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Aneurysmal bone cyst is a benign solitary lesion of unknown etiology. Its radiographic and histologic appearance can overlap with those tumors of malignant origin. It is imperative that clinical data, radiographs, and operative and pathological findings be correlated to ensure an accurate diagnosis. Aneurysmal bone cysts occur only 7% of the time in the foot. Recurrence rates are reported to be less than 12%. A case report of recurrence of aneurysmal bone cyst in the foot is reviewed, in addition to the etiology, differential diagnosis, and treatment alternatives.

We have used a broad range of primers for HPV detection, using the polymerase chain reaction (PCR) so as to compare PCR typing of HPV with the results of cytological diagnosis in a New Brunswick population referred to the out-patient clinic of the Saint John Regional Hospital. The primers selected were found to be capable of amplification with high efficiency, therefore we did not perform further hybridization analysis for specific identification of HPV types. Amplification of selected fragments for detection of HPV 6, 11, 16, 18, 31 and 33 was obtained from cervical swabs collected from 154 patients. Microscopic examination was performed in duplicate samples and the results compared with the DNA-typing analysis. HPV of any of the above types was detected in 43 out of 154 patients. Among these, 32 patients showed single or multiple infections with "high-risk" HPV strains 16, 18, 31 or 33. Cytologically normal or atypical samples with any of the HPV types tested amounted to 17%, but increased to 56% in patients with CIN I, and to 100% in patients with CIN II or III. Prevalence of "high-risk" types alone increased from 15% and 10%, for normal and atypical cases respectively, to 48% for CIN I, 75% for CIN II and 100% for CIN III. Our results indicate that HPV detection and typing by this simple procedure can be a valuable indicator of cancer progression and thus can help to identify individuals at high risk in pre-malignant stages of the disease.

A 9-yr-old girl developed delayed acute measles inclusion body encephalitis, which was different from subacute sclerosing panencephalitis (SSPE) in clinical course. Measles virus was demonstrated by electron microscopy, immunohistochemistry, and in situ hybridization. Contrary to the most previous reports, matrix (M) protein was present in the brain, cerebrospinal fluid, and serum and was demonstrated by Western blot analysis and in situ hybridization. The hybridization was performed by a nonradioactive digoxigenin method.

Plasma diazepam can be reliably estimated using a simple benzene extraction and gas-liquid chromatography with griseofulvin as internal standard. This gives reproducible results within the clinical range of plasma levels. Storage at minus 20 degrees C is recommended but is not essential for the 1st week.

A detailed analysis in which the blast furnace is considered as a continuous counter-current reactor. The stoichiometric and thermodynamic conditions are applied to individual reactions within the furnace as well as to the overall process.

In what follows I propose to give the history of two theorenis and to state some of the consequences that have been developed from them.The first theorem is:If a triangle be inscribed in a circle, and from any point in the circumference perpendiculars be drawn to the sides, the feet of these perpendiculars lie in a straight line.

A straight line KK′ meets the circumference of a circle at two real or two imaginary points K, K′, and H is the middle point of the real or imaginary chord KK′. If A, B, C, D be any four points on the circumference, and the pairs of straight lines AB, DC, AC, BD, AD, CB meet KK′ at the pairs of points E,E′, F,F′, G,G′; then if any one pair of points be equidistant from H, the two other pairs will also be equidistant.

The object of the present paper is merely to exhibit the methods employed by the ancient Greek geometers in their solution of this celebrated problem. A critical discussion of these methods, of the origin of the problem, and perhaps also an account of more recent researches and a notice of the literature connected therewith may form the subject of a subsequent paper.

The paper is entitled Solutio facilis problematum quorumdam geometricorum difficillimorum, and is printed in Novi Commentarii Academiae Scientiarum Imperialis Petropolitanae, Tom. xi., pp. 103–123. The volume is for the year 1765; the title-page is dated 1767.

In 1746, when he was a candidate for the Chair of Mathematics in the University of Edinburgh rendered vacant by the death of Maclaurin, Matthew Stewart published his first work, Some General Theorems of considerable use in the higher parts of Mathematics. In the preface to it he states that “the theorems contained in the following sheets . … are entirely new, save one or two at most,” but he does not specify the two. They are

The theorem is—The distance between the circumscribed and the inscribed centres of a triangle it a mean proportional between the circumscribed radius and its excess above the inscribed diameter.

A process for removing the superfine smokes from ferromanganese blast-furnace gases having low investment and low operating cost is described. This method solves both the air and stream-pollution problems. The ferro blast-furnace gas is cleaned from 10 to 15 grains per cu ft to less than 0.01 grains per cu ft by a wet-washing procedure in a Pease Anthony venturi scrubber. The alkali cyanide stream-pollution problem is solved by the control of pH and complete recycle of the liquors so that the cyanide is stripped by the incoming gas and is subsequently burnt in the stoves or boilerhouse. The liquor is separated from solids in a Dorr thickener. The solids are removed in the underflow as a thick slurry which is either returned to the furnace or dumped in a pit in the ore yard. The overflow is pumped back to the venturi. The chemistry and physical equipment of the process are described.

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

Is the following trifle worthy of a place in your Mathematical Notes ? I came on the puzzle in a volume of the letters of Dr W. Whewell, the well-known Master of Trinity College, Cambridge. At the end of a letter to Professor A. De Morgan, dated 18th January 1859, he says:“I can express every whole number from 1 to 15 (I think) by means of four nines. Thus Is it worth while working this out further ?”A note to the letter states that:“Two more examples from a fragment in Dr Whewell's handwriting will illustrate the meaning of this:Here are my solutions of the puzzle for the numbers 0 to 40, excepting 38. Some ingenious young mathematician may be instigated to complement my solutions, and to carry the matter still further.

The two problems are :—1. To divide a given straight line internally and externally so that the ratio between its segments may be equal to a given ratio.2. To divide a given straight line internally and externally so that the rectangle under its segments may be equal to a given rectangle.

Chasles in his Aperçu, Historique sur l'origine et le développement des Méthodes en Géométrie (seconde édition, 1875, pp. 214–215) makes the following statement:“Essays of the same kind as the geometry of the rule and that of the compasses, and which hold, so to speak, the mean between the two, had long previously engaged the attention of famous mathematicians. Cardan first of all in his book De Subtilitate had resolved several of Euclid's problems by the straight line and a single aperture of the compasses, as if one had in practice only a rule and invariable compasses. Tartalea was not long in following his rival on this field, and extended this mode of treatment to some new problems. (General trattato di numeri et misure; 5ta parte, libra terzo; in-fol. Venise, 1560). Finally, a learned Piedmontese geometer, J.–B. de Benedictis, made it the object of a treatise entitled: Resolutio omnium Euclidis problematum, aliorumque ad hoc necessario inventorum, una tantummodo circini data apertura; in-4°. Venise, 1553.”

Oral glucose tolerance tests were carried out on 51 men with atherosclerotic peripheral vascular disease, none of whom were known diabetics or had suffered recent myocardial infarction. The plasma insulin and blood sugar responses were compared with 47 age and sex-matched controls. There was no significant difference in obesity between the two groups. The patient group showed an increased plasma insulin response with a delay in return to fasting levels, and the blood sugar response was similar. These results suggest that hyperinsulinaemia and hyperglycaemia are often associated with atherosclerosis, and may have a role in its aetiology.

The following mnemonics, with one exception, consist of verses or sentences such that if the number of the letters in each word be written down in the order in which the words occur, the desired value will be obtained.

Plasma diazepam can be reliably estimated using a simple benzene extraction and gas-liquid chromatography with griseofulvin as internal standard. This gives reproducible results within the clinical range of plasma levels. Storage at minus 20 degrees C is recommended but is not essential for the 1st week.

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.

Three body numerical solutions to low thrust guidance and navigation for outer planet orbiter with nuclear-electric propulsion

Investigations conducted in several parts of the world have shown that residents of soft-water areas have a higher death rate from ischemic heart disease than residents of hard-water areas. The same pattern appears to exist in Ontario, but when deaths are divided into sudden and nonsudden (on the basis of whether or not the death certificate was signed by a coroner), the higher death rate in the soft-water areas is found to be due entirely to an excess of sudden deaths. This finding suggests that the correlation between cardiac mortality and water hardness may be the result of an increased susceptibility to lethal arrhythmias among residents of soft-water areas.

Ventilatory tests (F.E.V.(1)/F.V.C.) have been studied in 16 asthmatic subjects during intermittent administration of corticotrophin, and the responses correlated with the plasma cortisol levels. The improvement in respiratory function was found to last for a longer period than the enhanced adrenocortical activity.

A system is described for applying lateral forces to human teeth. The force patterns can reproduce those previously observed during any type of routine buccolingual activity. The technique permits continuous registration of the displacement patterns of teeth relative to surrounding intraoral structures. Threshold levels for the force/duration/displacement relationship have been examined, but summation, recovery, fatigue and maximal-displacement phenomena can also be recorded.

The incidence of abnormalities of fasting serum cholesterol and triglyceride levels and blood sugar and plasma insulin response to an oral glucose load have been investigated in a group of 51 male patients with atherosclerotic peripheral vascular disease. These have been compared with an age and sex matched group of 47 healthy controls. Both groups showed a similar degree of obesity. The most common single abnormality was a prolonged and increased plasma insulin response, which was much more frequently seen among patients than controls. Over 75% of the patients showed abnormality of blood sugar or insulin response. Elevation of fasting levels of serum lipids was considerably less common, although the mean serum cholesterol level of the patients was significantly higher than that of the controls. The relevance of these results is discussed.

Pythagoras was born in Samos about 580 B.C. The statements regarding his masters are destitute of solid historical foundation, and so are the accounts of his travels. It is known, however, that he visited Egypt. He may have taught in Samos, but whether he did not obtain sufficient consideration among his fellow-citizens, or whether he wished to withdraw from the tyranny of Polycrates, he removed to Croton about 540 B.C. There he founded an association, less scientific than politico-religious, which eventually became the nucleus of the aristocratic party.

Here is a pendant to Dr Gibson's beautiful dissection of the three squares. I am pretty sure that his proof is new to the world, but I am not sure that mine s so. There are about fifty proofs, differing more or less from each ither, but there are only some half a dozen worth remembering oreaching. The proof I submit (not one of the half dozen) was levised in 1859, when I was a young student in St Andrews, and b may probably have been given long before that date.

Mr J. F. Cameron of Gonville and Caius College, Cambridge, has suggested the use of factorial functions such as or n! to solve Whewell's problem. I had excluded them as beyond the bounds of ordinary arithmetic. I append half a score of my attempts with the factorials; they could be easily increased.

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

Of the following properties the first two are obvious; the third was communicated to the Royal Society of London by the Rev. Dr James Booth* in 1854; the others, obtained many years ago, have not as far as I know been remarked. They seem to be more curious than useful.