University of KashanMathematics Interdisciplinary Research2538-36396320210901Inverse Nodal Problem for Polynomial Pencil of a Sturm-Liouville Operator from Nodal Parameters17118311163410.22052/mir.2021.242239.1286ENSertacGoktasDepartment of Mathematics,
Mersin University,
Mersin, Turkey0000-0001-7842-6309EsengulBitenDepartment of Mathematics,
Mersin University,
Mersin, Turkey0000-0001-9754-3455Journal Article20210508A 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.University of KashanMathematics Interdisciplinary Research2538-36396320210901Fixed Point of Multivalued Mizoguchi-Takahashi's Type Mappings and Answer to the Rouhani-Moradi's Open Problem18519411162810.22052/mir.2021.240213.1227ENSirousMoradiDepartment of Mathematics, Faculty of Sciences, Lorestan University, Khorramabad 68151-4-4316, IranZahraFathiDepartment of Mathematics, Faculty of Science, Arak University, Arak 38156-8-8349, IranJournal Article20200722The 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.University of KashanMathematics Interdisciplinary Research2538-36396320210901Hopf-Zero Bifurcation in Three-Cell Networks with Two Discrete Time Delays19521411162710.22052/mir.2021.190015.1149ENZohrehDadiDepartment of Mathematics,
University of Bojnord,
Bojnord, I. R. IranZahraYazdaniDepartment of Mathematics,
University of Bojnord,
Bojnord, I. R. IranJournal Article20190614In 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.University of KashanMathematics Interdisciplinary Research2538-36396320210901A Note on the Lempel-Ziv Parsing Algorithm under Asymmetric Bernoulli Model21522311154010.22052/mir.2021.240429.1263ENHojjatNaeiniDepartment of Statistics,
Science and Research Branch,
Islamic Azad University,
Tehran, I. R. IranRaminKazemiDepartment of Statistics,
Imam Khomeini International University, Qazvin, I. R. IranMohammad HasanBehzadiDepartment of Statistics,
Science and Research Branch,
Islamic Azad University,
Tehran, I. R. IranJournal Article20210110In 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.University of KashanMathematics Interdisciplinary Research2538-36396320210901On the Hosoya Index of Some Families of Graph22523411153210.22052/mir.2021.240266.1238ENFatemeMovahediDepartment of Mathematics,
Faculty of Sciences, Golestan University, Gorgan, IranMohammad HadiAkhbariDepartment of Mathematics,
Estahban Branch, Islamic Azad University, Estahban, IranHailizaKamarulhailiSchool of Mathematical Sciences,
Universiti Sains Malaysia,
11800 USM Penang, MalaysiaJournal Article20200902We 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.University of KashanMathematics Interdisciplinary Research2538-36396320210901A Remark on the Factorization of Factorials23524211189510.22052/mir.2021.240348.1254ENMehdiHassaniDepartment of Mathematics,
University of Zanjan,
University Blvd., 45371-38791
Zanjan, I. R. Iran0000-0003-0363-524XMahmoudMarieDepartment of Mathematics,
University of Zanjan,
University Blvd., 45371-38791
Zanjan, I. R. IranJournal Article20201105The 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.