bluuebunny/crossref_metadata_2025 huggingface dataset:
Elementary Considerations relating to the Absolute
Authors: Sommerville Duncan M.Y.
Published: January 2009

Non-Euclidean geometry in the narrowest sense is that system of geometry which is usually associated with the names of Lobachevskij and Bolyai, and which arose from the substitution for Euclid's parallel-postulate of a postulate admitting an infinity of lines through a fixed point not intersecting a given line, the two limits between the intersectors and the non-intersectors being called the parallels to the given line through the fixed point. In a wider sense, any system of geometry which denies one or more of the fundamental assumptions upon which Euclid's system is based is a non-euclidean geometry. Of special interest are, however, those which touch only the question of parallel lines ; and there exists, in addition to Lobachevskij's geometry, another, commonly associated with the name of Riemann, in which the parallels to any line through a fixed point are imaginary. The three geometries, Lobachevskij's, Euclid's, and Riemann's, thus form a trio characterised by the existence of real, coincident, or imaginary pairs of parallels through a given point to a given line. With reference to this criterion, a consistent nomenclature was introduced by Klein, who called these three geometries respectively Hyperbolic, Parabolic, and Elliptic.
The Bolyai-Lobatschewsky Non-Euclidean Geometry: an Elementary Interpretation of this Geometry, and some Results which follow from this Interpretation
Authors: Carslaw H. S.
Published: January 2009

Much has been written in recent years on the foundations of geometry, chiefly in Germany and Italy, and the relations of the various Non-Euclidean geometries to the Euclidean system are now more generally known among mathematicians. But most of these writings involve a knowledge of more advanced mathematics, while it has been found difficult to represent even the simplest Non-Euclidean geometry—that of Bolyai-Lobatschewsky—in an elementary manner.
On Wilkinson's Method of treating the Nine-Points Circle, with Generalizations
Authors: Muirhead R. F.
Published: January 2009

Ever since I first became acquainted with Wilkinson's method of establishing the existence of the nine-points circle of a triangle (see Mackay's “Euclid,” Appendix to Bk. IV., Prop. 2, the lettering of which I have followed in the first three sections of this paper), its simple and fundamental character has pleased me. I propose to point out first that this method yields probably the most elementary proof of the concurrence of the perpendiculars from the vertices, and then, after restating the investigation of the nine-points circle, to sketch some generalizations.
Historical Note on Wallace's Line
Authors: Archibald R.C.
Published: January 2009

A friend, Professor Smith of Sackville, New Brunswick, has called my attention to the fact that the term “Wallace's Line,” as defined in the Century Dictionary, is employed by other scientists than mathematicians. In these days, when increasing attention is paid to the nomenclature of lines and curves, it may be of interest to add here a brief quotation from the dictionary: “Wallace's Line [so named after Alfred R. Wallace, who defined it] in Zoögeography, a line assumed to separate the Indomalayan from the Austromalyan Zoological region or faunal area. It passes between Borneo and Celebro, through the Strait of Macassar. Southward between Bali and Lombok, northeastward between Mindanao and Gilolo. This line divides the shallow waters of the Indomalayan region from the much deeper Austromalayan seas; and the character of the fauna is quite different on the two sides of it.”
On Certain Formulae connected with the Function (cosnα – cosnθ)/(cosα – cosθ)
Authors: Taylor D. G.
Published: January 2009

§ 1. This paper deals with certain formulae which, though probably not all new, have not appeared in the text-books. They were suggested to the writer while engaged in discussing the expression for the intensity of the transmitted beam in the Lummer Gehrcke Interference Spectroscope, viz.
Concurrency of lines joining vertices of a triangle to opposite vertices of triangles on its sides
Authors: Burgess A. G.
Published: January 2009

(1). Let ABC be the given triangle; A′BC, B′CA, C′BA triangles described externally on its sides, and let the angles of these triangles be A′BC=μ1, A′CB=v1, B′AC = λ2, B′CA = v2 C′AB = λ3, C′BA = μ3, (Fig. 1).
On a Difference Equation due to Stirling
Authors: Pairman Eleanor
Published: January 2009

In 1730 there was published Stirling's Methodus Differentialis, and in it (Prop. VIII., p. 44) he considers the Difference Equation

and shows that it is satisfied by an inverse factorial series
A Formula for the Solution of Algebraic or Transcendental Equations
Authors: Whittaker E. T.
Published: January 2009

Statement of the formula and numerical examples of it.

The object of the present note is to communicate the following formula for the solution of algebraic or transcendental equations:

The root of the equation
On Determinants whose elements are Determinants
Authors: Whittaker E. T.
Published: January 2009

The present paper is concerned with determinants whose elements are themselves determinants. The best-known determinants of this kind are those whose elements are minors of a given determinant; these are called the “adjugate” and the “compounds” of the given determinant. Determinants whose elements are themselves determinants also occur frequently in Muir's theory of Extensionals.

The determinants considered in the present paper are of a somewhat more general type than adjugates, compounds, and extensionals; the principal result obtained is “Theorem A” (at the end of § 2), which relates to determinants whose elements are formed from any number of arrays. It is shown in § 3 that many other formulae, both new and old, may be obtained by specialising the arrays in “Theorem A.”
Note on the Complete Jacobian Elliptic Integrals
Authors: Bowman F.
Published: January 2009

The complete elliptic integrals K and E are functions of their modulus k which satisfy the equations

respectively.
Determinantal Systems of Apolar Triads ia a Conic
Authors: Marr W. L.
Published: January 2009

The discovery of the configuration known as a Determinantal System of Points was made by Dr W. P. Milne while investigating the problem of the “Generation of a cubic curve by apolar pencils of lines.” In the Proc. L. M. S., Ser. 2, Vol. 15, Part 4, he obtained a complete solution, but in unsymmetrical form. He therefore suggested to me that as he was up to that time unable to find a symmetrical solution for the general cubic I should investigate Determinantal Systems for the case of rational curves. The results of my investigations are given in this and the ensuing paper, and have enabled Dr Milne to solve the general problem in symmetrical form in a paper which will appear in the Proc. L. M. S. at an early date. I commence from the result given in the paper by Dr Milne, entitled Determinantal Systems of Points, in the Proc. E. M. S., Vol XXXIV., Part 2.
Determinantal Systems of Apolar Triads in the Twisted Cubic
Authors: Marr W. L.
Published: January 2009

It has already been shown that nine points can be found on a conic to form six triads all apolar to a given triad (ABC), the hessian lines of these six triads and of ABC being concurrent.

The construction of the corresponding system in the twisted cubic is easy. In the first place, the poles of the six triads P1Q2R3, etc., will lie on the plane of the triad ABC to which they are all apolar. Secondly, the hessian lines of these triads, which in the conic were concurrent, will now be generating lines of a quadric circumscribing the twisted cubic. Now the pole of a triad is in the osculating plane at any of the points of the triad, hence the osculating plane at Pl will contain the poles of the triads P1Q2R3 and P1Q2R3
A Geometrical Proof of Professor Morley's Extension of Feuerbach's Theorem
Authors: Richmond Herbert W.
Published: January 2009

In the Proceedings of the National Academy of Sciences of the U.S.A., Vol. II. (1916), page 171, Professor F. Morley has established a theorem which both extends and simplifies the theorem of Feuerbach, viz., All curves of class three which (i) touch the six lines OP, OQ, OR, QR, RP, PQ joining four orthocentric points, O, P, Q, R, and (ii) pass through the circular points, also touch the common nine-points-circle of the triangles PQR, OQR, ORP, OPQ. Sixteen of these curves of class three break up into one of the four points aud a circle touching the sides of the triangle formed by the other three. Thus the sixteen instances of Feuerbach's theorem derivable from the four triangles are included as special cases, in Morley's theorem. A purely geometrical proof of the theorem may be worth consideration.
A Proof of the Binomial Theorem, with some Applications
Authors: Gibson
Published: January 2009

Many proofs of the Binomial Theorem have been given, and the proof which I give in this note has not the slightest claim to be considered new. My only object in giving it is to call attention to the fact that it depends merely on the rule of integration by parts, and provides a form of the remainder that in many applications is much simpler than any of the forms associated with Taylor's Theorem. Of its usefulness in this latter respect I give an example from the asymptotic expression for a Bessel function.
The Modified Bessel Function Kn(z)
Authors: MacRobert T. M.
Published: January 2009

Gray and Mathews, in their treatise on Bessel Functions, define the function Kn(z) to be

We shall denote this function by Vn(z). This definition only holds when z is real, and R(n)≧0. The asymptotic expansion of the function is also given; but the proof, which is said to be troublesome and not very satisfactory, is omitted. Basset (Proc. Camb. Phil. Soc., Vol. 6) gives a similar definition of the function.
Extension of Frenet's Formulae to a Curve in Flat Space of n Dimensions
Authors: Muirhead R. F.
Published: January 2009

A curve in n dimensions may be taken as the limit to which a polygonal figure ABCDE … tends, when the sides AB, BC, CD, etc., all diminish towards the limit zero.

The curvature at A is .
Note on the Polynomials which satisfy the Differential Equation
Authors: M'Arthur Neil
Published: January 2009

Laguerre has shown that if be expanded in ascending powers of t,

where fn(x) is a polynomial of degree n, satisfying the differential equation
On Direct and Inverse Interpolation by Divided Differences
Authors: Smeal Glenny
Published: January 2009

The general interpolation series, originated by Newton, has been studied mainly for its algebraic interest, only the special case of equidistant data being developed on the practical side. This is justified by the simplicity of this case, and by the numerous problems for which it suffices, but it may lead to undue simplification of data and to restrictions on experimental and computative methods. Thus tables of functions which are not in common use, or which are carried to many places, must often be limited to relatively few entries, and these might conceivably be not in arithmetical progression, with advantage both of easier tabulation and of more accurate interpolation. Data from experiment or statistics, again, are often fitted to a parabolic curve of arbitrarily chosen degree, and on rather inadequate grounds. The formation of a difference-table not only avoids the suppression of the original data, but supplies at a glance a useful analysis of them—indicating their consistency and regularity, showing with what accuracy a parabolic curve can represent them, and supplying its expression with minimum labour. For direct interpolation to new points Lagrange's formula, the usual alternative, fails in this respect and, when applied to unfamiliar data, is very apt to mislead. It is wasteful of labour and more liable to error, and cannot easily be extended to include fresh terms.
Multiply Perspective Polygons inscribed in a Plane Cubic Curve
Authors: Taylor D. G.
Published: January 2009

Prof. W. P. Milne has cited (Proc. Edin. Math. Soc., Vol. XXXI., p. 90) pairs of nonagons inscribed in a plane cubic curve, and in nonuple perspective. A part from this, and the familiar case of triangles, little attention appears to have been given to polygons in multiple perspective.
Some Extensions of Pincherle's Polynomials
Authors: Humbert Pierre
Published: January 2009

The polynomials which satisfy linear differential equations of the second order and of the hypergeometric type have been the object of extensive work, and very few properties of them remain now hidden; the student who seeks in that direction a subject for research is compelled to look, not after these functions themselves but after generalisations of them. Among these may be set in first place the polynomials connected with a differential equation of the third order and of the extended hypergeometric type, of which a general theory has been given by Goursat. The number of such polynomials of which properties have been studied in particular is rather small; in fact, Appell's polynomials

and Pincherle's polynomials, arising from the expansions

are, so far as I know, the only well-known ones. To show what can be done in these ways, I shall briefly give the definition and principal properties of some polynomials analogous to Pincherle's and of some allied functions.
Taylor's Theorem and Bernoulli's Theorem: A Historical Note
Authors: Gibson George A.
Published: January 2009

Brill and Noether in their Report, Die Entwicklung der Theorie der Algebraischen Functionen in äerer und nlteuerer Zeit, Abschnitt I., § 16, state in their remarks on Taylor's Theorem that “in its modern form the Theorem appears only as a Corollary (Prop. VII., Cor. II.) and is left without any application.”
On the Relation between Pincherle's Polynomials and the Hypergeometric Function
Authors: Baker Bevan B.
Published: January 2009

1. The Pincherle polynomials are defined as the coefficients in the expansion of {1 − 3 tx + t3}−½ in ascending powers of t. If the coefficient of tn be denoted by Pn(x), then the polynomials satisfy the difference equation

and Pn(x) satisfies the differential equation
Newton's Conception of a Limit as interpreted by Jurin and Robins respectively
Authors: Gibson George A.
Published: January 2009

In his recent book A History of the Conceptions of Limits and Fluxions in Great Britain from Neuton to Woodhouse (Chicago and London: The Open Court Publishing Company, 1919), as well as in a series of articles in the American Mathematical Monthly for 1915 on The History of Zeno's Arguments on Motion, Mr Cajori discusses certain aspects of the conception of a limit, and treats in considerable detail the controversy between Jurin and Robins that arose out of the publication of Berkeley's Analyst. I gave an account of the controversy in a paper that appears in Volume XVII. of our Proceedings, and as Mr Cajori's estimate of the respective merits of the contributions by Jurin and Robins differs greatly from mine, and as the conception of a limit is fundamental in modern mathematics I venture to draw the attention of the Society to the matter.
On Sylvester's Dialytic Method of Elimination
Authors: Whittaker E. T.
Published: January 2009

Consider any two algebraic equations, which for simplicity we shall take to be a cubic

whose roots are y1, y2, y3, and a quadratic

whose roots are x1, x2.
The Numerical Evaluation of Double Integrals
Authors: Aitken A. C. , Frewin G. L.
Published: January 2009

The present paper is concerned with formulae by which double integrals of functions of two independent variables may be evaluated approximately. The number of such formulae published hitherto is not great, and it has seemed desirable both to make a systematic search for new formulae, and to test the comparative merits of these, and of those previously known, by computing the numerical values of certain selected integrals.
The Linear Complexes belonging to the Invariant System of Three Quadrics
Authors: Williamson J.
Published: January 2009

In the Proceedings of the London Mathematical Society, Ser. 2, Vol. 20 (1921), pp. 465–489, Professor H. W. Turnbull has studied the projective invariant theory of three quadrics. The following paper is based on this work and develops one definite section of the theory. From the geometrical point of view the linear complex is now seen to be fundamental in the study of three arbitrary quadrics; particularly when their (2, 2, 2) invariant φ123 vanishes.
Geometrical Interpretation of a few concomitants of the cubic in the Argand Plane
Authors: Saddler W.
Published: January 2009

be the binary cubic whose coefficients a1, are complex numbers represented on the Argand Plane. Then if its roots are z1, z2, z3, the three corresponding points form the vertices of a triangle A1 A2 A3. Let this triad of points be said to represent the cubic. Then its Hessian

is represented by a certain pair of other points; likewise every first polar

associates a definite pair of points (z) with any given point (y).
Note on the Geometry of two Binary quadratics in the complex plane
Authors: Saddler W.
Published: January 2009

If

represent the points A, B and C, D respectively and if

then A, B, C, D are four harmonic points on a circle. If 0 is the mid point of AB then OA2 = OC. OD and ∠COB = ∠DOB.
A Proof of the Addition Theorem for the Legendre Functions
Authors: MacRobert T. M.
Published: January 2009

A Theorem of Dougall's. In Vol. XVIII. (p. 78) of these Proceedings Dr Dougall has established the theorem that, if m is a positive integer,
An Extension of Heaviside's Operational Method of Solving Differential Equations
Authors: Baker Bevan B.
Published: January 2009

An elegant symbolic method of solving differential equations was developed by Heaviside in his “Electrical Papers” and “Electromagnetic Theory,” chiefly in connexion with problems concerning electric currents in net-works of wires. Attention has recently been called to the method by Bromwich, who applied it to a wider range of problems and gave an extension of Heaviside's formula; another generalisation of the formula has been obtained by Carson.

In the present paper a formula is obtained which contains the formulae of Heaviside, Bromwich and Carson as particular cases, and whose form is such that it may be readily applied to physical problems.
On Self-Adjoint Partial Differential Equations of the Second Order
Authors: Copson E. T.
Published: January 2009

Let be a linear differential expression involving n independent variables xi the coefficients AikBi, and C being functions of the independent variables but not involving the dependent variable u. Associated with F(u) is the adjoint expression
Particular Solutions of the Equation of Conduction of Heat in One Dimension
Authors: Gray Marion C.
Published: January 2009

The problem of the conduction of heat in one dimension is usually concerned with the propagation of a thermal disturbance along a bar or rod of uniform cross section. The solution of the problem is required for a given initial distribution of temperature, and given boundary values, usually at each end of the rod. In most cases this solution is found by assuming a series solution and then proving that the series satisfies the equation of the disturbance well as all the assigned conditions. Other methods, for example the contour integral method developed by Carslaw, also introduce this arbitrary element of choice in choosing the integrand and the contour of integration. The object of the present paper is to develop the application of Heaviside's Operational method to the solution of the problem, and to show that it leads in all cases to solutions equivalent to the known forms, although initially no assumptions are made regarding the nature of the solution.
On the Relation between Inverse Factorial Series and Binomial Coefficient Series
Authors: Ferrar W. L.
Published: January 2009

The chief aim of this note is to investigate directly the relation between the inverse factorial series

and the binomial coefficient series, or Newton's interpolation formula,

which may also represent Ω(x), the sum of the series (1).
The Differentiation of an Indefinite Integral
Authors: Whittaker J. M.
Published: January 2009

Theorem 1 needs very little explanation. It is the converse of the well known theorem that the indefinite integral F(x) of a function f(x) possesses a derivate on the right at every point at which f(x + 0) exists. If f(x + 0) does not exist, nothing can be said as to the existence or otherwise of F+(x); but in a general way we might expect that the integral of a function which oscillates comparatively slowly, say sin (log x) at x = 0, would be more likely to possess a derivate than that of a function which oscillates more rapidly, say . It appears from Theorem 1 that this is not by any means the case. In fact the integral of sin (log x) has not a definite derivate at x = 0 while that of has such a derivate.
The Triangle and its Six Scribed Circles
Authors: Mackay John Sturgeon
Published: January 2009

When the Edinburgh Mathematical Society was founded, it was deemed impracticable, from the expense that would be involved, to print the papers read at its meetings. It was, however, resolved that copies of them should be deposited with the Secretary, and that these copies should as far as possible be made accessible to the members of the Society. Want of leisure during the first session prevented me from doing my part in carrying out this intention of the Society, and committing to writing the paper which was delivered at the second meeting. During its second session, the Society resolved to print its proceedings in whole or in abstract; and a beginning was made with the second volume, the first being left over for future consideration, as the cost of printing absorbed nearly the entire income of the Society.
The Shoemaker's Knife
Authors: Mackay J. S.
Published: January 2009

Some of the properties of the figure which, on account of its shape, the Greeks named the Shoemaker's Knife (ἄρβηλοσ) are given in the Lemmas attributed to Archimedes; others occur in the fourth book of Pappus's Mathematical Collection. The Lemmas (which are not extant in Greek, but have been translated from the Arabic) are generally considered to be spurious; it is, however, regarded as possible, if not probable, that the theorems among them relating to the Arbelos may be due to Archimedes. Whether they are or not, the figure and the principal proposition respecting it which Pappus gives are said by him to be “ancient.” It may be added that the Arbelos does not seem to have attracted much notice from geometers, few of them having treated of it, and fewer still having added to the properties known to the ancients. (See Steiner's Gesammelte Werke, Vol. I., pp. 47–76, and The Lady's and Gentleman's Diary for 1842 and 1845).
Failing Cases of Fourier's Double-Integral Theorem
Authors: Alexander Peter
Published: January 2009

Fourier's Theorem, as usually stated, is

Most writers give this without limitation, but De Morgan (Diff. and Int. Calc. pp. 618 &c.) directs attention to what he calls the apparent neglect by previous writers of the limitation of the theorem to functions which satisfy the condition
Note on a Function of two Integral Arguments
Authors: Muir Thomas
Published: January 2009

In the part just issued of the American Journal of Mathematics (vii, pp. 3, 4) Proffessor Cayley has occasion to deal with the function

where stands for i (i – 1)…(i – j + 1). He Points out that

expresses {i, 1}, {i, 2},…{i, 5} each in descending powers of i, and tabulates the function from {1, 1} to {5, 5}.
Note on the equation connecting the mutual distances of four points in a plane
Authors: Muir Thomas
Published: January 2009

If the distances (12), (13), (14), (23), (24), (34) between four points 1, 2, 3, 4 on the circumference of a circle be denoted by a, b, c, d, e, f respectively, then a certain relation (A) is known to connect a, b, c, d, e, f. The same four points, however, being points in a plane, there subsists between their mutual distances another relation (B). Now, it occurs to one that from these two relations some deduction ought to be possible regarding the mutual distances of four points on a circumference, and the problem is suggested of making the said deduction.
Note on a Plane Strain
Authors: Tait
Published: January 2009

The object of this note is to point out, by a few remarks on a single case, how well worth the attention of younger mathematicians is the full study of certain problems, suggested by physics, but limited (so far as that science is concerned) by properties of matter.
Gilbert's Method of Treating Tangents to Confocal Conicoids
Authors: Gibson George A.
Published: January 2009

The method of treating tangents to confocal conicoids, of which I propose to give an account, is discussed in the number for December 1867 of the Nouvelles Annales de Mathématiques. The writer of the paper referred to is M. Ph. Gilbert, Professor at the University of Louvain. The results arrived at are in nearly every case already well known, but the method of reaching them is somewhat novel, and I have thought that it might interest the members of this society if I were to give a statement of the chief methods and results of Gilbert's paper. In one or two cases I have altered the proofs, and I have added two or three propositions that seemed to follow naturally from the equations dealt with. Gilbert deals only with central conicoids; but I have put in an equation for the paraboloids that corresponds to Gilbert's fundamental one.
Note on the evaluation of functions of the form 0°
Authors: Sprague T. B.
Published: January 2009

Let f(t), ø(t), be two functions of t, such that they both vanish with t, that is, f(0) = 0, ø(0) = 0; and put
Historical Note on the so-called Simson line
Authors: Muir Thomas
Published: January 2009

The theorem that the feet of the perpendiculars drawn to the sides of a triangle from any point in the circumference of the circumscribing circle are collinear is ascribed (Gerg. Ann. iv., p. 250, ca. 1814) by Servois, though not with confident knowledge, to Simson. Baltzer, who gives us this information, refers also to Gerg. Ann. xiv., p. 28, p. 280, and to Poncelet. Fuller details, showing how the question of authority has hitherto stood, will be found in an extract from a letter of Mr Mackay's in Nature, xxx., p. 635. Mr Mackay has further stated that he has not found the property mentioned in any of Simson's published works.
Notes on the method of Orthogonal Projection
Authors: Dallas Robert J.
Published: January 2009

This paper is designed to call attention to certain extensions of this method, which do not seem to be generally recognised. Most writers consider the ellipse alone as amenable to orthogonal projection, whereas all the conic sections are so.

With the hyperbola we may use this method in three ways—

(1) By projecting a given diameter in the figure to be a transverse axis of the projected figure, when the result will follow by symmetry.

(2) By projecting the hyperbola into a rectangular one.

(3) By an imaginary orthogonal projection from the circle.
On a number of concurrent spheres
Authors: Allardice R. E.
Published: January 2009

This paper included an analytical proof of the following theorem:

If five spheres 1, 2, 3, 4, 5, pass through the same point, and if the four points in which the four spheres 1, 2, 3, 4, intersect in sets of three be coplanar; and if the same be true for the sets 1, 2, 3, 5; 1, 2, 4, 5; 1, 3, 4, 5; it will also be true for the remaining set 2, 3, 4, 5.

The same theorem is true for similar and similarly situated quadric surfaces.
On the Continued Fractions associated with the Hypergeometric Equation
Authors: Ince E. Lindsay
Published: January 2009

The present paper is based on a method attributed to Euler of expressing as a continued fraction the logarithmic derivate of a solu tion of a linear differential equation of the second order. The method is particularly applicable to equations of hypergeometric type, and, in that connection, was previously employed by the present author as a means of adding to the number of known transformations of continued fractions.
Triassic rift-related meta-granites in the Internal Hellenides, Greece
Authors: HIMMERKUS F. , REISCHMANN T. , KOSTOPOULOS D.
Published: January 2009

The Serbo-Macedonian Massif is a basement complex in the Internal Hellenides of northern Greece, situated between the Vardar Zone to the west and the Rhodope Massif to the east. The Serbo-Macedonian Massif comprises several distinct basement units interpreted as terranes, the largest of which is the Gondwana-derived Vertiskos Terrane in the northwestern and central parts of the massif. A series of leucocratic meta-granites intrude the Silurian orthogneiss basement of the Vertiskos Terrane. No similar granites are found in any of the other units of the Internal Hellenides. The meta-granites have a pronounced crustal within-plate signature which is visible in lithology, major- and trace-element geochemistry and the Sr isotopic compositions. These intrusions were dated using the Pb–Pb single-zircon evaporation method, and yielded a Triassic age of between 240.7 ± 2.6 Ma and 221.7 ± 1.9 Ma on 17 samples, with a mean age of 228.3 ± 5.6 Ma. The zircons are purely magmatic, indicating that ages are primary crystallization ages. A Rb–Sr errorchron of the whole-rock samples of the Arnea granite yielded an age of 231.6 ± 9.9 Ma (MSWD = 82), and a mean 87Sr/86Sr initial ratio is 0.7142, indicating a crust-dominated source, and suggesting an A-type origin for the granites. The A-type meta-granites together with mafic intrusive bodies (amphibolites) in the Vertiskos Terrane may be evidence of Triassic rifting that led to the formation of a branch of Neotethys (Vardar–Meliata Ocean). Similar rock associations are also exposed in the Cyclades, and in massifs of the wider eastern Mediterranean realm related to the Gondwana-derived Hun Terrane, indicating that the Arnea-type granites are representatives of a major regional rifting event in Triassic times.
Sheep handling and welfare standards in livestock markets in the UK
Authors: GREGORY N. G. , BENSON T. , SMITH N. , MASON C. W.
Published: January 2009

Some meat retailers have introduced a trade embargo on fat lambs sold through livestock markets on the grounds that welfare standards associated with live auction markets are said to be worse than standards associated with direct sale to abattoirs. The current study examined the handling difficulties and welfare standards at 24 UK livestock markets. Comparisons were made according to class of animal (store, fat, breeding animals, etc.) and throughput of the market: <100 livestock units (LU) per week, 100–300 LU per week and >300 LU per week. Handling problems examined included refusal to move, balking, slips, falls, impacts, isolation leading to apparent distress, confusion while loading onto vehicles and inappropriate handling such as wool pulling. The overall prevalence of each handling problem was low (usually <0·05 of the sheep). The most common difficulties were impacts, slips and falls when grading fat lambs, and confusion or refusal to load onto the vehicles after the sale in ewes. Store lambs were generally easier to handle than fat lambs. They were less prone to refusing to move, balking, impacts, slips and falls. In fat lambs, slips and falls during grading were more common at small markets, while at larger markets there were more impacts, slips and falls during selling. Confusion during loading onto vehicles after the sale was more common in breeding ewes and rams, and at small markets. Projections in the corridors that were considered to be potential bruising or impact points were found in 0·33 of the markets and 0·71 did not have a way of ensuring that legs could not get trapped between gates and gateposts if sheep attempted to jump out of a holding pen. In most other respects the prevalence of problems with the facilities and during handling was low and it was concluded that a trade embargo on selling fat lambs in markets might not be justified.
Analysis of plankton in the southern Great Barrier Reef: abundance and roles in throphodynamics
Authors: Sorokin Yu. I. , Sorokin P. Yu.
Published: January 2009

Wet biomass of principal plankton components and whole plankton standing stock were assessed in waters of the Heron Island ring reef and surrounding deep lagoon. Biomass of phytoplankton ranged between 30 to 120 mg m−3, without its pronounced depletion over the reef shallows. Picocyanobacteria and prochlorophyte algae contributed over 70% of this biomass. Biomass of bacterioplankton varied between 75 to 340 mg m−3, with its maximum over the reef flat. Biomass of planktonic protozoa's ciliates and zooflagellates ranged between 20 to 110 mg m−3. The daytime biomass of zooplankton varied between 490 to 1590 mg m−3in the deep lagoon in the zone of intense tidal currents. Over the reef shallows, it was 10–20 mg m−3. At night, it rose there up to 800 to 4000 mg m−3as the result of emerging demersal zooplankton from the benthic substrates. The time scale of nocturnal emerging by different taxa was also documented. Biomass of whole demersal zooplankton communities hiding by the daytime in bottom substrates at the reef flat was found to be over 100 g m−2. Problems of nutrition planktivore reef fauna related to the plankton production and abundance are discussed.
Seasonal variations in the phytoplankton community in the north-eastern Sea of Marmara and a species list
Authors: Deniz Niyazi , Taş Seyfettin
Published: January 2009

This paper describes phytoplankton abundance data collected in the Sea of Marmara in 2000 and identifies new species to the region. The quantitative sampling was carried out monthly at 3 stations and seasonally at 6 stations at depths of 0.5, 5, 10 and 20 m. Additionally, vertical samplings by plankton net from 15–0 m were carried out in order to determine the species diversity. Simultaneously measured physical (salinity, temperature and Secchi disc) and chemical parameters (dissolved oxygen, nitrate + nitrite, chlorophyll-a, phosphate and silicate) were evaluated together with phytoplankton data. One hundred and fifteen species were recorded which are members of 55 dinoflagellates, 42 diatoms, 11 silicoflagellates and 7 other groups. Those species include toxic species with high reproduction rates and species that are accepted as carrying risk. Blooms ofAnabaenasp.,Nitzschia longissima(Brébisson in Kützing) Ralfs in Pritchard andProrocentrum triestinumSchiller species were observed during the study.Dictyocha antarcticaLohmann 1919,Dictyocha cruxEhrenberg 1840 andNitzschia rectilongaTakano 1983 species were recorded for the first time from the coastal waters of Turkey. The maximum phytoplankton abundance has been observed during the winter and autumn seasons in the 0.5 and 5 m depths; the concentration of the diatoms was higher during late winter and autumn, however, the concentration of the dinoflagellates was always high during the whole year and they did not show a seasonal variation. The phytoplankton density was lower at the 20 m depths because of the low light penetration property of the Sea of Marmara.
Using morphological and molecular tools to identify megalopae larvae collected in the field: the case of sympatric Cancer crabs
Authors: Pardo Luis Miguel , Ampuero David , Véliz David
Published: January 2009

Studies of recruitment dynamics in meroplanktonic organisms are dependent on the correct identification of each ontogenic stage of each species. This is particularly difficult when studying the larval stages, which are not easy to identify due to their lack of resemblance to conspecific adults and their high degree of similarity with congenerics at the same stage of development. This is the case with the crustacean megalopae of the genus Cancer along the coast of the south-eastern Pacific. This fact represents a serious limitation on ecological studies of populations of these species which constitute a heavily exploited local resource. In this study we describe in detail field collected megalopae larvae of three sympatric crab species of the genus Cancer(C. edwardsii, C. setosus and C. coronatus). As a result of this analysis we were able to identify easily visible diagnostic characters which allow the species to be distinguished from one another. The megalopae were easily distinguished by the form of the cheliped and the presence of spines on these. Cancer edwardsii has an elongated globulose cheliped, whereas C. coronatus has a subquadrate one. Both species possess a prominent ischial spine, which is absent in C. setosus. We corroborated the utility of these diagnostic characters by comparing the COI gene sequences of mitochondrial DNA of larvae identified by morphology with sequences taken from samples of the adults of all species of Cancer found in the region. We discuss the morphological variations between larvae found across the region (i.e. at sites separated by more than 800 km) and between megalopae obtained from the field versus those cultivated in the laboratory. We conclude that the simultaneous use of morphological and molecular tools for identification of decapod larvae appears useful for the study of cryptic species.
MHC class II expression in skin biopsies from the franciscana dolphin Pontoporia blainvillei and the southern right whale Eubalaena australis
Authors: Heinzelmann Larissa , Tavares Maurício , Ott Paulo H. , Moreno Ignacio M.B. , Chies José Artur B.
Published: January 2009

Presently, there is no information about the functionality of the immune system in the franciscana dolphin (Pontoporia blainvillei), a small dolphin from southern Brazil. As in the case of the franciscana, the population of southern right whale (Eubalaena australis) which inhabits Brazilian waters has not yet been surveyed in what concerns MHC expression. For the first time it was possible to observe the DQB gene expression in skin of these two species of cetacean using RT-PCR. Skin pieces of the animals were collected to RNA extraction. The fragment corresponding to DQB exon 2 was amplified, cloned and sequenced. A total of five alleles were found, one to franciscana and four to southern right whale. The observed dN/dS ratio of 2.77 (P = 0.03) suggests that this gene is under balancing selection pressure (positive Darwinian selection). The sequences indicate that, in both species analysed, the DQB gene is functional.
Take-up and the Social Fund
Authors: Huby Meg , Whyley Claire
Published: January 2009

Non-application to the social fund can lead to a reduction in the resources available to some of the most vulnerable members of society. This article shows how traditional models of take-up are inadequate for examining why payments from the discretionary cash-limited social fund do not always reach the people for whom the benefit was designed. Nevertheless, it is crucial to examine why non-application to the social fund denies many people even a chance of meeting their needs. A new model of take-up is proposed that widens the debate beyond the level of claimant behaviour, allowing non-application to the social fund to be looked at as a variant of non-take-up. It provides a framework for examining the influence of structural and administrative factors on social fund application rates and highlights the extent to which policy makers and legislators play a part in non-application.
Reforming Aged Care in Australia: Change and Consequence
Authors: Gibson Diane
Published: January 2009

For the last ten years, the Australian system of services for frail elderly people has been undergoing significant reforms. Prior to that time, a series of government reviews and inquiries had repeatedly identified the same problems, including the dominance of institutional care, the inadequate supply of home and community based services, the lack of co-ordination, the inefficiency, and the unequal distribution of services by geographical area. Changes since the implementation of the Aged Care Reform Strategy in 1985 have been considerable, particularly with regard to the residential care sector. This article is concerned with the policy responses which emerged under the Strategy, and their impact on aged care service delivery in Australia.
Educational research and education policy
Authors: Glennerster Howard , Hoyle Eric
Published: January 2009

Education is absorbing an increasing share of the nation's resources. The body of research on the subject is vast. Yet its impact on policy has been diffuse and difficult to assess. Studies directly focused on policy issues are rare. The primary aim of this paper is to suggest some areas where research is needed in view of emerging policy considerations. To put such a discussion in its context we begin by briefly examining the extent to which research has had an impact on education policy. We use ‘policy’ here to mean political and administrative decision-making. We conclude with some remarks on the funding and initiation of educational research.
National Insurance Local Tribunals
Authors: Bell Kathleen , Collison Peter , Turner Stephen , Webber Susan
Published: January 2009

Tribunals are at the centre of a growing controversy concerning citizen rights in welfare. In the first of two articles, attention is drawn to some of the salient features of this controversy and particularly to those aspects concerning national insurance local tribunals (NILTs). A special analysis of D.H.S.S. records is presented giving a picture of the distribution of the work of NILTs over different benefit categories, of success rates, of the extent of attendance by appellants and of representation. Generally the analysis suggests that NILTs are more varions and less confined by law and regulation than is often assumed. Findings from surveys of chairmen, members and appellants are also presented. Men constitute the great majority of those concerned with NILTs and there are some striking contrasts between varions groups in age and education. People who serve NILTs are shown to be active in a wide range of community activities and particularly in professional organizations, trade unions and local politics.
Budget Allocation in the National Health Service
Authors: Maynard Alan , Ludbrook Anne
Published: January 2009

The objective of this article is to analyse the way in which budget allocation decisions have been made in the National Health Service (NHS) of Britain. Despite the criticisms of the pre-1948 health care system on the grounds of geographical inequity, it was not until nearly twenty-five years after the service's inception that explicit allocation formulae were devised and implemented in an attempt to achieve equity, defined as equal financial resources for health care for those in equal need.

The article is divided into four sections; the first analyses briefly the establishment of the NHS in 1948 and the failure of policy-makers to rectify the significant inequalities in the distribution of health care inputs between the regions. The second section is concerned with the official recognition of the policy problem of geographical inequality in resources and the first attempt to rectify it. In the third section the most recent set of resource allocation formulae for England, Scotland and Wales will be analysed and compared. The final section offers some brief conclusions.
Unemployment, Housing and Household Structure Among Young Adults
Authors: Murphy M. , Sullivan O.
Published: January 2009

Differentials in unemployment among young adult males are shown to be particularly associated with two factors: housing tenure and early childbearing. Even after controlling for factors such as social class and area of residence, local authority tenants have unemployment rates two or three times as high as owner-occupiers of a similar age. For movers between tenures these differentials are even greater; movers from owner-occupation to local authority tenancy have four times the unemployment rate of those moving in the opposite direction. Large differentials by the family situation of young people are also found, with childless married couples having particularly low unemployment rates. These two aspects are connected by the effect of childbearing filtering couples into different tenures. Finally, the implications for increased social polarization between the two major tenures, and the likely effect on future tenure levels, are discussed.
Workforce Restructuring, Social Insurance Coverage and the Black Economy
Authors: Hakim Catherine
Published: January 2009

The national insurance system of contributory work-related benefits was designed for a ‘core’ workforce in continuous full-time employment. It provides incomplete coverage for the rising numbers of people in the peripheral workforce: part-time jobs, temporary work and self-employment. National estimates are presented for workers whose earnings are below the national insurance threshold, and who are thus excluded from social security benefits such as unemployment, sickness and retirement benefits—roughly 2 million in the period 1985–87. It is estimated that another million workers at least are within the NI net, but outside the income tax net. In addition, there are up to 2 million non-working people who have trivial earnings that leave them outside the NI and tax nets. Homeworkers are found in both these groups. The paper discusses the implications of these findings for claims about the size of the black economy and the characteristics of people participating in the black economy, and for the future development of the social insurance system.
Coping With Change in the NHS: A Frontline District's Response to AIDS
Authors: Ferlie Ewan , Pettigrew Andrew
Published: January 2009

The core of this paper is a case study of how a District Health Authority (Paddington and North Kensington, now Parkside DHA following a recent merger with Brent DHA) in Inner London responded to a major new health care issue of the 1980s—Aids, but the paper also seeks to locate this case study material within wider debates. What theories are there of organisational change which could be used to illuminate policy and service change in the health care sector? How, indeed, do we best study change in health care organisations? The paper is thus in three parts. In the first section we identify some streams of literature which act as a frame of reference defining our initial research question and discuss implications for methodology. The second section presents the case itself, while the last section discusses some emerging findings.
Service Delivery By a Trade Union—Does It Pay?
Authors: Yanay Uri
Published: January 2009

A changing socio-economic environment and competition have led trade unions to extend their role and become service providers. This paper examines some of the issues of service delivery which arise. Four central implications are discussed: the trade union's need (1) to adapt to the competitive service provider's market, (2) to enlarge its consumer body, (3) to become an employer of workers, and (4) to expand its interests with business establishments and authorities over non-union matters. The paper focuses on the General Federation of Labour in Israel (the Histadrut), and its comprehensive health insurance scheme (Kupat Holim). The scheme is provided to all union members and their families as part of union membership. Nonetheless, alternative service systems seem sufficiently attractive for many union members to consider ‘deserting’ their union. The union depends on its members—consumers—to secure its broad base, universalistic image, source of income and legitimacy. Trying to attract consumers causes the union to bend some of its principles. Ultimately, service provision forces the union to adopt characteristics alien to, and even contradicting, its traditional, militant role as an organiser of labour.