Ramin Kazemi
Imam Khomeini International University
[ 1 ] - CONDITIONAL EXPECTATION IN THE KOPKA'S D-POSETS
The notion of a $D$-poset was introduced in a connection withquantum mechanical models. In this paper, we introduce theconditional expectation of random variables on theK^{o}pka's $D$-Poset and prove the basic properties ofconditional expectation on this structure.
[ 2 ] - The ratio and product of the multiplicative Zagreb indices
The first multiplicative Zagreb index $Pi_1(G)$ is equal to the product of squares of the degree of the vertices and the second multiplicative Zagreb index $Pi_2(G)$ is equal to the product of the products of the degree of pairs of adjacent vertices of the underlying molecular graphs $G$. Also, the multiplicative sum Zagreb index $Pi_3(G)$ is equal to the product of the sum...
[ 3 ] - On the first variable Zagreb index
The first variable Zagreb index of graph $G$ is defined as begin{eqnarray*} M_{1,lambda}(G)=sum_{vin V(G)}d(v)^{2lambda}, end{eqnarray*} where $lambda$ is a real number and $d(v)$ is the degree of vertex $v$. In this paper, some upper and lower bounds for the distribution function and expected value of this index in random increasing trees (rec...
[ 4 ] - On the Multiplicative Zagreb Indices of Bucket Recursive Trees
Bucket recursive trees are an interesting and natural generalization of ordinary recursive trees and have a connection to mathematical chemistry. In this paper, we give the lower and upper bounds for the moment generating function and moments of the multiplicative Zagreb indices in a randomly chosen bucket recursive tree of size $n$ with maximal bucket size $bgeq1$. Also, we consi...
[ 5 ] - The eccentric connectivity index of bucket recursive trees
If $G$ is a connected graph with vertex set $V$, then the eccentric connectivity index of $G$, $xi^c(G)$, is defined as $sum_{vin V(G)}deg(v)ecc(v)$ where $deg(v)$ is the degree of a vertex $v$ and $ecc(v)$ is its eccentricity. In this paper we show some convergence in probability and an asymptotic normality based on this index in random bucket recursive trees.
[ 6 ] - The Order Steps of an Analytic Combinatorics
Analytic combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures. This theory has emerged over recent decades as essential both for the analysis of algorithms and for the study of scientific models in many disciplines, including probability theory, statistical physics, computational biology and information theory. With a caref...
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