Eulerian Angles

Euler's angles are used to describe rotation using independent coordinates. They are useful in rotation spectroscopy studies, hence this introduction.

DeMoivre's Theorem

DeMoivre's theorem is of great utility in some parts of physical chemistry and is re-introduced here.

Briefe an eine deutsche Prinzessin über verschiedene Gegenstände aus der Physik und Philosophie

[Leonhard Euler]. Aus dem Franz. übers.

Die Gefäßkryptogamen der Schweiz

von Carl Gustav Bernoulli

The theory of runs with application to drought predictions

The primary interest was in predicting the distribution runs in a sequence of Bernoulli trials. Difference equation techniques were used to express the number of runs of a given length k in n trials under three assumptions (1) no runs of length greater than k, (2) no runs of length less than k, (3) no other assumptions about the length of runs. Generating functions were utilized to obtain the distributions of the future number of runs, future number of minimum run lengths and future number of the maximum run lengths unconditional on the number of successes and failures in the Bernoulli sequence. When applying the model to Texas hydrology data, the model provided an adequate fit for the data in eight of the ten regions. Suggested health applications of this approach to run theory are provided. ^

Kawasaki syndrome: Cluster analysis of incident cases presenting to a pediatric tertiary care hospital in Texas from January 1, 2005 to December 31, 2009

Background: Despite almost 40 years of research into the etiology of Kawasaki Syndrome (KS), there is little research published on spatial and temporal clustering of KS cases. Previous analysis has found significant spatial and temporal clustering of cases, therefore cluster analyses were performed to substantiate these findings and provide insight into incident KS cases discharged from a pediatric tertiary care hospital. Identifying clusters from a single institution would allow for prospective analysis of risk factors and potential exposures for further insight into KS etiology. ^ Methods: A retrospective study was carried out to examine the epidemiology and distribution of patients presenting to Texas Children’s Hospital in Houston, Texas, with a diagnosis of Acute Febrile Mucocutaneous Lymph Node Syndrome (MCLS) upon discharge from January 1, 2005 to December 31, 2009. Spatial, temporal, and space-time cluster analyses were performed using the Bernoulli model with case and control event data. ^ Results: 397 of 102,761 total patients admitted to Texas Children’s Hospital had a principal or secondary diagnosis of Acute Febrile MCLS upon over the 5 year period. Demographic data for KS cases remained consistent with known disease epidemiology. Spatial, temporal, and space-time analyses of clustering using the Bernoulli model demonstrated no statistically significant clusters. ^ Discussion: Despite previous findings of spatial-temporal clustering of KS cases, there were no significant clusters of KS cases discharged from a single institution. This implicates the need for an expanded approach to conducting spatial-temporal cluster analysis and KS surveillance given the limitations of evaluating data from a single institution.^

(Table 1) Stabile isotopes at DSDP Leg 55 Holes

Deep sea drilling on four seamounts in the Emperor Seamount chain revealed that Paleogene shallow-water carbonate sediments of the "bryozoan-algal" facies crown the basalt edifices. According to the biofacies model of Schlanger and Konishi (1966, 1975), this bryozoan- algal assemblage suggests that the seamounts formed in cooler, more northerly waters than those presently occupied by the island of Hawaii; i.e., the paleolatitudes of formation were greater than 20 °N. Moving southward toward the youngest member of the seamount chain, a facies gradient indicative of warmer waters was observed. This gradient is interpreted as a reflection of a northward shift in isotherms during the time span in which the seamounts were progressively formed (Savin et al., 1975). On all seamounts, sedimentation at the drilling sites occurred in a high-energy environment with water depths of approximately 20 meters. Early-stage carbonate diagenesis began in the phreatic zone in the presence of meteoric water, but proceeded after subsidence of the seamounts into intermediate sea waters, where the bulk, stable isotopic composition was determined. The subsidence into intermediate waters was rapid, and permitted establishment of an isotopic equilibrium which, like the facies gradient, reflects the northward shift in isotherms during the Paleogene. Calcite and zeolite cements comprise the later-stage diagenesis, and originated from solutions arising from the hydrolysis of the underlying basalt. In conclusion, the results of this study of the shallow-water carbonate sediments are not inconsistent with a paleolatitude of formation for Suiko Seamount (Site 433) of 26.9 ±3.5 °N, as determined by paleomagnetic measurements (Kono, 1980).

Distribution of diatoms in surface sediments and some limnological characteristics of studied lakes in the Siberian arctic

The investigation of the species composition and ecology of diatoms of modern bottom sediments in water bodies of arctic polygonal tundra in three subregions of North Yakutiya has been carried out. As a result, 161 taxons of diatoms were determined; the determinant role of the depth, conductivity, pH of the water, and geographic latitude in their distribution was confirmed, and two complexes of species with respect to the leading abiotic factors were distinguished. The diatoms of the first complex prefer shallow water bodies of high latitudes with neutral and slightly alkaline water and relatively high conductivity. The second complex is confined to the water bodies of lower latitudes with small conductivity, as well as neutral and slightly acidic water.