bluuebunny/crossref_metadata_2025_split huggingface dataset:
On a Nine-Point Conic, etc.
Authors: Pinkerton P. 
Published: January 2009

1. The Pole and Polar Theorem for the Circle may be proved as follows:—Let P be any point, and C the centre of a circle.Let AB be the diameter through P, and QQ′ any chord passing through P.Let AQ, BQ′ meet in M; AQ′, BQ in O; MO, AB in N; and MO, QQ′ in P′.
On the Pascal Hexagram
Authors: Jack J. 
Published: January 2009

ABCDEF is any cyclic hexagon;AB, DE meet in G,BC, EF „ „ H,CD, FA „ „ K; then G, H, K are in a straight line.Draw KLNM parallel to BC and produce DE, EF, AB to meet it in I, N, M. Join DA, DM and let BC, DE meet in P.
A Property of the Harmonic Triangle of the Complete Quadrangle formed by the four points of contact of the four tangents to the Cubic Curve from a point on it
Authors: Milne William P. 
Published: January 2009

The following two propositions are necessary for what is to follow, and are very easy to prove.I. If A, B, C be three points such that B and C are conjugate with respect to the Polar Conic of A, then are C and A conjugate points with respect to the Polar Conic of B, and similarly with regard to the third vertex.A triangle possessing the property defined above, viz. that each pair of vertices are conjugate points with respect to the Polar Conic of the third vertex, is called an Apolar Triangle.
The Focal and Bi-Tangent Properties of Bi-Circular Quartics
Authors: Milne William P. 
Published: January 2009

The following direct method of attack establishes the fundamental properties of the Foci and Bi-Tangents of a Bi-Circular Quartic very simply, using only the properties of a homographic correspondence. The method was suggested to me by my previous paper on the focal properties of Circular Cubics.I am indebted to Mr Peter Fraser, University of Bristol, for his criticism.
Note on a formula connected with Fourier Series
Authors: Macdonald H. M. 
Published: January 2009

An expression for the sum of a series of terms which takes account of the different rates of oscillation of the functions involved is of importance for series such as occur in the problems of diffraction, and a relation of this kind has been given by Poisson. This relation can be written in the formwhere Sm denotes the sum of m terms of the series Σun, beginning with the term un.
On Series for calculating Euler's Constant, and the Constant in Stirling's Theorem
Authors: Sanjana K. J. 
Published: January 2009

Let γn denote the value ofwhere n is a definite integer; and let γ denote the limit ofwhen the integer k is indefinitely increased. It is known that the expansion of γn – γ in ascending powers of 1/n iswhere B1, B3, B5… are the numbers of Bernoulli. The series (3) is, however, divergent, as B2r+1 not only increases indefinitely with r, but bears† an infinite ratio to B2r–1 in this case. It is proposed to find by elementary methods the expansion of γn – γ up to the term in nr and to estimate the error (of order l/nr+1) made in omitting further terms of series (3). I shall take the case of r = 9, but the process is quite general.
Historical Note on Wallace's Line
Authors: Archibald R.C. 
Published: January 2009

In earlier volumes of the Proceedings of the Edinburgh Mathematical Society (cf. III., 104; IX., 83) it has been shown by researches of Dr. J. S. Mackay that the “discovery of the Wallace line … dates back only to about the year 1799 or 1800.” This result is reproduced in Cantor's Vorlesungen über die Geschichte der Mathematik (III., 542, 2te Aufl.). It was arrived at by considering the two following theorems given by Professor Wallace in the old series of Leybourn's Mathematical Repository:Theorem A (Vol. I., p. 309 ; Vol. II., p. 54–5). If three straight lines touch a parabola, a circle described through their intersections shall pass through the focus of the parabola.
Approximations to the Length of an Arc
Authors: Sommerville D. M. Y. 
Published: January 2009

Dr E. M. Horsburgh has given the approximate expression for the length of an arc of the catenary:where C is the length of the chord and T the sum of the tangents at its extremities, analogous to Huygens' approximation to the length of a circular arc:where C′ is the sum of the chords of the two halves of the arc. These approximations are not confined to these particular curves, but hold, within wider or narrower limits, for any continuous curve. In fact, if s is regarded as a small quantity of the first order, as are also C, C′ and T, the difference between s and either of the quantities ⅓(2C + T) and ⅓(4C″ – C) is a small quantity of the fifth order. Other expressions of a similar form can be found involving the chords and tangents of the half-arcs.
Asymptotic Expressions for the Bessel Functions and the Fourier-Bessel Expansions
Authors: MacRobert T. M. 
Published: January 2009

Asymptotic Expressions for the Bessel Functions.From the asymptotic expansion for Ku(z) it follows that, if − π < amp z < π,This theorem is also true if amp z = ± π; to prove this consider the formula
Addition of a Third of a Period to the Argument of the Elliptic Function
Authors: Taylor D. G. 
Published: January 2009

1. If I is an inflexion on a non-singular plane cubic curve, a variable line IPP′ establishes a (1, 1) correspondence between points P, P′ on the curve. This correspondence defines a perspective transformation of the whole plane, with I for pole, and the harmonic polar of I for axis, of perspective; for, when I is projected to infinity on the y-axis, and its harmonic polar taken for x-axis, the resulting equationindicates a curve symmetrical with respect to the latter.
Determination of the Arbitrary Constants which appear in the Asymptotic Expansions for the Functions of the Elliptic Cylinder
Authors: Marshall William 
Published: January 2009

In an article, published some time since, the author of the present paper deduced an asymptotic expression for the functions of the elliptic cylinder, which expression took the following form:Here P and Q are certain asymptotic series, and C and a arbitrary constants. General expressions for these constants were not determined in the aforementioned article on account of the difficulties there set forth, though it was pointed out that their numerical calculation for any particular problem was simply a matter of arithmetic computation. It is the object of the present paper to deduce general expressions for these constants C and a in terms of the two parameters which appear in the defining equation for U.
The Equation of Telegraphy
Authors: Gray M. C. 
Published: January 2009

The equation of the propagation of electric signals along cables, generally known as the equation of telegraphy, may be writtenParticular solutions of this equation, adapted to various purposes have been found by Heaviside, Poincaré, A. G. Webster, T. W. Chaundy, § and others. The object of the present paper is to unify the theory of the equation by exhibiting the relations which these solutions bear to each other, and by obtaining them as particular cases of a general solution. The derivation of new particular solutions by the solution of integral equations is also discussed.
On an Asymptotic Expansion of the Hypergeometric Function
Authors: MacRobert T. M. 
Published: January 2009

In a previous paper the author has employed the expansionwhereandto establish the theorem that, if −π/2<amp γ<π/2, the function Ps/Ts+1 remains finite as γ→∞. This theorem is valid provided that z is not real and ≧ 1.
Note on Binet's Inverse Factorial Series for μ(x)
Authors: Copson E. T. 
Published: January 2009

Binet shewed that the functioncan be expanded as an inverse factorial series. This note furnishes a new and much simpler proof of his result, based on a formula which is an analogue of the Binomial Theorem for factorials.This formula is that, if we denote by [x]n the ratiothenwhere denotes the coefficient of xr in the expansion of (1 + x)m.
On Integral Relations connected with the Confluent Hypergeometric Function
Authors: Gibb D. 
Published: January 2009

In the Bulletin of the American Mathematical Society Whittaker defines the confluent hypergeometric function Wk,m(x) by the equationwhere the path of integration begins at t = + ∞, and after encircling the point t = Q in the counter-clockwise direction, returns to t = + ∞ again.
Functional oesophagoscopy: endoscopic evaluation of the oesophageal phase of deglutition
Authors: Belafsky P C , Rees C J 
Published: January 2009

AbstractBackground:The anatomy and function of the oropharynx and larynx during deglutition can be assessed using the flexible endoscope, but this evaluation does not provide information on the oesophagus. Guided observation of oesophageal swallowing enables extended dysphagia evaluation.Objective:To assess the diagnostic utility of guided observation of oesophageal swallowing in the evaluation of dysphagia.Study design:Retrospective case series.Methods:Procedures for guided observation of oesophageal swallowing were reviewed for oesophageal findings and compared with fluoroscopy and manometry.Results:Twenty-one patients underwent guided observation of oesophageal swallowing and concurrent videofluoroscopy and/or manometry. No complications of the former procedure occurred. The results of guided observation of oesophageal swallowing concurred with those of fluoroscopy in 15/21 cases (71 per cent) and with those of manometry in five of six (83 per cent) cases. Guided observation of oesophageal swallowing revealed anatomic pathology contributing to dysphagia in 15/21 (71 per cent) patients. The procedure identified pathology not detected by fluoroscopy and manometry in 13/21 (62 per cent) patients.Conclusion:Guided observation of oesophageal swallowing appears to be a safe diagnostic tool with which to evaluate the oesophageal phase of deglutition.
History of instruments used for mastoidectomy
Authors: Mudry A 
Published: January 2009

AbstractAim:To present the historical development of specific instruments used for mastoidectomy and their resulting implications for this surgery.Method:Compilation of original written documents, trade catalogues and collections of instruments used in mastoid surgery, with a review of the secondary literature on the subject.Results:The first surgical opening of the mastoid was performed by Petit in 1736 with a trepanation system. More than one and a half centuries later, in 1873, Schwartze codified the operation using chisels and gouges. At the end of the nineteenth century, Macewen introduced the electrical dental burr for mastoid surgery, but it remained largely unrecognised. At the beginning of the 1950s, the systematic use of the microscope in ear surgery allowed generalised use of the drill and improvement of the suction-irrigation system.Conclusion:Three instrumental periods are recognisable in the history of mastoidectomy: the trepan period, the chisel and gouge period, and the electrical drill period.
Pain versus bleeding risk following tonsillectomy: do patients and doctors agree?
Authors: Low T-H , Harris P , Esterman A , Carney A S 
Published: January 2009

AbstractObjective:To investigate the differing opinions of patients and medical practitioners regarding the relative priorities of pain relief versus bleeding prevention following tonsillectomy.Methods:Questionnaires were mailed out to adult patients, paediatric patients' parents, general practitioners and ENT surgeons.Results:A total of 72/112 (64.3 per cent) questionnaires were returned. Adult patients, paediatric patients' parents, general practitioners and ENT surgeons all ranked bleeding as the most important factor when assessing risks related to tonsillectomy. Most adult patients indicated that they would accept a bleeding risk of 2 per cent; however, parents indicated that they would accept a higher bleeding risk (3 per cent) for their children in exchange for better pain control.Conclusions:Adult patients, paediatric patients' parents and doctors were slightly more inclined to ‘trade-off’ an increased post-tonsillectomy bleeding risk in exchange for better post-tonsillectomy pain control, although concerns about post-operative haemorrhage remained the main priority for all groups.
Influence of temperature on the larval development of the edible crab, Cancer pagurus
Authors: Weiss Monika , Thatje Sven , Heilmayer Olaf , Anger Klaus , Brey Thomas , Keller Martina 
Published: January 2009

The influence of temperature on larval survival and development was studied in the edible crab, Cancer pagurus, from a population off the island of Helgoland, North Sea. In rearing experiments conducted at six different temperatures (6°, 10°, 14°, 15°, 18° and 24°C), zoeal development was only completed at 14° and 15°C. Instar duration of the Zoea I was negatively correlated with temperature. A model relating larval body mass to temperature and developmental time suggests that successful larval development is possible within a narrow temperature range (14° ± 3°C) only. This temperature optimum coincides with the highest citrate synthase activity found at 14°C. A comparison for intraspecific variability among freshly hatched zoeae from different females (CW 13–17 cm, N = 8) revealed that both body mass and elemental composition varied significantly. Initial larval dry weight ranged from 12.1 to 17.9 μg/individual, the carbon content from 4.6 to 5.8 μg/individual, nitrogen from 1.1 to 1.3 μg/individual, and the C:N ratio from 4.1 to 4.4. A narrow larval temperature tolerance range of C. pagurus as well as the indication of intraspecific variability in female energy allocation into eggs may indicate a potential vulnerability of this species to climate change. Large-scale studies on the ecological and physiological resilience potential of this commercially fished predator are needed.
Labours of Love: Voluntary Working in a Depressed Local Economy
Authors: MacDonald Robert 
Published: January 2009

ABSTRACTWhilst studies of employment have fuelled arguments about post-Fordism and questions of flexibility, recent debates about welfare have considered social polarization and the growth of an anti-social, anti-work ‘underclass’. In both cases, relatively little attention has been given to the ways in which people in depressed local economies now survive through precarious, marginal and informal work.This article explores how people deprived of jobs seek to re-create positive working lives for themselves through voluntary work. Drawing upon qualitative interviews with working-class men and women in Teesside, it explores the motivations and meanings of volunteering and the significance that voluntary action has for work and welfare in such communities. State intervention in the voluntary work sphere is assessed and a number of recommendations are made for policy and practice.
Policy Dilemmas in Belfast
Authors: Osborne R. D. 
Published: January 2009

ABSTRACTMajor policy developments in Northern Ireland concerned with socioeconomic differences between Protestants and Catholics have involved a concern with structural issues and the nature of the policy making process. These initiatives have raised considerable debate concerning the extent to which religion-specific policies are appropriate. In this article each of these initiatives is considered in detail. It is suggested that the debates in Northern Ireland could have significance in the light of proposals to develop race-specific policies in Britain.
Competition in the Mixed Economy of Care
Authors: Forder Julien , Knapp Martin , Wistow Gerald 
Published: January 2009

ABSTRACTThe 1990National Health Service and Community Care Actintroduced sweeping changes to health and social welfare services. The reforms to community care were dominated by the introduction of markets for social care. We argue that the new markets cannot be guaranteed to deliver the range of services required to meet community care objectives. When they began to assume their new responsibilities, few key purchasers had a basic understanding of the functioning and imperfections of markets. Consequently, they were poorly equipped to anticipate or ameliorate the sources of market failure that we identify. Like any other relatively ill-informed purchaser, local authorities risk being unable to buy what they want on behalf of their residents and at an appropriate volume, cost and quality. We discuss where and how market imperfections are likely to occur. In this context, we offer an economic framework to help in the shaping and managing of social care markets.
Combining Employment with Childcare: An Escape From Dependence?
Authors: Ward Clare , Dale Angela , Joshi Heather 
Published: January 2009

ABSTRACTThe availability of childcare is an important factor in enabling motherhood to be combined with paid employment. This article uses evidence from the fifth sweep of the National Child Development Study to analyse the use of childcare by a cohort of employed women who were aged 33 in 1991. There is a heavy reliance on informal care by women in partnerships and also by lone mothers. Formal care is most heavily used by women whose youngest child is under five, especially if the woman works full-time. Reported costs of childcare represent nearly a quarter of net weekly earnings for mothers with a child under five. Formal childcare is shown to play an important role in facilitating women's full-time employment. Full-time employment is the route by which women achieve financial independence from their partner. It also increases the likelihood of contributing to an occupational pension which, in turn, has implications for financial independence in later life. However, the majority of women in this cohort do not take the full-time route. For these women, low earnings potential and part-time working make paid childcare uneconomic and reinforces both their role as minor financial contributors within the family and their lack of pension provision in later life.
Compensation for Disability
Authors: Bolderson Helen 
Published: January 2009

ABSTRACTDifficulties encountered in the transfer of money to a minority group in society are explored. Should benefits for disabled people seek to mitigate earnings loss, functional incapacity or damage? Should they take the form of contingency benefits, merited payment, or compensatory and reparatory ‘gifts’? What are the reasons for the different approaches adopted in the War Pensions, Industrial Injuries, and Invalidity Benefit schemes?An historical account of the development of these schemes shows that payments related to attributed characteristics or ‘condition’ avoid the pitfalls of undue stress on status, performance and achievement inherent in alternative, and apparently more integrative, benefits. Payments related to condition accentuate ‘difference’ but if they represent a collective liability for society's vicariously caused diswelfares, they need not be experienced as stigmatizing. It may therefore be possible to conceive of a compensatory / reparatory payment for all disabled people, as of right, independent of insurance status, average life earnings, current wage, and other measured achievements. To avoid ‘physiological and psychological means testing’ the basic payment would be assessed on a disabled person's assumed ‘loss of faculty’ but, in the interest of equity, individual measurements of functional limitation may be necessary for additional cash benefits and services.
Diversity and Esteem in Higher Education
Authors: Eustace Rowland 
Published: January 2009

ABSTRACTThere are many calls for greater variety in the provision of higher education combined with greater transferability between courses and institutions – in short, that we should end the present hierarchy of esteem in which institutions and subjects of study are commonly held.Is this likely to be done easily? Too little consideration has been given to the size and strength of the social forces that create educational elitism. Some idea of this size and strength may be gained by looking, as a revealing example, at some educational history. Elitism has survived in times when the factors usually thought of as decisive have been strongly adverse to it. We should not hope that its virulence is any less now. New approaches are needed, and a concerted effort to decide what these approaches should be is now urgent.To have much hope of achieving perceived equality of esteem of diverse types of higher education, an intensive study of the causes of elitism in education, and of measures that would have some chance of reducing it, is needed. A single Royal Commission type of inquiry is unlikely to be enough. A structured set of parallel inquiries might offer more hope.
The Structure of Social Casework and Behavioural Change
Authors: Toren Nina 
Published: January 2009

ABSTRACTThe casework method practised in social work is assessed from a sociological-structural perspective. Social workers are viewed as agents of social control who wield power and authority in order to change their clients' attitudes and behaviour. It is argued that the main weaknesses of casework as a technique for personal change lie in its dyadic structure and isolation from the client's real-life environment. These characteristics impede the operation of the basic processes through which control and influence are generally accepted. It is proposed to substitute small groups of clients for the one-to-one casework setting, to link the treatment situation to real-life experiences, and to emphasize learning processes. It is believed that this restructuring of the worker-client encounter will increase the effectiveness of social work therapeutic intervention.
Workmen's Compensation in the United States: The Effects of Fifty Years of Local Control and Private Enterprise on the Administration of a Social Welfare Programme
Authors: Chambers Donald E. 
Published: January 2009

ABSTRACTFrom an examination of the available data it appears that the present Workmen's Compensation system in the United States is providing a deprivation livelihood for the work-injured and their survivors and is failing to meet its objectives as a service delivery system because it results in a gross misallocation of public costs. It is not providing coverage at all to many workers most exposed to industrial injury and is not getting benefits to an important proportion of those entitled to them. At the same time, it is providing dependable but undisclosed profits to private insurance carriers.
Living without the Mental Hospitals
Authors: Hewett Sheila , Ryan Peter , Wing John 
Published: January 2009

ABSTRACTChanges in the administrative structure of the National Health Service and in policy concerning the role of the psychiatric hospitals in the delivery of mental health care mean that local authorities have a growing responsibility for providing a range of supportive services for people who formerly would have lived for long periods in mental hospitals. Sheltered living environments will be an essential part of these services but there is little systematic information regarding the kind of care required in terms of the needs of the adult mentally ill. A pilot study is reported of the non-hospital residential care experienced by mentally ill adults who were financially assisted by three South London boroughs. The findings are related to a wider study of new long-stay patients in mental hospitals, some of whom could be discharged if alternative services were available. The appropriateness of short-term rehabilitation hostels as opposed to long-term maintenance environments of various kinds is discussed. The study is now being extended to include other forms of care including group homes, sheltered housing schemes and a wider range of local authority hostels than was encountered at the pilot stage.