University of Kashan Mathematics Interdisciplinary Research 2538-3639 5 2 2020 06 01 Numerical Calculation of Fractional Derivatives for the Sinc Functions via Legendre Polynomials 71 86 96936 10.22052/mir.2018.96632.1074 EN Abbas Saadatmandi ‎Department of Applied Mathematics‎, ‎Faculty of Mathematical Sciences‎, ‎‎University of Kashan, ‎Kashan‎, ‎Iran 0000-0002-7744-7770 Ali Khani Department of Mathematics, Faculty of Sciences, Azarbaijan Shahid Madani University, Tabriz, Iran Mohammad Reza Azizi Department of Mathematics, Faculty of Sciences, Azarbaijan Shahid Madani University, Tabriz, Iran Journal Article 2017 08 27 ‎This paper provides the fractional derivatives of‎ ‎the Caputo type for the sinc functions‎. ‎It allows to use efficient‎ ‎numerical method for solving fractional differential equations‎. ‎At‎ ‎first‎, ‎some properties of the sinc functions and Legendre‎ ‎polynomials required for our subsequent development are given‎. ‎Then‎ ‎we use the Legendre polynomials to approximate the fractional‎ ‎derivatives of sinc functions‎. ‎Some numerical examples are‎ ‎introduced to demonstrate the reliability and effectiveness of the‎ ‎introduced method‎.
University of Kashan Mathematics Interdisciplinary Research 2538-3639 5 2 2020 06 01 On L(d,1)-labelling of Trees 87 102 108519 10.22052/mir.2020.227370.1211 EN Irena Hrastnik Faculty of Mechanical Engineering, University of Maribor, Maribor, Slovenia Janez Žerovnik Faculty of Mechanical Engineering, University of Ljubljana, Ljubljana, Slovenia Journal Article 2020 04 17 Given a graph <em>G</em> and a positive integer <em>d</em>, an L(<em>d</em>,1)-labelling of <em>G</em> is a function <em>f</em> that assigns to each vertex of <em>G</em> a non-negative integer such that if two vertices u and v are adjacent, then |<em>f</em>(<em>u</em>)-<em>f</em>(<em>v</em>)|≥ <em>d</em> and if <em>u</em> and <em>v</em> are at distance two, then |<em>f</em>(<em>u</em>)-<em>f</em>(<em>v</em>)|≥ 1. The L(<em>d</em>,1)-number of <em>G</em>, <em>λ<sub>d</sub></em>(<em>G</em>), is the minimum <em>m</em> such that there is an L(<em>d</em>,1)-labelling of <em>G</em> with <em>f</em>(<em>V</em>)⊆ {0,1,… ,<em>m</em>}. A tree T is of type 1 if <em>λ<sub>d</sub></em>(<em>T</em>)= Δ +<em>d</em>-1 and is of type 2 if λ<sub>d</sub>(<em>T</em>)≥ Δ+<em>d</em>. This paper provides sufficient conditions for λ<sub>d</sub>(<em>T</em>)=Δ+<em>d</em>-1 generalizing the results of Wang  and Zhai, Lu, and Shu  for L(2,1)-labelling.
University of Kashan Mathematics Interdisciplinary Research 2538-3639 5 2 2020 06 01 The Zagreb Index of Bucket Recursive Trees 103 111 109509 10.22052/mir.2020.204312.1166 EN Ramin Kazemi Department of Statistics, Imam Khomeini International University, Qazvin, I. R. Iran Ali Behtoei Department of Pure Mathematics, Imam Khomeini International University, Qazvin, I. R. Iran Akram Kohansal Department of Statistics, Imam Khomeini International University, Qazvin, I. R. Iran https://orcid.org/0000-0002-1894-411X Journal Article 2019 10 07 ‎Bucket recursive trees are an interesting and natural generalization of recursive trees‎. ‎In this model the nodes are buckets that can hold up to b≥ 1 labels‎. ‎The (modified) Zagreb index of a graph is defined as the sum of‎ ‎the squares of the outdegrees of all vertices in the graph‎. ‎We give the mean and variance of this index in random bucket recursive trees‎. ‎Also‎, ‎two limiting results on this index are given‎.
University of Kashan Mathematics Interdisciplinary Research 2538-3639 5 2 2020 06 01 Tension Reduction between Planck data and LSS by Dynamical Dark Energy Model 113 130 110589 10.22052/mir.2019.176929.1127 EN Aghile Ebrahimi Department of Physics, University of Kashan,Kashan, I. R. Iran Majid Monemzadeh Department of Physics, University of Kashan,Kashan, I. R. Iran Hossein Moshafi Ibn-Sina Laboratory, Shahid Beheshti University, Velenjak, Tehran 19839, Iran Seyed Mohammad Sadegh Movahed Department of Physics, Shahid Beheshti University, Velenjak, Tehran 19839, Iran Journal Article 2019 03 24 In this paper, we consider the dynamical dark energy model (Feng model) to reveal the discrepancy between CMB and LSS data raised by ΛCDM model. In order to constrained free parameters, we utilize two combined sets namely the Planck TT 2015+Pol+BAO and the WL+RSD. We find that, there is a tension between the best fit values for both σ<sub>8</sub> and H<sub>0</sub> derived by the early and late time observations in the context of ΛCDM model, while the mentioned discrepancy is alleviated in the Feng model. Two dimensional likelihood analysis demonstrate that including dynamical dark energy model alleviates H<sub>0</sub> − Ω<sub>m</sub> and σ<sub>8</sub> − Ω<sub>m</sub> tension from 2σ to 1σ confidence level compared to that of given for ΛCDM. Besides these, the models satisfy fσ8 data in 0 < z < 0.4 redshift bin but for z > 0.4, the models behave differently rather than data for both data sets.<br /> <br />
University of Kashan Mathematics Interdisciplinary Research 2538-3639 5 2 2020 06 01 Toplogical and Geometric KM-Single Valued Neutrosophic Metric Spaces 131 155 110781 10.22052/mir.2020.227202.1209 EN Mohammad Hamidi ‎Department of Mathematics, University of Payame Noor, ‎Tehran‎, ‎Iran Mahdi Mollaei-Arani ‎Department of Mathematics, University of Payame Noor, ‎Tehran‎, ‎Iran Yousef Alipour-Fakhri ‎Department of Mathematics, University of Payame Noor, ‎Tehran‎, ‎Iran Journal Article 2020 04 15 ‎This paper introduces the novel concept of KM-single valued neutrosophic metric spaces as an especial generalization of KM-fuzzy metric spaces‎, ‎investigates several topological and structural properties and presents some of its applications‎. This study also considers the metric spaces and constructs KM-single valued neutrosophic spaces with respect to any given triangular norms and triangular conorms‎. ‎Moreover‎, ‎we try to extend the concept of KM-single valued neutrosophic metric spaces to a larger class of KM-single valued neutrosophic metric spaces such as union of KM-single valued neutrosophic metric spaces and product of KM-single valued neutrosophic metric spaces
University of Kashan Mathematics Interdisciplinary Research 2538-3639 5 2 2020 06 01 A New Efficient High Order Four-Step Multiderivative Method for the Numerical Solution of Second-Order IVPs with Oscillating Solutions 157 172 110786 10.22052/mir.2020.211603.1185 EN Ali Shokri Faculty of Mathematical Science, University of Maragheh, Maragheh, I. R. Iran 0000-0003-2699-1490 Mohammad Mehdizadeh Khalsaraei Faculty of Mathematical Science, University of Maragheh, Maragheh, I. R. Iran Journal Article 2019 12 12 In this paper, we present a new high order explicit four-step method of eighth algebraic order for solving second-order linear periodic and oscillatory initial value problems of ordinary differential equations such as undamped Duffing's equation. Numerical stability and phase properties of the new method is analyzed. The main structure of the method is multiderivative, and the combined phases were applied to expand the stability interval and to achieve P-stability. The advantage of the method in comparison with similar methods in terms of efficiency, accuracy, and stability is shown by its implementation in some well-known problems.