Wiener Polynomial Research Articles

A Two-Step Identification Approach for Twin-Box Models of RF Power Amplifier

We propose a two-step identification approach for twin-box model (Wiener or Hammerstein) of RF power amplifier. The linear filter block and the static nonlinearity block are extracted, respectively, based on least-squares method, by iterative calculation. Simulations show that the method can get quite accurate parameters to model different nonlinear models with memory such as Wiener, Hammerstein, Wiener-Hammerstein (W-H), and memory polynomial models, hence, demonstrating its robustness. Furthermore, experimental results show excellent agreement between measured output and modeled output, where one carrier WCDMA signal is used as the excitation for a wideband RF amplifier.

Formula omitted]-Wiener index of composite graphs

Eliasi and Taeri [Extension of the Wiener index and Wiener polynomial, Appl. Math. Lett. 21 (2008) 916–921] introduced the notion of y -Wiener index of graphs as a generalization of the classical Wiener index and hyper Wiener index of graphs. They obtained some mathematical properties of this new defined topological index. In this paper, the join, Cartesian product, composition, disjunction and symmetric difference of graphs under y -Wiener index are computed. By these results most parts of a paper by Sagan et al. [The Wiener polynomial of a graph, Int. J. Quant. Chem. 60 (1996) 959–969] and another paper by Khalifeh et al. [The hyper-Wiener index of graph operations, Comput. Math. Appl. 56 (2008) 1402–1407] are generalized.

Applications of the Matrix Package MATLAB in Computing the Wiener Polynomial of Armchair Polyhex Nanotubes and Nanotori

Applications of the Matrix Package MATLAB in Computing the Wiener Polynomial of Armchair Polyhex Nanotubes and Nanotori

SOME NEW RESULTS ON THE HOSOYA POLYNOMIAL OF GRAPH OPERATIONS

The Wiener index is a graph invariant that has found extensive application in chemistry. In addition to that a generating function, which was called the Wiener polynomial, who’s derivate is a q-analog of the Wiener index was defined. In an article, Sagan, Yeh and Zhang in [The Wiener Polynomial of a graph, Int. J. Quantun Chem., 60 (1996), 959969] attained what graph operations do to the Wiener polynomial. By considering all the results that Sagan et al. admitted for Wiener polynomial on graph operations for each two connected and nontrivial graphs, in this article we focus on deriving Wiener polynomial of graph operations, Join, Cartesian product, Composition, Disjunction and Symmetric difference on n graphs and Wiener indices of them.

Computing Wiener Polynomial, Wiener Index and Hyper Wiener Index of C80 Fullerene by GAP Program

In this article, we give a GAP program for computing the Wiener polynomial of any graph. Also we compute the Wiener index, hyper Wiener index, and Wiener polynomial of C80 fullerene by this program.

A Spectral Stochastic Semi-Lagrangian Method for Convection-Diffusion Equations with Uncertainty

Real life convection-diffusion problems are characterized by their inherent or externally induced uncertainties in the design parameters. This paper presents a spectral stochastic finite element semi-Lagrangian method for numerical solution of convection-diffusion equations with uncertainty. Using the spectral decomposition, the stochastic variational problem is reformulated to a set of deterministic variational problems to be solved for each Wiener polynomial chaos. To obtain the chaos coefficients in the corresponding deterministic convection-diffusion equations, we implement a semi-Lagrangian method in the finite element framework. Once this representation is computed, statistics of the numerical solution can be easily evaluated. These numerical techniques associate the geometrical flexibility of the finite element method with the ability offered by the semi-Lagrangian method to solve convection-dominated problems using time steps larger than its Eulerian counterpart. Numerical results are shown for a convection-diffusion problem driven with stochastic velocity and for an incompressible viscous flow problem with a random force. In both examples, the proposed method demonstrates its ability to better maintain the shape of the solution in the presence of uncertainties and steep gradients.

Extension of the Wiener index and Wiener polynomial

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 ) .

Distance distributions for graphs modeling computer networks

The Wiener polynomial of a graph G is a generating function for the distance distribution dd ( G ) = ( D 1 , D 2 , … , D t ) , where D i is the number of unordered pairs of distinct vertices at distance i from one another and t is the diameter of G. We use the Wiener polynomial and several related generating functions to obtain generating functions for distance distributions of unweighted and weighted graphs that model certain large classes of computer networks. These provide a straightforward means of computing distance and timing statistics when designing new networks or enlarging existing networks.

The Liner multiplexers for generalizing the distance of vehicle data from the complete statement with Some private data

It may be possible to find the Wiener polynomial with respect to a generalized distance of a compound graph constructed from two graphs having some kind of regularity. In this paper, we obtain the Wiener polynomials for a generalized distance of compound graphs constructed from a complete graph with some other special graph, such as a complete bipartite graph, a star, and a wheel, using binary operations defined by Gutman [4]. The Wiener index with respect to such generalized distance for each such compound graph is also obtained.الملخصإن وضع صیغة لمتعددة حدود وینر لتعمیم المسافة فی البیانات المرکبة یتطلب ان تکون البیانات المرکبة لها درجة من الانتظام, وهذا ینطبق على تراکیب بعض البیانات الخاصة التی لها انتظام معین, لذلک وجدنا من المناسب إیجاد حدودیات وینر لتعمیم المسافة للبیان المرکب من البیان التام مع بعض البیانات الخاصة مثلا البیان الثنائی التجزئة التام, وبیان النجمة, وبیان العجلة بإحدى العملیات الثنائیة المعرفة لـ[4] Gutman. وکذلک أوجدنا دلیل وینر لمتعددات الحدود لتعمیم المسافة لکل من البیانات المرکبة المذکورة سابقا.

The Wiener Polynomial of thekthPower Graph

We presented a formula for the Wiener polynomial of thekthpower graph. We use this formula to find the Wiener polynomials of thekthpower graphs of paths, cycles, ladder graphs, and hypercubes. Also, we compute the Wiener indices of these graphs.

The behavior of Wiener indices and polynomials of graphs under five graph decorations

The sum of distances between all vertex pairs in a connected graph is known as the Wiener index. It is an early index which correlates well with many physico-chemical properties of organic compounds and as such has been well studied over the last quarter of a century. A q -analogue of this index, termed the Wiener polynomial by Hosoya but also known today as the Hosoya polynomial, extends this concept by trying to capture the complete distribution of distances in the graph. Mathematicians have studied several operators on a connected graph in which we see a subdivision of the edges. In this work, we show how the Wiener index of a graph changes with these operations, and extend the results to Wiener polynomials.

Hyper‐Wiener vector, Wiener matrix sequence, and Wiener polynomial sequence of a graph

AbstractThe Wiener matrix and the hyper‐Wiener number of a tree (acyclic structure) were first introduced by Randic 1. Randic and Guo and colleagues 2, 3 further introduced the higher Wiener numbers of a tree that can be represented by a Wiener number sequence 1W, 2W, 3W, …, where 1W = W is the Wiener index, and ∑k=1,2, … kW = R is the hyper‐Wiener number. Later the definition of hyper‐Wiener number was extended by Klein et al. for application to any connected structure. In this study, the definition of higher Wiener numbers is extended to be applicable to any connected structure. The concepts of the Wiener vector and hyper‐Wiener vector of a graph are introduced. Moreover, a matrix sequence W(1), W(2), W(3), …, called the Wiener matrix sequence (or distance matrix sequence), and their sum ∑k=1,2, … W(k) = W(H), called the hyper‐Wiener matrix, are introduced, where W(1) = D is the distance matrix, and the sum of the entries of upper triangle of W(k) (resp. W(H)) is just equal to kW (resp. R). A Wiener polynomial sequence and a weighted hyper‐Wiener polynomial of a graph are also introduced. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006

Finite elements for elliptic problems with stochastic coefficients

We describe a deterministic finite element (FE) solution algorithm for a stochastic elliptic boundary value problem (sbvp), whose coefficients are assumed to be random fields with finite second moments and known, piecewise smooth two-point spatial correlation function. Separation of random and deterministic variables (parametrization of the uncertainty) is achieved via a Karhunen–Loève (KL) expansion. An O(NlogN) algorithm for the computation of the KL eigenvalues is presented, based on a kernel independent fast multipole method (FMM). Truncation of the KL expansion gives an (M,1) Wiener polynomial chaos (PC) expansion of the stochastic coefficient and is shown to lead to a high dimensional, deterministic boundary value problem (dbvp). Analyticity of its solution in the stochastic variables with sharp bounds for the domain of analyticity are used to prescribe variable stochastic polynomial degree r=(r1,…,rM) in an (M,r) Wiener PC expansion for the approximate solution. Pointwise error bounds for the FEM approximations of KL eigenpairs, the truncation of the KL expansion and the FE solution to the dbvp are given. Numerical examples show that M depends on the spatial correlation length of the random diffusion coefficient. The variable polynomial degree r in PC-stochastic Galerkin FEM allows to handle KL expansions with M up to 30 and r1 up to 10 in moderate time.

Wiener polynomials of some chemically interesting graphs

AbstractThe chemist Harold Wiener found 𝒲(G), the sum of distances between all pairs of vertices in a connected graph G, to be useful as a predictor of certain physical and chemical properties. The q‐analogue of 𝒲, called the Wiener polynomial 𝒲(G; q), is also useful, but it has few existing useful formulas. We will evaluate 𝒲(G; q) for certain graphs G of chemical interest. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004

Remarks on Distance Distributions for Graphs Modeling Computer Networks

Abstract The Wiener polynomial of a graph G is a generating function for the distance distribution dd ( G ) = ( D 1 , D 2 ,…, D t ), where D i is the number of unordered pairs of distinct vertices at distance i from one another and t is the diameter of G . We use the Wiener polynomial and several related generating functions to obtain generating functions for distance distributions of graphs that model certain large classes of computer networks. These provide a straightforward means of computing distance and timing statistics when designing new networks or enlarging existing networks.

The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations

We present a new method for solving stochastic differential equations based on Galerkin projections and extensions of Wiener's polynomial chaos. Specifically, we represent the stochastic processes with an optimum trial basis from the Askey family of orthogonal polynomials that reduces the dimensionality of the system and leads to exponential convergence of the error. Several continuous and discrete processes are treated, and numerical examples show substantial speed-up compared to Monte Carlo simulations for low dimensional stochastic inputs.

Quantitative Structure-Property Relationships Generated with Optimizable Even/Odd Wiener Polynomial Descriptors

Chemical structures of organic compounds are characterized numerically by a variety of structural descriptors, one of the earliest and most widely used being the Wiener index W, derived from the interatomic distances in a molecular graph. Extensive use of distance-based structural descriptors or topological indices has been made in QSPR and QSAR models, drug design, toxicology, virtual screening of combinatorial libraries, similarity and diversity assessment. Novel topological indices are introduced representing a partitioning of the Wiener polynomial based on counts of even and odd molecular graph distances. During the QSAR/QSPR modeling process the variables of the even and odd power functions are optimized in order to offer an improved mapping of the investigated property. These novel topological indices are tested in QSPR models for the boiling temperature, molar heat capacity, standard Gibbs energy of formation, vaporization enthalpy, refractive index, and density of alkanes. In many cases, the even/odd Wiener polynomial indices proposed here give notably improved correlations or suggest simpler QSPR models.

The Wiener polynomial of a graph

The Wiener index is a graphical invariant that has found extensive application in chemistry. We define a generating function, which we call the Wiener polynomial, whose derivative is a q-analog of the Wiener index. We study some of the elementary properties of this polynomial and compute it for some common graphs. We then find a formula for the Wiener polynomial of a dendrimer, a certain highly regular tree of interest to chemists, and show that it is unimodal. Finally, we point out a connection with the Poincaré polynomial of a finite Coxeter group. © 1996 John Wiley & Sons, Inc.

The Wiener polynomial of a graph

The Wiener index is a graphical invariant that has found extensive application in chemistry. We define a generating function, which we call the Wiener polynomial, whose derivative is a q-analog of the Wiener index. We study some of the elementary properties of this polynomial and compute it for some common graphs. We then find a formula for the Wiener polynomial of a dendrimer, a certain highly regular tree of interest to chemists, and show that it is unimodal. Finally, we point out a connection with the Poincare polynomial of a finite Coxeter group.