1 1735-4463 ACECR at Tarbiat Modares University 381 General The Subtree Size Profile of Bucket Recursive Trees Kazemi R. b b Imam Khomeini International University 1 4 2016 11 1 1 11 19 01 2013 02 03 2015 Kazemi (2014) introduced a new version of bucket recursive trees as another generalization of recursive trees where buckets have variable capacities. In this paper, we get the $p$-th factorial moments of the random variable $S_{n,1}$ which counts the number of subtrees size-1 profile (leaves) and show a phase change of this random variable. These can be obtained by solving a first order partial differential equation for the generating function correspond to this quantity.
430 Special Tangent Bundle of the Hypersurfaces in a Euclidean Space Deshmukh S. c Al-Shaikh S. B. d c King Saud University d King Saud University 1 4 2016 11 1 13 26 29 05 2013 15 11 2015 Let $M$ be an orientable hypersurface in the Euclidean space $R^{2n}$ with induced metric $g$ and $TM$ be its tangent bundle. It is known that the tangent bundle $TM$ has induced metric $overline{g}$ as submanifold of the Euclidean space $R^{4n}$ which is not a natural metric in the sense that the submersion $pi :(TM,overline{g})rightarrow (M,g)$ is not the Riemannian submersion. In this paper, we use the fact that $R^{4n}$ is the tangent bundle of the Euclidean space $R^{2n}$ to define a special complex structure $overline{J}$ on the tangent bundle $R^{4n}$ so that $% (R^{4n},overline{J}$,$leftlangle ,rightrangle )$ is a Kaehler manifold, where $leftlangle ,rightrangle $ is the Euclidean metric which is also the Sasaki metric of the tangent bundle $R^{4n}$. We study the structure induced on the tangent bundle $(TM,overline{g})$ of the hypersurface $M$, which is a submanifold of the Kaehler manifold $(R^{4n},overline{J}$,$% leftlangle ,rightrangle )$. We show that the tangent bundle $TM$ is a CR-submanifold of the Kaehler manifold  $(R^{4n},overline{J}$,$leftlangle ,rightrangle )$. We find conditions under which certain special vector fields on the tangent bundle $(TM,overline{g})$ are Killing vector fields. It is also shown that the tangent bundle $TS^{2n-1}$ of the unit sphere $% S^{2n-1}$ admits a Riemannian metric $overline{g}$ and that there exists a nontrivial Killing vector field on the tangent bundle $(TS^{2n-1},% overline{g})$. 451 Special Double Integral Characterization for Bergman Spaces Hassanlou M. e Vaezi H. f e University of Tabriz‎ f ‎Faculty of Mathematical Sciences‎, ‎University of Tabriz‎, ‎Tabriz‎, ‎Iran 1 4 2016 11 1 27 34 13 07 2013 22 11 2015 ‎In this paper we characterize Bergman spaces with‎ ‎respect to double integral of the functions $|f(z)‎ ‎-f(w)|/|z-w|$,‎ ‎$|f(z)‎ -‎f(w)|/rho(z,w)$ and $|f(z)‎ ‎-f(w)|/beta(z,w)$,‎ ‎where $rho$ and $beta$ are the pseudo-hyperbolic and hyperbolic metrics‎. ‎We prove some necessary and sufficient conditions that implies a function to be in Bergman spaces‎. 462 General Convergence of an Approach for Solving Fredholm Functional Integral Equations Aghazadeh N. g Fathi S. h g Azarbaijan Shahid Madani University h Azarbaijan Shahid Madani University 1 4 2016 11 1 35 46 18 08 2013 08 09 2014 In this work, we give a product Nyström method for solving a Fredholm functional integral equation (FIE) of the second kind. With this method solving FIE reduce to solving an algebraic system of equations. Then we use some theorems to prove the existence and uniqueness of the system. Finally we investigate the convergence of the method. 482 General The Representations and Positive Type Functions of Some Homogenous Spaces Raisi Tousi R. i Esmaeelzadeh F. j Kamyabi Gol R. A. k i Ferdowsi University Of Mashhad j Bojnourd Branch, Islamic Azad University k Ferdowsi University Of Mashhad 1 4 2016 11 1 47 56 14 09 2013 28 02 2015 ‎For a homogeneous spaces ‎$‎G/H‎$‎, we show that the convolution on $L^1(G/H)$ is the same as convolution on $L^1(K)$, where $G$ is semidirect product of a closed subgroup $H$ and a normal subgroup $K $ of ‎$‎G‎$‎. ‎Also we prove that there exists a one to one correspondence between nondegenerat $ast$-representations of $L^1(G/H)$ and representations of $G/H$‎. We propose a relation between cyclic representations of $L^1(G/H)$ and positive type functions on $G/H$‎. We prove that the Gelfand Raikov theorem for $G/H$ holds if and only if $H$ is normal‎. 587 Special Stability of $g$-Frame Expansions Abdollahi A. l Rahimi E. m l Shiraz University m DepaShiraz Branch, Islamic Azad University 1 4 2016 11 1 57 67 05 06 2014 22 12 2014 In this paper we investigate the stability of one-sided perturbation to g-frame expansions. We show that if $Lambda$ is a g-frame of a Hilbert space $mathcal{H}$, $Lambda_{i}^{a}=Lambda_{i}+Theta_{i}$ where $Theta_{i} in mathcal{L}(mathcal{H},mathcal{H}_{i})$, and $widetilde{f}=sum_{i in J}Lambda_{i}^{star}widetilde{Lambda}_{i}^{a}f$, $widehat{f}=sum_{i in J}(Lambda_{i}^{a})^{star}widetilde{Lambda_{i}}f$, then $|widehat{f}-f|leq alpha |f|$ and $|f-widetilde{f}|leq beta |f|$ for some $alpha$ and $beta$. 588 General An Explicit Viscosity Iterative Algorithm for Finding Fixed Points of Two Noncommutative Nonexpansive Mappings Sahebi H. R. n Razani A. o n DepartmenScience and Research Branch, Islamic Azad University o DepartmentScience and Research Branch, Islamic Azad University 1 4 2016 11 1 69 83 06 06 2014 17 01 2015 We suggest an explicit viscosity iterative algorithm for finding a common element in the set of solutions of the general equilibrium problem system (GEPS) and the set of all common fixed points of two noncommuting nonexpansive self mappings in the real Hilbert space.   597 Special On $(α, β)$−Linear Connectivity Ayatollah Zadeh Shirazi F. p Hosseini A. p Faculty of Mathematics, Statistics and Computer Science, ColUniversity of Tehran Farhangian University (Pardis Nasibe-Shahid Sherafat branch) 1 4 2016 11 1 85 100 11 07 2014 06 01 2015 In this paper we introduce $(alpha,beta)-$linear connected spaces for nonzero cardinal numbers $alpha$ and $beta$. We show that $(alpha,beta)-$linear connectivity approach is a tool to classify the class of all linear connected spaces. 620 General Coincidence Points and Common Fixed Points for Expansive Type Mappings in $b$-Metric Spaces Kumar Mohanta S. Department of Mathematics,West Bengal State University 1 4 2016 11 1 101 113 18 09 2014 05 05 2015 The main purpose of this paper is to obtain sufficient conditions for existence of points of coincidence and common fixed points for a pair of self mappings satisfying some expansive type conditions in $b$-metric spaces. Finally, we investigate that the equivalence of one of these results in the context of cone $b$-metric spaces cannot be obtained by the techniques using scalarization function. Our results extend and generalize several well known comparable results in the existing literature.   645 Special On Harmonic Index and Diameter of Unicyclic Graphs Amalorpava Jerline J. Benedict Michaelraj L. Holy Cross College Joseph’s College 1 4 2016 11 1 115 122 08 11 2014 23 05 2015 The Harmonic index $ H(G) $ of a graph $ G $ is defined as the sum of the weights $ dfrac{2}{d(u)+d(v)} $ of all edges $ uv $ of $G$, where $d(u)$ denotes the degree of the vertex $u$ in $G$. In this work, we prove the conjecture $dfrac{H(G)}{D(G)} geq dfrac{1}{2}+dfrac{1}{3(n-1)}  $ given by Jianxi Liu in 2013 when G is a unicyclic graph and give a better bound $ dfrac{H(G)}{D(G)}geq dfrac{1}{2}+dfrac{2}{3(n-2)}$, where $n$ is the order and $D(G)$ is the diameter of the graph $G$. 684 Special Fixed Point Results on $b$-Metric Space via Picard Sequences and $b$-Simulation Functions Demma M. Saadati R. Vetro P. Universit`a degli Studi di Palermo Iran University of Science and Technology Universit`a degli Studi di Palermo 1 4 2016 11 1 123 136 09 02 2015 20 06 2015 In a recent paper, Khojasteh emph{et al.} [F. Khojasteh, S. Shukla, S. Radenovi'c, A new approach to the study of fixed point theorems via simulation functions, Filomat, 29 (2015), 1189-–1194] presented a new class of simulation functions, say $mathcal{Z}$-contractions, with unifying power over known contractive conditions in the literature. Following this line of research, we extend and generalize their results on a $b$-metric context, by giving a new notion of  $b$-simulation function. Then, we prove and discuss some fixed point results in relation with existing ones. 891 Special Tricyclic and Tetracyclic Graphs with Maximum and Minimum Eccentric Connectivity Tavakoli M. Rahbarnia F. Ashrafi A. R Ferdowsi University of Mashhad Ferdowsi University of Mashhad University of Kashan 1 4 2016 11 1 137 143 02 05 2016 02 05 2016 Let $G$ be a connected graph on $n$ vertices. $G$ is called tricyclic if it has $n + 2$ edges, and tetracyclic if $G$ has exactly $n + 3$ edges. Suppose $mathcal{C}_n$ and $mathcal{D}_n$ denote the set of all tricyclic and tetracyclic $n-$vertex graphs, respectively. The aim of this paper is to calculate the minimum and maximum of eccentric connectivity index in $mathcal{C}_n$ and $mathcal{D}_n$. 898 General ABSTRACTS IN PERSIAN - Vol. 11, No. 1 In This Volume Name of Authors Tarbiat Modares University, Jahade Daneshgahi 1 4 2016 11 1 145 157 14 05 2016 14 05 2016 Please see the full text contains the Pesian abstracts for this volume.