scholarly journals On generalized series fields and exponential-logarithmic series fields with derivations

2014 ◽  
pp. 350-372 ◽  
Author(s):  
Mickaël Matusinski
Keyword(s):  
Author(s):  
Li Ma ◽  
Changpin Li

This paper is devoted to investigating the relation between Hadamard-type fractional derivatives and finite part integrals in Hadamard sense; that is to say, the Hadamard-type fractional derivative of a given function can be expressed by the finite part integral of a strongly singular integral, which actually does not exist. Besides, our results also cover some fundamental properties on absolutely continuous functions, and the logarithmic series expansion formulas at the right end point of interval for functions in certain absolutely continuous spaces.


2008 ◽  
Vol 27 (1) ◽  
pp. 63-73 ◽  
Author(s):  
Brent Wilson

Abstract. The taxocene of live epiphytal foraminifera was for one year monitored monthly on six phytal substrates in shallow water (<1 m) in two bays around Nevis, NE Caribbean Sea. Mosquito Bay was subject to a nutrient flux from a leaking septic tank. Long Haul Bay was comparatively undeveloped. SHE Community Structure Investigations (SHECSIs) revealed that the populations on five plants had logarithmic series distributions of species abundances, the slopes of lnS vs. lnE for these five time-series being within −1±0.3. In three time-series, they were within −1±0.05.Cluster analysis of twenty-five sediment samples in shallow water (<3 m) indicates that Nevis is largely surrounded by a single thanatacoenosis, for which SHECSI indicates a logarithmic series population structure. However, it is not possible to reconstruct perfectly the epiphytal population from the sediment thanatacoenosis. The thanatacoenosis included 40% allochthonous Amphistegina gibbosa, Archaias angulatus and Asterigerina carinata, washed in from offshore reefs, and few planorbulinids, although the latter dominates the biocoenosis on seagrass leaves in the backreef.


2021 ◽  
Vol 9 (3) ◽  
pp. 151-155
Author(s):  
Fehim J Wani ◽  

The Generalized Logarithmic Series Distribution (GLSD) adds an extra parameter to the usual logarithmic series distribution and was introduced by Jain and Gupta (1973). This distribution has found applications in various fields. The estimation of parameters of generalized logarithmic series distribution was studied by the methods of maximum likelihood, moments, minimum chi square and weighted discrepancies. The GLSD was fitted to counts of red mites on apple leaves and it was observed that all the estimation techniques perform well in estimating the parameters of generalized logarithmic series distribution but with varying degree of non-significance.


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