University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
6
3
2021
09
01
Inverse Nodal Problem for Polynomial Pencil of a Sturm-Liouville Operator from Nodal Parameters
171
183
EN
Sertac
Goktas
0000-0001-7842-6309
Department of Mathematics,
Mersin University,
Mersin, Turkey
srtcgoktas@gmail.com
Esengul
Biten
0000-0001-9754-3455
Department of Mathematics,
Mersin University,
Mersin, Turkey
esengulbiten@gmail.com
10.22052/mir.2021.242239.1286
A Sturm-Liouville problem with n-potential functions in the second order differential equation and which contains spectral parameter depending on linearly in one boundary condition is considered. The asymptotic formulas for the eigenvalues, nodal parameters (nodal points and nodal lengths) of this problem are calculated by the Prüfer's substitutions. Also, using these asymptotic formulas, an explicit formula for the potential functions are given. Finally, a numerical example is given.
Eigenvalues,Eigenfunctions,Prüfer's Substitutions,Sturm-Liouville problem,Inverse Nodal problem
https://mir.kashanu.ac.ir/article_111634.html
https://mir.kashanu.ac.ir/article_111634_89d6dc1051dd147639c7ebc8f42970d0.pdf
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
6
3
2021
09
01
Fixed Point of Multivalued Mizoguchi-Takahashi's Type Mappings and Answer to the Rouhani-Moradi's Open Problem
185
194
EN
Sirous
Moradi
Department of Mathematics, Faculty of Sciences, Lorestan University, Khorramabad 68151-4-4316, Iran
moradi.s@lu.ac.ir
Zahra
Fathi
Department of Mathematics, Faculty of Science, Arak University, Arak 38156-8-8349, Iran
zs.fathi62@gmail.com
10.22052/mir.2021.240213.1227
The fixed point theorem of Nadler (1966) was extended by Mizoguchi and Takahashi in 1989 and then for multi-valued contraction mappings, the existence of fixed point was demonstrated by Daffer and Kaneko (1995). Their results generalized the Nadler’s theorem. In 2009 Kamran generalized Mizoguchi-Takahashi’s theorem. His theorem improve Klim and Wadowski results (2007), and extended Hicks and Rhoades (1979) fixed point theorem. Recently Rouhani and Moradi (2010) generalized Daffer and Kaneko’s results for two mappings. The results of the current work, extend the previous results given by Kamram (2009), as well as by Rouhani and Moradi (2010), Nadler (1969), Daffer and Kaneko (1995), and Mizoguchi and Takahashi (1986) for tow multi-valued mappings. We also give a positive answer to the Rouhani-Moradi’s open problem.
fixed point,Mizoguchi-Takahashi fixed point theorem,multi-valued mapping,weak contraction
https://mir.kashanu.ac.ir/article_111628.html
https://mir.kashanu.ac.ir/article_111628_6092f5d4bd2792c664bd866be5b6928d.pdf
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
6
3
2021
09
01
Hopf-Zero Bifurcation in Three-Cell Networks with Two Discrete Time Delays
195
214
EN
Zohreh
Dadi
Department of Mathematics,
University of Bojnord,
Bojnord, I. R. Iran
dadizohreh@gmail.com
Zahra
Yazdani
Department of Mathematics,
University of Bojnord,
Bojnord, I. R. Iran
zahra.yazdani1369@yahoo.com
10.22052/mir.2021.190015.1149
In this paper, we study a delayed three-cell network which is introduced by coupled cell theory and neural network theory. We investigate this model with two different discrete delays. The aim is to obtain necessary conditions for the stability and the existence of Hopf-zero bifurcation in this model. Moreover, we find the normal form of this bifurcation by using linearization and the Multiple Time Scale method. Finally, the theoretical results are verified by numerical simulations.
Coupled cell theory,neural network,Stability,Hopf-zero bifurcation,Normal form
https://mir.kashanu.ac.ir/article_111627.html
https://mir.kashanu.ac.ir/article_111627_a1242026af2518358e53a9f6df503e78.pdf
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
6
3
2021
09
01
A Note on the Lempel-Ziv Parsing Algorithm under Asymmetric Bernoulli Model
215
223
EN
Hojjat
Naeini
Department of Statistics,
Science and Research Branch,
Islamic Azad University,
Tehran, I. R. Iran
kazemi@ikiu.ac.ir
Ramin
Kazemi
Department of Statistics,
Imam Khomeini International University, Qazvin, I. R. Iran
r.kazemi@sci.ikiu.ac.ir
Mohammad
Hasan
Behzadi
Department of Statistics,
Science and Research Branch,
Islamic Azad University,
Tehran, I. R. Iran
rst.kazemi@gmail.com
10.22052/mir.2021.240429.1263
In this paper, by applying analytic combinatorics, we obtain an asymptotics for the <em>t</em>-th moment of the number of phrases of length <em>l</em> in the Lempel-Ziv parsing algorithms built over a string generated by an asymmetric Bernoulli model. We show that the <em>t</em>-th moment is approximated by its Poisson transform.
Lempel-Ziv parsing algorithm,phrases,digital search tree,moment
https://mir.kashanu.ac.ir/article_111540.html
https://mir.kashanu.ac.ir/article_111540_e5431c1a549eefd99ebdb70f9041716e.pdf
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
6
3
2021
09
01
On the Hosoya Index of Some Families of Graph
225
234
EN
Fateme
Movahedi
Department of Mathematics,
Faculty of Sciences, Golestan University, Gorgan, Iran
f.movahedi@gu.ac.ir
Mohammad Hadi
Akhbari
Department of Mathematics,
Estahban Branch, Islamic Azad University, Estahban, Iran
mhakhbari20@gmail.com
Hailiza
Kamarulhaili
School of Mathematical Sciences,
Universiti Sains Malaysia,
11800 USM Penang, Malaysia
hailiza@usm.my
10.22052/mir.2021.240266.1238
We obtain the exact relations of the Hosoya index that is defined as the sum of the number of all the matching sets, on some classes of cycle-related graphs. Moreover, this index of three graph families, namely, chain triangular cactus, Dutch windmill graph, and Barbell graph is determined.
Hosoya Index,Helm graph,graph lotus,chain triangular cactus,Dutch windmill graph
https://mir.kashanu.ac.ir/article_111532.html
https://mir.kashanu.ac.ir/article_111532_6da7a8236e2c51a1927c9a9c74ddc8bb.pdf
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
6
3
2021
09
01
A Remark on the Factorization of Factorials
235
242
EN
Mehdi
Hassani
0000-0003-0363-524X
Department of Mathematics,
University of Zanjan,
University Blvd., 45371-38791
Zanjan, I. R. Iran
mehdi.hassani@znu.ac.ir
Mahmoud
Marie
Department of Mathematics,
University of Zanjan,
University Blvd., 45371-38791
Zanjan, I. R. Iran
mahmoud.marie@znu.ac.ir
10.22052/mir.2021.240348.1254
The subject of this paper is to study distribution of the prime factors p and their exponents, which we denote by v<sub>p</sub> (n!), in standard factorization of n! into primes. We show that for each θ > 0 the primes p not exceeding n<sup>θ</sup> eventually assume almost all value of the sum ∑<sub>p⩽n<sup>θ</sup> </sub>v<sub>p</sub>(n!). Also, we introduce the notion of θ-truncated factorial, defined by n!<sub>θ</sub> =∏<sub>p⩽n<sup>θ</sup> </sub> p<sup>v<sub>p</sub></sup> <sup>(n!) </sup>and we show that the growth of log n!<sub>1/2</sub> is almost half of growth of log n!1.
Factorial,Growth of arithmetic functions,Prime number
https://mir.kashanu.ac.ir/article_111895.html
https://mir.kashanu.ac.ir/article_111895_95cb4d730a26d08b2cc21d98d04876cb.pdf