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The theory of classical ergodic Markov genetic diffusion process, Feller genetic diffusion, and the genetic drift diffusion with and without selection and mutation for a single unlinked locus with two alleles, Kimura models, is studied. These genetic problems are numerically investigated on the long run. The approximates solutions of these models are described as the conditional probabilities to find the specific gene with frequencies between zero and one at generation T . As a surprise, we notice that the summation of these approximate solutions lose their unity rapidly as the number of generations increase than five, i.e. T > > 5 . The earlier biologists did due the reason to the migration, immigration and death of individuals. Till now, there is no mathematical proof to this phenomenon. In this paper, we solve this problem by extending the first order time derivative to the time fractional derivative, to study the effect of the memory on these models. This extension ensures that the summations of the approximate solutions, i.e. of the Non-Markov cases, are one at any number of generations. The time evolution of the approximate solutions are simulated and compared with other published papers, for different values of generations and for the Markov and Non-Markov cases with different values of the fractional order β . The convergence of the approximate descrete solutions and the reversibility property of these stochastic processes for both the Markov cases and Non-Markov cases are also numerically simulated and discussed.

A stochastic production technology that allows risk effects of factor inputs was estimated for maize farmers in Ethiopia. The results suggested that the promoted improved maize technology exhibits constant returns to scale whereas non-adopters use decreasing returns to scale technology. The study showed that timely planting is critical for maize yield stability among both adopters and non-adopters and suggests the importance of using oxen and higher efforts to achieve that. Nevertheless, the results showed that most of the factors under the control of the farmers do not offer powerful explanation to maize yield variability compared to natural factors such as rainfall, frost, pests and diseases.

The Kalabsha region at the northwest side of Lake Aswan has been a subject of seismological and geodetic investigations since 1981, after the 5.5 M earthquake on 14 November. The subsequent seismic activity was related to the effect of water-level oscillations in the Lake. Geodetic measurements provided indications of regional stress and of the local character of vertical movements. As crustal dynamics represents a potential hazard with respect to the size of the lake, other techniques have been applied to the monitoring system. Repeated gravity test measurements were already made in the late 1980s and in 1994, but only in 1997 was a new epoch of long-term investigation initiated. The measured data showed sufficient accuracy of approx. 5 μGal. Already the first difference of the two campaigns of the years 1997 and 2000 showed a few important features. First of all, the temporal non-tidal changes of gravity exceed the level of confidence significantly. The changes were compared with older available geodetic data, and it was concluded, that the gravity changes were not related directly to the vertical movements of the surface. On the contrary, a water loading effect may be expected on the eastern side of the network, especially in the Kalabsha local net. The development of the stress field is considered to be the main source of observed gravity changes. In both the Kalabsha and Seiyal nets the changes differ according to the relative positions of the particular measuring points with respect to the faults.

A simple method to simultaneously determine the shape (shape factor or structural index) and the depth of a buried structure from second horizontal derivative anomalies obtained from gravity data using filters of successive window lengths has been developed. The method is similar to Euler deconvolution, but it solves for shape and depth independently. For a fixed window length, the depth is determined using the least-squares method for each shape factor. The computed depths are plotted against the shape factors representing a continuous window curve. The solution for the shape and depth of the buried structure is read at the common intersection of window curves. The method involves using simple models convolved with the same numerical horizontal second derivative filter as applied to observed gravity data. As a result, the method can be applied not only to true residuals but also to measured Bouguer data of a short profile length. Finally, the validity of the method is tested on theoretical examples with and without random errors and field data from Senegal, west Africa.

The voltage collapse of a power system is analyzed as the result of the eventual push of the system operating point beyond the boundary of voltage security due to random fluctuations in the system load characteristics. The effect of different fluctuation intensity levels at load buses on the eventual voltage collapse of a power system is studied with the help of a stochastic based voltage collapse indicator. It is shown that this indicator, will provide further insights into the power system's vulnerability due to the high degree of uncertainty that exists in present day voltage collapse load models. >

The problem of bistable dynamic power systems driven by colored and Markov jump noise processes is analyzed. The authors address the development of specific stochastic models that reflect inherent fluctuations of power system parameters and characteristics. These models cover certain fluctuations, such as those due to the effect of random customer switching and ambient weather conditions. In addition, an example of a discrete stochastic model is presented to reflect other switching events, such as those due to transformer tap changers. One of the most important features of these models is the capability to properly represent prevailing conditions leading up to voltage collapse scenarios. >

This paper attempts to justify claims made by the authors concerning the application of a power system stochastic voltage collapse indicator (SVCI). Since the SVCI is an approximate solution to a system of stochastic differential equations, the authors present a scheme to evaluate its validity. The scheme involves the use of Monte-Carlo techniques where for a given confidence interval, samples representing different realizations of the modeled uncertain power system will be run with the goal of obtaining the sampled value of the SVCI. Accuracy and sensitivity of the indicator are compared to benchmark measurements obtained from Monte-Carlo runs of a dynamic power system perturbed by small-magnitude perturbations. Strong correlation between the two sets of values for the SVCI and its sampled counterpart will give credence to the application of the SVCI to voltage stability studies.

The mixed ligand complexes of Cd(II) and Pb(II) with thiosulphate as a primary ligand and chloride, bromide of iodide (individually) as a secondary ligand have been polarographically, investigated at 30°C and at a constant ionic strength of μ = 1.0 M (NaClO4). Two mixed ligand complexes were formed with the Cd(II) ion: log β12 = 4.77, 5.30 and 6.78 for the chloride, bromide and iodide ions, respectively; and log β21 = 5.36, 5.04 and 6.22 for the same ions. For the Pb(II)-Ts-Cl system, only one mixed ligand complex was formed with a log stability constant log β21 =4.35. For the Pb(II)-Ts-Br system, three mixed ligand complexes are obtained with log β11 = 3.63, log β12 = 4.51 and log β21 = 4.85.