AIP Conference Proceedings (0094243X)971pp. 105-111
In this paper we extend the 2-D directed graphical representation for DNA sequences. The main purpose is to making a directed graph corresponding to a DNA sequence which hasn't any complete coincidence of the edges. To prevent repetition of the edge e we define e→1 by using the outer product of two vectors and some mathematical concepts. Moreover, we have applied this method for some DNA sequences to show the advantage of this method over the some other methods. © 2008 American Institute of Physics.
Journal of Computational and Theoretical Nanoscience (15461955)4(6)pp. 1174-1178
Topological indices of nanotubes are numerical descriptors that are derived from graph of chemical compounds. Such indices based on the distances in graph are widely used for establishing relationships between the structure of nanotubes and their physico-chemical properties. The Balaban index of a molecular graph calculates the average distance sum connectivity index. Balaban index measures the ramification and it tends to increase with molecular ramification. In this paper we derive the exact expressions for Balaban index of zigzag polyhex nanotorus. Copyright © 2007 American Scientific Publishers. All rights reserved.
Taiwanese Journal of Mathematics (10275487)(1)pp. 95-105
We give some new generalized. R-KKM theorems in the nonconvexity setting of topological spaces. As an application we answer a question posed by Isac et al. for the lower and upper bounds equilibrium problem in topological spaces.
Ars Combinatoria (03817032)85pp. 307-318
The hyper Wiener index of a connected graph G is defined as WW(G) = 1/2 Σ{u,v}⊆V(G) d(u, v)+1/2 Σ{u, v}1/2V(G) d(u, v) where d(u, v) is the distance between vertices u, v E V(G). In this paper we find an exact expression for hyper Wiener index of HC6[p, q], the zigzag polyhex nanotori.
International Journal of Computer Mathematics (10290265)84(1)pp. 75-79
In this paper we propose new ideas for the implementation of the Adomian decomposition method to solve nonlinear Volterra integral equations. Numerical examples are presented to illustrate the method for nonlinear Volterra integral equations of the second kind.
Applied Mathematics and Computation (963003)189(1)pp. 341-345
In this paper, an application of homotopy perturbation method is applied to solve the nonlinear two-dimensional wave equation. The analytic solution of the nonlinear wave equation is calculated in the form of a series with easily computable components. The non-homogenous equation is effectively solved by employing the phenomena of the self-canceling "noise" terms, where sum of components vanishes in the limit. Comparing the methodology with some known techniques shows that the present approach is powerful and reliable. Its remarkable accuracy properties are finally demonstrated by an example. © 2006 Elsevier Inc. All rights reserved.
AIP Conference Proceedings (0094243X)929pp. 243-249
Topological indices of nanotube? are numerical descriptors that are derived from graph of chemical compounds. Such indices based on the distances in graph are widely used for establishing relationships between the structure of nanotubes and their physico-chemical properties. Harold Wiener in 1947 introduced the notion of path number of a graph as the sum of the distances between two carbon atoms in the molecules, in terms of carbon-carbon bound. The Wiener index of graph G is defined as W(G)= 1/2 ∑u,v∈V(G) d(u,v), where V(G) is the set of vertices of the graph and d(u,v) is the distance between two vertices u,v. The hyper Wiener index of G is defined by WW(G)= 1/2 W(G) +1/4 ∑uv∈V(G) d(u,v)2. In this paper we present some new results on topological indices of nanotubes and calculate hyper Wiener index of some nanotubes. © 2007 American Institute of Physics.
Utilitas Mathematica (03153681)74pp. 55-64
Schultz index of a molecular graph G is defined as 1/2 ∑ {u,v}⊂V(G)(deg (u) + deg (v))d(u,v), where d(u,v) is the distances between u and v in the graph G and deg (u) is the degree of the vertex u. In this paper we find an exact expression for Schultz index of TUHC6[2p,q], the zigzag polyhex nanotubes.
Journal of Theoretical and Computational Chemistry (17936888)7(5)pp. 1029-1039
Graph theory was successfully applied in developing a relationship between chemical structure and biological activity. The concept of distance in graphs is basic in the definition of various topological indices for chemical compounds, which determines some of the physicochemical properties of them. In this paper, we explain a method, using the concept of distance in the graph of zigzag polyhex nanotorus, which enables us to compute different topological indices simultaneously. © 2008 World Scientific Publishing Company.
Applied Mathematics Letters (18735452)21(9)pp. 916-921
The Wiener index W (G) of a connected graph G is defined as the sum of distances between all pairs of vertices. The Wiener polynomial H (G, x) has the property that its first derivative evaluated at x = 1 equals the Wiener index, i.e. H′ (G, 1) = W (G). The hyper-Wiener polynomial H H (G, x) satisfies the condition H H′ (G, 1) = W W (G), the hyper-Wiener index of G. In this paper we introduce a new generalization W (G, y) of the Wiener index and H (G, x, y) of the Wiener polynomial. One of the advantages of our definitions is that one can handle the Wiener and hyper-Wiener index (respectively polynomial) with the same formula, i.e. W (G) = W (G, 1), W W (G) = W (G, 2), H (G, x) = H (G, x, 1) and H H (G, x) = H (G, x, 2). © 2007 Elsevier Ltd. All rights reserved.
Journal of the Serbian Chemical Society (03525139)73(3)pp. 311-319
The Hosoya polynomial of a molecular graph G is defined as H(G,λ) = ∑{u, v}⊆V(G)λd(u,v), where d(u,v) is the distance between vertices u and v. The first derivative of H(G,λ) at λ = 1 is equal to the Wiener index of G, defined as W(G) = ∑ {u, v}⊆V(G)d(u,v). The second derivative of 1/2λH(G, λ) at λ = 1 is equal to the hyper-Wiener index, defined as WW(G) = 1/2W(G)+1/2∑{u, v}⊆V(G)d(u,v)2. Xu et al. 1 computed the Hosoya polynomial of zigzag open-ended nanotubes. Also Xu and Zhang2 computed the Hosoya polynomial of armchair open-ended nanotubes. In this paper, a new method was implemented to find the Hosoya polynomial of G = HC6[p,q], the zigzag polyhex nanotori and to calculate the Wiener and hyper Wiener indices of G using H(G,λ).
International Journal Of Molecular Sciences (14220067)9(10)pp. 2016-2026
The study of topological indices – graph invariants that can be used for describing and predicting physicochemical or pharmacological properties of organic compounds – is currently one of the most active research fields in chemical graph theory. In this paper we study the Schultz index and find a relation with the Wiener index of the armchair polyhex nanotubes T UV C6[2p, q]. An exact expression for Schultz index of this molecule is also found. © 2008 by the authors; licensee Molecular Diversity Preservation International, Basel, Switzerland.
Applicable Analysis and Discrete Mathematics (14528630)2(2)pp. 285-296
For a connected graph G, the Schultz and modified Schultz polynomials, introduced by I. Gutman: Some relations between distance-based polynomials of trees. Bulletin, Classe des Sciences Math́ematiques et Naturelles, Sciences math́ematiques, Vol. CXXXI, 30 (2005) 1-7, are defined as H1(G,x) = 1/2∑{(δu + δv)xd(u,v,|G) | u,v,∈ V(G), u ≠ v} and H2(G,x) = 1/2∑{(δuδv)xd(u,v,|G) | u,v,∈ V(G), u ≠ v}, respectively, where δu is the degree of vertex u, d(u, v|G) is the distance between u and v and V(G) is the vertex set of G. In this paper we find identities for the Schultz and modified Schultz polynomials of the sum, join and composition of graphs. As an application of our results we find the Schultz polynomial of C4 nanotubes.
Match (03406253)59(2)pp. 437-450
Topological indices of nanotubes are numerical descriptors that are derived from graph of chemical compounds. Such indices based on the distances in graph are widely used for establishing relationships between the structure of nanotubes and their physico-chemical properties. The Szeged index is obtained as a bond additive quantity where bond contributions are given as the product of the number of atoms closer to each of the two end points of each bond. In this paper we find an exact expression for Szeged index of TUVC6[2p, q], the armchair polyhex nanotubes, using a theorem of A. Dobrynin and I. Gutman on connected bipartite graphs (see Ref [1]).
Current Nanoscience (18756786)5(4)pp. 514-518
Chemical compounds are often modeled as polygonal shapes, where a vertex represents an atom and an edge symbolizes a bond. Topological properties of molecular graphs of chemical compounds can be correlated to their chemical properties and biological activities. Topological indices are the oldest and the most widely used to describing these activity relationships. Many topological indices can be expressed in terms of the distance concept in graphs. In this paper we explain a method, using the concept of distance in the graphs of zigzag polyhex nanotubes, which enables us to compute different topological indices simultaneously. © 2009 Bentham Science Publishers Ltd.
Discrete Applied Mathematics (0166218X)157(4)pp. 794-803
The Wiener index is the sum of distances between all vertex pairs in a connected graph. This notion was motivated by various mathematical properties and chemical applications. In this paper we introduce four new operations on graphs and study the Wiener indices of the resulting graphs. © 2008 Elsevier B.V. All rights reserved.
Digest Journal of Nanomaterials and Biostructures (18423582)4(4)pp. 757-762
The Harary index, H = H(G), of a molecular graph G is based on the concept of reciprocal distance and is defined, in parallel to the Wiener index, as the half-sum of the off-diagonal elements of the molecular distance matrix of G. In this paper we compute the Harary index of zigzag polyhex nanotorus.
ANZIAM Journal (14461811)50(1)pp. 75-86
The hyper-Wiener index of a connected graph G is defined as $WW(G)=(1/4)∑ (u,v) V(G)× V(G) (d(u,v)+d(u,v) ), where V (G) is the set of all vertices of G and d(u,v) is the distance between the vertices u,vV (G). In this paper we find an exact expression for the hyper-Wiener index of TUHC6[2p,q], the zigzag polyhex nanotube. Copyright © Australian Mathematical Society 2009.
Applied Mathematical Sciences (discontinued) (1312885X)3(13-16)pp. 693-700
We use the continuous Legendre multi-wavelets on the interval [0,1) to solve the linear integro-differential equation. To do so, we reduced the problem into a system of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique. Comparison has been done with two other methods and it shows that the accuracy of these results are higher than them.
Abbas, Z.,
Vahdati, S.,
Tavassoli kajani m., ,
Atan k.a., Applied Mathematics and Computation (18735649)210(2)pp. 473-478
In this paper, the properties of the floor function has been used to find a function which is one on the interval [0, 1) and is zero elsewhere. The suitable dilation and translation parameters lead us to get similar function corresponding to the interval [a, b). These functions and their combinations enable us to represent the stepwise functions as a function of floor function. We have applied this method on Haar wavelet, Sine-Cosine wavelet, Block-Pulse functions and Hybrid Fourier Block-Pulse functions to get the new representations of these functions. © 2009 Elsevier Inc. All rights reserved.
EXCLI Journal (16112156)30pp. 211-217
In this paper, a new approach for prediction of protein solvent accessibility is presented. The prediction of relative solvent accessibility gives helpful information for the prediction of na-tive structure of a protein. Recent years several RSA prediction methods including those that generate real values and those that predict discrete states (buried vs. exposed) have been de-veloped. We propose a novel method for real value prediction that aims at minimizing the prediction error when compared with existing methods. The proposed method is based on Pace Regression (PR) predictor. The improved prediction quality is a result of features of PSI-BLAST profile and the PR method because pace regression is optimal when the number of coefficients tends to infinity. The experiment results on Manesh dataset show that the pro-posed method is an improvement in average prediction accuracy and training time.
Asian Journal of Chemistry (09707077)21(2)pp. 931-941
The Schultz polynomial, S(G,x), of a molecular graph G has the property that its first derivative at x=l is equal to the Schultz index of graph. Ivan Gutman discovered that in the case of G is a tree, S(G,x), has closely related to the Wiener polynomial of G. In this paper, we find the exact expression for Schultz polynomial of TUHC6 [2p; q], the zigzag polyhex nanotubes, and obtain a relation between Schultz and Wiener polynomials of TUHC6 [2p; q].
Discrete Applied Mathematics (0166218X)158(6)pp. 659-665
In this paper, we investigate the best pixel expansion of various models of visual cryptography schemes. In this regard, we consider visual cryptography schemes introduced by Tzeng and Hu (2002) [13]. In such a model, only minimal qualified sets can recover the secret image and the recovered secret image can be darker or lighter than the background. Blundo et al. (2006) [4] introduced a lower bound for the best pixel expansion of this scheme in terms of minimal qualified sets. We present another lower bound for the best pixel expansion of the scheme. As a corollary, we introduce a lower bound, based on an induced matching of hypergraph of qualified sets, for the best pixel expansion of the aforementioned model and the traditional model of visual cryptography scheme realized by basis matrices. Finally, we study access structures based on graphs and we present an upper bound for the smallest pixel expansion in terms of strong chromatic index. © 2009 Elsevier B.V. All rights reserved.
Australian Journal of Basic and Applied Sciences (19918178)4(9)pp. 4193-4199
In this paper,We use the continuous Legendre multi-wavelets on the interval [0, 1) to solve Fredholm integral equations of the second kind. To do so, we reduced the solution of Fredholm integral equation to the solution of algebraic equations. Illustrative examples are included to show the high accuracy of the estimation, and to demonstrate validity and applicability of the technique. © 2010, INSInet Publication.
Optoelectronics and Advanced Materials, Rapid Communications (18426573)4(4)pp. 565-567
The multiplicative Wiener index, π (G), is equal to the product of the distances between all pairs of vertices of the underlying molecular graph G. In this paper we compute this index for zigzag polyhex nanotubes.
Physica A: Statistical Mechanics and its Applications (03784371)389(14)pp. 2733-2738
The quantum vibrational partition function has been obtained in the Tsallis statistics framework for the entropic index, q, between 1 and 2. The effect of non-extensivity on the population of states and thermodynamic properties have been studied and compared with their corresponding values obtained in the Boltzmann-Gibbs (BG) statistics. Our results show that the non-extensive partition function of harmonic oscillator at any temperature is larger than its corresponding values for an extensive system and that their differences increase with temperature and entropic index. Also, the number of accessible states increases with q but, compared to the BG statistics, the occupation number decreases for low energy levels while the population of the higher energy levels increases. The internal energy and heat capacity have also been obtained for the non-extensive harmonic oscillator system. Results indicate that the heat capacity is greater than its corresponding value in the extensive (BG) system at low temperatures but that this trend is reversed at higher temperatures. © 2010 Elsevier B.V. All rights reserved.
Fakharian a., ,
Hamidi beheshti m.t., ,
Davari, A. International Journal of Computer Mathematics (10290265)87(12)pp. 2769-2785
The aim of this research is to solve the Hamilton-Jacobi-Bellman equation (HJB) arising in nonlinear optimal problem using Adomian decomposition method. First Riccati equation with matrix variable coefficients, arising in linear optimal and robust control approach, is considered. By using the Adomian method, we consider an analytical approximation of the solution of nonlinear differential Riccati equation. An application in optimal control is presented. The solution in different order of approximations and different methods of approximation will be compared with respect to accuracy. Then the HJB equation, obtained in nonlinear optimal approach, is considered and an analytical approximation of the solution of it, using Adomian method, is presented. © 2010 Taylor & Francis.
