bluuebunny/crossref_metadata_2025 huggingface dataset:
Regulatory properties of 6-phosphofructokinase and control of glycolysis in boar spermatozoa
Authors: Kamp G , Schmidt H , Stypa H , Feiden S , Mahling C , Wegener G
Published: January 2007

Glycolysis is crucial for sperm functions (motility and fertilization), but how this pathway is regulated in spermatozoa is not clear. This prompted to study the location and the regulatory properties of 6-phosphofructokinase (PFK, EC 2.7.1.11), the most important element for control of glycolytic flux. Unlike some other glycolytic enzymes, PFK showed no tight binding to sperm structures. It could readily be extracted from ejaculated boar spermatozoa by sonication and was then chromatographically purified. At physiological pH, the enzyme was allosterically inhibited by near-physiological concentrations of its co-substrate ATP, which induced co-operativity, i.e. reduced the affinity for the substrate fructose 6-phosphate. Inhibition by ATP was reinforced by citrate and H+. Above pH 8, PFK lost all its regulatory properties and showed maximum activity. However, in the physiological pH range, PFK activity was very sensitive to small changes in effectors. At near-physiological substrate concentrations, PFK activity requires activators (de-inhibitors) of which the combination of AMP and fructose 2,6-bisphosphate (F2,6P2) was most efficient as a result of synergistic effects. The kinetics of PFK suggest AMP, F2,6P2, H+, and citrate as allosteric effectors controlling PFK activity in boar spermatozoa. Using immunogold labeling, PFK was localized in the mid-piece and principal piece of the flagellum as well as in the acrosomal area at the top of the head and in the cytoplasmic droplets released from the mid-piece after ejaculation.
Oocyte growth and follicular development in KIT-deficient Fas-knockout mice
Authors: Moniruzzaman Mohammad , Sakamaki Kazuhiro , Akazawa Yukiko , Miyano Takashi
Published: January 2007

In mammals, oocyte growth and follicular development are known to be regulated by KIT, a tyrosine kinase receptor. Fas is a member of the death receptor family inducing apoptosis. Here, we investigated germ cell survival, oocyte growth and follicular development in KIT-deficient (Wv/Wv:Fas+/+), Fas-deficient (+/+:Fas−/−), and both KIT- and Fas-deficient (Wv/Wv:Fas−/−) mice during fetal and postnatal periods. Further, the ovaries of these mice were transplanted in immunodeficient mice to compare oocyte growth and follicular development under a condition isolated from the extraovarian effects of KIT- and Fas-deficiency. Higher numbers of germ cells were found in the fetal and postnatal ovaries of Fas-deficient mice than in the same-aged wild-type mice. In KIT-deficient mice, ovaries at 13 days postcoitum (dpc) contained 1106±72 (n=3) germ cells, but the ovaries contained no oocytes after birth. Twenty-one days after transplantation of the ovaries at 13 dpc, no oocytes/germ cells were found. A higher number of germ cells (3843±108; n=3) were observed in the Wv/Wv:Fas−/− genotypes than in Wv/Wv:Fas+/+ mice at 13 dpc. Furthermore, Wv/Wv:Fas−/− mice contained 528±91 (n=3) oocytes at 2 days, and follicles developed to the antral stage at 14 days of age. After transplantation of fetal and neonatal ovaries from Wv/Wv:Fas−/− mice, increased numbers of growing oocytes and developing follicles were obtained compared with those in 14-day old ovaries in vivo. These results show that oocytes grow and follicles develop without KIT signaling, although KIT might be essential for the survival of germ cells/oocytes in mice.
Perturbation of spermatogenesis by androgen antagonists directly injected into seminiferous tubules of live mice
Authors: Nagaosa Kaz , Kishimoto Atsushi , Kizu Ryoichi , Nakagawa Akihisa , Shiratsuchi Akiko , Nakanishi Yoshinobu
Published: January 2007

Natural and artificial substances present in the environment can affect our health. Testicular toxicants in particular are troublesome, because they disturb gonadal function of males. Translocation of substances into the seminiferous epithelium where sperm production proceeds is restricted due to the blood–testis barrier, but this permeability barrier temporarily disappears under physiological and sub-physiological conditions. This means that any substance could enter the seminiferous epithelium and disturb sperm production. To reduce the risk posed by such toxins, it is important to accurately determine which substances possess the toxicity. However, existing assay systems are not satisfactory in terms of both accuracy and sensitivity. Here, we report the establishment of such a system. We injected the androgen antagonists, flutamide and vinclozolin, directly into seminiferous tubules of live mice, which had been treated with busulfan for a temporal arrest of spermatogenesis, and the testes were histologically examined to see the effect of the injected materials on spermatogenesis that was in the process of recovery. The injection of either substance brought about a severe impairment of spermatogenesis at an amount over a million times smaller than that used in the previous assay systems where animals are administered with test substances outside of the testis. In contrast, these androgen antagonists at the same doses showed lesser effects when intratubularly or intraperitoneally administered into mice that had not been pretreated with busulfan. We propose that the method adopted in this study is a novel assay system to identify potential testicular toxicants.
Agonia da história clínica e suas conseqüências para o ensino médico
Authors: Dichi Jane Bandeira , Dichi Isaias
Published: January 2007

A história clínica, cada vez mais, vem sendo subestimada como ferramenta indispensável à formação médica. Sendo esta desvalorização multifatorial, dois são os fatores que a tornam menos atraente aos olhos dos recém-egressos das universidades e mesmo para alguns profissionais já graduados: o deslumbramento diante de procedimentos high tech e a lenda intelectualista que valoriza apenas aspectos teórico-contemplativos do saber humano. O presente artigo de revisão tem por objetivo analisar as causas que levaram a esse quadro e contribuir com algumas sugestões para que ele possa ser ao menos minimizado.
Enzima e simbiótico para frangos criados nos sistemas convencional e alternativo
Authors: Sartori José Roberto , Pereira Kelly Almeida , Gonçalves Jane Cristina , Cruz Valquíria Cação da , Pezzato Antonio Celso
Published: January 2007

O objetivo deste trabalho foi estudar os efeitos da inclusão de enzima e simbiótico nas rações de frangos de corte criados nos sistemas convencional e alternativo sobre o desempenho, rendimento de carcaça, cortes e gordura abdominal e também avaliar economicamente o uso destes aditivos em ambos os sistemas de criação. Foram utilizados 720 pintos machos Cobb, com um dia de idade, distribuídos em um delineamento em blocos casualizados no esquema fatorial 2x3, com dois sistemas de criação: convencional (com promotor de crescimento) e alternativo (sem promotor de crescimento) e três aditivos: sem outro aditivo (SA), com simbiótico (SI) e com enzima + simbiótico (SIE), com 4 repetições de 30 aves cada. Aos 42 dias de idade, o fator de produção (FP) foi menor (P<0,05) para aves SA (324), quando comparadas às tratadas com SI (334) e SIE (337). Aves criadas no sistema convencional apresentaram maior (P<0,05) FP (338), quando comparadas às do sistema de criação alternativo (325). No sistema alternativo, a conversão alimentar foi melhor (P<0,05) para aves SI (1,77), quando comparadas às SIE (1,82) e SA (1,85). O uso de SI e SIE favorece o desempenho dos frangos aos 42 dias de idade e não influencia o rendimento de carcaça, cortes e gordura abdominal, tanto no sistema convencional como no alternativo, sendo que estes aditivos aumentam os custos de produção em ambos os sistemas. O sistema alternativo de criação proporciona maior retorno econômico, apesar do menor fator de produção.
Meadow Fescue and Tetraploid Perennial Ryegrass—Two New Species for Overseeding Dormant Bermudagrass Turf
Authors: Richardson M. D. , Hignight K. W. , Walker R. H. , Rodgers C. A. , Rush D. , McCalla J. H. , Karcher D. E.
Published: January 2007

Bermudagrass (Cynodon spp.) is often overseeded with a cool‐season turfgrass to provide a green, actively growing surface for winter and early‐spring sporting activities. Two grass species that have not been tested for overseeding include tetraploid (2n = 4x = 28) perennial ryegrass (Lolium perenne L.) and meadow fescue (Festuca pratensis Huds.). The objectives of this study were to test these two species in comparison to three standard overseeding species [diploid perennial ryegrass, intermediate ryegrass (L. perenne × L. multiflorum Lam.), and Poa trivialis L.] in three environments; Maricopa, AZ (arid), Fayetteville, AR (transition zone), and Auburn, AL (humid, subtropical). At all locations, overseeding grasses were seeded into dormant bermudagrass turf and managed according to standard overseeding practices. The tetraploid ryegrass had equal or superior turfgrass quality to all other overseeding species except the diploid ryegrass. Meadow fescue produced similar turfgrass quality to intermediate ryegrass and tetraploid ryegrass at Arkansas and Alabama, but had lower turf quality scores in Arizona. The meadow fescue and tetraploid ryegrass transitioned more quickly back to bermudagrass compared to the diploid ryegrass, intermediate ryegrass, and P. trivialis, which would be very favorable aspects of these new overseeding grasses. These trials clearly demonstrate the potential of two new species, meadow fescue and tetraploid ryegrass, for overseeding dormant bermudagrass turf.
Sententiousness in Fuente Ovejuna
Authors: Pring-Mill R. D. F.
Published: January 2007

Fuente Ovejuna is probably Lope de Vega's best-known work, perhaps because it can so easily be given an unintended slant: the nature of the central situation, in which the villagers of Fuente Ovejuna join together to kill their tyrannous overlord—the Comendador—and are ultimately pardoned by the King, has made it a favorite with left-wing producers. It is not really a proletarian manifesto, however, and should not be set against a Marxist background: Fuente Ovejuna—like all Spanish Golden Age plays—requires to be seen against the same structuralized vision of Creation as Elizabethan drama. Like so many Elizabethan plays, it is primarily concerned with order and disorder: social disorder seen as cosmic discord, and the restoration of order constituting a reestablishment of cosmic harmony.
The Incest of Amnon and Tamar
Authors: Rank Otto
Published: January 2007

In the Spanish drama the most important role, next to that of the homosexually tinged motif of disguise, is that of the love of siblings. Particularly so with Lope de Vega, whose parents died when he was extremely young; since he grew up with his sister Isabel and one brother, it is understandable that the parental complex could be replaced in him to such a dominant degree by the sibling complex. It may be remarked that Lope's first wife was also named Isabel, which will not seem accidental in the light of name-determination, and we may point to the circumstance, certainly significant for the psychic life of the dramatist, that his brother, wounded in a sea fight in 1588, died in his arms.

In Lope's play The Outrageous Saint (La fianza satisfecha) a young Sicilian named Leonido, whose every crime is committed out of the sheer love of sinning, attempts to rape his married sister.
Ibsen and Revolt
Authors: Brustein Robert
Published: January 2007

In 1869, Hendrik Ibsen, then 41, paused in his dramatic labors to compose a short poem. He had left his beloved Rome just one year before to settle in Dresden (he was to remain in exile from Norway until 1891), and he had just completed his first realistic prose play, The League of Youth, after having established his reputation as the author of Brand and Peer Gynt. Since The League of Youth contains strong satire on the hypocritical opportunism of the contemporary Norwegian Liberal, critics were beginning to charge Ibsen with having joined the Conservative faction. The poem—“To My Friend, the Revolutionary Orator”—is addressed to one of these critics, and is a polemical defense against the current charges. In these verses, Ibsen affirms that he is still a perfervid revolutionary—but he then proceeds to distinguish his own revolt from anything in recorded history.
Theme and Motif in La Guerre de Troie n’aura pas lieu
Authors: Falk Eugene H.
Published: January 2007

Flaubert once said that a theme imposes itself upon the writer, that it demands to be treated. And Curtius remarked that the choice of a theme reflects an author’s basic attitude toward the world, that it indicates his typical reactions to given situations. But he also pointed out that he who has only a theme will not necessarily create great literature. No doubt, the theme alone cannot assure literary value to any work; nor does the particular orientation, the point of view from which the theme is treated, endow the work with stature. Broadly considered, war is the theme of La Guerre de Troie n’aura pas lieu, and a despondent pacifism is its orientation. At first glance, the play appears to say either that war is in the hearts of men or that it is a pastime of gods indifferent to human will or human prayers.
The Madwoman of Chaillot: A Modern Masque
Authors: Brée Germaine
Published: January 2007

Until the curtain went up on The Madwoman of Chaillot in December 1945, Louis Jouvet, the producer and Giraudoux’ close collaborator since the production of Siegfried (1928), was tortured by uncertainty as to its reception. It was his opening play after a prolonged five-year absence from Paris. There were almost insuperable material difficulties, during this immediately post-war winter, in staging a play which requires some fifty highly fantastic characters to appear on stage. More serious, still, Jouvet suffered from the absence of Giraudoux who had unobtrusively died the year before, leaving his friend alone to select which of the two and sometimes three or more versions of scenes in the play was definitely to be adopted.

But most serious of all, the mood of The Madwoman of Chaillot, its lightness of touch, its colorful fantasy and ease seemed alien to the atmosphere of the day.
Battle for Bookings: Independents Challenge The Trust
Authors: Lippman Monroe
Published: January 2007

That once flourishing but now moribund institution, the road, has had a long and frequently exciting past. It can be traced back at least 200 years to the time when the Old American Company toured its repertory up and down the East Coast. As the country grew and the road expanded, the problems of booking became increasingly complex. By the middle of the nineteenth century, actors arid managers of attractions were finding it almost impossible to book a road season adequately, since they were forced to deal individually with the multitude of local theatre managers across the country. The local managers were finding it equally difficult to book their theatres profitably, since they had to book each attraction separately. The resultant confusion grew to the point of chaos, particularly among the many one-night stands.
The Approach to the Spanish Drama of the Golden Age
Authors: Parker A. A.
Published: January 2007

By the “approach” to the drama of the Golden Age I mean a guide to its understanding. I have thought that some remarks on this subject might be useful because the drama has not yet been satisfactorily handled in any histories of Spanish literature. This is mainly due, I believe, to the fact that our conceptions of what a play is and how it should be approached are derived from our inherited notions of the classical and Shakespearian dramas, and from the realistic theatre of more modern times, whereas Spanish literature offers us a form of drama that is in many respects different from any of these.

The Spanish drama of this period is not, of course, uniform in technique; there are very great differences between the last plays of Calderón and the first of Lope.
Mr. Duerrenmatt Buys New Shoes
Authors: Rogoff Gordon
Published: January 2007

The returns are in. A Swiss playwright has been “discovered.” A year ago the name of Friedrich Duerrenmatt suddenly studded the hopeful theatrical gossip of the alert drinkers in the Salisbury, Cranbourne, and Arts Theatre. No director worthy of the name “Peter” was without curiosity. To acquire the production rights for The Visit of the Old Lady would be considered a virtual coup d'état for any ambitious directorial career. Travelers from the continent regaled us with stories: one had seen the play in Munich with Therese Giehse, a famous Mother Courage seen here in Benedek's film Kinder, Mutter, und Ein General; another had seen the great Kathe Dorsch as the Old Lady; yet another the Paris production (not a notable success) with that delicate, withered little bundle remembered from many French films, Mme. Sylvie.
The Classic Theatre
Authors: Bentley Eric
Published: January 2007

My anthology The Modern Theatre — five volumes in Anchor Books—is made up of plays written between 1830 and 1950. The première of Victor Hugo's Hernani in 1830 has always been considered a landmark, though closer to my own thoughts were Musset, Büchner, and Gogol, all of whom wrote plays in the early eighteen thirties.

That anthology, readers will agree, was not just another bundle of famous plays. On the contrary, justly famous items—and unjustly famous ones—were omitted. Famous authors like O'Casey and Anouilh were represented only by non-famous works. It was an anthology of protest—against the standardization of the repertoire. For our theatres limit their range even more than our orchestras and our museums do. My anthology was issued in the hope of persuading some of them to look at other things, other kinds of things. The volumes serve a purpose even if that hope is vain.
The Criticism of Greek Tragedy
Authors: Arrowsmith William
Published: January 2007

My purpose here is to do a little superstitious rapping in the hope of persuading into existence something a little different in the kind of criticism we normally bring to bear upon Greek tragedy. If this seems pretentious, blame the subject in part: Greek tragedy requires, I think, a formidable apparition by way of an adequate criticism and certainly a larger one than I can summon up, though also a larger one than presently attends the scene. What I want to do is to outline the nature of the job to be done, as I see it, and to discuss what seems to me inadequate in both the traditional and contemporary ways of writing about Greek tragedy.
Ancient Tragedy In Modern Greece
Authors: Brown John Russell
Published: January 2007

A performance lasting ninety minutes, a language few of the audience can understand, a play more than 2,400 years old, and the immediate result—continuous applause for more than twenty minutes. This is a measure of the success of ancient tragedy in modern Greek translations and productions when on tour. In Greece itself, performances are frequently attended by audiences of twelve to fourteen thousand, most of whom have come from considerable distances, such as the 112 miles from Athens to Epidaurus.
The Ascension of John Osborne
Authors: Marowitz Charles
Published: January 2007

If one looks closely at the crotchety, constipated, hypercritical figure of Martin Luther in John Osborne's newest play, one is forcibly reminded of that fuming British malcontent, Jimmy Porter; a protestant who bitched against the Welfare State as vehemently as the theologian wrangled with the Pope. The similarities do not end there.

Despite the jump in time, the clerical context and the change of venue, the play is not (as has been charged here) a departure for Osborne. There is a clear link-up between Luther's sixteenth-century Germany and our time. In both, the sense of cosmic imminence is very strong. “The Last Judgement isn't to come. It's here and now,” says Luther, and the doomsday-mountain-squatters and the nuclear-psychotics echo his words.
Theatre in Eastern Europe
Authors: Popkin Henry
Published: January 2007

Right now, the East European theatre is the most exciting in the world. (When I say East Europe, I refer to the Soviet Union, Poland, Czechoslovakia, Hungary, Rumania, Bulgaria, East Germany, and Yugoslavia.) This theatre is not necessarily the most accomplished, although that is a defensible claim. I mean that theatrical creativity is blooming there, and that, in the theatre, encouragements and incitements outweigh efforts to keep creative people in check.

The most important single element is the existence of a cheap, subsidized theatre that has mass appeal. Of course, subsidies encourage the continued popularity of a great deal of junk, but they protect quality as well, and sometimes theatre of the highest standards is popular, too. If subsidy is one secret, the other is the relative absence of competition. Television is generally confined to a single channel and only to certain hours of the day.
Richard's Himself Again: Journey to an Actors’ Theatre
Authors: Rogoff Gordon
Published: January 2007

One measure of a revolution is the change in faces. At Edinburgh in the fall of 1963, Kenneth Tynan made himself host to ninety gentlemen and ladies of the theatre from several corners of the narrowing globe. The delegation from the United States was led by Harold Clurman and Lillian Hellman, spirits from our vital thirties, still active, and still representative of our theatre's leadership. (Leadership is a word chosen out of courtesy: taken against the delegates of other countries, the singular message of the conference was that America had no theatre leaders. As always, a visual image told the most chilling tale: every day, three ladies took seats next to one another on the platform, each hatted and veiled like three weird sisters at a club luncheon. They were Miss Hellman, Agnes Moorhead, and Judith Anderson.
Arden's Unsteady Ground
Authors: Gilman Richard
Published: January 2007

“An object of art is artistic only insofar as it is not real,” Ortega y Gasset once wrote, and meant something much broader than an attack upon naturalism. Until we are able to think of drama, for all its physical contingencies and aesthetic impurities, as existing in a different realm from the “real”—the way we are mostly able to think of poetry, painting, music—we will go on disputing over everything that is peripheral and secondary in the work of a playwright like Arden, in the effort to establish its “validity,” unconscious that this validity has already been established by the play's own internal processes and conquests.

There is something dispiriting about Arden's own vacillations between apology and peevish resentment. The prefaces to his plays are full of protests against his critics, but also of weakly enunciated and what can only be called supererogatory statements of his dramatic intentions.
Ten Years of the English Stage Company
Authors: Taylor John Russell
Published: January 2007

The facts are well enough known. On April 2, 1956, a new company began a term of management at the Royal Court Theatre, London. It called itself the English Stage Company, and announced its intentions of becoming a writer's theatre, playing new English plays and contemporary classics from abroad in repertory. This sounded brave and worthy, though enough similarly brave and worthy ventures had foundered in the years since the war for the few interested people to have no great confidence in the new company's survival. The first repertory season was to consist of five productions: first a play by the novelist Angus Wilson, The Mulberry Tree, which had already been tried out at Bristol, then the first British production of The Crucible, then Look Back in Anger, a new play by a young actor, then a double bill of poetic dramas about Don Juan by one of the company's directors, Ronald Duncan, and finally Nigel Dennis's adaptation of his novel Cards of Identity.
“Culture: Intercom” and Expanded Cinema: A Proposal and Manifesto
Authors: Vanderbeek Stan
Published: January 2007

It is imperative that we quickly find some way for the level of world understanding to rise to a new human scale. This scale is the world. The risks are the life or death of this world. Man is running the machines of his own invention, while the machine that is man runs the risk of running wild.
The Uses of Film in the New Theatre
Authors: Kirby Michael
Published: January 2007

The film experience is not necessarily a single rectangle of light and shadow that flickers at one end of a darkened room. Call this “movies” or “cinema”—that archetypal dream world in which the spectator, seated in a near-foetal position, attempts to ignore the physical space, the other spectators, the projector's shifting beam, to concentrate on the images and the sounds that accompany them. Of course, the movies are a film experience—and a theatre experience—but the use of motion pictures is not so limited, and theatre is just beginning to realize the possibilities inherent in film.

For many years, motion pictures have been used as elements in staged drama—epic and “total” theatre, the “living newspaper,” etc. In 1941, Robert Edmund Jones foresaw “in the simultaneous use of the living actor and the talking picture…a wholly new theatrical art, whose possibilities are as infinite as those of speech itself.”
On a Binomial Approximation
Authors: Steggall J. E. A.
Published: January 2007

The simple approximation for the rth root of a number which is nearly an exact rth power, given by Mr. Whipple last month, is found as a rule in Bonnycastle’s Arithmetic. Perhaps the most elegant form is this:
The Calculus as an Item in School Mathematics
Authors: Jackson C. S.
Published: January 2007

A bold induction by simple enumeration has been made. The graph when plotted confirms it. Let elementary algebra justify it. A little later the algebra will come first.

Just when to introduce the synlbol Δ is of course a question of knowing the class.

How the differences give the slope of certain chords will be evident. How far at this stage to allow the question of the tangent to arise is a question of tact.
Some New Theorems in Geometry of a Surface
Authors: Weatherburn C. E.
Published: January 2007

The elementary properties of generators of a ruled surface, and the existence of a line of striction when the surface is skew, are well known to readers of this journal. We propose to show that many of these properties do not belong exclusively to ruled surfaces; but that a family of curves on any surface possesses a line of striction and a focal curve or envelope, though these are not always real. When the surface is developable, and the “curves” are the generators of one system, the focal curve is the edge of regression. We shall also see that the properties to be established for a family of curves on a surface are analogous to some of the leading properties of congruences of curves in space, the line of striction corresponding to the surface of striction or orthocentric surface, and the focal curve to the focal surface of the latter.
Pythagoras
Authors: Ball W. W. Rouse
Published: January 2007

The Mathematical Gazette has commenced a series of articles, adapted for the use of school-teachers, on the great mathematicians of former days. No series of the kind could be complete were Pythagoras omitted, for it was he who raised mathematics to the rank of a science, made it a part of liberal education, and evolved a scheme on which it continued to be studied in Europe for more than 2000 years. But though his claim to inclusion is indisputable, the materials for describing his work are sadly lacking. We have a treatise by Aristotle on Pythagorean teaching, but the biography by the wife of Pythagoras is lost, and only fragments of the sketches by Aristoxenus, Dikaiarchus, and Philolaus exist, while the memoirs by Laertius Diogenes, Iamblichus, and Porphyry, on which we have mainly to rely for personal details, are late and include much that is palpably untrue. The reputation of Pythagoras far exceeded that of any of his contemporaries, and so great was it that in the credulous ages miracles and magical feats were freely attributed to him; later these additions tended to make men go to the other extreme, and doubt the truth of everything written about him. Within recent years, however, the available materials have been subjected to critical examination, and the researches of T. Gomperz of Vienna, J. Burnet of St. Andrews, G. J. Allman of Dublin, and P. Tannery of Paris enable us to speak with more confidence than was formerly possible.
Imaginaries in Geometry, and Their Interpretation in Terms of Real Elements
Authors: Rao C. V. H.
Published: January 2007

The principal ideas are due to Von Staudt and Luroth. There is also a paper by Prof. Mathews, though it does not go far enough; and a recent treatise in English on the subject makes no reference at all to the question. It may be useful therefore to put down a brief account of the leading ideas of the two writers first mentioned, together with some simple developments.
On Binal Fractions
Authors: Cunningham Allan
Published: January 2007

Binal Fractions. The reciprocals (1/N) of any number (N) will be termed Binal Fractions, or shortly Binals, when expressed in the binary scale. The notation used is similar to that of ordinary decimals. Thus (see table at end):

1°. A point is used to mark the beginning of the fraction.

2°. The binal (1/N) consists of a certain sequence of ciphers and units (the only digits used) to the right of the point; partly non-recurrent and partly recurrent.
Some New Circles Connected With a Triangle
Authors: Lowry H.V.
Published: January 2007

It is sometimes fascinating to return to the old geometry and try to find new properties of the triangle and quadrilateral. One of the most interesting ways of discovering such properties is to start with some well-known result and generalise it. The following notes are the result of an attempt to find circles in a triangle which satisfy the same kind of conditions as the Brocard circle.
Two Illustrations of Elimination
Authors: Davis R. F.
Published: January 2007

If A, B, C, G are four given points in a plane, it is possible to place masses x, y, z at A, B, C respectively, so that the centroid of the system is at G. This, it is to be observed, can only be done in one way as x, y, z must be proportional to the areal (or “barycentric”) co-ordinates of G with respect to the triangle ABC.
Correspondence of Operands to Functions
Authors: Elliott C.
Published: January 2007

In an article on models of functions in the October (1908) number of the Gazette it was suggested that some knowledge of one-to-one correspondence of operands ought to be acquired by means of models before going on to the correspondence of operands to functions, and of functions to functions. In particular, it is easy and of importance to make models of some of the roots of one. It is needless to say that the order of subjects actually adopted in schools is widely different from that here suggested. It is usual to begin with the addition and multiplication of numbers, that is, with a particular kind of correspondence not of operands but of functions. Even the words function and correspondence are not met with until a comparatively late stage, and the fact is ignored that the numbers 2, 3, 4, etc., are functions, though not one-to-one functions.
A New Cubic Connected with the Triangle
Authors: Trachtenberg H. L.
Published: January 2007

The locus of the points of contact of tangents from A to the conics of the confocal system with foci B, C is the same curve as the locus of the feet of normals from A to conies of the system. For any tangent AP to one of the conics is a normal AP to the orthogonal conic of the system through P. Hence if the coordinates of A referred to BC and the perpendicular bisector of BG be x0y0 the equation of this locus is the eliminant of λ between
How to Solve Differential Equations
Authors: Richardson Lewis F.
Published: January 2007

I.The first obstacle may be one of sentiment. It is said that in a certain grassy part of the world a man will walk a mile to catch a horse, whereon to ride a quarter of a mile to pay an afternoon call. Similarly, it is not quite respectable to arrive at a mathematical destination, under the gaze of a learned society, at the mere footpace of arithmetic. Even at the expense of considerable time and effort, one should be mounted on the swift steed of symbolic analysis.
Note on the Addition Formulae of Trigonometry
Authors: Leathem J. G.
Published: January 2007

Proofs of the addition formulae for angles of any magnitudes are sometimes rendered invalid by the way in which arguments are founded on a diagram which can represent only one of the many possible cases. When the two angles under consideration are represented in the usual manner as having a common vertex, the only angles in the diagram whose values it is safe to represent by formulae, if complete generality is to be preserved, are angles having this same vertex. The introduction of other angles may be avoided by a restatement of the definitions of sine and cosine.
The Need of a Sequence in Geometry
Authors: Child J. M.
Published: January 2007

Messrs. Godfrey and Siddons in the preface to their Geometry express both a hope and an expectation that a recognized sequence of propositions will ultimately be adopted not widely differing from that of Euclid. In the Athenœum of January 9th, 1904, the writer of a review on Messrs. Godfrey and Siddons’ book scouts the idea.
Sound-Ranging
Authors: Hope-Jones W.
Published: January 2007

“We are all pacifists now”; or if not, it is difficult to see what excuse we have for living in the modern world. I feel therefore that a word of apology is needed for a paper on a military subject. But I hope you will acquit me of any intention to revive the hatred and bloodthirsty panic that poisoned the years 1914 to 1918, because the activity that I have to tell you about is not concerned with the destruction of life but rather with the saving of it.
The Discovery of Logarithms by Napier.
Authors: Carslaw H. S.
Published: January 2007

A Little more than three hundred years ago Napier announced to the world his discovery of Logarithms in the Mirifici Logarithmorum Canonis Description “ I have always endeavoured,” we read in one of his works, “ according to my strength and the measure of my ability to do away with the difficulty and tediousness of calculations, the irksomeness of which is wont to deter very many from the study of mathematics. With this aim before me, I undertook the publication of the Canon of Logarithms which I had worked at for a long time in former years; this canon rejected the natural numbers and the more difficult operations performed by them, substituting others which bring out the same results by easy additions, subtractions and divisions by two and by three.” Soon after the publication of the Canon, what he calls “another and better kind of logarithms “occurred to him, practically logarithms to the base 10, as we now know them, and a similar change in his system also suggested itself to Briggs, then Gresham Professor of Geometry in London, one of the first to recognise the immense value of Napier’s discovery In the interval between 1614 and Napier’s death in 1617, they had devised several methods for the construction of the new Tables; but owing to Napier’s failing health he had decided to leave the actual computation to Briggs. As early as 1617 Briggs was able to publish the logarithms of the numbers from 1 to 1000 to eight places. In 1624 he followed this with the numbers from 1 to 20,000 and 90,000 to 100,000 to fourteen places. In 1628 Vlacq, a Dutchman, published the logarithms of all numbers from 1 to 100,000 to ten places, along with a Table of the Logarithms of the Trigonometrical Ratios for every minute, to the same number of places. These Tables of Briggs and Vlacq have never been superseded—their work was done for all time. They contain errors which have gradually been discovered and corrected, but all the Tables that have been published since their time, with one single exception, have been copied, directly or indirectly, from their work.
Notes on Elementary Dynamics. II
Authors: Muirhead R. F.
Published: January 2007

In problems where more than two bodies are simultaneously in collision, the rules usually stated in the text books are not, in general, sufficient for their solution. It has been suggested to me that I should continue the subject of Collision by a discussion of the method required in such cases.

In what follows I confine myself to the case of smooth spheres impinging on one another, or on fixed bodies, so that rotations do not fall to be considered.
Extension of the Theory of Inversion to Conics
Authors: Milne J. J.
Published: January 2007

Let t be the centre of a circle, radius r, p any point in its plane, and draw the diameter through p. Then the inverse of p is a point p′ on tp such that tp. tp′ =r2. This circle is called the circle of inversion, its centre t the pole of inversion and the square of its radius the constant of inversion, and each of the points p, p′ is the inverse of the other. This relation is a metric one: a descriptive relation can be obtained as follows.
Note on Systems of Conics Satisfying Four Conditions Treated by the Theory of Characteristics
Authors: Milne J. J.
Published: January 2007

The systematic treatment of these systems by this method has been strangely neglected hitherto by English writers, the only text-book, as far as I am aware, which deals at all with the subject being Salmon’s Conics, sixth edition, 1879, pp. 389, 390, where the states that the properties have been studied by de Jonquières, Chasles, Zeuthen, and Cayley, and that references to the original memoirs will be found in Cayley’s memoir (Phil. Trans., 1867, p. 75). This I have not had the opportunity of consulting. In this article I have followed the Danish mathematician, H. G. Zeuthen, who selected the subject for his Doctor’s Thesis of 1865, which was translated and published in the Nouvelles Annales de Mathématiques in 1866, p. 241, with the title “A New Method of Determining the Characteristics of Systems of Conics.”
Sign in Elementary Analytical Geometry
Authors: Brown F. G.
Published: January 2007

The question of sign constitutes a real difficulty to the intelligent boy at the outset of his study of Coordinate Geometry. At the beginning of his Trigonometry he is told OP must be considered always positive, but later on he will find some authorities giving a point in the third quadrant as ( - r, θ), while others prefer (r, θ + π). The perpendicular distance of (h, k) from ax + by + c = 0 is given by ± (ah + bk +c)/(a2 + b2)½, and sign seems to matter, but usually the pupil is told that he only wants to know how far off (h, k) is, and he is advised to stick to the absolute value. But a little later on he wants the equations of the bisectors of the angles between two given lines, and then he is blamed for not remembering that signs matter a good deal.
3. On Some Unrealised Possibilities in Mathematical Education
Authors: Carson G. ST. L.
Published: January 2007

The last half-century has seen a great and significant change in the popular estimation of mathematics. Formerly the subject was regarded as utterly unpractical, and therefore useless in the narrow sense of this term, though it was recognised as providing a training, unique in its character, in logical thought and accurate expression. Now it is regarded, and correctly regarded, as having enormous practical importance in science and engineering. Most, if not all, of those discoveries and inventions which are so profoundly modifying civic and national life have found their origin, or development, or both, in the labours of mathematicians, and this fact is widely known. The mathematician is no longer regarded as a dreamer of dreams; he is classed with the doctor, the engineer, the chemist and all those whose specialised labours have had immense import for the human race.
A Plea for the Earlier Introduction of the Calculus
Authors: Durell C. V.
Published: January 2007

All who are interested in educational matters cannot fail to be conscious of the widespread spirit of unrest that is abroad. The energy of this association and other similar bodies is proof enough of the increased interest in the efforts that are being made to examine and recast, in the light of modern work, the existing forms of secondary education, and to grapple with the new problems created by a changing system of external forces. Criticism within this sphere is as healthy as it is inevitable, just because it secures a careful scrutiny of the grounds for proposed alterations; and it should serve as a safeguard against fantastic and ill-considered developments of methods and ideas that under proper limitations may be both serviceable and stimulating. Any proposal to introduce a new variety of an old subject, and still more an apparently fresh theme, into the curriculum can only lead to beneficial results if a thorough investigation of the principles involved and the purpose in view has first led to a discrimination between the essential and non-essential, the useful and undesirable, elements of the subject.
The Greek Geometers Before Euclid
Authors: Mackay J. S.
Published: January 2007

The learned professor of Higher Geometry in the university of Genoa has undertaken to write a treatise on The Exact Sciences in Ancient Greece. The treatise will consist of five books, the first being devoted to the period of preparation, the second to the period of greatest splendour, the third to the period of decadence or the epoch of the commentators, the fourth will trace the mathematical discoveries incidentally made by the Greek astronomers and surveyors, and the fifth will treat of the arithmetic of the Greeks.
On Approximations and Reductions
Authors: Lodge A.
Published: January 2007

1.

It may not be generally known how much more rapidly such operations as multiplying or dividing by π, or reducing metres to yards, etc. can be effected by the methods of “Practice” than by direct multiplication and division.

2.

For example, the commonly used approximation for the value of π, though an excellent first approximation, is only true to three significant figures; but (i) is true to five significant figures, and thus yields a second approximation by a correction of the first. The value (ii) which is slightly higher, may be used as a useful check.
Answer to Query
Authors: Sheppard W. F
Published: January 2007

[71. vol. v. p. 330] Mr. Shovelton’s proof (vol. vii. p. 153) may be shortened by using central-difference operators. The theorem itself may be made clearer by splitting it up into two:
Notes on the Parallel-Axiom
Authors: Frankland W. Barrett
Published: January 2007

To begin at the beginning, Euclid built up a system of geometrical theory two thousand two hundred years ago. What perfect clearness there is in his logical procedure! The logic is not only sound, but evident. No wonder that Spinoza wanted to write a geometry of ethics ; the reason was that he wanted a perfect logical sequence.
Presidential Address.: Technical Education and its Relation to Science and Literature
Authors: Whitehead A. N.
Published: January 2007

The subject of this address is Technical Education. I wish to examine its essential nature and also its relation to a liberal education. Such an enquiry may help us to realise the conditions for the successful working of a national system of technical training. It is also a very burning question among mathematical teachers; for mathematics is included in most technical courses.
General Theory of Verniers
Authors: Heawood Percy J.
Published: January 2007

The practical use and working of a vernier is very simple. It is applicable to all measurements where minute accuracy is required, whether the quantity to be measured is itself a length, as the reading of a barometer, or is determined by the distance passed over by a moving point relatively to a uniformly divided scale straight or curved, as in the angular readings of an astronomical instrument. In its simplest form too, the principle on which it depends is very obvious. Supposing, for instance, we require to read a scale to the one hundredth of an inch. To graduate such a scale directly would require a large number of minute subdivisions, which would be troublesome to make with the requisite accuracy and very confusing to the eye in reading.
On Stirling's Theorem as a Definition of the Gamma Function
Authors: Egan F.
Published: January 2007

In the following note, Stirling’s formula for a factorial is first found by a very simple process. The expression so obtained has a meaning for non-integral as well as integral values of the variable. The function it defines is easily seen (§§ 3 ff.) to possess the fundamental properties of the Gamma function, and provides an easy and natural avenue of approach to its study.
Fractional Calculus
Authors: Fabian W.
Published: January 2007

We continue here our work on fractional integration and differentiation of functions of a real variable which we began in a previous paper. All quantities in the present paper are real.

We define a λth integral, or a (−λ)th differential coefficient, of f(x) over an interval (a, x)by

where D stands for and γ is the least integer greater than or equal to zero such that λ + γ>0, f(x) is bounded on the path of integration, and is continuous on this path except possibly for a finite number of ordinary discontinuities.
Remainders in Interpolation and Quadrature Formulae
Authors: Daniell P. J.
Published: January 2007

The determination of the errors involved in interpolation or quadrature formulae often involves complicated reasoning. There are many cases, however, where the remainder can be obtained very easily. These cases belong to the class which we call simplex.

In general a formula will be expressible in the form

L(f) =∑rArf(xr) + ∑sBsf'(xs)+ ∑tCtf''(xt) +… ......(1)

to a finite number of terms and it is assumed throughout that f(x) possesses derivatives as far as the remainder may require.
How ought a Logarithm to be defined?
Authors: Muirhead R. F.
Published: January 2007

Mr. Fletcher begins his article in the January number of the Gazette by giving two reasons why a logarithm ought not to be defined as the index of the power of the base which is equal to the number. But are these reasons well-founded? One is that it does not afford a basis for the more advanced parts of the theory of logarithms. That statement would require a proof that might be very difficult or perhaps impossible to produce.
Differentials
Authors: Temple G.
Published: January 2007

In the teaching of the Theory of Differentials the really difficult and important problem is not “how shall we teach a given theory?” but “which theory shall we teach?” There are, in fact, a number of rival theories, none of which has met with any general measure of acceptance. In these circumstances, the critical problem of considering the rival merits of these theories is much more urgent than the pedagogical problem of presenting them to students.
The Conjugate Hyperbola and the Involutory Ellipse
Authors: Freeman J. B.
Published: January 2007

N.B.—In what follows we consider the conic as the projection of the circle and assume only its descriptive (including cross-ratio) properties as known.

1. A circle, centre g1 is cut by a secant line at ww′. Any line cpp′ through c, the pole of ww′, cuts the circle at p and again at p′. The lines wp and w′p′ intersect at d. The locus of d for the variable secant line through c is a hyperbola touching the given circle at ww′ (If w′p and wp′ meet at d′, the locus of d′ is the same hyperbola.)
A Scale Change Calculator with Three Control Points
Authors: Green H. G.
Published: January 2007

A difficulty which is frequently met in dealing with examination results is that of bringing to a common standard the marks obtained from two different papers. The most common form of variation occurs when the mark distribution curves are correct in general character but the peaks are at different points of the scale. We describe a machine devised by the author which has been used for the adjustment of marks. Its theory has no statistical justification, but where the distortions are not excessive the results do not differ appreciably from those of the rather lengthy theoretical methods and are usually absorbed in the approximation of a fraction to its nearest unit.