Seven place logarithmic tables.

"October 1961."

Logarithmic and mathematical tables.

Chiefly tables.

Vierstellige Logarithmen der natürlichen Zahlen und Winkelfunctionen ... /

Mode of access: Internet.

Tables of applied mathematics in finance, insurance, statistics,

Mode of access: Internet.

Surveying manual; a manual of field and office methods for the use of students in surveying,

Mode of access: Internet.

Typing mineral deposits using their grades and tonnages in an artificial neural network

A test of the ability of a probabilistic neural network to classify deposits into types on the basis of deposit tonnage and average Cu, Mo, Ag, Au, Zn, and Pb grades is conducted. The purpose is to examine whether this type of system might serve as a basis for integrating geoscience information available in large mineral databases to classify sites by deposit type. Benefits of proper classification of many sites in large regions are relatively rapid identification of terranes permissive for deposit types and recognition of specific sites perhaps worthy of exploring further. Total tonnages and average grades of 1,137 well-explored deposits identified in published grade and tonnage models representing 13 deposit types were used to train and test the network. Tonnages were transformed by logarithms and grades by square roots to reduce effects of skewness. All values were scaled by subtracting the variable's mean and dividing by its standard deviation. Half of the deposits were selected randomly to be used in training the probabilistic neural network and the other half were used for independent testing. Tests were performed with a probabilistic neural network employing a Gaussian kernel and separate sigma weights for each class (type) and each variable (grade or tonnage). Deposit types were selected to challenge the neural network. For many types, tonnages or average grades are significantly different from other types, but individual deposits may plot in the grade and tonnage space of more than one type. Porphyry Cu, porphyry Cu-Au, and porphyry Cu-Mo types have similar tonnages and relatively small differences in grades. Redbed Cu deposits typically have tonnages that could be confused with porphyry Cu deposits, also contain Cu and, in some situations, Ag. Cyprus and kuroko massive sulfide types have about the same tonnages. Cu, Zn, Ag, and Au grades. Polymetallic vein, sedimentary exhalative Zn-Pb, and Zn-Pb skarn types contain many of the same metals. Sediment-hosted Au, Comstock Au-Ag, and low-sulfide Au-quartz vein types are principally Au deposits with differing amounts of Ag. Given the intent to test the neural network under the most difficult conditions, an overall 75% agreement between the experts and the neural network is considered excellent. Among the largestclassification errors are skarn Zn-Pb and Cyprus massive sulfide deposits classed by the neuralnetwork as kuroko massive sulfides—24 and 63% error respectively. Other large errors are the classification of 92% of porphyry Cu-Mo as porphyry Cu deposits. Most of the larger classification errors involve 25 or fewer training deposits, suggesting that some errors might be the result of small sample size. About 91% of the gold deposit types were classed properly and 98% of porphyry Cu deposits were classes as some type of porphyry Cu deposit. An experienced economic geologist would not make many of the classification errors that were made by the neural network because the geologic settings of deposits would be used to reduce errors. In a separate test, the probabilistic neural network correctly classed 93% of 336 deposits in eight deposit types when trained with presence or absence of 58 minerals and six generalized rock types. The overall success rate of the probabilistic neural network when trained on tonnage and average grades would probably be more than 90% with additional information on the presence of a few rock types.

Size-corrected BMD decreases during peak linear growth: Implications for fracture incidence during adolescence

Peak adolescent fracture incidence at the distal end of the radius coincides with a decline in size-corrected BMD in both boys and girls. Peak gains in bone area preceded peak gains in BMC in a longitudinal sample of boys and girls, supporting the theory that the dissociation between skeletal expansion and skeletal mineralization results in a period of relative bone weakness. Introduction: The high incidence of fracture in adolescence may be related to a period of relative skeletal fragility resulting from dissociation between bone expansion and bone mineralization during the growing years. The aim of this study was to examine the relationship between changes in size-corrected BMD (BMDsc) and peak distal radius fracture incidence in boys and girls. Materials and Methods: Subjects were 41 boys and 46 girls measured annually (DXA; Hologic 2000) over the adolescent growth period and again in young adulthood. Ages of peak height velocity (PHV), peak BMC velocity (PBMCV), and peak bone area (BA) velocity (PBAV) were determined for each child. To control for maturational differences, subjects were aligned on PHV. BMDsc was calculated by first regressing the natural logarithms of BMC and BA. The power coefficient (pc) values from this analysis were used as follows: BMDsc = BMC/BA(pc). Results: BMDsc decreased significantly before the age of PHV and then increased until 4 years after PHV. The peak rates in radial fractures (reported from previous work) in both boys and girls coincided with the age of negative velocity in BMDsc; the age of peak BA velocity (PBAV) preceded the age of peak BMC velocity (PBMCV) by 0.5 years in both boys and girls. Conclusions: There is a clear dissociation between PBMCV and PBAV in boys and girls. BMDsc declines before age of PHV before rebounding after PHV. The timing of these events coincides directly with reported fracture rates of the distal end of the radius. Thus, the results support the theory that there is a period of relative skeletal weakness during the adolescent growth period caused, in part, by a draw on cortical bone to meet the mineral demands of the expanding skeleton resulting in a temporary increased fracture risk.

Statnote 19: non-linear regression: fitting an exponential curve to data

Non-linear relationships are common in microbiological research and often necessitate the use of the statistical techniques of non-linear regression or curve fitting. In some circumstances, the investigator may wish to fit an exponential model to the data, i.e., to test the hypothesis that a quantity Y either increases or decays exponentially with increasing X. This type of model is straight forward to fit as taking logarithms of the Y variable linearises the relationship which can then be treated by the methods of linear regression.

Sobre a integração indefinida de funções racionais complexas: teoria e implementação de algoritmos racionais

We present indefinite integration algorithms for rational functions over subfields of the complex numbers, through an algebraic approach. We study the local algorithm of Bernoulli and rational algorithms for the class of functions in concern, namely, the algorithms of Hermite; Horowitz-Ostrogradsky; Rothstein-Trager and Lazard-Rioboo-Trager. We also study the algorithm of Rioboo for conversion of logarithms involving complex extensions into real arctangent functions, when these logarithms arise from the integration of rational functions with real coefficients. We conclude presenting pseudocodes and codes for implementation in the software Maxima concerning the algorithms studied in this work, as well as to algorithms for polynomial gcd computation; partial fraction decomposition; squarefree factorization; subresultant computation, among other side algorithms for the work. We also present the algorithm of Zeilberger-Almkvist for integration of hyperexpontential functions, as well as its pseudocode and code for Maxima. As an alternative for the algorithms of Rothstein-Trager and Lazard-Rioboo-Trager, we yet present a code for Benoulli’s algorithm for square-free denominators; and another for Czichowski’s algorithm, although this one is not studied in detail in the present work, due to the theoretical basis necessary to understand it, which is beyond this work’s scope. Several examples are provided in order to illustrate the working of the integration algorithms in this text

Análise conjunta de regressões : ajustamento e zonagem agrícola

A Análise conjunta de regressões, ACR, é uma técnica utitilizada para estudar a interação gentipo x ambiente baseada em regressões. Nesta técnica ajusta-se uma regressão linear por cultivar. Nestas regressões a variável controlada é o índice ambiental que mede a produtividade dos vários ambientes. Nas culturas anuais, os ambientes compreendem aos pares (local, ano). Os valores dos índices ambientais e dos coeficientes das regressões são ajustados simultaneamente. Até agora a ACR tem sido aplicada a uma única cultura de cada vez. Neste trabalho vamos procurar ultrapassar essa limitação através da modelação dos logaritmos dos índices ambientais tendo-se desenvolvido um modelo da forma: zi, j  v  l j  j , i  1,...,n, J  1,...,n onde zi , j é o logaritmo do índice ambiental para o i-essimo ambiente na j  essima cultura , v um valor médio geral , li j  essimo cultivar. o efeito do i  essimo local e  j o efeito do Ao utilizar esta modelação, os locais corresponderão a estações experimentais de forma a poder-se ter várias culturas no mesmo local. Ora, as estações experimentais são escolhidas por forma a serem representativas das regiões onde estão implantadas. Assim, os índices ambientais correspondentes às várias estações experimentais e, consequentemente, às respetivas regiões, pudesse ser utilizados para agrupar regiões contíguas com índices semelhantes obtendo-se assim, um elemento interessante para a Zonagem agrícola no que diz respeito às culturas que se trabalha. Pode-se ainda procurar uma Zonagem para grupos de cultivares. Por exemplo, adiante trabalharemos com dados da cevada e trigo os quais são cereais. ABSTRACT: Joint Regression Analysis, JRA, is one of the techniques for the study of genotypeXenvironment interaction based on the use of regressions .In JRA a linear regression of the yields of each cultivar on a controlled variable, the environment index ,is adjusted .The index miss erasures the productivity of each environment .In yearly cultures the environments correspond to the pairs (location ,years) .These indexes and the correlation coefficients are adjusted simultaneously. Up to now JRA has been applied to single crops .Now we try to overcome this restriction through modeling of the logarithms of the environmental indexes .We developed a model τ i , j = v + l j +λ j , i = 1,..., b, J = 1,...J where τ i , j is the logarithm of the environmental index for the i-th environment and the j-th crop , v is the general mean , li is the effect of the i-th environment and λ j is the effect of the j-th crop . When applying this model the location will correspond to experimental situations in order to have several crops in the same locations .Now experimental stations are chosen to be representative of the regions in which they are located .Then the l1 ,..., lb can be used to group contiguous regions with similar location effects .We thus get an useful tool for Agricultural Zoning for the crops we used or, even, for the group to which those crops belong . For instance we worked with barley and wheat that are cereals.

Next-to-soft radiative corrections in QCD and quantum gravity

The origin of divergent logarithmic contributions to gauge theory cross sections arising from soft and collinear radiation is explored and a general prescription for tackling next-to-soft logarithms is presented. The NNLO Abelian-like contributions to the Drell-Yan K-factor are reproduced using this generalised prescription. The soft limit of gravity is explored where the interplay between the eikonal phase and Reggeization of the graviton is explained using Wilson line techniques. The Wilson line technique is then implemented to treat the set of next-to-soft contributions arising from dressing external partons with a next-to-soft Wilson line.