Abstract: We present a theory for optimal filtering of infinite sets of random signals. There are several new distinctive features of the proposed approach. First, we provide a single optimal filter for processing any signal from a given infinite signal set. Second, the filter is presented in the special form of a sum with p terms where each term is represented as a combination of three operations. Each operation is a special stage of the filtering aimed at facilitating the associated numerical work. Third, an iterative scheme is implemented into the filter structure to provide an improvement in the filter performance at each step of the scheme. The final step of the concerns signal compression and decompression. This step is based on the solution of a new rank-constrained matrix approximation problem. The solution to the matrix problem is described in this paper. A rigorous error analysis is given for the new filter.
Abstract: An upwind difference approximation is used for a singularly perturbed problem in material science. Based on the discrete Green-s function theory, the error estimate in maximum norm is achieved, which is first-order uniformly convergent with respect to the perturbation parameter. The numerical experimental result is verified the valid of the theoretical analysis.
Abstract: We present a new quadrature rule based on the spline
interpolation along with the error analysis. Moreover, some error
estimates for the reminder when the integrand is either a Lipschitzian
function, a function of bounded variation or a function whose
derivative belongs to Lp are given. We also give some examples
to show that, practically, the spline rule is better than the trapezoidal
rule.
Abstract: Glomerular filtration rate (GFR) is a measure of
kidney function. It is usually estimated from serum concentrations of
cystatin C or creatinine although there has been considerable debate
in the literature about (i) the best equation to use and (ii) the
variability in the correlation between the concentrations of creatinine
and cystatin C. The equations for GFR can be written in a general
form and from these I calculate the error of the GFR estimates
associated with analyte measurement error. These show that the
error of the GFR estimates is such that it is not possible to distinguish
between the equations over much of the concentration range of either
analyte. The general forms of the equations are also used to derive
an expression for the concentration of cystatin C as a function of the
concentration of creatinine. This equation shows that these analyte
concentrations are not linearly related. Clinical reports of cystatin C
and creatinine concentration are consistent with the expression
derived.
Abstract: It is very important to determine reference temperature when convective temperature because it should be used to calculate the temperature potential. This paper deals with the development of a new method that can determine heat transfer coefficient and reference free stream temperature simultaneously, based on transient heat transfer experiments with using two narrow band thermo-tropic liquid crystals (TLC's). The method is validated through error analysis in terms of the random uncertainties in the measured temperatures. It is shown how the uncertainties in heat transfer coefficient and free stream temperature can be reduced. The general method described in this paper is applicable to many heat transfer models with unknown free stream temperature.
Abstract: A method for solving linear and non-linear Goursat
problem is given by using the two-dimensional differential transform
method. The approximate solution of this problem is calculated in
the form of a series with easily computable terms and also the exact
solutions can be achieved by the known forms of the series solutions.
The method can easily be applied to many linear and non-linear
problems and is capable of reducing the size of computational work.
Several examples are given to demonstrate the reliability and the
performance of the presented method.
Abstract: This study is designed to investigate errors emerged in written texts produced by 30 Turkish EFL learners with an explanatory, and thus, qualitative perspective. Erroneous language elements were identified by the researcher first and then their grammaticality and intelligibility were checked by five native speakers of English. The analysis of the data showed that it is difficult to claim that an error stems from only one single factor since different features of an error are triggered by different factors. Our findings revealed two different types of errors: those which stem from the interference of L1 with L2 and those which are developmental ones. The former type contains more global errors whereas the errors in latter type are more intelligible.
Abstract: In this paper, verified extension of the Ostrowski method which calculates the enclosure solutions of a given nonlinear equation is introduced. Also, error analysis and convergence will be discussed. Some implemented examples with INTLAB are also included to illustrate the validity and applicability of the scheme.
Abstract: The production of a plant can be measured in terms of
seeds. The generation of seeds plays a critical role in our social and
daily life. The fruit production which generates seeds, depends on the
various parameters of the plant, such as shoot length, leaf number,
root length, root number, etc When the plant is growing, some leaves
may be lost and some new leaves may appear. It is very difficult to
use the number of leaves of the tree to calculate the growth of the
plant.. It is also cumbersome to measure the number of roots and
length of growth of root in several time instances continuously after
certain initial period of time, because roots grow deeper and deeper
under ground in course of time. On the contrary, the shoot length of
the tree grows in course of time which can be measured in different
time instances. So the growth of the plant can be measured using the
data of shoot length which are measured at different time instances
after plantation. The environmental parameters like temperature, rain
fall, humidity and pollution are also play some role in production of
yield. The soil, crop and distance management are taken care to
produce maximum amount of yields of plant. The data of the growth
of shoot length of some mustard plant at the initial stage (7,14,21 &
28 days after plantation) is available from the statistical survey by a
group of scientists under the supervision of Prof. Dilip De. In this
paper, initial shoot length of Ken( one type of mustard plant) has
been used as an initial data. The statistical models, the methods of
fuzzy logic and neural network have been tested on this mustard
plant and based on error analysis (calculation of average error) that
model with minimum error has been selected and can be used for the
assessment of shoot length at maturity. Finally, all these methods
have been tested with other type of mustard plants and the particular
soft computing model with the minimum error of all types has been
selected for calculating the predicted data of growth of shoot length.
The shoot length at the stage of maturity of all types of mustard
plants has been calculated using the statistical method on the
predicted data of shoot length.