Necessary and sufficient conditions for the operator equation I AXAX n*, to have a real positive definite solution X are given. Based on these conditions, some properties of the operator A as well as relation between the solutions X andAare given.

This paper studies a novel technique based on the use of two effective methods like modified Laplace- variational method (MLVIM) and a new Variational method (MVIM)to solve PDEs with variable coefficients. The current modification for the (MLVIM) is based on coupling of the Variational method (VIM) and Laplace- method (LT). In our proposal there is no need to calculate Lagrange multiplier. We applied Laplace method to the problem .Furthermore, the nonlinear terms for this problem is solved using homotopy method (HPM). Some examples are taken to compare results between two methods and to verify the reliability of our present methods.

In this paper the modified trapezoidal rule is presented for solving Volterra linear Integral Equations (V.I.E) of the second kind and we noticed that this procedure is effective in solving the equations. Two examples are given with their comparison tables to answer the validity of the procedure.

Signal denoising is directly related to sample estimation of received signals, either by estimating the equation parameters for the target reflections or the surrounding noise and clutter accompanying the data of interest. Radar signals recorded using analogue or digital devices are not immune to noise. Random or white noise with no coherency is mainly produced in the form of random electrons, and caused by heat, environment, and stray circuitry loses. These factors influence the output signal voltage, thus creating detectable noise. Differential Evolution (DE) is an effectual, competent, and robust optimisation method used to solve different problems in the engineering and scientific domains, such as in signal processing. This paper looks

Algorithms using the second order of B -splines [B (x)] and the third order of B -splines [B,3(x)] are derived to solve 1' , 2nd and 3rd linear Fredholm integro-differential equations (F1DEs). These new procedures have all the useful properties of B -spline function and can be used comparatively greater computational ease and efficiency.The results of these algorithms are compared with the cubic spline function.Two numerical examples are given for conciliated the results of this method.

In this paper, a self-tuning adaptive neural controller strategy for unknown nonlinear system is presented. The system considered is described by an unknown NARMA-L2 model and a feedforward neural network is used to learn the model with two stages. The first stage is learned off-line with two configuration serial-parallel model & parallel model to ensure that model output is equal to actual output of the system & to find the jacobain of the system. Which appears to be of critical importance parameter as it is used for the feedback controller and the second stage is learned on-line to modify the weights of the model in order to control the variable parameters that will occur to the system. A back propagation neural network is appl

Rutting in asphalt mixtures is a very common type of distress. It occurs due to the heavy load applied and slow movement of traffic. Rutting needs to be predicted to avoid major deformation to the pavement. A simple linear viscous method is used in this paper to predict the rutting in asphalt mixtures by using a multi-layer linear computer programme (BISAR). The material properties were derived from the Repeated Load Axial Test (RLAT) and represented by a strain-dependent axial viscosity. The axial viscosity was used in an incremental multi-layer linear viscous analysis to calculate the deformation rate during each increment, and therefore the overall development of rutting. The method has been applied for six mixtures and at different tem

Translation is a vital process that needs much more understanding and mutual background knowledge on the part of ESL or EFL learners in terms of grammar , meaning and context of both the SL and TL . Thus , the main aim of the current research paper is to identify and figure out the techniques used by ESL or EFL learners when translating English barnyard verbs into Arabic . The main problem of this study is attributed to the fact that ESL or EFL learners may not be able to identify and understand the connotative meaning of barnyard verbs since these verbs are onomatopoeic (i.e,) a word that phonetically imitates, or suggests the source of sound that it describes. Therefore they may be unable to translate these verbs appropriately and accura

Motivation is one of the most important factors that influence students learning and has a great effect on their success and achievement. For this reason, in this paper, the researcher is going to investigate the motivational teaching strategies used by EFL Iraqi school teachers. To achieve the aim of the study, the researcher adapted a questionnaire with some changes and modification’s. This questionnaire with five point scale (always, often, sometimes, rarely and never). To achieve face validity, the questionnaire items are given to a jury of experts. Alpha Cronbach formula is used to achieve the questionnaire reliability. After that, the questionnaire was applied on a sample of 38 teachers during the academic year 2019-2020. Th

The current study is concerned with investigating the difficulties that Iraqi EFL learners of English may face when translating English collective nouns. Such collective nouns as committee, government, , jury , Parliament , etc. are considered singular when the concept of the unity as a group is emphasized , but when the concept of the individuals or numbers is emphasized they are treated as plural. A sample of twenty undergraduate students have been selected randomly to translate certain English collective nouns in some selected political texts in order to find out the difficulties they might face in rendering them into Arabic. It is hypothesized that most of the testees have used the singular form rather than the plural ignoring the