The occurrence of halloysite and/or kaolinite in clay-rich, vein-like zones in saprolites in Hong Kong has provided the opportunity to examine the conditions determining the formation of one kaolin mineral or the other and also the nature of their particles. Clay-rich zones within tuffaceous or granitic saprolites from six different hillside sites have been examined in replicate samples by optical and scanning electron microscopy, X-ray diffraction, and thermal analysis. Kaolin minerals, sometimes together with Mn oxides and Fe oxides/oxyhydroxides, have formed within discontinuities within the altered host rocks. The fabrics of kaolin infills generally indicated several generations of kaolin formation and that shear and deformation have commonly occurred within the infills. The infills were either light or dark in color. Light-colored infills often comprised pure, or nearly pure, halloysite or kaolinite. Dark Mn- and Fe-rich infills all contained kaolinite, while including some halloysite. The very halloysitic, light-colored infills occurred in saprolites in both granite and tuff as long tubular shapes in parallel bunches. The light-colored, very kaolinitic infills occurred in tuff only, in large platy or near-platy shapes within vermiform packets. In dark-colored infills, early kaolin mineral crystallization was limited by impurities from the breakdown of primary minerals leaving dissolved and re-precipitated compounds of Mn and Fe within the infill. Kaolin minerals in infill at all the sites except one are considered to have formed as a result of weathering. The exception comprises white infills in tuff that are composed of extremely small, closely packed particles, suggesting formation by hydrothermal action. Generally, the kaolin minerals have formed by neogenesis out of solution in the discontinuities. Drying, with the formation of Mn and/or Fe oxides/oxyhydroxides, had occurred several times, indicating enhanced drainage. Where drying had occurred, kaolinite had formed. Where indications of drying in infills were absent, halloysite was predominant.

Infants and children born with CHD are at significant risk for neurodevelopmental delays and abnormalities. Individualised developmental care is widely recognised as best practice to support early neurodevelopment for medically fragile infants born premature or requiring surgical intervention after birth. However, wide variability in clinical practice is consistently demonstrated in units caring for infants with CHD. The Cardiac Newborn Neuroprotective Network, a Special Interest Group of the Cardiac Neurodevelopmental Outcome Collaborative, formed a working group of experts to create an evidence-based developmental care pathway to guide clinical practice in hospital settings caring for infants with CHD. The clinical pathway, “Developmental Care Pathway for Hospitalized Infants with Congenital Heart Disease,” includes recommendations for standardised developmental assessment, parent mental health screening, and the implementation of a daily developmental care bundle, which incorporates individualised assessments and interventions tailored to meet the needs of this unique infant population and their families. Hospitals caring for infants with CHD are encouraged to adopt this developmental care pathway and track metrics and outcomes using a quality improvement framework.

In order to state our primary results, we must first establish some notation. Let S-1 (x) = sin x and C-1 (x) = cos x, then for each non-negative integer n, let

these are the remainders of the Maclaurin series for sine and cosine, respectively. Note that for each and for each . It is known that

See [1] for several different proofs of the well-known fact that

the values of αn and βn for then follow rather easily using induction and integration by parts. (Details are provided in the Appendix.)

The set of solutions to the equation xy = yx has been studied extensively over the past three centuries, including work by well known mathematicians such as Daniel Bernoulli (1700–1782), Leonhard Euler (1707–1783), and Christian Goldbach (1690–1764). Various mathematicians have focused on the integer, rational, real, and complex solutions. For example, it has been shown (see [1]) that the equality 24 = 42 gives the only distinct integer solutions. Our exposition below presents some of the key ideas behind the positive real solutions to this equation and illustrates how rational solutions can be found. To learn more about the various solutions, the reader can consult the articles listed at the end of this paper, as well as the extensive references given in these articles. It is also possible to find some of this material on the Web.

Finding an expression for the length of a curve is one of the simpler geometric applications of the integral. If f is a function with a continuous derivative, then the expression gives the length of the curve y = f (x) on an interval [a, b]. However, after writing out the integrand for familiar functions such as y = x2 and y = sin x, it quickly becomes apparent that, in general, finding an antiderivative is a challenge. Of course, a computer can give accurate approximations for the value of the integral for the length of a curve, but it would be nice to find the exact length rather than a decimal approximation. In his work on geometry (from 1637), Descartes stated that he believed it was not possible to determine the exact lengths of curves. However, just twenty years later, William Neile was able to find the length of arcs of semicubical parabolas (see Katz [1]). These curves have the form y = kx3/2 and are usually the first examples or exercises given to students since the resulting integral is very easy to compute. In this paper, we are going to examine this curve and other related curves and consider problems such as the following: find rational numbers a and b so that the length of the curve over the interval is an [a, b] integer. As we shall see, problems such as this provide a variety of opportunities for undergraduate students to explore some interesting mathematics arising from a few simple and accessible questions.

Following large declines in tuberculosis transmission the United States, large-scale screening programs targeting low-risk healthcare workers are increasingly a source of false-positive results. We report a large cluster of presumed false-positive tuberculin skin test results in healthcare workers following a change to 50-dose vials of Tubersol tuberculin.

Infect Control Hosp Epidemiol 2018;39:750–752

Let T be a triangle and let A be the area of T. Given a point p inside the triangle and a number r that satisfies 0 < r ≤ ½, we seek to count the number N (p, r) of straight lines that pass through p and cut T into two pieces so that one piece has area rA. As the point p and the ratio r vary, the value of N (p, r) ranges from 0 to 6. Given a ratio r, we want to determine the regions within T for which the function N (p, r) assumes various integer values. For example, a region inside T for which N (p, r) = 6 only exists for values of r between and ½, and we would like to quantify the area of this region (as a fraction of the total area of the triangle) as r varies.

The aberrancy of a plane curve is a property of the curve that is invariant under both translation and rotation. It provides a numerical measure for the non-circularity of the curve at each point of the curve. (Recall that curvature gives an invariant numerical measure of nonlinearity.) The concept of aberrancy has been around for two centuries, but it has received very little attention. We hope to stir a little interest in the concept by presenting four different derivations of the formula for aberrancy. This may appear to be redundant, but there are some good reasons for doing so. First of all, the only derivation for aberrancy in the literature is a bit confusing and makes a few unjustified assumptions. Secondly, the derivations we present are all significantly different from each other and involve some interesting ideas in elementary real analysis. Finally, although the basic idea behind each derivation is simple, the details can become extremely messy unless a proper path is chosen. We encourage the reader to find one or two approaches of particular interest and use the concept of aberrancy as an extended problem set in an undergraduate analysis course or even a further mathematics class in an English school.

This paper reviews the results of several years' study by a multidisciplinary team comprising geneticists, physiologists, ecologists and statisticians of abiotic stress tolerance in barley. The strategy involves genetic fingerprinting of wild barley lines (Hordeum spontaneum C. Koch) from a range of habitats and testing these for responses to abiotic stresses under controlled conditions. Multiple regression analysis is used to identify genetic markers associated with experimentally determined stress responses. These data are related to site-of-origin ecogeographic data and used to identify areas of useful wild variation. Markers associated with traits of interest can be mapped in genetic mapping populations, revealing areas of the barley genome carrying genes controlling stress responses. This paper highlights our work on associations of amplied fragment length polymorphisms with salt tolerance and describes some initial results of the use of SSRs in studying drought tolerance in barley.

In adult male rats fed on a cholesterol-free synthetic diet, plasma cholesterol concentrations were lowest with oat bran, intermediate with cellulose and highest with wheat bran. Plasma triacylglycerols (TAG) were similar with wheat bran and cellulose but higher with oat bran. The concentrations and pools of caecal volatile fatty acids (VFA) were lowest with cellulose and equally higher with oat bran and wheat bran. Plasma VFA concentrations in the hepatic portal vein reflected those in caecal digesta and were unrelated to plasma cholesterol. Feeding oat bran after extraction with n-pentane gave plasma cholesterol concentrations similar to that found with wheat bran. Reconstitution of oat bran with extracted lipids did not restore the cholesterol-lowering effect. Addition of the extracted material to a wheat-bran diet had no effect on plasma cholesterol. Plasma TAG were higher with the oat bran and reconstituted-oatbran diets than with wheat-bran or cellulose diets. However, extracted oat bran+safflower oil gave similar TAG concentrations to that with wheat bran. These extractions and additions did not change caecal bile acid or neutral sterol concentrations. Effects of these diets on plasma cholesterol were unrelated to their tocotrienol or tocopherol content. Addition of n-pentane to oat bran followed by evaporation of solvent gave plasma cholesterol concentrations that were significantly higher than untreated oat bran but lower than similarly treated wheat bran. It is concluded that oat bran affects cholesterol metabolism through a pentane-soluble component as well as non-starch polysaccharides. It appears that the activity of this lipid is not transferable by simple addition of the solvent extract to the whole diet.

When the diagnosis of epilepsy is made, the patient must first of all be investigated to make sure that the epilepsy is not symptomatic of a disease that will need some special line of treatment. For example, epilepsy starting at any age may be the first indication of a cerebral tumour, although this will obviously be more likely among the older patients. The nature and extent of these investigations will depend on such factors as the age of onset, the type of seizure and the associated positive physical signs. However, even in the cases where there is no evidence whatsoever that the epilepsy is symptomatic, an electroencephalogram may help in differentiating the type of epilepsy from which any particular patient is suffering, and so aid in deciding on the form of treatment most likely to be beneficial. When any necessary investigations have been carried out and the form that treatment is to take has been settled, the social implication of this diagnosis has then to be faced. This often resolves itself into a discussion of the patient's employment.

It has been shown by a number of workers that in a large proportion of cases the E.E.G.s of schizophrenic patients are abnormal. This paper is an attempt to increase our knowledge of the hereditary background of schizophrenia by recording the E.E.G.s not only of those suffering from the disease but also those of their near relatives.