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Numerical Solution of Fractional Partial Differential Equations with Normalized Bernstein Wavelet Method
Get PDFIn this paper, normalized Bernstein wavelets are presented. Next, the fractional order integration and Bernstein wavelets operational matrices of integration are derived and finally are used for solving fractional partial differential equations. The operational matrices merged with the collocation method are used in order to convert fractional problems to a number of algebraic equations. In the suggested method the boundary conditions are automatically taken into consideration. An assessment of the error of function approximation based on the normalized Bernstein wavelet is also presented. Some numerical instances are given to manifest the versatility and applicability of the suggested method. Founded numerical results are correlated with the best reported results in the literature and the analytical solutions in order to prove the accuracy and applicability of the suggested method
Birkhoff’s Ergodic Theorem For Weighted Variable Exponent Amalgam Spaces
Get PDFIn this study, we consider some properties of weighted variable exponent Lebesgue and amalgam spaces. It is known these spaces are considerably used in harmonic and time-frequency analysis including elastic mechanics, electrorheological fluids, image processing, etc. Ergodic theory investigates the long-term averaging properties of measure preserving dynamical systems. This theory has also several applications and problems of statistical physics and mechanics. Moreover, it has influence on many areas of mathematics, especially probability theory and dynamical systems as well as Fourier analysis, functional analysis, and group theory. Therefore, we investigate Ergodic theorem for unweighted variable exponent Lebesgue spaces and also an amalgam space whose local component is weighted one
On General Matrix Application of Quasi Power Increasing Sequences
Get PDFIn this paper, we give a general theorem dealing with absolute matrix summability by using quasi-power increasing sequences. This theorem includes some results concerning absolute summability methods
MHD Boundary Layer Slip Flow over a Flat Plate with Soret and Dufour Effects
Get PDFThe present paper studies the effects of Soret and Dufour on MHD boundary layer slip flow over a flat plate. The governing partial differential equations are converted to a set of nonlinear ordinary differential equations by using similarity transformations. Then, these equations are solved numerically by implicit Finite Difference Scheme. The numerical solutions for Velocity, Temperature and Concentration profiles for the related essential physical parameters are visualized through graphs and discussed. Results show that the velocity rises whereas the temperature and concentration reduces with the respective slip parameters. The increase in Soret number or decrease in Dufour number reduces the temperature and enhances the concentration of the fluid
Convergence theorems for common fixed point of the family of nonself and nonexpansive mappings in real Banach spaces
Get PDFIn this paper, we construct cyclic-Mann type of iterative method for approximating a common fixed point of the finite family of nonself and nonexpansive mappings satisfying inward condition on a non-empty, closed and convex subset of a real uniformly convex Banach space . We also construct the averaging algorithm to the class of nonexpansive mappings in 2-uniformly smooth Banach space. We prove weak and strong convergence results for the iterative method. The results of this work extend results in the literature
Associated Matrix Polynomials with the Second Kind Chebyshev Matrix Polynomials
Get PDFThis paper deals with the study of the associated Chebyshev matrix polynomials. Associated matrix polynomials with the Chebyshev matrix polynomials are defined here. Some properties of the associated Chebyshev matrix polynomials are obtained here. Further, we prove that the associated Chebyshev matrix polynomials satisfy a matrix differential equation of the second order
Resonance in the Motion of a Geocentric Satellite Due to Poynting-Robertson Drag and Equatorial Ellipticity of the Earth
Get PDFIn this paper, the problem of resonance in a motion of a geocentric satellite is numerically investigated under the consolidated gravitational forces of the Sun, the Earth including Earth’s equatorial ellipticity parameter and Poynting-Robertson (P-R) drag. We are presuming that bodies lying on an ecliptic plane are the Sun and the Earth, and satellite on orbital plane. Resonance is monitored between satellite’s mean motion and average angular velocity of the Earth around the Sun, and also between satellite’s mean motion and equatorial ellipticity parameter of the Earth. We also perform a systematic and thorough analysis in an attempt to understand the effect of Earth’s equatorial ellipticity parameter and P-R drag on time period and amplitude of oscillations at different critical points
On Ordered (p; q)-Lateral Ideals in Ordered Ternary Semigroups
Get PDFIn this paper, we study some useful results of ordered (p; q)-lateral ideals in ordered ternary semigroups. Also, some properties of (p; q)-lateral simple ordered ternary semigroup have been examined. Further, we characterize the relationship between minimal (resp., maximal) ordered (p; q)- lateral ideals and (p; q)-lateral simple ordered ternary semigroups
Jones Polynomial for Graphs of Twist Knots
Get PDFWe frequently encounter knots in the flow of our daily life. Either we knot a tie or we tie a knot on our shoes. We can even see a fisherman knotting the rope of his boat. Of course, the knot as a mathematical model is not that simple. These are the reflections of knots embedded in threedimensional space in our daily lives. In fact, the studies on knots are meant to create a complete classification of them. This has been achieved for a large number of knots today. But we cannot say that it has been terminated yet. There are various effective instruments while carrying out all these studies. One of these effective tools is graphs. Graphs are have made a great contribution to the development of algebraic topology. Along with this support, knot theory has taken an important place in low dimensional manifold topology. In 1984, Jones introduced a new polynomial for knots. The discovery of that polynomial opened a new era in knot theory. In a short time, this polynomial was defined by algebraic arguments and its combinatorial definition was made. The Jones polynomials of knot graphs and their applications were introduced by Murasugi. T. U˘gur and A. Kopuzlu found an algorithm for the Jones polynomials of torus knots K(2; q) in 2006. In this paper, first of all, it has been obtained signed graphs of the twist knots which are a special family of knots. We subsequently compute the Jones polynomials for graphs of twist knots. We will consider signed graphs associated with each twist knot diagrams
Development Of Deep Learning Based Recommendation Engine For Embedded Programmer
No full textMicrocontroller based embedded devices have been widely used in the Internet of Things (IoT). In the IoT, the embedded based microcontroller unit (MCU) plays an irreplaceable role because of its advantages of real-time processing and low power consumption. Many successful embedded Integrated circuits (IC) designs are still being utilized and updated at a very fast speed, which brings big trouble and challenge to the coder. In this design, a smart embedded code recommendation system is developed to assist embedded programmers to quickly search high quality embedded code segments with precise tags.
In the beginning, a largescale embedded code database was built and reorganized as a code description dataset and code content dataset. In addition, a tag correlated machine-learning-based auto code classifier was implemented to label the embedded code with precise tags. Finally, the Modular Hierarchical Convolution Neural Network (MHCNN) deep learning model was presented to achieve the dynamic recommendation level by level. The detail design of the system included the code database structure, the classifier enhancement, and the promising performances of the MHCNN model were provided. The experimental results demonstrated that the proposed dataset structure outperformed the traditional dataset; the proposed tag correlated classifier could enhance the precision of labeling, and the MHCNN model showed performance that is more promising in embedded code recommendation