University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
5
2
2020
06
01
Numerical Calculation of Fractional Derivatives for the Sinc Functions via Legendre Polynomials
71
86
EN
Abbas
Saadatmandi
0000-0002-7744-7770
Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, Iran
a.saadatmandi@gmail.com
Ali
Khani
Department of Mathematics, Faculty of Sciences, Azarbaijan Shahid Madani University, Tabriz, Iran
khani@azaruniv.ac.ir
Mohammad Reza
Azizi
Department of Mathematics, Faculty of Sciences, Azarbaijan Shahid Madani University, Tabriz, Iran
mohamadrezaazizi52@gmail.com
10.22052/mir.2018.96632.1074
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.
Sinc functions,Fractional derivatives,Collocation method,caputo derivative
https://mir.kashanu.ac.ir/article_96936.html
https://mir.kashanu.ac.ir/article_96936_06da74b6baa7fbe772ca4a6139f4606c.pdf
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
5
2
2020
06
01
On L(d,1)-labelling of Trees
87
102
EN
Irena
Hrastnik
Faculty of Mechanical Engineering,
University of Maribor,
Maribor, Slovenia
irena.hrastnik@um.si
Janez
Žerovnik
Faculty of Mechanical Engineering,
University of Ljubljana,
Ljubljana, Slovenia
janez.zerovnik@imfm.si
10.22052/mir.2020.227370.1211
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 [11] and Zhai, Lu, and Shu [12] for L(2,1)-labelling.
L(d,1)-labelling,tree,Distance,Δ-vertex
https://mir.kashanu.ac.ir/article_108519.html
https://mir.kashanu.ac.ir/article_108519_7a815e176ecf64051ff8ea4e1a552bac.pdf
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
5
2
2020
06
01
The Zagreb Index of Bucket Recursive Trees
103
111
EN
Ramin
Kazemi
Department of Statistics, Imam Khomeini International University, Qazvin, I. R. Iran
r.kazemi@sci.ikiu.ac.ir
Ali
Behtoei
Department of Pure Mathematics, Imam Khomeini International University, Qazvin, I. R. Iran
a.behtoei@sci.ikiu.ac.ir
Akram
Kohansal
https://orcid.org/0000-0002-1894-411X
Department of Statistics, Imam Khomeini International University, Qazvin, I. R. Iran
kohansal@sci.ikiu.ac.ir
10.22052/mir.2020.204312.1166
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.
Bucket recursive tree,the Zagreb index,Limiting rule
https://mir.kashanu.ac.ir/article_109509.html
https://mir.kashanu.ac.ir/article_109509_f3b0cb23045fab361dda93a3b444fa84.pdf
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
5
2
2020
06
01
Tension Reduction between Planck data and LSS by Dynamical Dark Energy Model
113
130
EN
Aghile
Ebrahimi
Department of Physics, University of Kashan,Kashan, I. R. Iran
aghileh.ebrahimi@gmail.com
Majid
Monemzadeh
Department of Physics, University of Kashan,Kashan, I. R. Iran
monem@kashanu.ac.ir
Hossein
Moshafi
Ibn-Sina Laboratory, Shahid Beheshti University, Velenjak, Tehran 19839, Iran
hosseinmoshafi@gmail.com
Seyed Mohammad Sadegh
Movahed
Department of Physics, Shahid Beheshti University, Velenjak, Tehran 19839, Iran
m.s.movahed@ipm.ir
10.22052/mir.2019.176929.1127
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 />
Dynamical Dark Energy Models,Tension,Structure Formation
https://mir.kashanu.ac.ir/article_110589.html
https://mir.kashanu.ac.ir/article_110589_0d0bb4cabe5815f5d85dd91484d4b278.pdf
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
5
2
2020
06
01
Toplogical and Geometric KM-Single Valued Neutrosophic Metric Spaces
131
155
EN
Mohammad
Hamidi
Department of Mathematics, University of Payame Noor, Tehran, Iran
m.hamidi@pnu.ac.ir
Mahdi
Mollaei-Arani
Department of Mathematics, University of Payame Noor, Tehran, Iran
m.mollaei@pnu.ac.ir
Yousef
Alipour-Fakhri
Department of Mathematics, University of Payame Noor, Tehran, Iran
y_alipour@pnu.ac.ir
10.22052/mir.2020.227202.1209
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
KM-single valued neutrosophic metric,left-continuous triangular (co)norm,Cauchy sequence
https://mir.kashanu.ac.ir/article_110781.html
https://mir.kashanu.ac.ir/article_110781_a0449f237421dc7bb3437d2ff15d7d16.pdf
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
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
EN
Ali
Shokri
0000-0003-2699-1490
Faculty of Mathematical Science, University of Maragheh, Maragheh, I. R. Iran
shokri2090@gmail.com
Mohammad
Mehdizadeh Khalsaraei
Faculty of Mathematical Science, University of Maragheh, Maragheh, I. R. Iran
mehdizadeh@maragheh.ac.ir
10.22052/mir.2020.211603.1185
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.
Phase-lag error,Initial value problems,P-stable,Symmetric multistep methods,Periodicity interval
https://mir.kashanu.ac.ir/article_110786.html
https://mir.kashanu.ac.ir/article_110786_a6223df3def795862c0f681d78805671.pdf