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Tytuł:
Π(G,x) polynomial and (G) index of Armchair Polyhex Nanotubes TUAC6 [m,n]
Autorzy:
Farahani, M. R.
Powiązania:
https://bibliotekanauki.pl/articles/412239.pdf
Data publikacji:
2014
Wydawca:
Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
Tematy:
Molecular Graph
Armchair Polyhex Nanotubes and Nanotori
Omega polynomial
Pi polynomial
Pi index
Opis:
Let G be a simple connected graph with the vertex set V = V(G) and the edge set E = E(G), without loops and multiple edges. For counting qoc strips in G, Omega polynomial was introduced by Diudea and was defined as Ω(G,x ) = [wzór] where m(G,c) be the number of qoc strips of length c in the graph G. Following Omega polynomial, the Sadhana polynomial was defined by Ashrafi et al as Sd(G,x) = [wzór]. In this paper we compute the Pi polynomial Π(G,x) =[wzór] and Pi index Π(G ) = [wzór] of an infinite class of “Armchair Polyhex Nanotubes TUAC 6 [m,n]”.
Źródło:
International Letters of Chemistry, Physics and Astronomy; 2014, 17, 2; 201-206
2299-3843
Pojawia się w:
International Letters of Chemistry, Physics and Astronomy
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A characterization of \((t_1,\dots,t_n)\)-Wright affine functions
Autorzy:
Olbryś, Andrzej
Powiązania:
https://bibliotekanauki.pl/articles/745883.pdf
Data publikacji:
2007
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
polynomial functions
Opis:
In 1998 K.Lajkó [5] gave a characterization of \(t\)−Wright affine functions. Now, we extend this result to \((t_1 ,\dots, t_n)\)-Wright affine functions of an arbitrary order.
Źródło:
Commentationes Mathematicae; 2007, 47, 1
0373-8299
Pojawia się w:
Commentationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A counterexample to a conjecture of Drużkowski and Rusek
Autorzy:
van den Essen, Arno
Powiązania:
https://bibliotekanauki.pl/articles/1311428.pdf
Data publikacji:
1995
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
polynomial automorphisms
Jacobian Conjecture
Opis:
Let F = X + H be a cubic homogeneous polynomial automorphism from $ℂ^n$ to $ℂ^n$. Let $p$ be the nilpotence index of the Jacobian matrix JH. It was conjectured by Drużkowski and Rusek in [4] that $deg F^{-1} ≤ 3^{p-1}$. We show that the conjecture is true if n ≤ 4 and false if n ≥ 5.
Źródło:
Annales Polonici Mathematici; 1995, 62, 2; 173-176
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A dynamic bi-orthogonal field equation approach to efficient Bayesian inversion
Autorzy:
Tagade, P. M.
Choi, H. L.
Powiązania:
https://bibliotekanauki.pl/articles/330516.pdf
Data publikacji:
2017
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
Bayesian framework
stochastic partial differential equation
Karhunen–Loève expansion
generalized polynomial chaos
dynamically biorthogonal field equations
ramy Bayesa
stochastyczne równanie różniczkowe
przekształcenie Karhunena-Loeve'a
chaos wielomianowy
Opis:
This paper proposes a novel computationally efficient stochastic spectral projection based approach to Bayesian inversion of a computer simulator with high dimensional parametric and model structure uncertainty. The proposed method is based on the decomposition of the solution into its mean and a random field using a generic Karhunen–Loève expansion. The random field is represented as a convolution of separable Hilbert spaces in stochastic and spatial dimensions that are spectrally represented using respective orthogonal bases. In particular, the present paper investigates generalized polynomial chaos bases for the stochastic dimension and eigenfunction bases for the spatial dimension. Dynamic orthogonality is used to derive closed-form equations for the time evolution of mean, spatial and the stochastic fields. The resultant system of equations consists of a partial differential equation (PDE) that defines the dynamic evolution of the mean, a set of PDEs to define the time evolution of eigenfunction bases, while a set of ordinary differential equations (ODEs) define dynamics of the stochastic field. This system of dynamic evolution equations efficiently propagates the prior parametric uncertainty to the system response. The resulting bi-orthogonal expansion of the system response is used to reformulate the Bayesian inference for efficient exploration of the posterior distribution. The efficacy of the proposed method is investigated for calibration of a 2D transient diffusion simulator with an uncertain source location and diffusivity. The computational efficiency of the method is demonstrated against a Monte Carlo method and a generalized polynomial chaos approach.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2017, 27, 2; 229-243
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A locally polynomial method for solving a system of linear inequalities
Autorzy:
Evtushenko, Yuri
Szkatuła, Krzysztof
Tretyakov, Alexey
Powiązania:
https://bibliotekanauki.pl/articles/2183463.pdf
Data publikacji:
2021
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
linear programming
system of linear inequalities
computational complexity
locally-polynomial algorithm
convergence rate
Opis:
The paper proposes a method for solving systems of linear inequalities. This method determines in a finite number of iterations whether the given system of linear ineqalities has a solution. If it does, the solution for the given system of linear inequalities is provided. The computational complexity of the proposed method is locally polynomial.
Źródło:
Control and Cybernetics; 2021, 50, 2; 301--314
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A necessary and sufficient condition for sigma-Hurwitz stability of the convex combination of the polynomials
Autorzy:
Białas, S.
Powiązania:
https://bibliotekanauki.pl/articles/255228.pdf
Data publikacji:
2005
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
convex sets of polynomials
stability of polynomial
Hurwitz stability
sigma-stability
Opis:
In the paper are given a necessary and sufficent condition for sigma-Hurwitz stability of the convex combination of the polynomials.
Źródło:
Opuscula Mathematica; 2005, 25, 2; 165-168
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A new and fast approximation algorithm for vertex cover using a maximum independent set (VCUMI)
Autorzy:
Khan, I.
Riaz, N.
Powiązania:
https://bibliotekanauki.pl/articles/406436.pdf
Data publikacji:
2015
Wydawca:
Politechnika Wrocławska. Oficyna Wydawnicza Politechniki Wrocławskiej
Tematy:
non-deterministic polynomial
vertex cover
independent set
benchmark
error ratio
Opis:
The importance of non-deterministic polynomial (NP) problems in real world scenarios has compelled researchers to consider simple ways of finding approximate solutions to these problems in polynomial time. Minimum vertex cover is an NP complete problem, where the objective is to cover all the edges in a graph with the minimal number of vertices possible. The maximal independent set and maximal clique problems also belong to the same class. An important property that we have analyzed while considering various approaches to find approximate solutions to the minimum vertex cover problem (MVC) is that solving MVC directly can result in a bigger error ratio. We propose a new approximation algorithm for the minimum vertex cover problem called vertex cover using a maximum independent set (VCUMI). This algorithm works by removing the nodes of a maximum independent set until the graph is an approximate solution of MVC. Based on empirical results, it can be stated that VCUMI outperforms all competing algorithms presented in the literature. Based on all the benchmarks used, VCUMI achieved the worst case error ratio of 1.033, while VSA, MDG and NOVAC-1 gave the worst error ratios of 1.583, 1.107 and 1.04, respectively.
Źródło:
Operations Research and Decisions; 2015, 25, 4; 5-18
2081-8858
2391-6060
Pojawia się w:
Operations Research and Decisions
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A note about irreducibility of a resultant
Uwaga dotycząca nierozkładalności rugownika
Autorzy:
Hejmej, Beata
Powiązania:
https://bibliotekanauki.pl/articles/699792.pdf
Data publikacji:
2018
Wydawca:
Łódzkie Towarzystwo Naukowe
Tematy:
Galois theory, separable extension, embedding, polynomial, irreducibility, resultant
teoria Galois, rozszerzenie rozdzielcze ciał, zanurzenie ciał, nierozkładalność wielomianu, rugownik
Opis:
https://doi.org/10.26485/0459-6854/2018/68.1/2 W pracy przedstawiono twierdzenie dotyczące nierozkładalności wielomianu, który jest rugownikiem dwóch innych wielomianów. Dowód tego twierdzenia oparty jest na teorii ciał. Ponadto, udowodniono pewien wariant twierdzenia odwrotnego oraz zaprezentowano kilka przykładów.
https://doi.org/10.26485/0459-6854/2018/68.1/2 We present a theorem about irreducibility of a polynomial that is the resultant of two others polynomials. The proof of this fact is based on the field theory. We also consider the converse theorem and some examples.
Źródło:
Bulletin de la Société des Sciences et des Lettres de Łódź, Série: Recherches sur les déformations; 2018, 68, 1
1895-7838
2450-9329
Pojawia się w:
Bulletin de la Société des Sciences et des Lettres de Łódź, Série: Recherches sur les déformations
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A note on a broken-cycle theorem for hypergraphs
Autorzy:
Trinks, Martin
Powiązania:
https://bibliotekanauki.pl/articles/31231998.pdf
Data publikacji:
2014-08-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
Broken-cycle Theorem
hypergraphs
cycles
chromatic polynomial
graph polynomials
Opis:
Whitney’s Broken-cycle Theorem states the chromatic polynomial of a graph as a sum over special edge subsets. We give a definition of cycles in hypergraphs that preserves the statement of the theorem there.
Źródło:
Discussiones Mathematicae Graph Theory; 2014, 34, 3; 641-646
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A Note on Polynomial Algorithm for Cost Coloring of Bipartite Graphs with Δ ≤ 4
Autorzy:
Giaro, Krzysztof
Kubale, Marek
Powiązania:
https://bibliotekanauki.pl/articles/31526308.pdf
Data publikacji:
2020-08-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
bipartite graph
chromatic sum
cost coloring
NP-completeness
polynomial algorithm
Opis:
In the note we consider vertex coloring of a graph in which each color has an associated cost which is incurred each time the color is assigned to a vertex. The cost of coloring is the sum of costs incurred at each vertex. We show that the minimum cost coloring problem for n-vertex bipartite graph of degree Δ ≤ 4 can be solved in O(n2) time. This extends Jansen’s result [K. Jansen, The optimum cost chromatic partition problem, in: Proc. CIAC’97, Lecture Notes in Comput. Sci. 1203 (1997) 25–36] for paths and cycles to subgraphs of biquartic graphs.
Źródło:
Discussiones Mathematicae Graph Theory; 2020, 40, 3; 885-891
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A note on the order of polynomial-like iterative equations
Autorzy:
Draga, Szymon
Powiązania:
https://bibliotekanauki.pl/articles/746204.pdf
Data publikacji:
2016
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
continuous solution
iterate
polynomial-like iterative equation
recurrence relation
Opis:
We show that, under reasonable assumptions, two negative roots can be eliminated from the characteristic equation of a polynomial-like iterative equation. This result gives a new case where we may lower the order of such an equation.
Źródło:
Commentationes Mathematicae; 2016, 56, 2
0373-8299
Pojawia się w:
Commentationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A Note on the Permanental Roots of Bipartite Graphs
Autorzy:
Zhang, Heping
Liu, Shunyi
Li, Wei
Powiązania:
https://bibliotekanauki.pl/articles/30147218.pdf
Data publikacji:
2014-02-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
permanent
permanental polynomial
permanental roots
Opis:
It is well-known that any graph has all real eigenvalues and a graph is bipartite if and only if its spectrum is symmetric with respect to the origin. We are interested in finding whether the permanental roots of a bipartite graph G have symmetric property as the spectrum of G. In this note, we show that the permanental roots of bipartite graphs are symmetric with respect to the real and imaginary axes. Furthermore, we prove that any graph has no negative real permanental root, and any graph containing at least one edge has complex permanental roots.
Źródło:
Discussiones Mathematicae Graph Theory; 2014, 34, 1; 49-56
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A primal-infeasible interior point algorithm for linearly constrained convex programming
Autorzy:
Wang, Y.
Fei, P.
Powiązania:
https://bibliotekanauki.pl/articles/969664.pdf
Data publikacji:
2009
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
linearly constrained convex programming
primal-infeasible interior point algorithm
polynomial complexity
Opis:
In this paper a primal-infeasible interior point algorithm is proposed for linearly constrained convex programming. A positive primal-infeasible dual-feasible point can be taken as the starting point of this algorithm in a large region. At each iterates it requires to solve approximately a nonlinear system. The polynomial complexity of the algorithm is obtained. It is shown that, after finite iterations a sufficiently good approximation to the optimal point is found, or there is no optimal point in a large region.
Źródło:
Control and Cybernetics; 2009, 38, 3; 687-704
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A quadrature-free Legendre polynomial approach for the fast modelling guided circumferential wave in anisotropic fractional order viscoelastic hollow cylinders
Autorzy:
Zhang, X.
Liang, S.
Shao, S.
Yu, J.
Powiązania:
https://bibliotekanauki.pl/articles/38615994.pdf
Data publikacji:
2021
Wydawca:
Instytut Podstawowych Problemów Techniki PAN
Tematy:
guided wave
fractional order derivative
anisotropic viscoelastic hollow cylinder
quadrature-free Legendre polynomial approach
dispersion
attenuation
Opis:
Compared to the traditional integer order viscoelastic model, a fractional order derivative viscoelastic model is shown to be advantageous. The characteristics of guided circumferential waves in an anisotropic fractional order Kelvin–Voigt viscoelastic hollow cylinder are investigated by a quadrature-free Legendre polynomial approach combining the Weyl definition of fractional order derivatives. The presented approach can obtain dispersion solutions in a stable manner from an eigenvalue/eigenvector problem for the calculation of wavenumbers and displacement profiles of viscoelastic guided wave, which avoids a lot of numerical integration calculation in a traditional polynomial method and greatly improves the computational efficiency. Comparisons with the related studies are conducted to validate the correctness of the presented approach. The full three dimensional spectrum of an anisotropic fractional Kelvin–Voigt hollow cylinder is plotted. The influence of fractional order and material parameters on the phase velocity dispersion and attenuation curves of guided circumferential wave is discussed in detail. Moreover, the difference of the phase velocity dispersion and attenuation characteristics between the Kelvin–Voigt and hysteretic viscoelastic models is also illustrated. The presented approach along with the observed wave features should be particularly useful in non-destructive evaluations using waves in viscoelastic waveguides.
Źródło:
Archives of Mechanics; 2021, 73, 2; 121-152
0373-2029
Pojawia się w:
Archives of Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A refinement of Schwarzs lemma and its applications
Autorzy:
Jain, V. K.
Powiązania:
https://bibliotekanauki.pl/articles/357788.pdf
Data publikacji:
2016
Wydawca:
Politechnika Rzeszowska im. Ignacego Łukasiewicza. Oficyna Wydawnicza
Tematy:
Schwarz lemma
polynomial
inequalities
lemat Schwarza
wielomian
nierówność
Opis:
By using the value of the second derivative of the function at 0, along with the values of the function and its first derivative at 0, we have obtained a refinement of well known Schwarz’s lemma and have used this refinement to obtain refinements, of Aziz and Rather’s inequalities [2004] for a polynomial of degree n having no zeros in |z| < k, (k ≥ 1).
Źródło:
Journal of Mathematics and Applications; 2016, 39; 69-80
1733-6775
2300-9926
Pojawia się w:
Journal of Mathematics and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł

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