scholarly journals A unified approach to the Clenshaw summation and the recursive computation of very high degree and order normalised associated Legendre functions

2002 ◽  
Vol 76 (5) ◽  
pp. 279-299 ◽  
Author(s):  
S. A. Holmes ◽  
W. E. Featherstone
2018 ◽  
Vol 8 (1) ◽  
pp. 162-173
Author(s):  
T. Fukushima

Abstract In order to accelerate the spherical/spheroidal harmonic synthesis of any function, we developed a new recursive method to compute the sine/cosine series coefficient of the 4π fully- and Schmidt quasi-normalized associated Legendre functions. The key of the method is a set of increasing-degree/order mixed-wavenumber two to four-term recurrence formulas to compute the diagonal terms. They are used in preparing the seed values of the decreasing-order fixed-degree, and fixed-wavenumber two- and three-term recurrence formulas, which are obtained by modifying the classic relations. The new method is accurate and capable to deal with an arbitrary high degree/ order/wavenumber. Also, it runs significantly faster than the previous method of ours utilizing the Wigner d function, say around 20 times more when the maximum degree exceeds 1,000.


Author(s):  
Cecil E. Hall

The visualization of organic macromolecules such as proteins, nucleic acids, viruses and virus components has reached its high degree of effectiveness owing to refinements and reliability of instruments and to the invention of methods for enhancing the structure of these materials within the electron image. The latter techniques have been most important because what can be seen depends upon the molecular and atomic character of the object as modified which is rarely evident in the pristine material. Structure may thus be displayed by the arts of positive and negative staining, shadow casting, replication and other techniques. Enhancement of contrast, which delineates bounds of isolated macromolecules has been effected progressively over the years as illustrated in Figs. 1, 2, 3 and 4 by these methods. We now look to the future wondering what other visions are waiting to be seen. The instrument designers will need to exact from the arts of fabrication the performance that theory has prescribed as well as methods for phase and interference contrast with explorations of the potentialities of very high and very low voltages. Chemistry must play an increasingly important part in future progress by providing specific stain molecules of high visibility, substrates of vanishing “noise” level and means for preservation of molecular structures that usually exist in a solvated condition.


2011 ◽  
Vol E94-C (10) ◽  
pp. 1548-1556 ◽  
Author(s):  
Takana KAHO ◽  
Yo YAMAGUCHI ◽  
Kazuhiro UEHARA ◽  
Kiyomichi ARAKI

Genetics ◽  
1996 ◽  
Vol 144 (2) ◽  
pp. 635-645 ◽  
Author(s):  
David A Kirby ◽  
Wolfgang Stephan

Abstract We surveyed sequence variation and divergence for the entire 5972-bp transcriptional unit of the white gene in 15 lines of Drosophila melanogaster and one line of D. simulans. We found a very high degree of haplotypic structuring for the polymorphisms in the 3′ half of the gene, as opposed to the polymorphisms in the 5′ half. To determine the evolutionary mechanisms responsible for this pattern, we sequenced a 1612-bp segment of the white gene from an additional 33 lines of D. melanogaster from a European and a North American population. This 1612-bp segment encompasses an 834bp region of the white gene in which the polymorphisms form high frequency haplotypes that cannot be explained by a neutral equilibrium model of molecular evolution. The small number of recombinants in the 834bp region suggests epistatic selection as the cause of the haplotypic structuring, while an investigation of nucleotide diversity supports a directional selection hypothesis. A multi-locus selection model that combines features from both-hypotheses and takes the recent history of D. melanogaster into account may be the best explanation for these data.


1977 ◽  
Vol 27 (1) ◽  
pp. 81-90
Author(s):  
S.A. Filfilan ◽  
D.C. Sigee

The uptake of tritiated thymine into cells of a heterogeneous population of Prorocentrum micans was investigated using light-microscope and electron-microscope autoradiography. Specificity of thymine uptake into DNA was demonstrated by the specific removal of label from wax-embedded material using DNase and by the high degree of localization of nuclear label to chromosomes in the electron-microscope autoradiographs. All nuclei, including both dividing and non-dividing cells, showed a substantial uptake of label, indicating that nuclear DNA synthesis in Prorocentrum micans is a continuous process. The level of DNA synthesis does show considerable variation, however, with very high levels in some interphase nuclei. The continuous replication of nuclear DNA provides further evidence of dinoflagellate affinity to the prokaryotes, and indicates that Prorocentrum micans is a very primitive eukaryote cell.


Author(s):  
Arthur Yosef ◽  
Eli Shnaider ◽  
Rimona Palas ◽  
Amos Baranes

This study presents a decision-support method to estimate the next year performance of corporate Operating Income Margin (OIM). It is based on a unique combination of cross-section model and the rules-based evaluation mechanism. The estimate is done in terms of broad categories, and not precise numerical values. The model is constructed as follows: its dependent variable (OIM) is one year ahead vs. the corresponding explanatory variables. This structure of the model allows us to view explanatory variables as reflecting financial potential of corporations. The evaluation component consists of a set of rules designed to identify the companies whose “potential” clearly points to an opportunity to invest. For the method presented here to succeed, it is necessary to utilize a highly reliable modeling method, even if it is “Fuzzy”. We apply Soft Regression (SR), which is a Soft Computing modeling tool based on Fuzzy Logic, and utilize all available proxy variables by creating intervals of values. Advantages of utilizing SR, and the intervals’-based modeling are extensively discussed. Modeling results for five consecutive years are consistent and stable, thus indicating high degree of reliability. Testing indicates very high success rate for the stock market related domain, the lowest being 87.9%.


1962 ◽  
Vol 15 (3) ◽  
pp. 525-534 ◽  
Author(s):  
M. Rabinovitch ◽  
W. Plaut

The incorporation of tritiated thymidine in Amoeba proteus was reinvestigated in order to see if it could be associated with microscopically detectable structures. Staining experiments with basic dyes, including the fluorochrome acridine orange, revealed the presence of large numbers of 0.3 to 0.5 µ particles in the cytoplasm of all cells studied. The effect of nuclease digestion on the dye affinity of the particles suggests that they contain DNA as well as RNA. Centrifugation of living cells at 10,000 g leads to the sedimentation of the particles in the centrifugal third of the ameba near the nucleus. Analysis of centrifuged cells which had been incubated with H3-thymidine showed a very high degree of correlation between the location of the nucleic acid-containing granules and that of acid-insoluble, deoxyribonuclease-sensitive labeled molecules and leads to the conclusion that cytoplasmic DNA synthesis in Amoeba proteus occurs in association with these particles.


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