In this paper, our aim is to study variational formulation and solutions of 2-dimensional integrodifferential equations of fractional order. We will give a summery of representation to the variational formulation of linear nonhomogenous 2-dimensional Volterra integro-differential equations of the second kind with fractional order. An example will be discussed and solved by using the MathCAD software package when it is needed.
The Caputo definition of fractional derivatives introduces solution to the difficulties appears in the numerical treatment of differential equations due its consistency in differentiating constant functions. In the same time the memory and hereditary behaviors of the time fractional order derivatives (TFODE) still common in all definitions of fractional derivatives. The use of properties of companion matrices appears in reformulating multilevel schemes as generalized two level schemes is employed with the Gerschgorin disc theorems to prove stability condition. Caputo fractional derivatives with finite difference representations is considered. Moreover the effect of using the inverse operator which tr
<abstract><p>Many variations of the algebraic Riccati equation (ARE) have been used to study nonlinear system stability in the control domain in great detail. Taking the quaternion nonsymmetric ARE (QNARE) as a generalized version of ARE, the time-varying QNARE (TQNARE) is introduced. This brings us to the main objective of this work: finding the TQNARE solution. The zeroing neural network (ZNN) technique, which has demonstrated a high degree of effectiveness in handling time-varying problems, is used to do this. Specifically, the TQNARE can be solved using the high order ZNN (HZNN) design, which is a member of the family of ZNN models that correlate to hyperpower iterative techniques. As a result, a novel
... Show MoreObjectives. The current study aimed to predict the combined mesiodistal crown widths of maxillary and mandibular canines and premolars from the combined mesiodistal crown widths of maxillary and mandibular incisors and first molars. Materials and Methods. This retrospective study utilized 120 dental models from Iraqi Arab young adult subjects with normal dental relationships. The mesiodistal crown widths of all teeth (except the second molars) were measured at the level of contact points using digital electronic calipers. The relation between the sum mesiodistal crown widths of the maxillary and mandibular incisors and first molars and the combined mesiodistal crown widths of the maxillary and mandibular canines and premolars was as
... Show Moreهناك دائما حاجة إلى طريقة فعالة لتوليد حل عددي أكثر دقة للمعادلات التكاملية ذات النواة المفردة أو المفردة الضعيفة لأن الطرق العددية لها محدودة. في هذه الدراسة ، تم حل المعادلات التكاملية ذات النواة المفردة أو المفردة الضعيفة باستخدام طريقة متعددة حدود برنولي. الهدف الرئيسي من هذه الدراسة هو ايجاد حل تقريبي لمثل هذه المشاكل في شكل متعددة الحدود في سلسلة من الخطوات المباشرة. أيضا ، تم افتراض أن مقام النواة
... Show More<span>Digital audio is required to transmit large sizes of audio information through the most common communication systems; in turn this leads to more challenges in both storage and archieving. In this paper, an efficient audio compressive scheme is proposed, it depends on combined transform coding scheme; it is consist of i) bi-orthogonal (tab 9/7) wavelet transform to decompose the audio signal into low & multi high sub-bands, ii) then the produced sub-bands passed through DCT to de-correlate the signal, iii) the product of the combined transform stage is passed through progressive hierarchical quantization, then traditional run-length encoding (RLE), iv) and finally LZW coding to generate the output mate bitstream.
... Show MoreIn this study, a fast block matching search algorithm based on blocks' descriptors and multilevel blocks filtering is introduced. The used descriptors are the mean and a set of centralized low order moments. Hierarchal filtering and MAE similarity measure were adopted to nominate the best similar blocks lay within the pool of neighbor blocks. As next step to blocks nomination the similarity of the mean and moments is used to classify the nominated blocks and put them in one of three sub-pools, each one represents certain nomination priority level (i.e., most, less & least level). The main reason of the introducing nomination and classification steps is a significant reduction in the number of matching instances of the pixels belong to the c
... Show MoreIn this paper, wavelets were used to study the multivariate fractional Brownian motion through the deviations of the random process to find an efficient estimation of Hurst exponent. The results of simulations experiments were shown that the performance of the proposed estimator was efficient. The estimation process was made by taking advantage of the detail coefficients stationarity from the wavelet transform, as the variance of this coefficient showed the power-low behavior. We use two wavelet filters (Haar and db5) to manage minimizing the mean square error of the model.
The fractional free volume (Fh) in polystyrene (PS) as a function of neutron -irradiation dose has been measured, using positron annihilation lifetime (PAL) method. The results show that Fh values decreased with increasing n-irradiation dose up to a total dose of 501.03× 10-2 Gy.
A percentage reduction of 2.14 in Fh values is noticed after the initial n-dose corresponding to a percentage reduction in the free volume equal to 42.14/Gy.
The total n-dose induces a percentage reduction of 7.26, corresponding to a percentage reduction of 1.45/Gy. These results indicate that cross -linking is the predominant process induced by n-irradiation.
The results suggest that n-irradiation induces structure changes in PS, causing cross-linking
The inverse kinematic equation for a robot is very important to the control robot’s motion and position. The solving of this equation is complex for the rigid robot due to the dependency of this equation on the joint configuration and structure of robot link. In light robot arms, where the flexibility exists, the solving of this problem is more complicated than the rigid link robot because the deformation variables (elongation and bending) are present in the forward kinematic equation. The finding of an inverse kinematic equation needs to obtain the relation between the joint angles and both of the end-effector position and deformations variables. In this work, a neural network has been proposed to solve the problem of inverse kinemati
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