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Search Results: 1 - 10 of 413065 matches for " M. Mohammad-Noori "
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Some remarks about the derivative operator and generalized Stirling numbers
M. Mohammad-Noori
Mathematics , 2010,
Abstract: Studying expressions of the form $(f(x)D)^p$, where $D={\displaystyle \frac{d}{dx}}$ is the derivative operator, goes back to Scherk's Ph.D. thesis in 1823. We show that this can be extended as ${\displaystyle\sum \gamma_{p;a} (f^{(0)})^{a(0)+1} (f^{(1)})^{a(1)}...(f^{(p-1)})^{a(p-1)}D^{p-\sum_i i a(i)}}$}, where the summation is taken over the $p$-tuples $(a_0, a_1,..., a_{p-1})$, satisfying $\sum_{i}a(i)=p-1,\, \sum_{i}i a(i)
Distance-balanced closure of some graphs
N. Ghareghani,B. Manouchehrian,M. Mohammad-Noori
Mathematics , 2010,
Abstract: In this paper we prove that any distance-balanced graph $G$ with $\Delta(G)\geq |V(G)|-3$ is regular. Also we define notion of distance-balanced closure of a graph and we find distance-balanced closures of trees $T$ with $\Delta(T)\geq |V(T)|-3$.
Intersection matrices revisited
N. Ghareghani,E. Ghorbani,M. Mohammad-Noori
Mathematics , 2009,
Abstract: Several intersection matrices of $s$-subsets vs. $k$-subsets of a $v$-set are introduced in the literature. We study these matrices systematically through counting arguments and generating function techniques. A number of new or known identities appear as natural consequences of this viewpoint; especially, appearance of the derivative operator $d/dz$ and some related operators reveals some connections between intersection matrices and the "combinatorics of creation-annihilation". As application, the eigenvalues of several intersection matrices including some generalizations of the adjacency matrices of the Johnson scheme are derived; two new bases for the Bose--Mesner algebra of the Johnson scheme are introduced and the associated intersection numbers are obtained as well. Finally, we determine the rank of some intersection matrices.
Inclusion Matrices and Chains
E. Ghorbani,G. B. Khosrovshahi,Ch. Maysoori,M. Mohammad-Noori
Mathematics , 2007,
Abstract: Given integers $t$, $k$, and $v$ such that $0\leq t\leq k\leq v$, let $W_{tk}(v)$ be the inclusion matrix of $t$-subsets vs. $k$-subsets of a $v$-set. We modify slightly the concept of standard tableau to study the notion of rank of a finite set of positive integers which was introduced by Frankl. Utilizing this, a decomposition of the poset $2^{[v]}$ into symmetric skipless chains is given. Based on this decomposition, we construct an inclusion matrix, denoted by $W_{\bar{t}k}(v)$, which is row-equivalent to $W_{tk}(v)$. Its Smith normal form is determined. As applications, Wilson's diagonal form of $W_{tk}(v)$ is obtained as well as a new proof of the well known theorem on the necessary and sufficient conditions for existence of integral solutions of the system $W_{tk}\bf{x}=\bf{b}$ due to Wilson. Finally we present anotherinclusion matrix with similar properties to those of $W_{\bar{t}k}(v)$ which is in some way equivalent to $W_{tk}(v)$.
Enumeration of closed random walks in the square lattice according to their areas
Morteza Mohammad-Noori
Mathematics , 2010,
Abstract: We study the area distribution of closed walks of length $n$, beginning and ending at the origin. The concept of area of a walk in the square lattice is generalized and the usefulness of the new concept is demonstrated through a simple argument. It is concluded that the number of walks of length $n$ and area $s$ equals to the coefficient of $z^s$ in the expression $(x+x^{-1}+y+y^{-1})^n$, where the calculations are performed in a special group ring $R[x,y,z]$. A polynomial time algorithm for calculating these values, is then concluded. Finally, the provided algorithm and the results of implementation are compared with previous works.
Enhanced Regulatory Sequence Prediction Using Gapped k-mer Features
Mahmoud Ghandi ,Dongwon Lee ,Morteza Mohammad-Noori,Michael A. Beer
PLOS Computational Biology , 2014, DOI: doi/10.1371/journal.pcbi.1003711
Abstract: Oligomers of length k, or k-mers, are convenient and widely used features for modeling the properties and functions of DNA and protein sequences. However, k-mers suffer from the inherent limitation that if the parameter k is increased to resolve longer features, the probability of observing any specific k-mer becomes very small, and k-mer counts approach a binary variable, with most k-mers absent and a few present once. Thus, any statistical learning approach using k-mers as features becomes susceptible to noisy training set k-mer frequencies once k becomes large. To address this problem, we introduce alternative feature sets using gapped k-mers, a new classifier, gkm-SVM, and a general method for robust estimation of k-mer frequencies. To make the method applicable to large-scale genome wide applications, we develop an efficient tree data structure for computing the kernel matrix. We show that compared to our original kmer-SVM and alternative approaches, our gkm-SVM predicts functional genomic regulatory elements and tissue specific enhancers with significantly improved accuracy, increasing the precision by up to a factor of two. We then show that gkm-SVM consistently outperforms kmer-SVM on human ENCODE ChIP-seq datasets, and further demonstrate the general utility of our method using a Na?ve-Bayes classifier. Although developed for regulatory sequence analysis, these methods can be applied to any sequence classification problem.
Numerical Solution of a Class of Nonlinear Optimal Control Problems Using Linearization and Discretization  [PDF]
Mohammad Hadi Noori Skandari, Emran Tohidi
Applied Mathematics (AM) , 2011, DOI: 10.4236/am.2011.25085
Abstract: In this paper, a new approach using linear combination property of intervals and discretization is proposed to solve a class of nonlinear optimal control problems, containing a nonlinear system and linear functional, in three phases. In the first phase, using linear combination property of intervals, changes nonlinear system to an equivalent linear system, in the second phase, using discretization method, the attained problem is converted to a linear programming problem, and in the third phase, the latter problem will be solved by linear programming methods. In addition, efficiency of our approach is confirmed by some numerical examples.
A New Approach for a Class of Optimal Control Problems of Volterra Integral Equations  [PDF]
Mohammad Hadi Noori Skandari, Hamid Reza Erfanian, Ali Vahidian Kamyad
Intelligent Control and Automation (ICA) , 2011, DOI: 10.4236/ica.2011.22014
Abstract: In this paper, we propose a new approach for a class of optimal control problems governed by Volterra integral equations which is based on linear combination property of intervals. We convert the nonlinear terms in constraints of problem to the corresponding linear terms. Discretization method is also applied to convert the new problems to the discrete-time problem. In addition, some numerical examples are presented to illustrate the effectiveness of the proposed approach.
A New Definition for Generalized First Derivative of Nonsmooth Functions  [PDF]
Ali Vahidian Kamyad, Mohammad Hadi Noori Skandari, Hamid Reza Erfanian
Applied Mathematics (AM) , 2011, DOI: 10.4236/am.2011.210174
Abstract: In this paper, we define a functional optimization problem corresponding to smooth functions which its optimal solution is first derivative of these functions in a domain. These functional optimization problems are applied for non-smooth functions which by solving these problems we obtain a kind of generalized first derivatives. For this purpose, a linear programming problem corresponding functional optimization problem is obtained which their optimal solutions give the approximate generalized first derivative. We show the efficiency of our approach by obtaining derivative and generalized derivative of some smooth and nonsmooth functions respectively in some illustrative examples.
Petrology and Geochemistry of Ophiolitic Host Rocks of Copper Mineralization in Dowlat Abad-Tang e Hana Area (Neyriz-Iran)  [PDF]
Pedram Attarzadeh, Mohammad Yazdi, Mehrdad Karimi, Kamal Noori Khankahdani
Open Journal of Geology (OJG) , 2016, DOI: 10.4236/ojg.2016.68054
Abstract: Dowlat Abad-Tang e Hana area is a part of Neyriz ophiolite zone, parallel to the Zagros thrust, SW of Iran. It is also a part of obduction thrusting belt over the edge of the Arabian continent during the late Cretaceous. Petrographic investigation indicates the main host rocks are harzburgite, dunite, pyroxenite, basalt, gabbro and pelagic marine sediments. The main magma type of this ophiolite complex is sub-alkaline. The geochemical data of analysed samples show depletion of Na and K, and enrichment in Ca. Copper mineralization in Dowlat Abad-Tang e Hana is hosted mainly in peridotite rocks. The mineralizations are vein type and are associated as copper carbonate (malachite and less azurite). The average of Cu grade is 2.3 wt%. The geochemical and mineralogical data show that the primary source of copper is ortho-magmatic (from ultra-basic rocks and ferro magnesium minerals), which later influenced by hydrothermal processes.
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