Transportation of ferromagnetic powder using linear motor devices

The travelling magnetic wave of a linear induction motor induces eddy currents in a secondary circuit (usually a sheet consisting at least partly of a non-magnetic metal, often aluminium), which cause the unrestrained member to move linearly in the direction of the travelling wave. A linear motor can also transport ferromagnetic powder, although this travels in the opposite direction to the travelling magnetic field. The motion is therefore due to a mechanism other than the eddy currents flowing in the sheet secondary. Expressions for the forces acting on an iron particle due to a travelling magnetic field are derived in the thesis. Preliminary experiments support the assumptions made in the derivations of the force expressions and lead to the formation of an hypothesis. This is shown to be capable of predicting both linear and rotational particle speeds and, with greater accuracy, the distance travelled and the rotation experienced by the particles. Experiments conducted on tubular and transverse flux motors have enabled different linear motors to be identified as suitable for a number of powder transportation applications. The results obtained show also the importance of large flux density values, the tangential to normal flux density ratio and large pole-pitch winding arrangements, with the latter lending support to the original hypothesis. The results of a finite element investigation of the tubular motor did not closely agree with the results from the experimental motor although similar trends were evident. Flux density values within particles were found to be considerably greater than those outside, as assumed in the hypothesis

Semilocal convergence of a continuation method with Hölder continuous second derivative in Banach spaces

AbstractIn this paper, the semilocal convergence of a continuation method combining the Chebyshev method and the convex acceleration of Newton’s method used for solving nonlinear equations in Banach spaces is established by using recurrence relations under the assumption that the second Frëchet derivative satisfies the Hölder continuity condition. This condition is mild and works for problems in which the second Frëchet derivative fails to satisfy Lipschitz continuity condition. A new family of recurrence relations are defined based on two constants which depend on the operator. The existence and uniqueness regions along with a closed form of the error bounds in terms of a real parameter α∈[0,1] for the solution x∗ is given. Two numerical examples are worked out to demonstrate the efficacy of our approach. On comparing the existence and uniqueness regions for the solution obtained by our analysis with those obtained by using majorizing sequences under Hölder continuity condition on F″, it is found that our analysis gives improved results. Further, we have observed that for particular values of the α, our analysis reduces to those for the Chebyshev method (α=0) and the convex acceleration of Newton’s method (α=1) respectively with improved results

Exploration and Production Thesaurus : its helpfulness in indexing in a Library and information System

Exploration and Production (E & P) thesaurus published by the Information Service Department, University of Tulsa, is one of the most comprehensive thesaurus in its coverage on the exploration, development and production of crude oil and natural gas. The thesaurus is in continuous use in the Library of the Oil and Natural Gas Commission for indexing the literature and in the development of special schemes of classification for local use. The paper indicates the usefulness of the thesaurus for indexing the entries covered in the various bibliographies and for the preparation of a special scheme of classification for Exploration Geophysic

A hybrid algorithm for university course timetabling problem

A hybrid algorithm combining the genetic algorithm with the iterated local search algorithm is developed for solving university course timetabling problem. This hybrid algorithm combines the merits of genetic algorithm and iterated local search algorithm for its convergence to global optima at the same time avoiding being get trapped into local optima. This leads to intensification of the involved search space for solutions. It is applied on a number of benchmark university course timetabling problem instances of various complexities. Keywords: timetabling, optimization, metaheuristics, genetic algorithm, iterative local searc

Simultaneous approximation by certain Baskakov–Durrmeyer–Stancu operators

AbstractIn the present paper, we establish some direct results in simultaneous approximation for Baskakov–Durrmeyer–Stancu (abbr. BDS) operators Dn(α,β)(f,x). We establish point-wise convergence, Voronovskaja type asymptotic formula and an error estimate in terms of second order modulus of continuity of the function

Directional k-Step Newton Methods in n Variables and its Semilocal Convergence Analysis

[EN] The directional k-step Newton methods (k a positive integer) is developed for solving a single nonlinear equation in n variables. Its semilocal convergence analysis is established by using two different approaches (recurrent relations and recurrent functions) under the assumption that the first derivative satisfies a combination of the Lipschitz and the center-Lipschitz continuity conditions instead of only Lipschitz condition. The convergence theorems for the existence and uniqueness of the solution for each of them are established. Numerical examples including nonlinear Hammerstein-type integral equations are worked out and significantly improved results are obtained. It is shown that the second approach based on recurrent functions solves problems failed to be solved by first one using recurrent relations. This demonstrates the efficacy and applicability of these approaches. This work extends the directional one and two-step Newton methods for solving a single nonlinear equation in n variables. Their semilocal convergence analysis using majorizing sequences are studied in Levin (Math Comput 71(237): 251-262, 2002) and Ioannis (Num Algorithms 55(4): 503-528, 2010) under the assumption that the first derivative satisfies the Lipschitz and the combination of the Lipschitz and the center-Lipschitz continuity conditions, respectively. Finally, the computational order of convergence and the computational efficiency of developed method are studied.The authors thank the referees for their fruitful suggestions which have uncovered several weaknesses leading to the improvement in the paper. A. Kumar wishes to thank UGC-CSIR(Grant no. 2061441001), New Delhi and IIT Kharagpur, India, for their financial assistance during this work.Kumar, A.; Gupta, D.; Martínez Molada, E.; Singh, S. (2018). Directional k-Step Newton Methods in n Variables and its Semilocal Convergence Analysis. Mediterranean Journal of Mathematics. 15(2):15-34. https://doi.org/10.1007/s00009-018-1077-0S1534152Levin, Y., Ben-Israel, A.: Directional Newton methods in n variables. Math. Comput. 71(237), 251–262 (2002)Argyros, I.K., Hilout, S.: A convergence analysis for directional two-step Newton methods. Num. Algorithms 55(4), 503–528 (2010)Lukács, G.: The generalized inverse matrix and the surface-surface intersection problem. In: Theory and Practice of Geometric Modeling, pp. 167–185. Springer (1989)Argyros, I.K., Magreñán, Á.A.: Extending the applicability of Gauss–Newton method for convex composite optimization on Riemannian manifolds. Appl. Math. Comput. 249, 453–467 (2014)Argyros, I.K.: A semilocal convergence analysis for directional Newton methods. Math. Comput. 80(273), 327–343 (2011)Ortega, J.M., Rheinboldt, W.C.: Iterative solution of nonlinear equations in several variables. SIAM (2000)Argyros, I.K., Hilout, S.: Weaker conditions for the convergence of Newton’s method. J. Complex. 28(3), 364–387 (2012)Argyros, I.K., Hilout, S.: On an improved convergence analysis of Newton’s method. Appl. Math. Comput. 225, 372–386 (2013)Tapia, R.A.: The Kantorovich theorem for Newton’s method. Am. Math. Mon. 78(4), 389–392 (1971)Argyros, I.K., George, S.: Local convergence for some high convergence order Newton-like methods with frozen derivatives. SeMA J. 70(1), 47–59 (2015)Martínez, E., Singh, S., Hueso, J.L., Gupta, D.K.: Enlarging the convergence domain in local convergence studies for iterative methods in Banach spaces. Appl. Math. Comput. 281, 252–265 (2016)Argyros, I.K., Behl, R. Motsa,S.S.: Ball convergence for a family of quadrature-based methods for solving equations in banach Space. Int. J. Comput. Methods, pp. 1750017 (2016)Parhi, S.K., Gupta, D.K.: Convergence of Stirling’s method under weak differentiability condition. Math. Methods Appl. Sci. 34(2), 168–175 (2011)Prashanth, M., Gupta, D.K.: A continuation method and its convergence for solving nonlinear equations in Banach spaces. Int. J. Comput. Methods 10(04), 1350021 (2013)Parida, P.K., Gupta, D.K.: Recurrence relations for semilocal convergence of a Newton-like method in banach spaces. J. Math. Anal. Appl. 345(1), 350–361 (2008)Argyros, I.K., Hilout, S.: Convergence of Directional Methods under mild differentiability and applications. Appl. Math. Comput. 217(21), 8731–8746 (2011)Amat, S, Bermúdez, C., Hernández-Verón, M.A., Martínez, E.: On an efficient k-step iterative method for nonlinear equations. J. Comput. Appl. Math. 302, 258–271 (2016)Hernández-Verón, M.A., Martínez, E., Teruel, C.: Semilocal convergence of a k-step iterative process and its application for solving a special kind of conservative problems. Num. Algorithms, pp. 1–23Argyros, M., Hernández, I.K., Hilout, S., Romero, N.: Directional Chebyshev-type methods for solving equations. Math. Comput. 84(292), 815–830 (2015)Davis, P.J., Rabinowitz, P.: Methods of numerical integration. Courier Corporation (2007)Cordero, A, Torregrosa, J.R.: Variants of Newton’s method using fifth-order quadrature formulas. Appl. Math. Computation . 190(1), 686–698 (2007)Weerakoon, S., Fernando, T.G.I.: A variant of Newton’s method with accelerated third-order convergence. Appl. Math. Lett. 13(8), 87–93 (2000

Siamese Tracking of Cell Behaviour Patterns

Tracking and segmentation of biological cells in video sequences is a challenging problem, especially due to the similarity of the cells and high levels of inherent noise. Most machine learning-based approaches lack robustness and suffer from sensitivity to less prominent events such as mitosis, apoptosis and cell collisions. Due to the large variance in medical image characteristics, most approaches are dataset-specific and do not generalise well on other datasets. In this paper, we propose a simple end-to-end cascade neural architecture that can effectively model the movement behaviour of biological cells and predict collision and mitosis events. Our approach uses U-Net for an initial segmentation which is then improved through processing by a siamese tracker capable of matching each cell along the temporal axis. By facilitating the re-segmentation of collided and mitotic cells, our method demonstrates its capability to handle volatile trajectories and unpredictable cell locations while being invariant to cell morphology. We demonstrate that our tracking approach achieves state-of-the-art results on PhC-C2DL-PSC and Fluo-N2DH-SIM+ datasets and ranks second on the DIC-C2DH-HeLa dataset of the cell tracking challenge benchmarks