Abstract: Aim. We have introduced the notion of order to multinormed spaces and countable union spaces and their duals. The topology of bounded convergence is assigned to the dual spaces. The aim of this paper is to develop the theory of ordered topological linear
spaces La,b, L(w, z), the dual spaces of ordered multinormed spaces
La,b, ordered countable union spaces L(w, z), with the topology of bounded convergence assigned to the dual spaces. We apply Laplace transformation to the ordered linear space of Laplace transformable
generalized functions. We ultimately aim at finding solutions to nonhomogeneous
nth order linear differential equations with constant
coefficients in terms of generalized functions and comparing different
solutions evolved out of different initial conditions.
Method. The above aim is achieved by
• Defining the spaces La,b, L(w, z).
• Assigning an order relation on these spaces by identifying a
positive cone on them and studying the properties of the cone.
• Defining an order relation on the dual spaces La,b, L(w, z) of La,b, L(w, z) and assigning a topology to these dual spaces which makes the order dual and the topological dual the same. • Defining the adjoint of a continuous map on these spaces
and studying its behaviour when the topology of bounded
convergence is assigned to the dual spaces.
• Applying the two-sided Laplace Transformation on the ordered
linear space of generalized functions W and studying some
properties of the transformation which are used in solving
differential equations.
Result. The above techniques are applied to solve non-homogeneous
n-th order linear differential equations with constant coefficients in
terms of generalized functions and to compare different solutions of the differential equation.
Abstract: We present new finite element methods for Helmholtz and Maxwell equations on general three-dimensional polyhedral meshes, based on domain decomposition with boundary elements on the surfaces of the polyhedral volume elements. The methods use the lowest-order polynomial spaces and produce sparse, symmetric linear systems despite the use of boundary elements. Moreover, piecewise constant coefficients are admissible. The resulting approximation on the element surfaces can be extended throughout the domain via representation formulas. Numerical experiments confirm that the convergence behavior on tetrahedral meshes is comparable to that of standard finite element methods, and equally good performance is attained on more general meshes.
Abstract: Solution of some practical problems is reduced to the
solution of the integro-differential equations. But for the numerical
solution of such equations basically quadrature methods or its
combination with multistep or one-step methods are used. The
quadrature methods basically is applied to calculation of the integral
participating in right hand side of integro-differential equations. As
this integral is of Volterra type, it is obvious that at replacement with
its integrated sum the upper limit of the sum depends on a current
point in which values of the integral are defined. Thus we receive the
integrated sum with variable boundary, to work with is hardly.
Therefore multistep method with the constant coefficients, which is
free from noted lack and gives the way for finding it-s coefficients is
present.
Abstract: In this paper, a wavelet based method is proposed to
identify the constant coefficients of a second order linear system and
is compared with the least squares method. The proposed method
shows improved accuracy of parameter estimation as compared to the
least squares method. Additionally, it has the advantage of smaller
data requirement and storage requirement as compared to the least
squares method.
Abstract: Salinity is a measure of the amount of salts in the
water. Total Dissolved Solids (TDS) as salinity parameter are often
determined using laborious and time consuming laboratory tests, but
it may be more appropriate and economical to develop a method
which uses a more simple soil salinity index. Because dissolved ions
increase salinity as well as conductivity, the two measures are
related. The aim of this research was determine of constant
coefficients for predicting of Total Dissolved Solids (TDS) based on
Electrical Conductivity (EC) with Statistics of Correlation
coefficient, Root mean square error, Maximum error, Mean Bias
error, Mean absolute error, Relative error and Coefficient of residual
mass. For this purpose, two experimental areas (S1, S2) of Khuzestan
province-IRAN were selected and four treatments with three
replications by series of double rings were applied. The treatments
were included 25cm, 50cm, 75cm and 100cm water application. The
results showed the values 16.3 & 12.4 were the best constant
coefficients for predicting of Total Dissolved Solids (TDS) based on
EC in Pilot S1 and S2 with correlation coefficient 0.977 & 0.997 and
191.1 & 106.1 Root mean square errors (RMSE) respectively.
Abstract: As is known, one of the priority directions of research
works of natural sciences is introduction of applied section of
contemporary mathematics as approximate and numerical methods to
solving integral equation into practice. We fare with the solving of
integral equation while studying many phenomena of nature to whose
numerically solving by the methods of quadrature are mainly applied.
Taking into account some deficiency of methods of quadrature for
finding the solution of integral equation some sciences suggested of
the multistep methods with constant coefficients. Unlike these papers,
here we consider application of hybrid methods to the numerical
solution of Volterra integral equation. The efficiency of the suggested
method is proved and a concrete method with accuracy order p = 4
is constructed. This method in more precise than the corresponding
known methods.