AUT Journal of Mathematics and ComputingAUT Journal of Mathematics and Computing
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Feed provided by AUT Journal of Mathematics and Computing. Click to visit.$(alpha,beta)$-Metrics with Killing $beta$ of Constant Length
http://ajmc.aut.ac.ir/article_3038_0.html
Articles in Press, Accepted Manuscript , Available Online from 29 August 2018<br><br>The class of $(alpha,beta)$-metrics is a rich and important class of Finsler metrics, which is extensively studied. Here, we study $(alpha,beta)$-metrics with Killing of constant length 1-form $beta$ and find a simplified formula for their Ricci curvatures. Then, weshow that if $F=alpha+abeta+b,frac{beta^2}{alpha}$ is an Einstein Finsler metric, then $alpha$ is an Einstein Riemann metric.Tue, 28 Aug 2018 19:30:00 +0100On Sobolev spaces and density theorems on Finsler manifolds
http://ajmc.aut.ac.ir/article_3039_0.html
Articles in Press, Accepted Manuscript , Available Online from 29 August 2018<br><br>Here, a natural extension of Sobolev spaces is defined for a Finsler structure $F$ and it is shown that the set of all real $C^{infty}$ functions with compact support on a forward geodesically complete Finsler manifold $(M, F)$, is dense in the extended Sobolev space $H_1^p (M)$.As a consequence, the weak solutions $u$ of the Dirichlet equation $Delta u=f$ can be approximated by $C^infty$ functions with compact support on $M$.Moreover, let $W subset M$ be a regular domain with the $C^r$ boundary $partial W$, then the set of all real functions in $C^r (W) cap C^0 (overline W)$ is dense in $H_k^p (W)$, where $kleq r$. Finally, several examples are illustrated and sharpness of the inequality $kleq r$ is shown.Tue, 28 Aug 2018 19:30:00 +0100The bimodal standard normal density and kurtosis
http://ajmc.aut.ac.ir/article_3040_0.html
Articles in Press, Accepted Manuscript , Available Online from 29 August 2018<br><br>In this article, rst a density by the name "The bimodal standard normal density" is introduced and denoted by bphi(z). Then, a dention for the kurtosis of bimodal densities relative to bphi(z) is presented. Finally, to illustrate the introduced kurtosis, a few examplesare provided and a real data set is studied,too.Tue, 28 Aug 2018 19:30:00 +0100Approximate symmetries and invariant solutions for a family of the generalizations of the ...
http://ajmc.aut.ac.ir/article_3041_0.html
Articles in Press, Accepted Manuscript , Available Online from 29 August 2018<br><br>In this paper a family of the generalizations of the Burgers-Korteweg-de Vries model with small parameter derived by Kudryshov et al[ N.A. Kudryashov, D.I. Sinelshchikov. Extended models of non-linear waves in liquid with gas bubbles, International Journal of Non-Linear Mechanics 63 (2014) 31-38] is studied. By the method initiated by Baikov et al [V.A. Baikov, R.K. Gazizov, N.kh Ibragimov. Perturbation methods in group analysis. J. Sov. Math 1991;55:1450-90] a comprehensive study on the approximate symmetry analysis of the waves models is presented. We construct symmetries that are stable with respect to small perturbations. Subsequently, in a physical application, using the first-order approximate symmetries, corresponding approximate invariant solutions to the perturbed non-linear models are obtained.Tue, 28 Aug 2018 19:30:00 +0100A real-time decision support system for bridge management based on the rules generalized by ...
http://ajmc.aut.ac.ir/article_3043_0.html
Articles in Press, Accepted Manuscript , Available Online from 29 August 2018<br><br>Under dynamic conditions on bridges, we need a real-time management. To this end, this paper presents a rule-based decision support system in which the necessary rules are extracted from simulation results made by Aimsun traffic micro-simulation software. Then, these rules are generalized by the aid of fuzzy rule generation algorithms. Then, they are trained by a set of supervised and the unsupervised learning algorithms to get an ability to make decision in real cases. As a pilot case study, Nasr Bridge in Tehran is simulated in Aimsun and WEKA data mining software is used to execute the learning algorithms. Based on this experiment, the accuracy of the supervised algorithms to generalize the rules is greater than 80%. In addition, CART decision tree and sequential minimal optimization (SMO) provides 100% accuracy for normal data and these algorithms are so reliable for crisis management on bridge. This means that, it is possible to use such machine learning methods to manage bridges in the real-time conditions.Tue, 28 Aug 2018 19:30:00 +0100A simple greedy approximation algorithm for the unit disk cover problem
http://ajmc.aut.ac.ir/article_3044_0.html
Articles in Press, Accepted Manuscript , Available Online from 29 August 2018<br><br>Given a set P of n points in the plane, the unit disk cover problem, which is known as an NP-hard problem, seeks to find the minimum number of unit disks that can cover all points of P. In this paper, we present a new 4-approximation algorithm with running time O(n log n) for this problem. Our proposed algorithm uses a simple greedy approach and is easy to understand and implement.Tue, 28 Aug 2018 19:30:00 +0100