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The student must compute the arc length for each of her three functions, and the winner of the contest is the one who has the function with the smallest arc length on the unit interval. This is an interesting open-ended problem for most students since they do not have much experience in constructing functions that satisfy required conditions. I am often surprised by some of the ingenuity students use in coming up with their contest entries. The contest requires evaluation of two integrals for each function, one for the area and one for the arc length. Moreover, it is important for the students to recognize when one of their functions gives rise to an improper integral for the arc length since such an integral may be difficult to approximate accurately. Thus the contest provides an opportunity to combine several topics from the typical calculus syllabus. The shortest closed curve enclosing an area of 1 is a circle of radius 1/ √ π. Its arc length is 2 √ π. Since a unit area is bounded by any curve in our contest together with the interval [0, 1], the length of a contest curve cannot be less than 2 √ π − 1 = 2. 5449. If one imagines an ideal inextensible string of length L > 1 nailed down at the points (0, 0) and (1, 0), and pushed outward by a uniform pressure, then the equilibrium curve (where the force due to the pressure is balanced by the tension in the string in each small arc) has constant curvature in any portion where it is smooth, so it is a circular arc. This suggests that an arc of a circle joining the points (0, 0) and (1, 0) will yield the smallest arc length for a curve satisfying the three conditions, as illustrated in figure 1. To achieve the area of 1, we would need

This article explores the ways that a computer algebra system may be used in conjunction with plotting software to allow students to investigate the convergence properties of Riemann sums for functions of one or two variables in a way that is not possible with just numerical calculations. Explicit formulas for the Riemann sums suggest algebraic combinations that lead to the trapezoid and Simpson's rules as a way to improve the rate of convergence.

The traditional approach to introducing the study of the derivative is through the tangent line as the limiting behavior of secant lines. This geometric discussion leads to the definition of the derivative, after which the differentiation formulas are developed and tangent lines can finally be computed. Unfortunately, this approach seldom gives the students any idea of what tangent lines actually are and why they might be of interest. Today's computer-graphics capabilities, however, allow exciting new ways to introduce the derivative. Topics from dynamical systems serve as interesting applications that are accessible even to students in precalculus courses (see, e.g., Devaney [1990]). Coupled with modern graphing technology, the iteration of functions, especially linear functions, not only allows an instructor to illustrate ideas from an area of great current mathematical interest but also affords an excellent opportunity to introduce the derivative and tangent lines.

This study was undertaken to characterize the population pharmacokinetics (PK), therapeutic dose, and preferred route of administration for pyrazinamide (PZA) in elephants. Twenty-three African (Loxodonta africana) and Asian (Elephas maximus) elephants infected with or in contact with others culture positive for Mycobacterium tuberculosis were dosed under treatment conditions. PZA was dosed daily at 20-30 mg/kg via oral (fasting or nonfasting state) or rectal (enema or suppository) administration. Blood samples were collected 0-24 h postdose. Population PK was estimated using nonlinear mixed effect modeling. Drug absorption was rapid with T(max) at or before 2 h regardless of the method of drug administration. C(max) at a mean dose of 25.6 (+/-4.6) mg/kg was 19.6 (+/-9.5 microg/mL) for PZA given orally under fasting conditions. Under nonfasting conditions at a mean dose of 26.1 +/- 4.2 mg/kg, C(max) was 25% (4.87 +/- 4.89 microg/mL) and area under concentration curve (AUC) was 30% of the values observed under fasting conditions. Mean rectal dose of 32.6 +/- 15.2 mg/kg yielded C(max) of 12.3 +/- 6.3 microg/mL, but comparable AUC to PZA administered orally while fasting. Both oral and rectal administration of PZA appeared to be acceptable and oral dosing is preferred because of the higher C(max) and lower inter-subject variability. A starting dose of 30 mg/kg is recommended with drug monitoring between 1 and 2 h postdose. Higher doses may be required if the achieved C(max) values are below the recommended 20-50 microg/mL range.

We recently described the clinical presentation and treatment of 18 elephants from six herds infected with TB. Treatment protocols and methods varied between herds to include both oral and rectal dosing using multiple drug doses and formulations. In this paper we present information regarding the pharmacokinetics (PK) of isoniazid (INH) in elephants and provide suggestions regarding initial treatment regimens. Forty-one elephants received INH daily by either oral or rectal administration with different formulations. Population PK analysis was performed using Non-linear Mixed Effect Modeling (NONMEM). Results of oral administration indicated that compared with premixed INH solution, the drug exposure was highest with a suspension prepared freshly with INH powder. When INH was concomitantly given as an admixture over food, Tmax was delayed and variability in drug absorption was significantly increased. Compared with oral administration, similar drug exposures were found when INH was dosed rectally. The data generated suggest that a starting dose of 7.5 mg/kg of INH is appropriate for initial TB treatment in elephants when premixed solution is administered directly into the oropharynx or rectal vault and 4 mg/kg are when INH is administered following immediate suspension from powdered form.

In [1], Sheldon Gordon described several investigations that he has calculus students perform on polynomials whose coefficients are determined by the digits of the students’ social security numbers. He remarks that the use of individualized projects are designed to get the students to take a personal interest in the topic under study and that the students seem to enjoy these types of investigations. In this note I would like to build upon this theme by describing a project that I have used in multivariable calculus classes. The goal of the project is to investigate a function of two variables built from the student’s social security number. First the student is asked to take each of the nine digits of the number and compute its value mod 3 (to keep the digits small). Writing the new number as ABC-DE-FGHI, the student constructs a function by substituting the digits into the expression

Self-assessment of clerkship performance in obstetrics and gynecology was completed by 142 medical students and compared with departmental evaluations. Significant positive correlations existed between self- and departmental assessments for each of seven parameters in three categories of evaluation (clinical activities, written examination, and oral examinations). Students graded themselves lower than the actual faculty ratings and higher than the actual resident ratings. There was no difference in self- or departmental evaluations in regard to student gender. The amount of previous clerkship experience did not correlate with either the actual or perceived grades. Overall, self-assessments are consistent with those rendered by the department.

(1991). An Occurrence of the Ballot Numbers in Operator Theory. The American Mathematical Monthly: Vol. 98, No. 7, pp. 613-617.

The effects of short pulses of cycloheximide on the traversal of the G1 phase of the cell cycle of the yeast Saccharomyces cerevisiae were examined. Cells were released from a block at the regulatory stage of G1, termed ‘start’, and pulsed with cycloheximide. Delays in budding which were considerably longer than the length of the pulse were observed. During the delay the cells remained blocked at ‘start’. No delay in budding was observed after cycloheximide pulses, when cells were released from a cdc 24 block which arrests the budding process but not ‘start’. Overall protein synthesis did not show an additional delay after the pulse. The extra lag following cycloheximide pulses appears to reflect a unique feature of ‘start’. It may be accounted for by a requirement at ‘start’ for a labile protein with a half-life time of about 6 min.

Major proteins synthesized by Swiss 3T3 cells at different stages of the cell cycle have been analyzed using double isotope labeling and one-dimensional SDS-polyacrylamide slab gels. The synthesis of actin was previously shown to be markedly enhanced a few hours after quiescent cells initiated growth following addition of serum. In contrast, the synthesis of actin remained at a constant rate, similar to that in quiescent cells, relative to synthesis of other proteins during the entire cell cycle. We conclude that enhanced actin synthesis is a process specific for the G0 to S transit, and may serve as a marker event during this interval. In contrast, three other proteins (90,000, 57,000, and 33,000 daltons) were synthesized throughout the cell cycle at higher rates than in G0 cells, and thus, are markers characteristic of cells traversing the cell cycle. A transient increase, such as seen for actin synthesis, by cells emerging from quiescence, may represent a process that these cells must perform before they can enter the G1 portion of the cell cycle. A transient event such as this need not be a periodic event that occurs during each cycle.

Geometric characterizations in terms of trees, extreme points and dentability are presented for weak*-compact absolutely convex sets that have the Radon-Nikodym property for the Pettis integral.

Both serum factors and protein synthesis are required for normal cell growth. Swiss 3T3 cells require the serum growth factors insulin and EGF (epidermal growth factor) during the initial part of the G1 period, until they pass a restriction point about 2 h before the initiation of DNA synthesis. Concentrations of cycloheximide that inhibit protein synthesis by as much as 70% dramatically lengthen the cell cycle before the restriction point, while the cell cycle after the restriction point remains nearly constant. These results are consistent with a model in which labile proteins are required for transit of cells past the serum-sensitive restriction point. The relation of these findings to the growth control of transformed cells is discussed.

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A method of accurately determining the tensile strength of porcelain has been developed. The ratio of tensile to compression strength was found to be 5.9 for the special porcelain studied. Triaxial porcelains gave an average ratio of 7.66. The tensile strength tests show in general a little more variation than compression strength tests. The tensile strength is of more significance in judging the quality of porcelain than it has been commonly considered.

Repeated firing of several aluminum-silicate minerals to the same temperatures show that the specific gravities of the fired products do not drop at the same rate. Petrographic-microscopic examinations show that this is due to different rates of dissociation in the minerals. While these rates of reaction or dissociation can not be measured accurately, some idea of the relative rates can be obtained by comparison of the sizes of completely dissociated grains of the minerals or of the widths of the borders of the dissociation products formed around the grains. Furthermore, the effect of repeated firing upon the increase in size of mullite crystals formed when the minerals dissociate gives evidence concerning the rate of growth or probable refractoriness of the minerals. These are described in some detail and close correlation between them and the specific gravity changes are pointed out.

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The variable nature of the raw materials and the intricate methods involved in manufacture make it difficult to secure uniformity in ceramic ware. The elimination of variable factors is helped by adherence to the following rules: (1) Careful analysis of each operation. (2) Development of written standards for each operation, describing the methods and conditions found best. (3) Enforcement of the standards by careful inspection, using accurate tests after each operation to measure the results just obtained. (4) Division of the body as it is made, into homogeneous units or batches, which remain separate through the rest of the production operations. (5) Complete records readily available covering each step through which a batch passes in production. (6) Strict adherence to standard procedure even though tempted by expediency to somewhat let down the bars. The application of the above principles to body-making at the Champion Porcelain Company is described.

Advantage was taken of an eighteen months' continuous run of the Dressler kiln of the Champion Porcelain Company firing to cones between 17 and 18, to observe the effect of the temperatures and the gas conditions in various parts of the kiln upon a large number of standard bodies and experimental mixes. The kiln and conditions within it are briefly described, as well as the types of bodies used. The observed changes in outward physical properties of the bodies are supplemented by petrographic-microscopic examinations in order to determine or explain the reasons for the behavior of the bodies. Three instances of the production of deposits of artificial minerals formed in the kiln during firing are also described and explanations for their occurrence are given.

Calcined mixtures of kaolin and alumina were prepared by grinding for different lengths of time and firing the several grinds at different temperatures ranging from slightly above dehydration temperature of clay to 1700°C. The X-ray diffraction patterns revealed several interesting points relative to the degree of combination of the oxides present.

Foreword It was with a feeling of deep humility that I received the invitation to be the Edward Orton, Jr., Fellow Lecturer this year. Every year, when the program of the Annual Meeting is announced in The Bulletin, my first interest in it is the Orton Lecture, and the significant honor bestowed upon the man chosen to give it. The availability of the literature of The American Ceramic Society to me when I was graduated from high school and began to work in an art pottery helped me to decide to go to college and to choose the course in ceramics at Ohio State University. In doing so, I was very fortunate in having been closely associated with Doctor Orton both as a student and as an instructor. We became friends, and this friendship continued through the years. I am very grateful to have this opportunity to acknowledge the assistance and counsel of Edward Orton, Jr., and his associates.

The synthesis of both cytoplasmic and nuclear proteins has been studied as quiescent, serum-deprived Swiss mouse 3T3 cells are stimulated to transit the cell cycle. In serum-arrested cells a 200,000 dalton cytoplasmic protein and a 51,000 dalton nuclear protein were found to be preferentially synthesized. In serum-stimulated cells the first major protein whose synthesis was seen to increase had a molecular mass of 42,000 daltons. This protein also showed the greatest change in synthesis during the transit from G0 to S phase. Its synthesis rose to a maximum 4--6 hr after stimulation and then declined as cells entered S phase. The protein was present in both nuclear and cytoplasmic extracts. It was identified as actin on the basis of its mobility on sodium dodecyl sulfate and isoelectric focusing polyacrylamide gels. Other proteins synthesized preferentially by stimulated cells had molecular masses of 57,000 daltons (cytoplasmic), 33,000 daltons (cytoplasmic and nuclear), and 15,000 daltons (nuclear). The synthesis of the 57,000 and 33,000 dalton proteins increased gradually after stimulation and remained high during S phase. The 15,000 dalton proteins began to be synthesized as cells entered S phase. The preferential synthesis of these proteins provides biochemical markers for the transition from quiescence to proliferation.

We present a model to account for several major observations on growth control of animal cells in culture. This model is tested by means of kinetic experiments which show that exponentially growing animal cells whose ability to synthesize total protein has been inhibited with cycloheximide (by up to 70%) grow at rates approximately proportional to their rates of protein synthesis. However, virtually the entire elongation of the cell cycle occurs in the part of the G 1 phase that depends on a high concentration of serum in the medium. This part of the cycle has earlier been suggested to lie prior to the restriction point—i.e., the point beyond the main regulatory processes of G 1 . The remainder of the cycle, from restriction point to mitosis, is markedly insensitive to these concentrations of cycloheximide as well as to growth regulation. We quantitatively account for the specific lengthening of that part of the cycle involved in growth regulation by assuming that cells must accumulate a specific protein in a critical amount before they can proceed beyond the restriction point. The lability of this protein (half-life about 2 hr) makes its accumulation unusually sensitive to inhibition of total protein synthesis by cycloheximide. Its production appears to depend on growth factors provided by serum. The model can also account for greater variations of G 1 durations as the growth of cell populations is made slower. It also predicts two sorts of quiescence: one of cells slowly traversing G 1 , in slightly suboptimal conditions; the other of cells that enter G 0 under inadequate conditions. Transformation of different sorts could create cells with altered variables for initiation, synthesis, or inactivation of the regulatory protein or could altogether eliminate the need for the protein.

This paper describes the organization and evaluation of a third-year clerkship in obstetrics and gynecology conducted in a multiple-hospital setting. No difference was detected in objective test performance of students based on the site of the clerkship or in the subjective evaluation of students by faculty in the community hospitals. Students do spend their time in the various hospitals differently, but this seems more attributable to the individuality of specific hospitals than to the university-community dichotomy. PG 1 performance of graduates of the program compares favorably with that of graduates of other schools. It was concluded that community hospitals can carry out their primary responsibility of patient care while making an effective contribution to a university teaching program.