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In recent times the wavelet methods have obtained a great popularity for solving differential and integral equations. From different wavelet families we consider here the Haar wavelets. Since the Haar wavelets are mathematically most simple to be compared with other wavelets, then interest to them is rapidly increasing and there is a great number of papers,where thesewavelets are used tor solving problems of calculus. An overview of such works can be found in the survey paper by Hariharan and Kannan [1] and also in the text-book by Lepik and Hein [2]. The aim of the present paper is more narrow: we want to popularize our method of solution, which is published in 19 papers and presented in the text-book [2]. This method is quite universal, since a large group of problems can be solved by a unit approach. The paper is organised as follows. In Section 1 fundamentals of the wavelet method are described. In Section 2 the Haar wavelet method and solution algorithms are presented. In Sections 3-9 different problems of calculus and structural mechanics are solved. In Section 10 the advantageous features of the Haar wavelet method are summed up.
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We present the history of the conference Applications of Algebra in Logic and Computer Science, whose twenty-third edition will be held in March, 2019. At the end we outline some plans for the future.
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The objective of this paper is to present and make a comparative study of several inverse kinematics methods for serial manipulators, based on the Jacobian matrix. Besides the well-known Jacobian transpose and Jacobian pseudo-inverse methods, three others, borrowed from numerical analysis, are presented. Among them, two approximation methods avoid the explicit manipulability matrix inversion, while the third one is a slightly modified version of the Levenberg-Marquardt method (mLM). Their comparison is based on the evaluation of a short distance approaching the goal point and on their computational complexity. As the reference method, the Jacobian pseudo-inverse is utilized. Simulation results reveal that the modified Levenberg-Marquardt method is promising, while the first order approximation method is reliable and requires mild computational costs. Some hints are formulated concerning the application of Jacobian-based methods in practice.
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