bluuebunny/crossref_metadata_2025 huggingface dataset:
Body Weight Has Limited Influence on the Safety, Tolerability, Pharmacokinetics, or Pharmacodynamics of Rivaroxaban (BAY 59‐7939) in Healthy Subjects
Authors: Kubitza Dagmar , Becka Michael , Zuehlsdorf Michael , Mueck Wolfgang
Published: January 2007

Anticoagulants are often dose adjusted, or their use restricted, in patients with extremes of body weight. Rivaroxaban (BAY 59‐7939) is a novel, oral, direct factor Xa inhibitor in clinical development. This was a randomized, single‐blind, placebo‐controlled, parallel‐group study in healthy male and female subjects to assess the effect of extreme body weight (≤50 kg and >120 kg), and gender, on the safety, tolerability, pharmacokinetics, and pharmacodynamics of rivaroxaban 10 mg, compared with subjects of normal weight (70–80 kg). Rivaroxaban was well tolerated. Cmax of rivaroxaban was unaffected in subjects >120 kg but was increased by 24% in subjects weighing ≤5 0 kg, resulting in a small (15%) increase in prolongation of prothrombin time, which was not considered clinically relevant. The area under the curve was unaffected by body weight or gender. No other clinically relevant differences were observed, suggesting that rivaroxaban is unlikely to require dose adjustment for body weight or gender.
Pharmacokinetics of Maribavir, a Novel Oral Anticytomegalovirus Agent, in Subjects With Varying Degrees of Renal Impairment
Authors: Swan Suzanne K. , Smith William B. , Marbury Thomas C. , Schumacher Mary , Dougherty Carolyn , Mico Bruce A. , Villano Stephen A.
Published: January 2007

The effect of renal function on the pharmacokinetics of maribavir, a novel anticytomegalovirus agent, was evaluated in 12 adults with normal renal function (creatinine clearance [CrCl] >80 mL/min) and 19 adults with renal impairment classified as mild (n = 5), moderate (n = 5), or severe (n = 9), as measured by CrCl 50–80, 30–49, and <30 mL/min, respectively. After a single oral dose of maribavir 400 mg, the pharmacokinetics of maribavir, based on total and unbound plasma concentrations, showed no statistically significant difference between subjects with normal renal function and subjects with mild/moderate or severe renal impairment. Renal impairment was associated with an increase in area under the plasma concentration‐time curve (AUC) values for an inactive metabolite of maribavir, VP 44469. Results were consistent with those of previous studies, which showed that very little maribavir was excreted unchanged in urine, whereas about 22% of an oral dose of maribavir is recovered in urine as VP 44469.
An expression signature of syndecan-1 (CD138), E-cadherin and c-met is associated with factors of angiogenesis and lymphangiogenesis in ductal breast carcinoma in situ
Authors: Götte Martin , Kersting Christian , Radke Isabel , Kiesel Ludwig , Wülfing Pia
Published: January 2007

Introduction

Heparan sulphate proteoglycan syndecan-1 modulates cell proliferation, adhesion, migration and angiogenesis. It is a coreceptor for the hepatocyte growth factor receptor c-met, and its coexpression with E-cadherin is synchronously regulated during epithelial-mesenchymal transition. In breast cancer, changes in the expression of syndecan-1, E-cadherin and c-met correlate with poor prognosis. In this study we evaluated whether coexpression of these functionally linked prognostic markers constitutes an expression signature in ductal carcinoma in situ (DCIS) of the breast that may promote cell proliferation and (lymph)angiogenesis.

Methods

Expression of syndecan-1, E-cadherin and c-met was detected immunohistochemically using a tissue microarray in tumour specimens from 200 DCIS patients. Results were correlated with the expression patterns of angiogenic and lymphangiogenic markers. Coexpression of the three prognostic markers was evaluated in human breast cancer cells by confocal immunofluorescence microscopy and RT-PCR.

Results

Coexpression and membrane colocalization of the three markers was confirmed in MCF-7 cells. E-cadherin expression decreased, and c-met expression increased progressively in more aggressive cell lines. Tissue microarray analysis revealed strong positive staining of tumour cells for syndecan-1 in 72%, E-cadherin in 67.8% and c-met in 48.6% of DCIS. E-cadherin expression was significantly associated with c-met and syndecan-1. Expression of c-met and syndecan-1 was significantly more frequent in the subgroup of patients with pure DCIS than in those with DCIS and a coexisting invasive carcinoma. Levels of c-met and syndecan-1 expression were associated with HER2 expression. Expression of c-met significantly correlated with expression of endothelin A and B receptors, vascular endothelial growth factor (VEGF)-A and fibroblast growth factor receptor-1, whereas E-cadherin expression correlated significantly with endothelin A receptor, VEGF-A and VEGF-C staining.

Conclusion

Syndecan-1, E-cadherin and c-met constitute a marker signature associated with angiogenic and lymphangiogenic factors in DCIS. This coexpression may reflect a state of parallel activation of different signal transduction pathways, promoting tumour cell proliferation and angiogenesis. Our findings have implications for future therapeutic approaches in terms of a multiple target approach, which may be useful early in breast cancer progression.
Emergency Presentation of Abdominal Hernias: Outcome and Reasons for Delay in Treatment – A Prospective Study
Authors: Davies Mark , Chris Davies , Gareth Morris-Stiff , Ken Shute
Published: January 2007

INTRODUCTION

Emergency hernia surgery is associated with a higher postoperative complication and a less favourable outcome. The aim of this study was to audit emergency presentations of abdominal hernias prospectively in order to identify delays in patient treatment.

PATIENTS AND METHODS

Prospective audit was carried out between January and September 2003 of all patients presenting acutely with symptomatic hernias. In total, 55 patients presented, 39 of whom needed surgical intervention. The emergency repairs were compared with a cohort of elective repairs performed in the trust at the same time.

RESULTS

The median age was 77 years (range, 5–92 years; 35 male, 20 female). The distribution of the hernias, requiring surgery, was inguinal (19), para-umbilical (10), incisional (5) and femoral (5). The overall complication rate was 46.2% and the in-patient stay was 4 days (range, 1–49 days). Six patients required small bowel resection. Conservative management was identified as a key contributing factor in the delay of treatment. There was a significant increase in the in-patient stay, the early complication rate and the small bowel resection rate in the emergency repairs.

DISCUSSION

Patients with a symptomatic hernia should be offered elective, surgical repair. Non-operative management is inappropriate for the vast majority of cases, especially when many repairs may be performed with local anaesthetic infiltration. Clinicians should be aware of the high morbidity associated with the emergency repair of abdominal hernias in the elderly.
Symmetry reduction and cation ordering in alum solid solutions
Authors: Shtukenberg Alexander G. , Euler Harald , Kirfel Armin
Published: January 2007

Kinetic ordering of cations in solid solutions of alums showing anomalous birefringence was studied by means of single crystal X-ray diffraction. The crystal structures of two samples of K(Al0.6Cr0.4)(SO4)2 · 12 H2O and (K0.45(NH4)0.55)Al(SO4)2 · 12 H2O, respectively, taken from {111} growth sectors were refined in the ideal space group Pa-3 and in two of its subgroups – trigonal R-3 and triclinic P-1 with R1 = 0.028 – 0.032. The final choice of trigonal symmetry is based on the analysis of the diffraction patterns and of the cation distributions over the crystallographic sites. The correctness of the crystal structure refinements is supported by the disappearance of both ordering and birefringence upon crystal annealing. Also, an optically isotropic sample of (Rb0.3(NH4)0.7)Al(SO4)2 · 12 H2O (growth sector {111}) exhibiting random cation distribution is found to have cubic symmetry (space group Pa-3, R1 = 0.027).
Two N-[(3′-4-aryl)prop-2′-ynyl]-N,N′-1,2-phenylenedi-p-tosylamides: synthesis, spectroscopic and X-ray structural studies
Authors: Chowdhury Krishna , Mukherjee Monika , Mukhopadhyay Rupa , Helliwell Madeleine , Mukherjee Alok Kumar
Published: January 2007

Two N-substituted phenylene diamines, C30H28N2S2O4 (I) and C30H28N2S2O5 (II), have been synthesized, and characterized by spectroscopic and single crystal X-ray analyses. Intermolecular N—H···O and C—H···O hydrogen bonds link the molecules of (I) into centrosymmetric dimers, which are further joined by C—H···O hydrogen bonds to form one-dimensional polymeric chain propagating along the [100] direction. The two molecules, A and B, in the asymmetric unit of (II) are connected by a pair of N—H···O hydrogen bonds forming a characteristic R
2
2(14) dimeric ring centered at (0.245, 0.510, 0.252). The interlinking of adjacent dimers in (II) via C—H···O hydrogen bonds generates infinite one-dimensional ABBAAB… polymeric chain along the [101] direction.
Immunogenicity and contraceptive potential of three infertility-relevant zona pellucida 2 epitopes in the marsupial brushtail possum (Trichosurus vulpecula)
Authors: Duckworth Janine A , Wilson Kathryn , Cui Xianlan , Molinia Frank C , Cowan Phil E
Published: January 2007

In a previous study, three infertility-relevant epitopes of possum ZP2 (Pep12 (amino acids 111–125), Pep31 (amino acids 301–315), and Pep44 (amino acids 431–445)) were identified using sera from possums (Trichosurus vulpecula) immunized with recombinant possum zona pellucida 2 (ZP2) constructs, and a synthetic peptide library of possum ZP2 protein. In this study, the three peptides were conjugated to keyhole limpet hemocyanin and 300 μg of each conjugated peptide were administered subcutaneously to female possums (n = 20 per peptide) in complete Freund’s adjuvant. Immunogen doses were repeated 3 and 6 weeks later using incomplete Freund’s adjuvant. Control animals were immunized with either phosphate-buffered saline only (n = 10) or 300 μg keyhole limpet hemocyanin (n = 10), administered with the same adjuvants. Serum antibodies from animals immunized against these three epitopes bound to the corresponding possum ZP2 peptides, recombinant possum ZP2 protein constructs, and native zona. Possum fertility was assessed following superovulation and artificial insemination. Peptides Pep12 and Pep31 had no significant effects on fertility parameters (P > 0.05). However, animals immunized with Pep44 had lower egg fertilization rates (immunized 19.5% versus control 60.5%, P < 0.05) and produced significantly fewer embryos than control animals (immunized 0.5 embryos versus control 2.4 embryos, P < 0.05). The number of Pep44-immunized females that produced embryos was reduced by 64%. Identification and characterization of possum infertility-relevant epitopes on possum ZP2 protein will assist development of safe, humane, and possum-specific immunocontraceptive vaccines for controlling the introduced possums in New Zealand.
The long-term actions of etonogestrel and levonorgestrel on decidualized and non-decidualized endometrium in a mouse model mimic some effects of progestogen-only contraceptives in women
Authors: Morison Naomi B , Zhang Jin , Kaitu’u-Lino Tu’uhevaha J , Fraser Ian S , Salamonsen Lois A
Published: January 2007

Breakthrough bleeding (BTB), a major side effect of long-acting progestogen (p)-only contraceptives in women, is the main reason for discontinuation of their use. To understand the mechanisms of BTB, a mouse model of endometrial breakdown and repair was adapted to evaluate the effects of long-term progestogens on the endometrium. Appropriately prepared mice received either an etonogestrel (ENG)- or levonorgestrel (LNG)-releasing subdermal implant. Forty eight hours after decidualization was induced in one uterine horn the majority of tissues were highly decidualized, designated 0 day (0d). Uteri were collected subsequently at 5-day intervals (to 45d) and both decidualized and non-decidualized horns were analysed for morphological changes, leukocyte infiltration and matrix metalloproteinase expression (MMP). In decidualized horns, large blood vessels (BV) developed and disturbance of tissue integrity was observed at 5d with substantial stromal breakdown by 10d, progressing until 25d when re-epithelialization was initiated. By 45d, the tissue was restored to its pre-decidualized state but with considerable tortuosity of the luminal epithelium. Tissue remodelling was not apparent in the non-decidualized horns before 35d, when hyperproliferation of the luminal epithelium resulted in tortuosity. Changes in morphology were similar with the two progestogens, but occurred more rapidly with LNG. Apart from macrophages, few leukocytes were present in non-decidualized horns but large infiltrates of neutrophils and uterine natural killer cells (uNK) were associated with tissue breakdown in decidualized tissue, many of these cells were MMP9-positive. MMP7 was primarily associated with tissue repair. Therefore, this model mimics some of the changes observed in endometria of women using p-only contraceptives and provides an opportunity for functional studies.
Jet-grouting solution to link a tunnel to a cut-and-cover excavation
Authors: Candeias M. A. S. , Brito J. A. M. , Matos Fernandes M. , Lopes P. G.
Published: January 2007

The paper presents a solution executed for the connection of a pre-existing metro tunnel made with a tunnel-boring machine to the structure of a station constructed by the cut-and-cover method. The geotechnical conditions of the site were very difficult: 26 m of man-made fill and alluvial soft silty clay and loose sands, with the water level close to the surface. The tunnel was completely covered by these soft soils. The solution consisted mainly in extending the retaining wall of the station beyond the planes of the portals, in order to confine the tunnel in the stretches adjacent to the station, and creating a volume of treated soil by jet grouting limited by the tunnel lining, the stiff layer underlying the alluvial soft ground, the lateral confining walls and the station wall. The paper presents details of the execution and of the performance of the system. Some conclusions are extracted, emphasising the main advantages of the solution.

Cet article présente l'exécution d'une solution destinée à connecter un tunnel de métro préexistant creusé au moyen d'un appareil de forage de tunnels à la structure d'une station construite par la méthode de déblai-remblai. Les conditions géotechniques sur le site étaient particulièrement difficiles: 26 m de remblais, de sédiments d'argile silteuse molle et de sables meubles, avec un niveau d'eau proche de la surface. Le tunnel était complètement envahi par ces sols mous. La solution apportée a consisté essentiellement à étendre la paroi de soutènement de la station au-delà des plans des portails, afin de confiner le tunnel dans les extensions adjacentes à la station et à créer un volume de sol, traité par injection par jet, délimité par le revêtement du tunnel, la couche rigide sous-jacente au sol meuble de sédiments, les parois latérales de confinement et le mur de la station. Cet article présente les détails de la mise en oeuvre et les performances du système. Plusieurs conclusions sont avancées, qui soulignent les principaux avantages de la solution apportée.
Use of Primitive Derived Cotton Accessions for Agronomic and Fiber Traits Improvement: Variance Components and Genetic Effects
Authors: McCarty Jack C. , Wu Jixiang , Jenkins Johnie N.
Published: January 2007

Upland cotton (Gossypium hirsutum L.) is cultivated in warmer climates throughout the world. The genetic base of modern upland cultivars is narrow. As yield and fiber quality traits are improved, the genetic base should be extended by the incorporation of new germplasm into cultivars. In this study, 114 day‐neutral derived primitive accessions were crossed to two cultivars, Stoneville 474 and Sure‐Grow 747 (female parents). In a 2‐yr study, parents and F2 hybrids were evaluated in field plots where agronomic and fiber traits were measured. An extended additive‐dominance genetic model was used, and the data were analyzed on the basis of the mixed model approach. Dominance effects were the primary genetic effects controlling agronomic and fiber traits, while additive effects were small for most of these traits. Consequently, strong heterosis in some F1 and F2 hybrids for most traits would be expected. The genetic resources from the primitive accessions, determined on the basis of cluster analyses, did not show any consistent pattern for collection location or taxonomic classification. Even though dominance effects were the most common for traits measured, results indicate that these day‐neutral derived primitive accessions provide genes with significant additive effects for fiber quality traits, while the additive effects for yield improvement was not significantly decreased. Thus, these derived germplasm accessions can provide favorable gene resources for developing high yielding cultivars or hybrids with improved fiber quality.
Eugene O'Neill's Quest
Authors: Parks Edd Winfield
Published: January 2007

For some twenty years (1936-1956), Eugene O'Neill's expressionistic dramas with their symbolic distortion of objective facts to reveal inner experiences were more popular in South America and especially in the Scandinavian countries than they were at home. The dramatist who in the 1920s had been awarded three Pulitzer Prizes was regarded mainly as of historical importance when in 1936 he was the recipient of the Nobel Prize. To many critics, it seemed a recognition (belated or, perhaps, undeserved) of work that might once have been exciting but that no longer seemed vital or particularly relevant. In the main, we failed to see in his work what the Scandinavians found in it.
The Theatre Of The Thittles
Authors: Clurman Harold
Published: January 2007

There is a tendency nowadays to downgrade the thirties. The reason for this is that the prevailing mood of the thirties was what used to be called “left of center.” Beginning with the late forties— from the time the phrase about the “iron curtain” became part of the common vocabulary—our “intelligentsia” sounded the retreat. The Roosevelt administration, subjected to sharp criticism not infrequently close to slander, seemed to be in bad odor. “Left of center” might be construed as something worse than liberalism. To be “radical” implied that one might be tainted with some degree of “pink.“

A good many of the writers, artists and theatre folk in the thirties were inclined to radicalism. (Had not the Roosevelt administration sponsored the Projects for writers, artists and theatre?) In the early forties the fervor of the thirties was gradually absorbed by the pressures of the war.
Guerrilla Theatre
Authors: Davis R. G.
Published: January 2007

Art is almost always harmless and beneficent; it does not seek to be anything else but an illusion. Save in the case of a few people who are, one might say, obsessed by art, it never dares to make any attacks on the realm of reality.

Freud defines theatre in America, and Che Guevara tells us what to do about it:

The guerrilla fighter needs full help from the people of the area…. From the very beginning of the struggle he has the intention of destroying an unjust order and therefore an intention, more or less hidden, to replace the old with something new.

This society, our society—America, U.S.A.—is chock-full o'ennui. Distracted by superficial values, and without a sense of humanness, we let machines rule; it is easier to kill from a B-52 than to choke every Viet Cong.
The Teaching of Calculus
Authors: Godfrey C.
Published: January 2007

Questions Proposed by the Sub-Commission A of the International Commission on Mathematical Teaching, with regard to the position now occupied by the Elements of Differential and Integral Calculus in the programmes of Public and Secondary Schools.

Note 1. The object of the Central Committee in formulating these enquiries has been solely that of acquiring information. The Committee does not itself take up any definite standpoint in the matter as to how far the teaching of the subject in the schools is desirable.
The Achievements of Great Britain in the Realm of Mathematics
Authors: Loria Gino
Published: January 2007

In England the sceptre of Mathematics passed from the hands of Wallis to the man who was to raise the exact sciences to a height hitherto unattained—Isaac Newton (1642-1727), that sovereign genius before whom the world of science will ever bow with the profoundest reverence.
My Lecture Notes on Calculus
Authors: Bryan G. H.
Published: January 2007

In view of the recent discussions and papers in the Gazette, it may not be out of place for me to sketch the methods by which the Calculus is approached in my lectures. The class includes not only students qualifying for a degree in mathematics, but also others requiring a working knowledge of the use of the Calculus for the purposes of their courses in physics and chemistry.
Term-by-Term Integration of Infinite Series
Authors: Carslaw H. S.
Published: January 2007

1. The English student of Mathematics finds in his text-books a proof that the uniform convergence of a series of continuous functions is a sufficient condition for term-by-term integration. He knows that there are convergent series which cannot be integrated term-by-term,f and that there are series, not uniformly convergent in the interval of integration, which can be thus integrated. The last remark applies particularly to the Fourier’s Series of an ordinary function with discontinuities.
The Sequence of Theorems in School Geometry
Authors: Nunn T. P.
Published: January 2007

The subject of my address has recently been “ventilated” in more than one organ of educational opinion; and it is stated that a committee will shortly be assembled to explore the possibility of an escape from the present chaos to the sweet simplicity of an agreed and authoritative sequence.

I know nothing about the constitution of the committee nor about the proposals that are likely to be brought before it; nor had it been announced or foreshadowed when I suggested the subject for discussion to-night. My intention in suggesting that subject was merely to revive and develop further certain proposals brought forward in an address given to the Association at a time when many of its members were engaged in a vastly more serious discussion elsewhere. I venture, however, to hope that the circumstances I have referred to may add materially to the usefulness of our debate.
Differential Equations in Mechanics and in Physics
Authors: Forsyth A. R.
Published: January 2007

In accepting the honour of being your President, I was told that the office carried only a single duty—that of delivering an address at a then distant date: even the selection of the topic could be deferred for a time. So there lay before me a primrose path of dalliance. I had some hesitation about the selection of a topic. One decision, however, was immediate; my determination was instantly framed to avoid any discussion of the place of mathematics in education, an unending subject, of which perhaps you have heard only too much. It would have been possible to select some special topic, such as functionality, in its historical development; and you would have had a mere mathematical lecture. I have preferred to choose a general subject: my text seems highly technical in phrase, but I shall not keep very closely to it; my purpose rather is to fall back upon my own experience over a wide range of teaching and to exhibit for your consideration some reflexions based on that experience. Moreover, technical as its title is, my address will contain no mathematical symbols. Though my work as a teacher and writer is largely associated with differential equations—probably in the course of a year I receive (with a request for solution) a greater number of insoluble equations than any one here—the reason for its selection is not to be found in any specially personal relation. The reason is that the particular processes affect many subjects in mathematics, and consequently allow general comparisons to be made, as well as particular inferences to be drawn: they constitute a method as powerful in operation and effective in results as any within our domain.
Graphs of Trigonometrical Expressions
Authors: Hall F. G.
Published: January 2007

A Study of the questions on this subject set in the recent geometry papers of the London Intermediate Examinations will show that there is considerable danger that what should be the chief aim in the subject may be subordinated to the subsidiary aim of affording practice in evaluating and plotting results.

The chief aim should be, I think, a careful study of those important curves in Physics and in Higher Mathematics which best lend themselves to trigonometrical rather than to algebraic treatment. In the actual plotting of these curves much varied practice in the use of tables will, of course, be obtained; but this should be considered of distinctly minor importance.
Tripolar Coordinates
Authors: Bates G. N.
Published: January 2007

The tripolar coordinates of a point P are defined as the squares of its distances from the angular points of the triangle of reference.

The equation of the first degree in x, y, z (x = PA2, etc.) has been considered by E. Lucas (Mathesis, 1889) and by de Poulain (Journal de Mathématiques spéciales, 1889). I am also indebted to Mr. R. F. Davis for a note in accordance with which a portion of this paper has been rewritten.

In what follows x, y, z will denote the tripolar coordinates; α, β, γ the trilinear coordinates of a point with respect to a triangle of reference ABC; while ξ and η will denote Cartesian coordinates referred to B as origin and BC as the axis of x.
Notes on the Theory of the Reversible Pendulum. (Part II.)
Authors: Allen A. O.
Published: January 2007

We may now turn our attention to the questions which arise specially in connection with a reversible pendulum, such as Kater’s. Of course the object in view is so to place two knife-edges on opposite sides of the C.G. that the period shall be the same from either, the two positions being selected according to the rule at the end of § 4. But the usual procedure will be to decide on the distance between the knife-edges at the start, say one metre; then to clamp them to the more or less uniform bar of the pendulum, using a standard distance-piece to secure the proper interval between them, and finally to adjust a sliding weight in such a position as to make the period the same for both. We have seen in § 2 how the period, or rather the length of the equivalent S.P., varies with the position of the sliding weight, but it will be convenient now to change the notation. Let I1, I2, ... denote the moments of inertia of the various masses making up the pendulum, each about its own C.G., M1, M2.. the masses; x1, x2... the co-ordinates of the centres of gravity, referred to one of the knife-edges as origin; let the co-ordinate of the other knife-edge be d, and let the letters I, M, x without suffixes refer to a moveable mass which is being adjusted. We shall at once see how much simpler it is to discuss the graph whose ordinate is the length of the S.P., than the one where the period is used, for the position which the moveable mass should occupy of course corresponds to the intersection of the two graphs relating respectively to the two knife-edges: and it is surely better to have to deal with the intersections of conics than of cubics.
The Elementary Arithmetic of the Theory of Numbers
Authors: Jackson C. S.
Published: January 2007

That every person in the realm who teaches mathematics should be a member of our Association is an ideal towards which we are converging non-uniformly, if at all. Were this ideal state of things a reality no apology would be needed for a paper dealing with topics which though educationally important are from a mathematical point of view very familiar. As it is, the feeling haunted me as I wrote that I was writing a sermon, and that the people whom it might benefit would not be in the room, were not even members of our Association. As, however, other writers of sermons must, I suppose, sometimes find themselves in a similar position, 1 have ventured to go on.
Feuerbach’s Theorem as a Corollary
Authors: Neville E. H.
Published: January 2007

The solution of the problem of drawing a circle to touch a given line BC at a given point X and to touch also a given circle v is very familiar; it is obvious that this solution must lead to an elementary verification of Eeuerbach’s theorem, but the extreme simplicity of this verification is commonly overlooked.
The Teaching of Easy Calculus to Boys. (Continued from p. 208.)
Authors: Knowles W.
Published: January 2007

Another useful application is that the parabola, in the form y = –k.x2, represents the path of a projectile. The boys at this stage have already dealt with equations of the form y= ±(x–a)(x–b), and are able to find the points where the curve is cut by the x or the y-axis.
The Graphical Treatment of Differential Equations
Authors: Brodetsky S.
Published: January 2007

The subject of this Paper is one that presented itself in a piece of work of a practical nature. The development of aeroplane flight naturally suggested the investigation of the motion of a body in a resisting medium. In general this problem was too difficult for solution. One therefore looked for legitimate means of simplifying it. One simple type of motion allied somewhat to aeroplane motion was that of a plane lamina moving in air under the earth’s attraction. Even here difficulties arose in the solution of the resulting equations of motion; yet further simplification was not quite permissible, for care had to be taken that the simplified problem did bear some relation to the actual problem presented by nature.
Co-Ordinate Geometry in Schools
Authors: Dobbs W. J.
Published: January 2007

In the Report of t h e Education Reform Council, published in 1917 under the title “Education Reform,” it is suggested on page 83 that for boys of 14 to 16 years of age attending a secondary school it is desirable that the mathematical course should be directed towards an elementary use of calculus methods, so that those who remain at school to a later stage may be able to use effectively the elements of infinitesimal calculus. On the next page it is further suggested that boys of 16 to 18 years of age who take up mathematics and science may pursue the study of differential and integral calculus, including the easy parts of differential equations, and apply these with advantage to higher algebra, trigonometry, co-ordinate geometry, solid geometry and mechanics; that the co-ordinate geometry requires a muchbroader treatment than that commonly adopted—a treatment in which the calculus is freely used and in which some “geometrical” conies, when elegant and convenient, is dovetailed into the analysis.
The Use of Vectors in Practical Mathematics
Authors: Benny L. B.
Published: January 2007

The uses of vectors are many and varied. The value of the vector notation and of vector methods of calculation is becoming recognised in mechanics and physics, but few teachers use them to any extent in teaching pure mathematics, although they appear to be equally useful in this sphere.

I have found vector methods especially useful for students who require a “practical” knowledge; they are well adapted to numerical work, and often provide a welcome change from the drudgery of memorising formulae, and calculating results by substitution of numerical values of the symbols—a dull task, lacking in educational value, which forms such a large part of the work of the technical student. Vector solutions are usually short and simple, and proceed from first principles ; they should thus be preferred on logical grounds.
Note on the Treatment of Conic Sections and Conicoids By Pure Geometry
Authors: Rumsey C. A.
Published: January 2007

The object of the following note is to derive Pascal’s theorem and the Anharmonic and Harmonic properties of Conic Sections directly from the focus and directrix definition by the early introduction of an extended form of Carnot’s theorem, viz. “the product of the ratios in which the sides of a closed polygon, taken in order, are cut by a conic = +1.” When the above have been demonstrated the simpler properties are known to be easily deducible. Subsequently the treatment of Conicoids by Pure Geometry is introduced by means of the same theorem.
The Trigonometry of the Tetrahedron
Authors: Richardson G.
Published: January 2007

So far as I know the properties of a tetrahedron are not given in any mathematical text-book. In the late Dr. Wolstenholme’s Examples for Practice in the use of Seven-figure Logarithms, the formulae which are necessary to determine the plane and dihedral angles and the volume of the tetrahedron, having given the six edges, are stated, but nothing beyond this. Dr. Wolstenholme worked at the subject for some years, and several of his results were sent as problems to the Educational Times, where they appeared for the most part after his death. In one set of questions he remarks that they are “the equations I have been looking for for years,” and so I think we may fairly infer that these questions represent the more advanced results of his investigations. The solutions of these questions, so far as I have been able to find them, are practically all given in this paper. “With regard to the rest of the matter, I hardly dare claim any originality. Wolstenholme must have known all or nearly all the results, and any one seriously attacking the subject must come upon them. All I can say is that I have never seen them in print, and that under any circumstances the bringing of them together must be helpful to students in many branches of mathematics.
Can the Range of Geometry Taught in Schools Be Widened?
Authors: Baker H. R.
Published: January 2007

The following, written at the reguest of the Editor of the Gazette, gives an account of the mathematical part of the remarks made by the lecturer at the Annual Meeting of the Association last January. There are added some words dealing with geometry on a sphere, in regard to which some questions were raised at the meeting.
General Theory of Verniers
Authors: Heawood Percy J.
Published: January 2007

We have seen the connection between the general theory of verniers and the indeterminate equation of the form pn − qm = r; the equation pn + qm = r might be illustrated in much the same way. But, taking the case originally considered, we observe that it is the same question as before, from a different point of view, if instead of starting with an interval AB between divisions of two contiguous scales, and asking how far we must go to reach a coincidence, we suppose the zeros of two scales to coincide and ask how far we have to go to reach a certain interval, between divisions of the two. The question only differs in so far as it suggests the simultaneous consideration of more than one such interval. But further if, instead of repeated divisions of each kind, we take a circle whose entire circumference = one of the larger divisions, a say, and from a fixed point A on the circumference measure off continually arcs = to the smaller division 6, (figs. 5, 6), the question how far we have to go to reach a certain approximation to the starting point is the same thing in another form, although the arrangement brings to light many new relations, which in their turn throw light on the result. We have the subdivisions of the different a-intervals superposed as it were upon one a-interval, and the circle is thus continually divided into more and more parts until (if a and b are commensurable) exact coincidence with the starting point is reached.
Some Incidental Writings by de Morgan
Authors: Morgan A. de
Published: January 2007

While gathering the materials for something in the nature of a ‘Companion’ to De Morgan’s “Budget of Paradoxes,” I came across a considerable number of his notes, short papers, and other contributions to the famous English periodical known as “Notes and Queries.” The first number appeared on Nov. 3, 1849, and from that date “N. & Q.” has been a household word among those who are afflicted with the insatiable desire to penetrate into the bye-ways of Literature, Genealogy, Heraldry, Antiquarian Lore, the Science of History and the History of Science—all formed grist for those who came to that mill. By the kind permission of the Editor of this invaluable publication, I have been permitted to reproduce from its columns what is presented to the reader in the following pages. The early numbers of “N. & Q.” are exceedingly scarce, and a complete set is hardly to be obtained by those who live at a distance from the great libraries.
On a Supposed Solution of the “Four-Colour Problems”
Authors: Wilson J. Cook
Published: January 2007

It appears from the recently published life of Archbishop Temple that he is supposed to have found a proof of the proposition that any map can be coloured with four colours, no two adjacent segments of it being coloured alike. The writer had heard of this before the publication of the Life, but had not succeeded in finding what the proof was, and was under the impression that it had never been published, especially as it was not mentioned in Mr. Rouse Ball’s book. As stated in the Life the supposed solution was published in the Journal of Education, June 1, 1889. It turns out to be what one has learned from experience (and the writer owns that he has spent much time on the subject) to expect from any theory which looks like a short solution of this extremely elusive problem.
The Postulate of Parallels
Authors: Hill M. J. M.
Published: January 2007

There are in the Mathematical Gazette for October 1924, three communications on the above subject.

It will make my remarks on these clearer if I refer to the contents of my paper on the Postulate of Parallels in the Gazette for December 1923, and make an addition thereto. In that paper the demonstrations of Euc. I. 27 and 29 are deduced from Wallis’s Postulate of Similarity, viz.: “To every figure there exists a similar figure of arbitrary magnitude” taken as a substitute for Euclid’s Postulate of Parallels. The demonstration of Euc. I. 27 in this manner was first given (I believe) by Professor Nunn in the Gazette of May 1922. He has not, however, published in full his demonstration of Euc. I. 29. He was so kind as to communicate it to me, but I hope he will some day publish it in full. It is entirely different from the demonstration of Euc. I. 29 which I published in the Gazette of December 1923, which involves three successive applications of the Postulate of Similarity and makes use of Euc. I. 27 as proved by Professor Nunn, but does not include the proof of any other proposition.
On a Problem in Mechanics and the Number of its Solutions
Authors: Macaulay F S.
Published: January 2007

To find the position of equilibrium of a particle which is acted on by forces of given magnitudes directed towards given points.

This problem was suggested by Mr. P A. Hillhouse, and arose in the first instance from the consideration of forces acting in a crane. The following note does not offer a solution of the problem, but contains a proof by Mr. A. L. Jones that there is at most one position of equilibrium when the forces are all of one sign, i.e. either all tensions or all thrusts. This is followed by an investigation of the total number of solutions, real and imaginary, for all combinations of thrusts and tensions, when the magnitude only of each force, and not its sign, is given. This number is surprisingly large. It would of course be of more practical interest to find the number of real solutions for each particular combination of thrusts and tensions, but I have only succeeded in doing this when the given points are in a straight line, and in one or two other special cases. The results for these are stated without proof at the end of the note.
On the Theory of the Plane Complex with Simple Geometrical and Kinematical Illustrations
Authors: Genese R. W.
Published: January 2007

OA,OB = x1, x2, being distances, carrying signs, along an axis, the “Bearing” of B with respect to A (called a vector, or step, or displacement) is given by AB = OB – OA = x2 – x1 in all cases, and is independent of the position of O.

If we wish to add two such steps, a construction is necessary, viz. they are placed “ end on ” in either order; and the sum is dependent on the position of O ; if M be the mid-point of AB, the sum = 20M.
The Presidential Address: Mathematics and Individuality
Authors: Nunn T. P.
Published: January 2007

In the ancient story of Barlaam and Ioasaph, which edified and delighted our medieval forefathers through many centuries, there is a charming apologue of a fowler and a nightingale whom the former had snared and was about to slay. “Free me from my fetters,” said the nightingale, “and I will give thee three precepts by the keeping of which thou shalt be greatly benefited all thy life long.” The astonished fowler accepted the terms and set the bird free, receiving as his reward the precepts : “Never try to attain to the unattainable; never regret the thing past and gone; and never believe the word that passes belief.” But as the bird flew aloft she cried to her captor, “Shame, sir, on thy recklessness! What a treasure thou hast lost to-day! For I have inside me a pearl larger than an ostrich egg.” When the fowler heard this he was distraught and would fain have taken her again. “Come hither,” he said, “into my house; I will make thee right welcome, and send thee forth with honour.” But the nightingale replied, “Now I know thee to be a mighty fool. Though thou didst receive my words readily and gladly, thou hast gained no profit thereby. I bade thee never regret the thing past and gone; and behold thou art distraught with grief because I am escaped out of thy hands. I charged thee not to try to attain to the unattainable; and thou triest to catch me again. Besides which I bade thee never believe a word past belief; and behold thou hast believed that I had in me a pearl exceeding the size of my whole body.”
Non-Commutative Algebra
Authors: Turnbull H. W.
Published: January 2007

The whole of ordinary algebra, dealing with real or complex numbers a, b, c, is based on three fundamental laws which are usually called:

I.

The Associative Law,

II.

The Distributive Law,

III.

The Commutative Law.
The Best Method of Examining School Mathematics, with Special Reference to the School Certificate Examination of the Oxford and Cambridge Schools Examination Board.
Authors: Siddons A. W.
Published: January 2007

Ladies and Gentlemen,—Before this meeting commenced, Professor Lodge asked me if I was doing much examining now, to which I answered “No, none.” Then he asked what qualification I thought I had got for speaking on the best method of examining. I do not want to speak much on the best method, but I think it is time that members of this Association had the opportunity of blowing off a lot of steam, and I hope that many will have something to say about the school certificate examinations. My desire is that many different people should give their views and their criticisms.
A Conversation on Right Angles
Authors: Elliott T. C. J.
Published: January 2007

Following a method more popular in the seventeenth century than now, I propose to explain certain views on the definition of a right angle by an imaginary conversation between an inventor of mathematical models and a student.
The Teaching of Limits and Convergence to Scholarship Candidates. (Continued.)
Authors: Milne W P
Published: January 2007

8. The following application of Dedekind’s principle is the most important one in practice.

If s1, s2, s3, sn … be a sequence of positive rational nucmbers which steadily increase and never become greater than a given positive number K, then the given sequence approximates to a definite limit, K being rational.
The Stroud System of Teaching Dynamics
Authors: Henderson James B.
Published: January 2007

Very few teachers ever have the chance of noting the advantage or disadvantage of a change, introduced into their methods of teaching, and of profiting by the same. I desire now to put on record the results of such a change and the method by which they were attained.

The number of systems of teaching dynamics is great, and still the results are deplorable as judged by the knowledge possessed by the average engineer some years after he leaves college. Teachers are either biassed in favour of the Gaussian system or the Perry system, or some other system of their own, and are loath to change because they can train their students to solve the necessary problems, and if a mistake is made by omitting g or some other quantity it is merely a mistake and costs nothing. It is not so with the poor student, however, when he is launched on the world without his teacher to help him.
Note on Desargues’ Theorem
Authors: Sommerville D. M. Y.
Published: January 2007

Major Dixon has given in the Gazette for May an interesting representation, suggested, perhaps, by Hilbert's example of a non-desarguesian geometry, of a plane geometry, in which straight lines are represented by closed curves on a closed convex surface devoid of singularitles. Employing his theory of order and “collation,” he constructs this geometry so as to be desarguesian.
Aeroplane Mathematics
Authors: Brodetsky S.
Published: January 2007

1. The dynamics of aeroplane motion is a comparatively new subject, and one that arouses interest in all students of mechanics. Although a full study of aeronautics involves the use of complicated analysis, yet some really useful information about aeroplane motion can be obtained with quite simple mathematics. It is the object of this paper to draw attention to such methods and results. It will be seen that some of the investigations can be understood by mere beginners in mechanics; others are more suitable for such students as have had considerable experience of mechanics.
The Discussion of Certain Power-Series
Authors: Bromwich T. J. I’a.
Published: January 2007

I Quite agree with Mr. Hardy (Gazette, vol. 3, p. 284) in his contention that the real basis of the power-series for sin x; and cos x is given by the two equations

But I am inclined to doubt whether at present the difficulties of exposition will not outweigh the advantages of his method (iii); and for this reason the following method may be worth considering, although it is a fairly obvious modification of my previous note (Gazette, vol. 3, p. 85). The only preliminary knowledge implied is that of the elementary differential calculus, and of Argand’s diagram.