striking variety of narrative forms; 14 different narrative types were distinguished and defined, six of which have not previously been reported in the literature on children's narratives. Seventy per cent of the recorded narratives took anecdotal form; original fantasy narratives occurred only rarely. A significant proportion of the narratives were collaboratively created.
The connective ‘and’: do older children use it less as they learn other connectives?
Authors: Peterson Carole , McCabe Allyssa
Published: February 2009

The connective and has frequently been described as a useful allpurpose connective that is used as a vehicle for introducing new inter-sentential semantic relationships. As new and more specific connectives are acquired, they are matched to these meanings. An assumption is that as children get older, and should be used less to express the various meanings for which more specific connectives exist; rather, it should be increasingly reserved for simple co-ordination. This hypothesis was tested by examining narratives produced by children between 4 and 9 years old; contrary to expectation, and was used no differently by 9-year-olds than by 4-year-olds, and simple co-ordination constituted no more than 20% of the relationships. The role of and may be to indicate cohesion between sentences, without regard to semantic relationship.
Locative terms and Warlpiri acquisition
Authors: Bavin Edith L.
Published: February 2009

Cognitive complexity and complexity of linguistic structure have been found to influence the order of acquisition of locatives. In Warlpiri, locative terms are nominals and they are used in combination with a locative case marker on the reference object; directional affixes may be added to them. Data from a series of tests of Warlpiri children's comprehension and production of the Warlpiri expressions that may be translated as ‘in’, ‘on’, ‘under’, ‘in front of’, ‘behind’ and ‘between’ indicate that the locative case forms are used first without the more specific locative nominals; young children distinguish an ‘up-down’ dimension but not ‘in’, and the reference object influences how the locative term is interpreted; kamparru-pirdangirli (‘front-behind’) is not one dimension for children aged four to five years; kulkurru ‘between’ is understood before kamparru ‘front’ and pirdangirli ‘behind’; the use of features on a reference object for orientation develops at around six, but the orientation of the reference object, as well as features on the placed object may affect interpretation.
Maternal speech and the child's development of syntax: a further look
Authors: Hoff-Ginsberg Erika
Published: February 2009

The present study compared four categories of maternal utterances that were found in a previous study (Hoff-Ginsberg, 1986) to predict children's rates of syntax development to a category of maternal utterances that was unrelated to syntax development. The comparisons were designed to test the hypotheses that maternal utterances which benefit syntax development do so by providing syntactically rich data or by eliciting conversation from the child. Data-providing and conversation-eliciting characteristics of the selected categories of maternal utterances were assessed from the same transcripts of 22 mothers interacting with their 2½-year-old children that had provided the database for the earlier study of predictive relations. Each of the three positive predictor categories of maternal utterances differed from the unrelated category — in more frequently illustrating the affected aspect of syntax development, in eliciting more speech from the child, or both. Neither of these characteristics was true of the negative predictor category. The pattern of results suggested that maternal speech supports the child's development of syntax by engaging the child in linguistic interaction and also by providing illustrations of the structures the child acquires.
Second-language acquisition via immersion in daycare
Authors: Karniol Rachel
Published: February 2009

This paper presents a case study of second-language acquisition of Hebrew via immersion in daycare between 1;10 and 3;0. A period of silence was followed by rapid onset of L2 production simultaneously with many references to language itself. Eight types of language awareness were identified, and of these, several types may be prerequisites for starting L2 production. The nature of L2 speech during the first stages of production suggests that to crack the sematic code of L2, the child relies on identifiable contingencies between utterances and subsequent behaviours by speakers and listeners. As a result there are many more imperatives and interrogatives in L2 than are evident in L1 speech, and these appear to be learned by rote in an unanalysed manner. The transition to complex constructions occurs via the juxtaposition of known but syntactically unanalysed chunks, and results in patterns of syntactic errors similar to those of adult second-language learners. Reliance on L1 as a fall-back strategy was also evident. Several implications of these data for cognitive development in general are discussed.
Early lexical acquisition: rate, content, and the vocabulary spurt
Authors: Goldfield Beverly A. , Reznick J. Steven
Published: February 2009

The transition from slow to rapid word-learning was examined in a longitudinal study of 18 children. Beginning at age 1;2, mothers kept a diary of children's words. Diary entries were discussed during phone calls to the home every 2½ weeks. A chronological record of nouns and other word classes was coded from the diary records.

Thirteen children evidenced a prolonged period of up to three months during which rate of acquisition markedly increased. Almost threequarters of the words learned during this period were nouns. Five children evidenced more gradual word-learning, and acquired a balance of nouns and other word classes. These results suggest that the terms ‘vocabulary spurt’ and ‘naming explosion’ best describe children who focus their early linguistic efforts on a single strategy: learning names for things. Other children may attempt to encode a broad range of experience with a more varied lexicon, a strategy that results in more gradual lexical growth.
Similarity neighbourhoods of words in young children's lexicons
Authors: Charles-Luce Jan , Luce Paul A.
Published: February 2009

Similarity neighbourhoods for words in young children's lexicons were investigated using three computerized databases. These databases were representative of three groups of native English speakers: 5-year-olds, 7-year-olds, and adults. Computations relating to the similarity neighbourhoods of words in the children's and adult's lexicon revealed that words in the 5- and 7-year-olds' lexicons have many fewer similar neighbours than the same words analyzed in the adult lexicon. Thus, young children may employ more global recognition strategies because words are more discriminable in memory. The neighbourhood analyses provide a number of insights into the processes of auditory word recognition in children and the possible structural organization of words in the young child's mental lexicon.
Children's understanding of adverbs denoting degree of likelihood
Authors: Hoffner Cynthia , Cantor Joanne , Badzinski Diane M.
Published: February 2009

Two studies were conducted to examine children's understanding of three terms that denote different degrees of likelihood: possibly, probably and definitely. In Study 1, children in preschool, and first, third and fourth grade completed a comparison task involving pairs of likelihood terms. Twelve stories were created that described the likelihood that each of two children would participate in an activity, and subjects judged which of the two children actually participated. In Study 2, children in preschool, and first, third and fifth grade evaluated separate statements describing three different children, each of whom was said to have a different estimate of the likelihood that a scary event depicted in a movie would actually occur. Subjects rated how scared each of the three children felt. The results of the two studies revealed that preschoolers showed very little comprehension of the meaning of any of the three words, but by fourth grade the majority of children distinguished among all three terms. Children understood the distinction between definitely and both of the other terms (possibly, probably) better than they understood the distinction between possibly and probably. This finding is consistent with research on the development of children's understanding of probability concepts. Unexpectedly, the distinction between probably and definitely seems to emerge at a younger age than the distinction between possibly and definitely. The findings are discussed in terms of their implications for communicating verbal messages to children.
A cross-linguistic perspective on the development of temporal systems
Authors: Weist Richard M. , Wysocka Hanna , Lyytinen Paula
Published: February 2009

The purpose of this research was to evaluate the development of temporal location within a cross-linguistic experimental design. The research focused on the transition from a temporal system based on absolute temporal relations involving speech time and event time to a more complex system involving relative temporal relationships and reference time. A comprehension test was constructed with problems which were diagnostic of two salient distinctions within each of three temporal systems. The procedure was based on a two-choice sentence–picture matching task. The children who participated were from Poland, the USA and Finland, and there were 12 children at each of the following age levels: 2;6, 3;6, 4;6, 5;6, and 6;6. The Polish and American children solved problems requiring absolute temporal location at 2;6, and the older children eventually solved most of the problems requiring relative location. The Finnish children followed a different pattern taking longer to comprehend both types of problems. A second experiment confirmed the Finnish pattern of development. The results of the comprehension test were compared to observations of conversational and narrative discourse which were the product of two elicitation procedures. The research demonstrates the way in which conceptual development places a universal constraint on the developmental process and how the specific properties of individual languages also have an effect.
Children's communicative abilities revisited: verbal versus perceptual disambiguating strategies in referential communication
Authors: Pynte Joel , Girotto Vittorio , Baccino Thierry
Published: February 2009

The way seven- and nine-year-old French children and adults interpret ambiguous object descriptions was studied in four experiments. All four experiments followed the same basic procedure and consisted of two phases. During the training phase, plastic blocks varying in shape, colour and size were associated with fruit names. Some objects were always given just one label, the generic term, whereas others could be given either the generic or the specific label. For example, large circles were referred to as ‘pommes’ (‘apples’), and large BLUE circles as ‘reinettes’ (a kind of apple). Still others were given no name at all. During the test phase of the experiment, subjects were presented with referentially ambiguous messages and asked to point to a given object (Experiments 1, 2 and 3) or to draw an object (Experiment 4). The messages consisted of either a generic term preceded by an article (e.g. ‘(la pomme’ – ‘the apple’) or a verbal description based on a colour adjective (e.g. ‘le bleu’ – ‘the blue one’). When presented with the generic term, older children and adults persistently chose the object for which no specific term had been given during the training phase. When presented with an adjective description, they chose the referent for which no fruit name had been given during the training phase. Younger children's choices depended on whether the article preceding the description was definite or indefinite. These results are consistent with the Gricean approach to referential communication proposed by Jackson & Jacobs (1982) and with an extended version of the principle of contrast proposed by Clark (1987, 1988).
How the prosodic cues in motherese might assist language learning
Authors: Nelson Deborah G. Kemler , Hirsh-Pasek Kathy , Jusczyk Peter W. , Cassidy Kimberly Wright
Published: February 2009

The function of motherese has become a pivotal issue in the language-learning literature. The current research takes the approach of asking whether the prosodic characteristics that are distinctive to motherese could play a special role in facilitating the acquisition of syntax. Hirsh-Pasek, Kemler Nelson, Jusczyk, Cassidy, Druss & Kennedy (1987) showed that infants aged 0;7–0;10 are sensitive to prosodic cues that would help them segment the speech stream into perceptual units that correspond to clauses. The present study shows that infants' sensitivity to segment-marking cues in ongoing speech holds for motherese but not for adult-directed speech. The finding is that, for motherese only, infants orient longer to speech that has been interrupted at clausal boundaries than to matched speech that has been interrupted at within-clause locations. This selective preference indicates that the prosodie qualities of motherese provide infants with cues to units of speech that correspond to grammatical units of language – a potentially fundamental contribution of motherese to the learning of syntax.
The systematic acquisition of word forms by a child during the first-fifty-word stage
Authors: French Ann
Published: February 2009

This paper sets out to examine two findings reported in the literature: one, that during the one-word stage a child's word productions are highly phonetically variable, and two, that the one-word stage is qualitatively distinct from subsequent phonological development. The complete set of word forms produced by a child at the one-word stage were collected and analysed both cross-sectionally (month by month) and longitudinally (looking for changes over time). It was found that the data showed very little variability, and that phonological development during the period studied was qualitatively continuous with subsequent development. It is suggested that the phonologically principled development of this child's first words is related to his late onset of speech.
Alternative explanations for the relationship between maternal verbal interaction style and child language development
Authors: Yoder Paul J. , Kaiser Ann P.
Published: February 2009

The present study analysed formerly unexamined indirect routes for relationships between time 1 maternal speech and later child language development. Ten normally developing children in Brown's early stage 1 and their mothers were the subjects. For each dyad, two free-play sessions occurring five months apart were videotaped in the subjects' homes. Mothers' pragmatic language use was coded from time 1 sessions. Child language level was coded at both sessions. Even though time 1 scores of the outcome were controlled, seven of the ten relationships involving mother speech and child language development were indirectly related through one of two time 1 child language measures. The results indicate that a mother-driven, direct influence model may be inappropriate for many mother speech–child language development relationships. We argue that child-driven and mother-driven explanatory models for the indirect relationships are equally feasible.
On the developmental contour of child language: a reply to Smith & Weist
Authors: Bloom Lois , Harner Lorraine
Published: February 2009

A developmental perspective in child language research begins with a focus on the child and the processes that contribute to change in the child's knowledge of language. Developmental change occurs in an organized, systematic way, with later changes influenced at least in part by developments at an earlier time. The acquisition of tense and aspect provides a relevant example. Data previously published by Weist, Wysocka, Witkowska-Stadnik, Buczowska & Konieczna (1984) are reanalysed here to show, statistically, that children learning Polish are influenced by aspect in aquiring verb tense, just as children are in learning English, Italian, Hebrew, Turkish and other languages. Children beginning to learn verb inflections find aspectual contour particularly compelling in leading them to learn tense distinctions.
From babbling towards the sound systems of English and French: a longitudinal two-case study
Authors: Levitt Andrea G. , Aydelott Utman Jennifer G.
Published: February 2009

The utterances of one French and one American infant at 0;5, 0;8, 0;11, and 1;2 were transcribed and acoustically analysed for syllable duration and vowel formant values. Both general and language-specific effects emerged in the longitudinal study. Initial similarities in the consonantal repertoires of both infants, increasing control in producing targetF1andF2values, and developmental changes in babbling characteristics over time seem to reflect universal patterns. Yet the babbling of the infants differed in ways that appear to be due to differences in their language environments. Shifts in the infants' sound repertoires reflected phoneme frequencies in the adult languages. The English-learning infant produced more closed syllables, which is characteristic of English, than the French-learning infant. The French-learning infant tended to produce more regularly-timed nonfinal syllables and showed significantly more final-syllable lengthening (both characteristic of French) than the English-learning infant.
Analysis of pronominal errors: a case-study
Authors: Oshima-Takane Yuriko
Published: February 2009

The present paper reports a case-study of a normally developing boy who made pronominal errors for about ten months. Comprehension and production of first- and second-person pronouns were longitudinally examined from 1; 7 to 2; 10 to test three hypotheses concerning pronominal errors: pronominal errors are a result of either (a) semantic confusion, (b) simple imitation, or (c) confusion between self and others. The results showed that the child began using first- and second-person pronouns at about 1; 8 and mastered the correct usage by 2; 10. Consistent errors for the first- and the second-person pronouns were observed from 1; 11 to 2; 4, but proportions of errors occurring in his imitative language were low. The comprehension and production data clearly indicated that the child persistently made pronominal errors due to semantic confusion. That is, first-person pronouns referred to a person with whom the child conversed and second-person pronouns referred to himself.
Beyond the basics: preschool children label objects flexibly at multiple hierarchical levels
Authors: Waxman Sandra R. , Hatch Thomas
Published: February 2009

Although preschoolers typically accept the basic level label for an object (e.g. dog) and tend to resist all others (e.g. collie, animal), this tendency is not inviolable. Under certain circumstances, children accept more than one label per object. In this experiment, with 20 three- and 20 four-year-old children, we extended this body of research in three ways. We examined (1) children's production of multiple, hierarchically related labels; (2) the pragmatic consequences of the inherent asymmetry of inclusion relations; and (3) the influence of morphology (modifier + noun constructions vs. simple lexemes) at the subordinate level. Children labelled objects most frequently at the basic level, but also readily produced many non-basic level terms. Children, like adults, may prefer to label objects at the basic level, but they exhibit no general prohibition against also labelling at other, non-basic levels. Their performance challenges the notion that the ability to label objects flexibly at multiple levels is beyond the young child's capacity.
Children's understanding of the evidential connotation of ‘know’ in relation to overestimation of their own knowledge
Authors: Mitchell Peter , Robinson Elizabeth J.
Published: February 2009

This study examined five- to seven-year-olds' assumptions about the experiential connotation of ‘I know that's X’. In Experiment 1 children tried to identify which of a set of unfamiliar targets had a given name (X), and after they had chosen, we enquired either whether they KNEW their chosen item was (X) or whether they were SURE. Six- to seven-year-olds (N = 39) judged that they were sure more often than they judged that they knew, which suggests that although they experienced confidence that they had chosen correctly, they assumed it would be inappropriate to judge ‘know’, because this would imply an experiential basis, which was absent. Five- to six-year-olds (N = 36) did not discriminate between the two kinds of question. In Experiment 2, children could infer which item was a named unfamiliar cartoon character by ruling out familiar distractors. Six- to seven-year-olds (N = 35) judged that they knew they had picked the right one much more often than they judged that they knew their chosen picture was (target name). Again, five- to six-year-olds (N = 44) did not discriminate between the two kinds of question. This demonstrates powerfully that the older children held an experiential connotation of ‘I know that's X’, since they avoided such judgements even when they knew by inference they had chosen correctly.
Phonetic variation in multisyllable babbling
Authors: Mitchell Pamela R. , Kent Raymond D.
Published: February 2009

This investigation examined phonetic variation in multisyllable babbling of infants from 0;7 to 0;11. The basis of this investigation was to examine assumptions present in major models of infant vocal development which suggest systematic developmental increases in phonetic variation of these babbles, and posit separate stages of repetitive (multisyllables with non-varied phonetic elements) and non-repetitive (phonetically varied multisyllables) babbling. Eight infants were audiotaperecorded in their homes at ages 0;7, 0;9 and 0;11. The multisyllable vocalizations were categorized based on the presence or absence of phonetic variation, and the source of that variation (place change, manner change or both). Multisyllables were produced with phonetic variation at or near the beginning of multisyllable babbling, which failed to support the existence of distinct stages of repetitive and nonrepetitive babbling.
Homonymy and reduplication: on the extended availability of two strategies in phonological acquisition
Authors: Lleó Conxita
Published: February 2009

In the literature on phonological acquisition certain strategies such as homonymy and reduplication are viewed as phenomena appearing at a very early age, resulting from a deficient sound-inventory and sound-distribution. Data on homonymy and reduplication from a longitudinal study will be considered, which show that: (a) such strategies can appear later in the child's linguistic development than it has been proposed; (b) the lexical item has to be considered a central unit, beyond the earliest stages, in the acquisition of phonology.
Lexical assignability and perspective switch: the acquisition of verb subcategorization for aspectual inflections
Authors: Rispoli Matthew
Published: February 2009

This paper explores how children learn the range of aspect inflections to which a verb is amenable. The data considered are from observations of three Japanese boys aged between 1; 10 and 2; 1. Analyses focus on the children's mastery of Aktionsart specific intersentential patterns. For example, in one pattern, a caregiver asksnani shiteiru? ‘What is someone or something doing’. The conventional answer is with the continuative-te iruform of a verb that expresses an activity. Three conclusions are drawn. First, lexical assignment had begun before aspectual inflections were used to signal temporal perspective switch. Secondly, lexical assignment began with anchorpoints tying certain lexical contrasts to the Aktionsart of minimal sentences. Thirdly, overgeneralizations of aspect inflections are due to the difficulty of acquiring devices that signal temporal perspective switch.
Children's use of information in word learning
Authors: Au Terry Kit-Fong
Published: February 2009

Whenever children hear a novel word, the context supplies information about its meaning. One way children may cope with so much information is to use whatever seems to make sense, given their prior knowledge and beliefs, while ignoring or quickly forgetting the rest. This work examined if and how children's beliefs about word meanings may affect their use of contrastive linguistic information in the input in word learning. In Study 1, some 3- and 4-year-olds were introduced to a novel material or shape name and heard it contrasted with familiar words. Others merely heard the novel word used for referring to an object. These children were then tested to determine what they had learned about their new word meaning. In Study 2, another group of 3-and 4-year-olds were asked to name the materials and shapes used for introducing these novel terms. Children made use of linguistic contrast only in some situations. They benefited more when the novel term did not overlap much in denotation with any terms commonly known by 3-and 4-year-olds. These results suggest that children can use information in the input very efficiently in learning a term for an as-yet-unnamed category, but not in learning a term similar in denotation to a word they already know. Thus, the results are consistent with the claim that children believe every word has a unique denotation.
The who, when and where of early narratives
Authors: Peterson Carole
Published: February 2009

To be well understood, narratives need to be embedded within appropriate contextual information. The early development of key orientation (participants, location and time) was traced with an 18-month longitudinal study of real-experience narratives produced by 10 children aged approximately 2–3; 6. Listener knowledge or inference was required to decode most named participants and many were not specified at all. There was no developmental improvement. Orientation to when was rare at first and involved formula words indiscriminately applied. There was steady developmental improvement in frequency as well as differentiation of time references. where information was more common at all ages, particularly when the narrated events occurred away from home. It also showed developmental improvement, but only for away-from-home locations. Overall, very young children can produce narratives in an unscaffolded context to adults unfamiliar with their experiences. The potential role of parental scaffolding in teaching orientation skills is discussed.
An update on the CHILDES/BIB (formerly ISU/CHILDES) database*
Authors: Higginson Roy
Published: February 2009

A description is given of the CHILDES/BIB database, its contents, and its relationship to the CHILDES database. CHILDES is a depository of child language corpora, and the publisher of CHAT (a transcription manual), and CLAN (an electronic package for child language research). CHILDES/BIB is an electronic bibliographic database that is an autonomous unit of CHILDES.
Children's deictic and nondeictic interpretations of the spatial locatives in front of and behind
Authors: Cox Maureen V. , Isard Sarah
Published: February 2009

A younger group (mean age 5;10) and an older group (mean age 9;11) of children were asked to place a toy man IN FRONT OF or BEHIND a car which either faced away from them or faced sideways. When the observer's viewpoint was not emphasized in the instructions, or was merely implied, both age groups responded in a nondeictic way. When the viewpoint of the observer was an essential component of the task and the spatial term was omitted, both age groups selected a deictic location. However, when the viewpoint was emphasized but when the spatial term was also included the responses were split between deictic and nondeictic locations.
Stiff systems of ordinary differential equations. Part 1. Completely stiff, homogeneous systems
Authors: Mahony J. J. , Shepherd J. J.
Published: February 2009

For the completely stiff real homogeneous system

where e is a small positive parameter, a method is given for the construction of a basis for the solution space.

If A has n linearly independent eigenvector functions, then there exists a choice of these, {si}, with corresponding eigenvalue functions {λi}, such that there is a local basis for solution, that takes the form

where vi is a vector that tends to zero with e. In general, a basis of this form exists only on an interval in which the distinct eigenvalues have their real parts ordered. A construction is provided for continuing any solution across the boundaries of any such interval. These results are proved for a finite or infinite interval for which there are only a finite number of points at which the ordering of the real parts of eigenvalues changes.
Equations for periodic solutions of a logistic difference equation
Authors: Brown A.
Published: February 2009

The paper is concerned with periodic solutions of the difference equation un + 1 = 2aun, where a and b are constants, with and b > 0. A new method is developed for dealing with this problem and, for period lengths up to 6, polynomial equations are given which allow the periodic solutions to be determined in a precise and practical manner. These equations apply whether the periodic solutions are stable or unstable and the elements of the cycle can be determined with an accuracy which is not affected by instability of the cycle.

A simple transformation puts the equation into the form , where A = a2 − a, and the detailed discussion is based on this simpler form. The discussion includes details such as the number of cyclic solutions for a given value of A, the pattern of the cycles and their stability. For practical purposes, it is enough to consider a restricted range of values of A, namely , although the equations obtained are valid for A > 2.
The response to a hot spot in a combustion problem
Authors: Tam K. K. , Kiang M. T.
Published: February 2009

A simple model for a problem in combustion theory has multiple steady state solutions when a parameter is in a certain range. This note deals with the initial value problem when the initial temperature takes the form of a hot spot. Estimates on the extent and temperature of the spot for the steady state solution to be super-critical are obtained.
Optimal control theory with general constraints
Authors: Blatt John M.
Published: February 2009

We consider an optimal control problem with, possibly time-dependent, constraints on state and control variables, jointly. Using only elementary methods, we derive a sufficient condition for optimality. Although phrased in terms reminiscent of the necessary condition of Pontryagin, the sufficient condition is logically independent, as can be shown by a simple example.
Non-destructive testing of optical-fibre preforms
Authors: Anderssen R. S. , Calligaro R. B.
Published: February 2009

When optical fibres are made by first constructing optical-fibre preforms, the fibre which is pulled from the heated preform is simply a scaled down version of the original preform structure. The expansion coefficient profile α(r) of the preform, which relates directly to the fabrication variables, can be determined from non-destructive optical retardation measurements δ(r) performed on the preform. In addition, the residual elastic stress distributions in a fabricated preform, which can be used to compare different fabrication procedures, have simple definitions as linear functionals of the expansion coefficients α(r). Thus, through the use of optical retardation data, an examination of different manufacturing procedures for preform fabrication is reduced to a problem in non-destructive manufacturing procedures for preform fabrication is reduced to a problem in non-destructive testing and analysis. The underlying numerical problem of evaluating the stres distributions reduces to solving and Abel-type integral equation for α(r), which involves an indeterminacy, followed by the evaluation of linear functionals defined on α(r). It is shown how the known inversion formulae for the Abel-type integral equation can be used formally to reduce the numerical problem of evaluating the radial stress to the evaluation of a linear functional defined on the data δ(r) which bypasses the indeterminacy. When only the radial stress is required, the problem of actually solving the Abel-type integral equation is avoided. Methods for evaluating the non-radial stresses, which avoid the indeterminacy, are also derived.
Stiff systems of ordinary differential equations
Authors: Mahony J. J. , Shepherd J. J.
Published: February 2009

Solutions of the stiff system of linear differential equations

are obtained in a form yielding tight estimates of their properties, and conditions are obtained under which the operator norm of the map from r to the solution x does not become exponentially large for small values of ε. When these conditions are satisfied, the solutions are shown to be close to those of Ax + r = 0, save at any singular points of A, and in boundary layers. The behaviour of solutions near admissible singular points is also obtained.

The results are used to characterize those boundary-value problems for the above system in which the solution defines maps from the data that are of “moderate” operator norm. This leads to a constructive existence theory for a limited class of boundary-value problems for the nonlinear system

It is suggested that the treatment of more general classes of boundary-value problems may be simplified using these results. By the use of simple examples, the problems involving large operator norms are shown to be related to the stability properties of the possible branches of the outer solutions close to those of
Extended optima and equilibria for continuous games
Authors: Gates D. J. , Westcott M.
Published: February 2009

For the class of continuous games where σi and fi {σi, φ(σ1, …, σN)} are the strategy of and payoff to player i for i = 1, …, N, it is proved that the set of weak type I optima defined in Paper I conicide with the set of solution of a matrix condition. The latter condition restricts the equilibrium solutions of an adjustment process. Numerical results for N = 2 and N = 3 indicate that the set of all equilibrium solutions coincides with the above sets. The optima of types I to IV from Paper I are described fairly completely for the given class of games.
Linearized planing-surface theory with surface tension. Part II: Detachment with discontinuous slope
Authors: Tuck E. O.
Published: February 2009

In Part I of this series, surface tension was included in the classical two-dimensional planing-surface problem, and the usual smooth-detachment trailing-edge condition enforced. However, the results exhibited a paradox, in that the classical results were not approached in the limit as the surface tension approached zero. This paradox is resolved here by abandoning the smooth-detachment condition, that is, by allowing a jump discontinuity in slope between the planing surface and the free surface at the trailing edge. A unique solution is obtainable for any input planing surface at fixed wetted length if one allows such jumps at both leading and trailing edges. If, as is the case in practice, the wetted length is allowed to vary, uniqueness may be restored by requiring either, but not both, of these slope discontinuities to vanish. The results of Part I correspond to the seemingly more-natural choice of making the trailing-edge detachment continuous, but it appears that the correct choice is to require the leading-edge attachment to be continuous.
An inviscid theory for sliding flexible sheets
Authors: Tuck E. O.
Published: February 2009

This paper demonstrates feasibility of aerodynamically-supported motion of a thin sheet near to a plane wall. Steady equilibrium is possible for uniform sheets only if they are deformable, and a set of possible equilibrium shapes is determined.
A transformation to linearity of some non-linear differential-difference equations
Authors: Bracken A. J.
Published: February 2009

The problem of solving a differential-difference equation with quadratic non-linearities of a certain type is reduced to the problem of solving an associated linear differential-difference equation.
The commutation relation i[Y, Z] = 2Y and the absolutely continuous spectrum of Y
Authors: Corbett J. V.
Published: February 2009

A relation between positive commutators and absolutely continuous spectrum is obtained. If i[Y, Z] = 2Y holds on a core for Z and if Y is positive then we have a system of imprimitivity for the group on , from which it follows that Y has no singular continuous spectrum.
Suboptimality in linear control systems with time delay
Authors: Chan W. L.
Published: February 2009

For the linear quadratic control problem with delay, a lower bound for the performance index is obtained by elementary methods. Using this bound, two important a posteriori error estimates are derived. The first one measures the deviation of the performance index while the second is for the deviation of the state and control variables from the optimal solution.
Selective withdrawal from stratified streams
Authors: Yih Chia-Shun , Zhu Songping
Published: February 2009

Selective withdrawal from a stratified stream is considered. The average density of the withdrawn fluid and the flow pattern are found, within the limitations on the densimetric Froude number and the withdrawal rate specified in this paper, to depend on the strength and location of the sink, and very little on any slight variation in the velocity distribution far upstream and the densimetric Froude number. The upstream density distribution is assumed linear, but many other density distributions can be similarly treated.
Nonlinear free-surface flows emerging from vessels and flows under a sluice gate
Authors: Asavanant J. , Vanden-Broeck J.-M.
Published: February 2009

Steady two-dimensional flows in a domain bounded below by an infinite horizontal wall and above by a semi-infinite horizontal wall, a vertical wall and a free surface are considered. The fluid is assumed to be inviscid and incompressible, and gravity is taken into account. The problem is solved numerically by series truncation. It is shown that for a given length of the vertical wall, there are two families of solutions. One family is characterized by a continuous slope at the separation point and a limiting configuration with a stagnation point and a 120° angle corner at the separation point. The other family is characterized by a stagnation point and a 90° angle corner at the separation point. Flows under a sluice gate with and without a rigid lid approximation upstream are also considered.
The sputtering temperature of a cooling cylindrical rod without and with an insulated core in a two-fluid medium
Authors: Bera R. K. , Chakrabarti A.
Published: February 2009

Utilising Jones' method associated with the Wiener-Hopf technique, explicit solutions are obtained for the temperature distributions on the surface of a cylindrical rod without an insulated core as well as that inside a cylindrical rod with an insulated inner core when the rod, in either of the two cases, is allowed to enter, with a uniform speed, into two different layers of fluid with different cooling abilities. Simple expressions are derived for the values of the sputtering temperatures of the rod at the points of entry into the respective layers, assuming the upper layer of the fluid to be of finite depth and the lower of infinite extent. Both the problems are solved through a three-part Wiener-Hopf problem of special type and the numerical results under certain special circumstances are obtained and presented in tabular forms.
Variance Minimization – Relationship between Completion-Time Variance and Waiting-Time Variance
Authors: Zhou S. , Cai X.
Published: February 2009

The completion-time variance (CTV) and the waiting-time variance (WTV) are two performance measures which are commonly used in optimization of single-machine scheduling systems. This paper shows that when the number of jobs is large the two measures are nearly equivalent in a probabilistic environment.
On generalised convex multi-objective nonsmooth programming
Authors: Mishra S. K. , Mukherjee R. N.
Published: February 2009

We extend the concept of V-pseudo-invexity and V-quasi-invexity of multi-objective programming to the case of nonsmooth multi-objective programming problems. The generalised subgradient Kuhn-Tucker conditions are shown to be sufficient for a weak minimum of a multi-objective programming problem under certain assumptions. Duality results are also obtained.
Oscillatory and asymptotic behavior of solutions of nonlinear neutral-type difference equations
Authors: Graef John R. , Miciano Agnes , Spikes Paul W. , Sundaram P. , Thandapani E.
Published: February 2009

The authors consider the higher-order nonlinear neutral delay difference equation

and obtain results on the asymptotic behavior of solutions when (pn) is allowed to oscillate about the bifurcation value –1. We also consider the case where the sequence {pn} has arbitrarily large zeros. Examples illustrating the results are included, and suggestions for further research are indicated.
A two-sided shooting method in computation of travelling combustion waves of a solid material
Authors: Andonowati
Published: February 2009

Numerical solutions for travelling combustion waves of a solid material are sought. The algorithm of computation is based on a two-sided shooting method. It is found that there is a lower bound of the wave speed c, say c*, such that for c < c* no numerical solution can be constructed. This c* is a function of the activation energy of the medium.
Subharmonic orbits in an anharmonic oscillator
Authors: Christie J. R. , Gopalsamy K. , Panizza M. P.
Published: February 2009

In a recent paper, Christie and Gopalsamy [2] used Melnikov's method to establish a sufficient condition for the existence of chaotic behaviour, in the sense of Smale, in a particular time-periodically perturbed planar autonomous system of ordinary differential equations. They then concluded with an application to the dynamics of a one-dimensional anharmonic oscillator. In this paper, the same system is considered and a condition for the existence of subharmonic orbits in the perturbed system is deduced, using the subharmonic Melnikov theory. Finally, an application is given to the dynamical behaviour of the one-dimensional anharmonic oscillator system.
Some integral inequalities, with application to bounds for moments of a distribution
Authors: Varošanec Sanja , Pečarić Josip
Published: February 2009

The resolution of many problems in probability depends on being able to provide sufficiently good upper or lower bounds to certain moments of distributions. A striking example from the literature of a result that can offer such bounds was given by Pó1ya over sixty years ago as the following theorem (see [7, Vol. II, p. 144] and [7, Vol. I, p. 94]).
A C0-Collocation-like method for elliptic equations on rectangular regions
Authors: Leyk Zbigniew
Published: February 2009

We describe a C0-collocation-like method for solving two-dimensional elliptic Dirichlet problems on rectangular regions, using tensor products of continuous piecewise polynomials. Nodes of the Lobatto quadrature formula are taken as the points of collocation. We show that the method is stable and convergent with order hr(r ≥ 1) in the H1–norm and hr+1(r ≥ 2) in the L2–norm, if the collocation solution js a piecewise polynomial of degree not greater than r with respect to each variable. The method has an advantage over the Galerkin procedure for the same space in that no integrals need be evaluated or approximated.
Combustion waves
Authors: Weber R. O. , Watt S. D.
Published: February 2009

Finding critical phenomena in two-dimensional combustion is normally done numerically. By using a centre-manifold reduction, we can find a reduced equation in one dimension. Once we have found the reduced equation, it is simpler to find critical phenomena. We consider two different problems. One is spontaneous ignition. We compare our results with known critical parameters to give some validity to our reduction technique. We also look at a combustion model with three equilibrium states. For this model, the possible transitions can occur as travelling waves between the unstable to either of the stable equilibrium or from one stable to the other stable state. For the latter transition, the direction of the transition tells us whether we have an extinction or ignition wave. We find the critical parameters when the direction of the wave changes.
Numerical study of a problem in the combustion of a porous medium
Authors: Tam K. K. , Andonowati
Published: February 2009

A spectral method is used to consider the porous medium combustion in an infinite slab. The infinite system of ordinary differential equations for the amplitude functions is truncated and comparisons are made for different numbers of modes included in the numerical computation. It is shown that the qualitative behaviour of the solution is captured by the first eigenmode. Dependence of the solution on initial data and a parameter is also considered.
Markov decision programming–the moment optimal problem for the first-passage model
Authors: Jianyong Liu , Ke Liu
Published: February 2009

In this paper, we discuss MDP-the moment optimal problem for the first-passage model. A policy improvement iteration algorithm is given for finding the k-moment optimal stationary policy.
Existence of solutions of plane traction problems for inextensible transversely isotropic elastic solids
Authors: Morland L. W.
Published: February 2009

A plane strain or plane stress configuration of an inextensible transversely isotropic linear elastic solid with the axis of symmetry in the plane, leads to a harmonic lateral displacement field in stretched coordinates. Various displacement and mixed displacement-traction boundary conditions yield standard boundary-value problems of potential theory for which uniqueness and existence of solutions are well established. However, the important case of prescribed tractions at each boundary point gives a non-standard potential problem involving linking of boundary values at opposite ends of chords parallel to the axis of material symmetry. Uniqueness and existence of solutions, within arbitrary rigid motions, are now established for the traction problem for general domains.
The measurement of blood pressure
Authors: Patterson J. C. , Fitz-Gerald J. M.
Published: February 2009

In this paper, the procedure of the clinical measurement of blood pressure is modelled by the application of a uniform pressure band to a long, homogeneous, isotropic cylinder. The deformations are assumed to be infinitesimal, and transform methods are used to analyse the resulting equations. The inversion of the resulting transforms is carried out numerically. It is shown that, in spite of the fairly crude assumptions of the model, the actual load on the artery may be markedly different from that applied to the surface, leading to inaccuracies in the measured blood pressure. The parameter of importance is shown to be the ratio of pressure band width to arm diameter.