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Статті в журналах з теми "Wiener polynomial"

Автор: Grafiati

Опубліковано: 3 червня 2025

Оновлено: 31 липня 2025

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1

AbuGhneim, Omar A., Hasan Al-Ezeh, and Mahmoud Al-Ezeh. "The Wiener Polynomial of thekthPower Graph." International Journal of Mathematics and Mathematical Sciences 2007 (2007): 1–6. http://dx.doi.org/10.1155/2007/24873.

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Анотація:

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.

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2

GOREV, Vyacheslav, Alexander GUSEV, Valerii KORNIIENKO, Yana SHEDLOVSKA, and Ivan LAKTIONOV. "POLYNOMIAL SOLUTIONS FOR THE KOLMOGOROV–WIENER PREDICTION OF MODELED SMOOTHED HEAVY-TAIL PROCESS." Information Technology: Computer Science, Software Engineering and Cyber Security, no. 1 (June 12, 2024): 28–34. http://dx.doi.org/10.32782/it/2024-1-4.

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Анотація:

Nowadays telecommunication traffic in systems with data packet transfer is considered as a heavy-tail random process. In a couple of rather simple models traffic is considered to be stationary one. In our recent papers we generated modeled heavy-tail data, which is based on the smoothing of the fractional Gaussian noise. In particular, the applicability if the continuous Kolmogorov–Wiener filter to the prediction of such data was investigated, the corresponding Wiener–Hopf integral equation was solved on the basis of the truncated Walsh function expansion. However, a question occurs – may anot

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3

Jabir, Azeez Lafta, AbdulJalil M. Khalaf, and Emad A. Jaffar AL-Mulla. "Hosoya Polynomials Of Some Semiconducotors." Journal of Kufa for Mathematics and Computer 2, no. 2 (2014): 49–55. http://dx.doi.org/10.31642/jokmc/2018/020208.

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Анотація:

The Hosoya polynomial of a graph G is a graphical invariant polynomial that its first derivative at x = 1 is equal to the Wiener index and second derivative at x =1 is equal to the hyperï€Wiener index. In this paper we compute the Hosoya polynomial of some semiconducotors [Caesium Chloride, Perovskite structure, Zinc blende structure, Rock-salt(Nacl)structure, Wurtzite structure, Chalcopyrite structure], Wiener index and hyper-Wiener index for then.The Hosoya polynomial of a graph G is a graphical invariant polynomial that its first derivative at x = 1 is equal to the Wiener index and second

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4

Gorev, Vyacheslav, Alexander Gusev, and Valerii Korniienko. "INVESTIGATION OF THE KOLMOGOROV-WIENER FILTER FOR CONTINUOUS FRACTAL PROCESSES ON THE BASIS OF THE CHEBYSHEV POLYNOMIALS OF THE FIRST KIND." Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska 10, no. 1 (2020): 58–61. http://dx.doi.org/10.35784/iapgos.912.

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Анотація:

This paper is devoted to the investigation of the Kolmogorov-Wiener filter weight function for continuous fractal processes with a power-law structure function. The corresponding weight function is sought as an approximate solution to the Wiener-Hopf integral equation. The truncated polynomial expansion method is used. The solution is obtained on the basis of the Chebyshev polynomials of the first kind. The results are compared with the results of the authors’ previous investigations devoted to the same problem where other polynomial sets were used. It is shown that different polynomial sets p

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5

Cheng, Zhong-Lin, Ashaq Ali, Haseeb Ahmad, Asim Naseem, and Maqbool Ahmad Chaudhary. "Hosoya and Harary Polynomials of Hourglass and Rhombic Benzenoid Systems." Journal of Chemistry 2020 (April 9, 2020): 1–14. http://dx.doi.org/10.1155/2020/5398109.

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Анотація:

In the fields of chemical graph theory, topological index is a type of a molecular descriptor that is calculated based on the graph of a chemical compound. In 1947, Harry Wiener introduced “path number” which is now known as Wiener index and is the oldest topological index related to molecular branching. Hosoya polynomial plays a vital role in determining Wiener index. In this report, we compute the Hosoya polynomials for hourglass and rhombic benzenoid systems and recover Wiener and hyper-Wiener indices from them.

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6

GOREV, Vyacheslav, Alexander GUSEV, and Valerii KORNIIENKO. "ON THE ACCURACY OF SOME APPROXIMATIONS FOR THE KOLMOGOROV–WIENER FILTER WEIGHT FUNCTION FOR POWER–LAW STRUCTURE FUNCTION PROCESSES." Information Technology: Computer Science, Software Engineering and Cyber Security, no. 1 (September 8, 2022): 9–13. http://dx.doi.org/10.32782/it/2022-1-2.

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Анотація:

The paper is devoted to the investigation of the accuracy of some polynomial approximations for the Kolmogorov– Wiener filter weight function. The corresponding filter is applied to the prediction of stationary random processes with a power-law structure function. In our previous investigations the Kolmogorov–Wiener filter weight function was obtained on the basis of the truncated polynomial expansion method based on the Chebyshev polynomials of the first kind. It was obtained that some approximations lead to good results; however, some approximations (i.e. the approximations of 9–15 polynomia

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7

Sheikh, Umber, Sidra Rashid, Cenap Ozel, and Richard Pincak. "On Hosoya Polynomial and Subsequent Indices of C4C8(R) and C4C8(S) Nanosheets." Symmetry 14, no. 7 (2022): 1349. http://dx.doi.org/10.3390/sym14071349.

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Анотація:

Chemical structures are mathematically modeled using chemical graphs. The graph invariants including algebraic polynomials and topological indices are related to the topological structure of molecules. Hosoya polynomial is a distance based algebraic polynomial and is a closed form of several distance based topological indices. This article is devoted to compute the Hosoya polynomial of two different atomic configurations (C4C8(R) and C4C8(S)) of C4C8 Carbon Nanosheets. Carbon nanosheets are the most stable, flexible structure of uniform thickness and admit a vast range of applications. The Hos

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8

Chen, Lian, Abid Mehboob, Haseeb Ahmad, Waqas Nazeer, Muhammad Hussain, and M. Reza Farahani. "Hosoya and Harary Polynomials of TOX(n),RTOX(n),TSL(n) and RTSL(n)." Discrete Dynamics in Nature and Society 2019 (July 16, 2019): 1–18. http://dx.doi.org/10.1155/2019/8696982.

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Анотація:

In the fields of chemical graph theory, topological index is a type of a molecular descriptor that is calculated based on the graph of a chemical compound. In 1947, Wiener introduced “path number” which is now known as Wiener index and is the oldest topological index related to molecular branching. Hosoya polynomial plays a vital role in determining Wiener index. In this report, we computed the Hosoya and the Harary polynomials for TOX(n),RTOX(n),TSL(n), and RTSL(n) networks. Moreover, we computed serval distance based topological indices, for example, Wiener index, Harary index, and multiplic

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9

Azari, Mahdieh, and Ali Iranmanesh. "Joins, coronas and their vertex-edge Wiener polynomials." Tamkang Journal of Mathematics 47, no. 2 (2016): 163–78. http://dx.doi.org/10.5556/j.tkjm.47.2016.1824.

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Анотація:

The vertex-edge Wiener index of a simple connected graph $G$ is defined as the sum of distances between vertices and edges of $G$. The vertex-edge Wiener polynomial of $G$ is a generating function whose first derivative is a $q-$analog of the vertex-edge Wiener index. Two possible distances $D_1(u, e|G)$ and $D_2(u, e|G)$ between a vertex $u$ and an edge $e$ of $G$ can be considered and corresponding to them, the first and second vertex-edge Wiener indices of $G$, and the first and second vertex-edge Wiener polynomials of $G$ are introduced. In this paper, we study the behavior of these indice

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10

Liu, Yonghong, Abdul Rauf, AdnanAslam, Saira Ishaq та Abudulai Issa. "Computing Wiener and Hyper-Wiener Indices of Zero-Divisor Graph of ℤ ℊ 3 × ℤ I 1 I 2". Journal of Function Spaces 2022 (19 вересня 2022): 1–11. http://dx.doi.org/10.1155/2022/2046173.

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Анотація:

Let S = ℤ ℊ 3 × ℤ I 1 I 2 be a commutative ring where ℊ , I 1 and I 2 are positive prime integers with I 1 ≠ I 2 . The zero-divisor graph assigned to S is an undirected graph, denoted as Y S with vertex set V( Y (S)) consisting of all Zero-divisor of the ring S and for any c, d ∈ V( Y (S)), c d ∈ E Y S if and only if cd =0. A topological index/descriptor is described as a topological-invariant quantity that transforms a molecular graph into a mathematical real number. In this paper, we have computed distance-based polynomials of Y R i-e Hosoya polynomial, Harary polynomial, and the topological

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11

Gorev, V. N., A. Yu Gusev, and V. I. Korniienko. "KOLMOGOROV-WIENER FILTER FOR CONTINUOUS TRAFFIC PREDICTION IN THE GFSD MODEL." Radio Electronics, Computer Science, Control, no. 3 (October 1, 2022): 31. http://dx.doi.org/10.15588/1607-3274-2022-3-3.

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Анотація:

Context. We investigate the Kolmogorov-Wiener filter weight function for the prediction of continuous stationary telecommunication traffic in the GFSD (Gaussian fractional sum-difference) model. Objective. The aim of the work is to obtain an approximate solution for the corresponding weight function and to illustrate the convergence of the truncated polynomial expansion method used in this paper. Method. The truncated polynomial expansion method is used for the obtaining of an approximate solution for the KolmogorovWiener weight function under consideration. In this paper we used t

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12

Eliasi, Mehdi, and Bijan Taeri. "Extension of the Wiener index and Wiener polynomial." Applied Mathematics Letters 21, no. 9 (2008): 916–21. http://dx.doi.org/10.1016/j.aml.2007.10.001.

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13

Gorev, V. N., A. Yu Gusev, and V. I. Korniienko. "APPROXIMATE SOLUTIONS FOR THE KOLMOGOROV-WIENER FILTER WEIGHT FUNCTION FOR CONTINUOUS FRACTIONAL GAUSSIAN NOISE." Radio Electronics, Computer Science, Control 1, no. 1 (2021): 29–35. http://dx.doi.org/10.15588/1607-3274-2021-1-3.

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Анотація:

Context. We consider the Kolmogorov-Wiener filter for forecasting of telecommunication traffic in the framework of a continuous fractional Gaussian noise model. Objective. The aim of the work is to obtain the filter weight function as an approximate solution of the corresponding WienerHopf integral equation. Also the aim of the work is to show the convergence of the proposed method of solution of the corresponding equation. Method. The Wiener-Hopf integral equation for the filter weight function is a Fredholm integral equation of the first kind. We use the truncated polynomial expa

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14

ROBERTS, A. P., and M. M. NEWMANN. "Polynomial approach to Wiener filtering." International Journal of Control 47, no. 3 (1988): 681–96. http://dx.doi.org/10.1080/00207178808906046.

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15

Eliasi, Mehdi, and Bijan Taeri. "Hosoya polynomial of zigzag polyhex nanotorus." Journal of the Serbian Chemical Society 73, no. 3 (2008): 311–19. http://dx.doi.org/10.2298/jsc0803311e.

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Анотація:

The Hosoya polynomial of a molecular graph G is defined as H(G,?)=?{u,v}V?(G) ?d(u,v), where d(u,v) is the distance between vertices u and v. The first derivative of H(G,?) at ?=1 is equal to the Wiener index of G, defined as W(G)?{u,v}?V(G)d(u,v). The second derivative of 1/2 ?H(G, ?) at ?=1 is equal to the hyper-Wiener index, defined as WW(G)+1/2?{u,v}?V(G)d(u,v)?. 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 polynomia

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16

Shaheen, Ramy, Suhail Mahfud, and Qays Alhawat. "Hosoya, Schultz, and Gutman Polynomials of Generalized Petersen Graphs P n , 1 and P n , 2." Journal of Mathematics 2023 (July 3, 2023): 1–18. http://dx.doi.org/10.1155/2023/7341285.

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Анотація:

The graph theory has wide important applications in various other types of sciences. In chemical graph theory, we have many topological polynomials for a graph G through which we can compute many topological indices. Topological indices are numerical values and descriptors which are used to quantify the physiochemical properties and bioactivities of the chemical graph. In this paper, we compute Hosoya polynomial, hyper-Wiener index, Tratch–Stankevitch–Zefirov index, Harary index, Schultz polynomial, Gutman polynomial, Schultz index, and Gutman index of generalized Petersen graphs P n , 1 and P

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17

Ahila Jeyanthi, D., and T. M. Selvarajan. "WIENER POLYNOMIAL AND DEGREE DISTANCE POLYNOMIAL OF SOME GRAPHS." Advances in Mathematics: Scientific Journal 9, no. 9 (2020): 6863–69. http://dx.doi.org/10.37418/amsj.9.9.45.

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18

Johar, Dwindi Agryanti, Asep Kuswandi Supriatna, and Ema Carnia. "Wiener Index Calculation on the Benzenoid System: A Review Article." Jurnal Matematika Integratif 19, no. 1 (2023): 13. http://dx.doi.org/10.24198/jmi.v19.n1.44487.13-28.

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Анотація:

The Weiner index is considered one of the basic descriptors of fixed interconnection networks because it provides the average distance between any two nodes of the network. Many methods have been used by researchers to calculate the value of the Wiener index. starting from the brute force method to the invention of an algorithm to calculate the Wiener index without calculating the distance matrix. The application of the Wiener index is found in the molecular structure of organic compounds, especially the benzenoid system. The value of the Wiener index of a molecule is closely related to its ph

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19

Johar, Dwindi Agryanti, Asep Kuswandi Supriatna, and Ema Carnia. "Wiener Index Calculation on the Benzenoid System: A Review Article." Jurnal Matematika Integratif 19, no. 1 (2023): 13. http://dx.doi.org/10.24198/jmi.v19.n1.44487.13-30.

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Анотація:

The Weiner index is considered one of the basic descriptors of fixed interconnection networks because it provides the average distance between any two nodes of the network. Many methods have been used by researchers to calculate the value of the Wiener index. starting from the brute force method to the invention of an algorithm to calculate the Wiener index without calculating the distance matrix. The application of the Wiener index is found in the molecular structure of organic compounds, especially the benzenoid system. The value of the Wiener index of a molecule is closely related to its ph

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20

HOANG, VIET HA, and CHRISTOPH SCHWAB. "N-TERM WIENER CHAOS APPROXIMATION RATES FOR ELLIPTIC PDEs WITH LOGNORMAL GAUSSIAN RANDOM INPUTS." Mathematical Models and Methods in Applied Sciences 24, no. 04 (2014): 797–826. http://dx.doi.org/10.1142/s0218202513500681.

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Анотація:

We consider diffusion in a random medium modeled as diffusion equation with lognormal Gaussian diffusion coefficient. Sufficient conditions on the log permeability are provided in order for a weak solution to exist in certain Bochner–Lebesgue spaces with respect to a Gaussian measure. The stochastic problem is reformulated as an equivalent deterministic parametric problem on ℝℕ. It is shown that the weak solution can be represented as Wiener–Itô Polynomial Chaos series of Hermite Polynomials of a countable number of i.i.d standard Gaussian random variables taking values in ℝ1. We establish suf

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21

Guo, Xiaofeng, D. J. Klein, Weigen Yan, and Yeong-Nan Yeh. "Hyper-Wiener vector, Wiener matrix sequence, and Wiener polynomial sequence of a graph." International Journal of Quantum Chemistry 106, no. 8 (2006): 1756–61. http://dx.doi.org/10.1002/qua.20958.

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22

Shaheen, Ramy. "The Hosoya polynomial, Wiener index, and Hyper-Wiener index of Jahangir Graph \(J_{8,m}\)." Online Journal of Analytic Combinatorics, no. 15 (December 31, 2020): 1–9. https://doi.org/10.61091/ojac-1515.

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Анотація:

Let \( G(V,E) \) be a simple connected graph with vertex set \( V \) and edge set \( E \). The Wiener index in the graph is \(W(G) = \sum_{\{u,v\} \subseteq V} d(u,v),\) where \( d(u,v) \) is the distance between \( u \) and \( v \), and the Hosoya polynomial of \( G \) is \(H(G, x) = \sum_{\{u,v\} \subseteq V} x^{d(u,v)}.\) The hyper-Wiener index of \( G \) is \(WW(G) = \frac{1}{2} \left( W(G) + \sum_{\{u,v\} \subseteq V} d^2(u,v) \right).\) In this paper, we compute the Wiener index, Hosoya polynomial, and hyper-Wiener index of Jahangir graph \( J_{8,m} \) for \( m \geq 3 \).

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23

Mohammad, Reza Farahani. "HOSOYA POLYNOMIAL, WIENER AND HYPERWIENER INDICES OF SOME REGULAR GRAPHS." Informatics Engineering, an International Journal (IEIJ) 01, dec (2013): 01–05. https://doi.org/10.5281/zenodo.1435656.

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Анотація:

Let G be a graph. The distance d(u,v) between two vertices u and v of G is equal to the length of a shortest path that connects u and v. The Wiener index W(G) is the sum of all distances between vertices of G, whereas the hyper-Wiener index WW(G) is defined as ( ) ( ) ( ) ( ) ( ) 2 {u,v} V G WW G d v u d v u , , . ∈ = + ∑ Also, the Hosoya polynomial was introduced by H. Hosoya and define ( ) ( ) ( ) , {u,v} V G , . d v u H G x x ∈ = ∑ In this paper, the Hosoya polynomial, Wiener index and Hyper-Wiener index of some regular graphs are determined.

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24

Informatics, Engineering an International Journal (IEIJ). "HOSOYA POLYNOMIAL, WIENER AND HYPERWIENER INDICES OF SOME REGULAR GRAPHS." Informatics Engineering, an International Journal (IEIJ) 1, no. 1 (2013): 1–5. https://doi.org/10.5281/zenodo.14382082.

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Анотація:

Let G be a graph. The distance d(u,v) between two vertices u and v of G is equal to the length of a shortest path that connects u and v. The Wiener index W(G) is the sum of all distances between vertices of G,whereas the hyper-Wiener index WW(G) is defined as ( ) ( ) ( ) ( ) ( )2{u,v} V GWW G d v u d v u , , .∈= + ∑ Also, theHosoya polynomial was introduced by H. Hosoya and define ( )( )( ),{u,v} V G, .d v u H G x x∈= ∑ In this paper, the Hosoya polynomial, Wiener index and Hyper Wiener index of some regular graphs are determined.  

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25

Ahlen, A., and M. Sternad. "Wiener filter design using polynomial equations." IEEE Transactions on Signal Processing 39, no. 11 (1991): 2387–99. http://dx.doi.org/10.1109/78.97994.

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26

Sagan, Bruce E., Yeong-Nan Yeh, and Ping Zhang. "The Wiener polynomial of a graph." International Journal of Quantum Chemistry 60, no. 5 (1996): 959–69. http://dx.doi.org/10.1002/(sici)1097-461x(1996)60:5<959::aid-qua2>3.0.co;2-w.

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27

Al-Rumaima, Mahmoud, Abdu Alameri, Mohammed Al-Sharafi, et al. "Computation of wiener polynomial and index of line subdivision friendship and line subdivision bifriendship graphs using matlab program." Proyecciones (Antofagasta) 43, no. 1 (2024): 163–87. http://dx.doi.org/10.22199/issn.0717-6279-5584.

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Анотація:

A topological index is a branch of chemical graph theory that is vital to analyzing the physio-chemical characteristics of chemical compound structures divided into a degree-based molecular structure such as Zagreb indices, a distance-based molecular structure such as Wiener index, and a mixed such as Gutman index. In this paper, some definitions, results, and examples of Wiener polynomial and index for subdivision graph of friendship, bifriendship graphs, line subdivision graph of friendship, and bifriendship graphs were introduced. Moreover, we used the MATLAB program to calculate the Wiener

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28

Iranmanesh, Ali, Y. Alizadeh, and S. Mirzaie. "Computing Wiener Polynomial, Wiener Index and Hyper Wiener Index of C80Fullerene by GAP Program." Fullerenes, Nanotubes and Carbon Nanostructures 17, no. 5 (2009): 560–66. http://dx.doi.org/10.1080/15363830903133204.

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29

Knor, Martin, and Niko Tratnik. "A Method for Computing the Edge-Hosoya Polynomial with Application to Phenylenes." match Communications in Mathematical and in Computer Chemistry 89, no. 3 (2023): 605–29. http://dx.doi.org/10.46793/match.89-3.605k.

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Анотація:

The edge-Hosoya polynomial of a graph is the edge version of the famous Hosoya polynomial. Therefore, the edge-Hosoya polynomial counts the number of (unordered) pairs of edges at distance k ≥ 0 in a given graph. It is well known that this polynomial is closely related to the edge-Wiener index and the edge-hyper-Wiener index. As the main result of this paper, we greatly generalize an earlier result by providing a method for calculating the edge-Hosoya polynomial of a graph G which is obtained by identifying two edges of connected bipartite graphs G1 and G2. To show how the main theorem can be

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30

Arockiaraj PS, Mary U. "A Study on Wiener Polynomial for Steiner n - distance of some graphs." Mapana - Journal of Sciences 12, no. 3 (2013): 9–16. http://dx.doi.org/10.12723/mjs.26.5.

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31

GOREV, Vyacheslav, Yana SHEDLOVSKA, Ivan LAKTIONOV, and Grygorii DIACHENKO. "KOLMOGOROV– WIENER PREDICTION OF MFSD PROCESS BASED ON THE CHEBYSHEV POLYNOMIALS OF THE SECOND KIND." Information Technology: Computer Science, Software Engineering and Cyber Security, no. 1 (April 30, 2025): 257–61. https://doi.org/10.32782/it/2025-1-34.

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Анотація:

As is known, the telecommunication traffic in systems with packet data transfer is considered to be a heavytail process. Moreover, as is known, heavy-tail models may describe processes in agriculture. So, the problem of heavy-tail process prediction is an urgent problem for several fields of knowledge. For example, the so-called MFSD model may describe traffic in some of the above-mentioned telecommunication systems. Recently we investigated prediction of the continuous heavy-tail MFSD process which is based on the Kolmogorov-Wiener filter, constructed on the basis of the Chebyshev polynomials

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32

Das, Shibsankar, and Shikha Rai. "On the Hosoya polynomial of the third type of the chain hex-derived network." Journal of the Belarusian State University. Mathematics and Informatics, no. 3 (December 23, 2022): 67–78. http://dx.doi.org/10.33581/2520-6508-2022-3-67-78.

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Анотація:

A topological index plays an important role in characterising various physical properties, biological activities, and chemical reactivities of a molecular graph. The Hosoya polynomial is used to evaluate the distance-based topological indices such as the Wiener index, hyper-Wiener index, Harary index, and Tratch – Stankevitch – Zefirov index. In the present study, we determine a closed form of the Hosoya polynomial for the third type of the chain hex-derived network of dimension n and derive the distance-based topological indices of the network with the help of their direct formulas and altern

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33

Su, Liyun, and Fenglan Li. "Deconvolution of Defocused Image with Multivariate Local Polynomial Regression and Iterative Wiener Filtering in DWT Domain." Mathematical Problems in Engineering 2010 (2010): 1–14. http://dx.doi.org/10.1155/2010/605241.

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Анотація:

A novel semiblind defocused image deconvolution technique is proposed, which is based on multivariate local polynomial regression (MLPR) and iterative Wiener filtering (IWF). In this technique, firstly a multivariate local polynomial regression model is trained in wavelet domain to estimate defocus parameter. After obtaining the point spread function (PSF) parameter, iterative wiener filter is adopted to complete the restoration. We experimentally illustrate its performance on simulated data and real blurred image. Results show that the proposed PSF parameter estimation technique and the image

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34

FRANTZIKINAKIS, NIKOS. "Uniformity in the polynomial Wiener–Wintner theorem." Ergodic Theory and Dynamical Systems 26, no. 04 (2006): 1061. http://dx.doi.org/10.1017/s0143385706000204.

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35

Xu, Peng, Muhammad Numan, Aamra Nawaz, Saad Ihsan Butt, Adnan Aslam, and Asfand Fahad. "Computing the Hosoya Polynomial of M-th Level Wheel and Its Subdivision Graph." Journal of Chemistry 2021 (November 27, 2021): 1–7. http://dx.doi.org/10.1155/2021/1078792.

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The determination of Hosoya polynomial is the latest scheme, and it provides an excellent and superior role in finding the Weiner and hyper-Wiener index. The application of Weiner index ranges from the introduction of the concept of information theoretic analogues of topological indices to the use as major tool in crystal and polymer studies. In this paper, we will compute the Hosoya polynomial for multiwheel graph and uniform subdivision of multiwheel graph. Furthermore, we will derive two well-known topological indices for the abovementioned graphs, first Weiner index, and second hyper-Wiene

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36

Janczak, Andrzej, and Józef Korbicz. "Two–Stage Instrumental Variables Identification of Polynomial Wiener Systems with Invertible Nonlinearities." International Journal of Applied Mathematics and Computer Science 29, no. 3 (2019): 571–80. http://dx.doi.org/10.2478/amcs-2019-0042.

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Abstract A new two-stage approach to the identification of polynomial Wiener systems is proposed. It is assumed that the linear dynamic system is described by a transfer function model, the memoryless nonlinear element is invertible and the inverse nonlinear function is a polynomial. Based on these assumptions and by introducing a new extended parametrization, the Wiener model is transformed into a linear-in-parameters form. In Stage I, parameters of the transformed Wiener model are estimated using the least squares (LS) and instrumental variables (IV) methods. Although the obtained parameter

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37

Chung, Hyun Soo. "Basic Fundamental Formulas for Wiener Transforms Associated with a Pair of Operators on Hilbert Space." Mathematics 9, no. 21 (2021): 2738. http://dx.doi.org/10.3390/math9212738.

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Segal introduce the Fourier–Wiener transform for the class of polynomial cylinder functions on Hilbert space, and Hida then develop this concept. Negrin define the extended Wiener transform with Hayker et al. In recent papers, Hayker et al. establish the existence, the composition formula, the inversion formula, and the Parseval relation for the Wiener transform. But, they do not establish homomorphism properties for the Wiener transform. In this paper, the author establishes some basic fundamental formulas for the Wiener transform via some concepts and motivations introduced by Segal and used

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38

Mihai, Talmaciu, and Nechita Elena. "BRAIN Journal - Optimization Problems on Threshold Graphs." Brain Journal 1, SPECIAL ISSUE ON COMPLEXITY IN SCIENCES AND ARTIFICIAL INTELLIGENCE (2010): 61–68. https://doi.org/10.5281/zenodo.1036727.

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ABSTRACT During the last three decades, different types of decompositions have been processed in the field of graph theory. Among these we mention: decompositions based on the additivity of some characteristics of the graph, decompositions where the adjacency law between the subsets of the partition is known, decompositions where the subgraph induced by every subset of the partition must have predeterminate properties, as well as combinations of such decompositions. In this paper we characterize threshold graphs using the weakly decomposition, determine: density and stability number, Wiener in

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39

Sharyn, S. V. "Paley-Wiener-type theorem for polynomial ultradifferentiable functions." Carpathian Mathematical Publications 7, no. 2 (2015): 271–79. http://dx.doi.org/10.15330/cmp.7.2.271-279.

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The image of the space of ultradifferentiable functions with compact supports under Fourier-Laplace transformation is described. An analogue of Paley-Wiener theorem for polynomial ultradifferentiable functions is proved.

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40

Makki, Makkiah Suleiman. "Topological Indices of Inverse Graph for Generalized Quaternion Group." International Journal of Analysis and Applications 22 (December 9, 2024): 226. https://doi.org/10.28924/2291-8639-22-2024-226.

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In this paper, some of the famous and known topological indices for the inverse graph of Generalized quaternion group, including: Hosoya polynomial, Wiener index, hyper-Wiener index, first Zagreb index, second Zagreb index, ABC index, eccentric index, eccentric-connectivity index, total eccentric index, first Zagreb eccentric index, second Zagreb Eccentric index, graph energy index, and Estrada index.

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41

Naito, Riu, and Toshihiro Yamada. "A third-order weak approximation of multidimensional Itô stochastic differential equations." Monte Carlo Methods and Applications 25, no. 2 (2019): 97–120. http://dx.doi.org/10.1515/mcma-2019-2036.

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Abstract This paper proposes a new third-order discretization algorithm for multidimensional Itô stochastic differential equations driven by Brownian motions. The scheme is constructed by the Euler–Maruyama scheme with a stochastic weight given by polynomials of Brownian motions, which is simply implemented by a Monte Carlo method. The method of Watanabe distributions on Wiener space is effectively applied in the computation of the polynomial weight of Brownian motions. Numerical examples are shown to confirm the accuracy of the scheme.

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42

Moir, T. J. "Polynomial Wiener LQG Controllers based on Toeplitz Matrices." Journal of Physics: Conference Series 2224, no. 1 (2022): 012114. http://dx.doi.org/10.1088/1742-6596/2224/1/012114.

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Abstract This paper re-examines the discrete-time Linear Quadratic Gaussian (LQG) regulator problem. The normal approach to this problem is to use a Kalman filter state estimator and Kalman control state feedback. Though quite successful, an alternative approach in the frequency domain was employed later. That method used z-transfer functions or polynomials in the z-domain. The transfer function approach is similar to the method used in Wiener filtering and requires the use of Diophantine equations (sometimes bilateral) to find the optimal controller. The contribution here uses a similar appro

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43

Piroddi, Luigi, Marcello Farina, and Marco Lovera. "Polynomial NARX Model Identification: a Wiener–Hammerstein Benchmark." IFAC Proceedings Volumes 42, no. 10 (2009): 1074–79. http://dx.doi.org/10.3182/20090706-3-fr-2004.00178.

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44

Poklukar, Darja Rupnik, and Janez Žerovnik. "Reliability Hosoya-Wiener Polynomial of Double Weighted Trees*." Fundamenta Informaticae 147, no. 4 (2016): 447–56. http://dx.doi.org/10.3233/fi-2016-1416.

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45

Fan, Ai-hua. "Topological Wiener-Wintner ergodic theorem with polynomial weights." Chaos, Solitons & Fractals 117 (December 2018): 105–16. http://dx.doi.org/10.1016/j.chaos.2018.10.015.

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46

Mykhailenko, Oleksii. "Modeling and simulating dynamics of lithium-ion batteries using block-oriented models with piecewise linear static nonlinearity." E3S Web of Conferences 280 (2021): 05004. http://dx.doi.org/10.1051/e3sconf/202128005004.

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The article deals with the research of the efficiency of modelling the dynamics of voltage change in lithium-ion rechargeable batteries in charging/discharging modes using nonlinear block-oriented systems. Drawing on experimental data, a structural and parametric identification of the Hammerstein, Wiener and Hammerstein-Wiener models with a polynomial structure of the linear dynamic block and piecewise linear static nonlinearities was performed. It has been established that the best modelling accuracy was ensured by using the Hammerstein-Wiener system with a linear model having the 6th order o

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47

Yan, Jun, Bo Li, Hai-Feng Ling, Hai-Song Chen, and Mei-Jun Zhang. "Nonlinear State Space Modeling and System Identification for Electrohydraulic Control." Mathematical Problems in Engineering 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/973903.

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The paper deals with nonlinear modeling and identification of an electrohydraulic control system for improving its tracking performance. We build the nonlinear state space model for analyzing the highly nonlinear system and then develop a Hammerstein-Wiener (H-W) model which consists of a static input nonlinear block with two-segment polynomial nonlinearities, a linear time-invariant dynamic block, and a static output nonlinear block with single polynomial nonlinearity to describe it. We simplify the H-W model into a linear-in-parameters structure by using the key term separation principle and

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48

Xiu, Dongbin, Didier Lucor, C. H. Su, and George Em Karniadakis. "Stochastic Modeling of Flow-Structure Interactions Using Generalized Polynomial Chaos." Journal of Fluids Engineering 124, no. 1 (2001): 51–59. http://dx.doi.org/10.1115/1.1436089.

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We present a generalized polynomial chaos algorithm to model the input uncertainty and its propagation in flow-structure interactions. The stochastic input is represented spectrally by employing orthogonal polynomial functionals from the Askey scheme as the trial basis in the random space. A standard Galerkin projection is applied in the random dimension to obtain the equations in the weak form. The resulting system of deterministic equations is then solved with standard methods to obtain the solution for each random mode. This approach is a generalization of the original polynomial chaos expa

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49

Lee, Hoon, Xue-gang Chen, and Moo Young Sohn. "A Note on “Wiener Index of a Fuzzy Graph and Application to Illegal Immigration Networks”." Applied Sciences 12, no. 1 (2021): 304. http://dx.doi.org/10.3390/app12010304.

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Connectivity parameters have an important role in the study of communication networks. Wiener index is such a parameter with several applications in networking, facility location, cryptology, chemistry, and molecular biology, etc. In this paper, we show two notes related to the Wiener index of a fuzzy graph. First, we argue that Theorem 3.10 in the paper “Wiener index of a fuzzy graph and application to illegal immigration networks, Fuzzy Sets and Syst. 384 (2020) 132–147” is not correct. We give a correct statement of Theorem 3.10. Second, by using a new operator on matrix, we propose a simpl

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50

Liu, You-Jiang, Bang-Hua Zhou, Jie Zhou, and Yi-Nong Liu. "A Two-Step Identification Approach for Twin-Box Models of RF Power Amplifier." International Journal of Microwave Science and Technology 2011 (September 18, 2011): 1–5. http://dx.doi.org/10.1155/2011/468497.

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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, wher

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