Example 1. An exponential curve. My topic is best introduced by an example. I take it from the correspondence between Leibniz and Huygens in 1690-1691. Leibniz wrote about his new differential and integral calculus. Huygens was very skeptical and proposed problems for Leibniz to solve. In the course of this exchange Leibniz came to use an exponential equation to represent a curve. This was enti...

We reconsider the problem of producing fair and accurate tariffs based on aggregated insurance data giving numbers of claims and total costs for the claims. Jorgensen and de Souza (Scand. Actuarial J., 1994) assumed Poisson arrival of claims and gamma distributed costs for individual claims. Jorgensen and de Souza (1994) directly modelled the risk or expected cost of claims per insured unit, p ...

Rotation curves of spiral galaxies are known with reasonable precision for a large number of galaxies with similar morphologies. The data implies that non-Keplerian fall–off is seen. This implies that (i) large amounts of dark matter must exist at galactic scales or (ii) that Newtonian gravity must somehow be corrected.We present a method for inverting the integral relation between an elemental...

In many economic problems, we are often interested in the growth rate of a variable. Of particular importance is the situation where the rate of growth is constant or approximately constant. This often entails a model which assumes that a unit increase in the independent variable will be accompanied by a fixed proportional increase in the dependent variable, apart from random fluctuations. Unde...

The present study utilizes nine years of measurements taken from a Joss–Waldvogel disdrometer (JWD). From this dataset, thirty six rainfall events, were selected and categorized, respectively, in convective and stratiform types, according to specific criteria. Six statistical distributions namely the oneand two-parameter exponential, the twoand three-parameter lognormal and finally the twoand t...

Corn stover, a major crop‐based lignocellulosic biomass feedstock, is required to be at an optimum moisture content for efficient bioconversion processes. Environmental conditions surrounding corn stover, as in storage facilities, affect its moisture due to hygroscopic sorption or desorption. The measurement and modeling of sorption characteristics of corn stover and its leaf, husk, and stalk f...

We describe a new set of self-consistent, equilibrium disk galaxy models that incorporate an exponential disk, a Hernquist model bulge, an NFW halo and a central supermassive black hole. The models are derived from explicit distribution functions for each component and the large number of parameters permit detailed modeling of actual galaxies. We present techniques that use structural and kinem...

As a major part of the daily operation in an enterprise, purchasing frequency is of constant change. Recent approaches on the human dynamics can provide some new insights into the economic behaviors of companies in the supply chain. This paper captures the attributes of creation times of purchase orders to an individual vendor, as well as to all vendors, and further investigates whether they ha...

Temperature variations of the kinetics of the electrochemical and homogeneous oxidation of the title compounds give rise to Arrhenius plots, the slopes of which give access to the heavy-atom (including solvent) reorganization energies. Information on the role of proton transfer in the dynamics of the concerted proton-electron transfer reaction (CPET) is potentially contained in the pre-exponent...