2022-05-17T06:08:45Z
https://mir.kashanu.ac.ir/?_action=export&rf=summon&issue=15309
Mathematics Interdisciplinary Research
Math. Interdisc. Res.
2538-3639
2538-3639
2021
6
3
Inverse Nodal Problem for Polynomial Pencil of a Sturm-Liouville Operator from Nodal Parameters
Sertac
Goktas
Esengul
Biten
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
2021
09
01
171
183
https://mir.kashanu.ac.ir/article_111634_89d6dc1051dd147639c7ebc8f42970d0.pdf
Mathematics Interdisciplinary Research
Math. Interdisc. Res.
2538-3639
2538-3639
2021
6
3
Fixed Point of Multivalued Mizoguchi-Takahashi's Type Mappings and Answer to the Rouhani-Moradi's Open Problem
Sirous
Moradi
Zahra
Fathi
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
2021
09
01
185
194
https://mir.kashanu.ac.ir/article_111628_6092f5d4bd2792c664bd866be5b6928d.pdf
Mathematics Interdisciplinary Research
Math. Interdisc. Res.
2538-3639
2538-3639
2021
6
3
Hopf-Zero Bifurcation in Three-Cell Networks with Two Discrete Time Delays
Zohreh
Dadi
Zahra
Yazdani
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
2021
09
01
195
214
https://mir.kashanu.ac.ir/article_111627_a1242026af2518358e53a9f6df503e78.pdf
Mathematics Interdisciplinary Research
Math. Interdisc. Res.
2538-3639
2538-3639
2021
6
3
A Note on the Lempel-Ziv Parsing Algorithm under Asymmetric Bernoulli Model
Hojjat
Naeini
Ramin
Kazemi
Mohammad
Behzadi
In this paper, by applying analytic combinatorics, we obtain an asymptotics for the t-th moment of the number of phrases of length l in the Lempel-Ziv parsing algorithms built over a string generated by an asymmetric Bernoulli model. We show that the t-th moment is approximated by its Poisson transform.
Lempel-Ziv parsing algorithm
phrases
digital search tree
moment
2021
09
01
215
223
https://mir.kashanu.ac.ir/article_111540_e5431c1a549eefd99ebdb70f9041716e.pdf
Mathematics Interdisciplinary Research
Math. Interdisc. Res.
2538-3639
2538-3639
2021
6
3
On the Hosoya Index of Some Families of Graph
Fateme
Movahedi
Mohammad Hadi
Akhbari
Hailiza
Kamarulhaili
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
2021
09
01
225
234
https://mir.kashanu.ac.ir/article_111532_6da7a8236e2c51a1927c9a9c74ddc8bb.pdf
Mathematics Interdisciplinary Research
Math. Interdisc. Res.
2538-3639
2538-3639
2021
6
3
A Remark on the Factorization of Factorials
Mehdi
Hassani
Mahmoud
Marie
The subject of this paper is to study distribution of the prime factors p and their exponents, which we denote by vp (n!), in standard factorization of n! into primes. We show that for each θ > 0 the primes p not exceeding nθ eventually assume almost all value of the sum ∑p⩽nθ vp(n!). Also, we introduce the notion of θ-truncated factorial, defined by n!θ =∏p⩽nθ pvp (n!) and we show that the growth of log n!1/2 is almost half of growth of log n!1.
Factorial
Growth of arithmetic functions
Prime number
2021
09
01
235
242
https://mir.kashanu.ac.ir/article_111895_95cb4d730a26d08b2cc21d98d04876cb.pdf