Abstract: Analysis of real life problems often results in linear
systems of equations for which solutions are sought. The method to
employ depends, to some extent, on the properties of the coefficient
matrix. It is not always feasible to solve linear systems of equations
by direct methods, as such the need to use an iterative method
becomes imperative. Before an iterative method can be employed
to solve a linear system of equations there must be a guaranty that
the process of solution will converge. This guaranty, which must
be determined apriori, involve the use of some criterion expressible
in terms of the entries of the coefficient matrix. It is, therefore,
logical that the convergence criterion should depend implicitly on the
algebraic structure of such a method. However, in deference to this
view is the practice of conducting convergence analysis for Gauss-
Seidel iteration on a criterion formulated based on the algebraic
structure of Jacobi iteration. To remedy this anomaly, the Gauss-
Seidel iteration was studied for its algebraic structure and contrary
to the usual assumption, it was discovered that some property of the
iteration matrix of Gauss-Seidel method is only diagonally dominant
in its first row while the other rows do not satisfy diagonal dominance.
With the aid of this structure we herein fashion out an improved
version of Gauss-Seidel iteration with the prospect of enhancing
convergence and robustness of the method. A numerical section is
included to demonstrate the validity of the theoretical results obtained
for the improved Gauss-Seidel method.
Abstract: Saturated hydraulic conductivity is one of the soil
hydraulic properties which is widely used in environmental studies
especially subsurface ground water. Since, its direct measurement is
time consuming and therefore costly, indirect methods such as
pedotransfer functions have been developed based on multiple linear
regression equations and neural networks model in order to estimate
saturated hydraulic conductivity from readily available soil
properties e.g. sand, silt, and clay contents, bulk density, and organic
matter. The objective of this study was to develop neural networks
(NNs) model to estimate saturated hydraulic conductivity from
available parameters such as sand and clay contents, bulk density,
van Genuchten retention model parameters (i.e. r
θ , α , and n) as well
as effective porosity. We used two methods to calculate effective
porosity: : (1) eff s FC φ =θ -θ , and (2) inf φ =θ -θ eff s , in which s
θ is
saturated water content, FC θ is water content retained at -33 kPa
matric potential, and inf θ is water content at the inflection point.
Total of 311 soil samples from the UNSODA database was divided
into three groups as 187 for the training, 62 for the validation (to
avoid over training), and 62 for the test of NNs model. A commercial
neural network toolbox of MATLAB software with a multi-layer
perceptron model and back propagation algorithm were used for the
training procedure. The statistical parameters such as correlation
coefficient (R2), and mean square error (MSE) were also used to
evaluate the developed NNs model. The best number of neurons in
the middle layer of NNs model for methods (1) and (2) were
calculated 44 and 6, respectively. The R2 and MSE values of the test
phase were determined for method (1), 0.94 and 0.0016, and for
method (2), 0.98 and 0.00065, respectively, which shows that method
(2) estimates saturated hydraulic conductivity better than method (1).
Abstract: Investigation of soil properties like Cation Exchange
Capacity (CEC) plays important roles in study of environmental
reaserches as the spatial and temporal variability of this property
have been led to development of indirect methods in estimation of
this soil characteristic. Pedotransfer functions (PTFs) provide an
alternative by estimating soil parameters from more readily available
soil data. 70 soil samples were collected from different horizons of
15 soil profiles located in the Ziaran region, Qazvin province, Iran.
Then, multivariate regression and neural network model (feedforward
back propagation network) were employed to develop a
pedotransfer function for predicting soil parameter using easily
measurable characteristics of clay and organic carbon. The
performance of the multivariate regression and neural network model
was evaluated using a test data set. In order to evaluate the models,
root mean square error (RMSE) was used. The value of RMSE and
R2 derived by ANN model for CEC were 0.47 and 0.94 respectively,
while these parameters for multivariate regression model were 0.65
and 0.88 respectively. Results showed that artificial neural network
with seven neurons in hidden layer had better performance in
predicting soil cation exchange capacity than multivariate regression.
Abstract: The optimization and control problem for 4D trajectories
is a subject rarely addressed in literature. In the 4D navigation
problem we define waypoints, for each mission, where the arrival
time is specified in each of them. One way to design trajectories for
achieving this kind of mission is to use the trajectory optimization
concepts. To solve a trajectory optimization problem we can use
the indirect or direct methods. The indirect methods are based on
maximum principle of Pontryagin, on the other hand, in the direct
methods it is necessary to transform into a nonlinear programming
problem. We propose an approach based on direct methods with a
pseudospectral integration scheme built on Chebyshev polynomials.
Abstract: The purposes of researches - to estimate implicit ethnic attitudes by direct and indirect methods, to determine the accordance of two types measuring, to investigate influence of task type used in an experiment, on the results of measuring, as well as to determine a presence or communication between recent episodic events and chronologic correlations of ethnic attitudes. Method of the implicit measuring - an evaluative priming (EPT) carried out with the use of different SOA intervals, explicit methods of research are G.Soldatova-s types of ethnic identity, G.Soldatova-s index of tolerance, E.Bogardus scale of social distance. During five stages of researches received results open some aspects of implicit measuring, its correlation with the results of self-reports on different SOA intervals, connection of implicit measuring with emotional valence of episodic events of participants and other indexes, presenting a contribution to the decision of implicit measuring application problem for study of different social constructs
Abstract: A new stochastic algorithm called Probabilistic Global Search Johor (PGSJ) has recently been established for global optimization of nonconvex real valued problems on finite dimensional Euclidean space. In this paper we present convergence guarantee for this algorithm in probabilistic sense without imposing any more condition. Then, we jointly utilize this algorithm along with control
parameterization technique for the solution of constrained optimal control problem. The numerical simulations are also included to illustrate the efficiency and effectiveness of the PGSJ algorithm in the solution of control problems.