Results 31 to 40 of about 131,499 (275)

Polynomial Spline Collocation Method for Solving Weakly Regular Volterra Integral Equations of the First Kind

Известия Иркутского государственного университета: Серия "Математика", 2022
The polynomial spline collocation method is proposed for solution of Volterra integral equations of the first kind with special piecewise continuous kernels.
Aleksandr Tynda, Samad Noeiaghdam, Denis Sidorov   +2 more
doaj   +1 more source

Liouvillian first integrals for Liénard polynomial differential systems [PDF]

Proceedings of the American Mathematical Society, 2010
Summary: We characterize the Liouvillian first integrals for the Liénard polynomial differential systems of the form \(x^{\prime } = y, y^{\prime } = -cx-f(x)y\), with \(c \in \mathbb{R}\) and \(f(x)\) is an arbitrary polynomial. For obtaining this result we need to find all the Darboux polynomials and the exponential factors of these systems.
Llibre, J., Valls, C.
openaire   +1 more source

A class of polynomial planar vector fields with polynomial first integral

Journal of Mathematical Analysis and Applications, 2015
We give an algorithm for deciding whether a planar polynomial differential system has a first integral which factorizes as a product of defining polynomials of curves with only one place at infinity. In the affirmative case, our algorithm computes a minimal first integral. In addition, we solve the Poincar problem for the class of systems which admit
A. Ferragut, C. Galindo, F. Monserrat
openaire   +10 more sources

Darboux theory of integrability in the sparse case [PDF]

, 2014
International audienceDarboux's theorem and Jouanolou's theorem deal with the existence of first integrals and rational first integrals of a polynomial vector field. These results are given in terms of the degree of the polynomial vector field.
Christopher, Christopher, Cox, Darboux, Darboux, Dumortier, Gelfand, Goriely, Guillaume Chèze, Jouanolou, Llibre, Llibre, Llibre, Llibre, Llibre, Moulin Ollagnier, Ostrowski, Rosenlicht, Schlomiuk, Singer, Valls, Weil   +21 more
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Heavy-hole bilayer trions of transition metal dichalcogenides by analytical treatment to model He-isoelectronic ions upto dipole factor of Green’s function expansion of Coulomb interaction

Physics Open, 2022
Electronic structures of heavy-hole trions and He-isoelectronic ions show dependence on transitions among two-electron bound states constituted of hydrogenic orbitals for which Coulomb (exchange) interaction causes nontrivial secular divergence to ...
Shivalika Sharma, Bharti Kapil, Priyanka Aggarwal, Ram Kuntal Hazra   +3 more
doaj   +1 more source

Painleve property and the first integrals of nonlinear differential equations

, 2004
Link between the Painleve property and the first integrals of nonlinear ordinary differential equations in polynomial form is discussed. The form of the first integrals of the nonlinear differential equations is shown to determine by the values of the ...
Ablowitz, Conte, Conte, Cosgrove, Drach, Dubrovin, Elwakil, Fan, Fordy, Fordy, Hone, Hénon, Kudryashov, Kudryashov, Kudryashov, Kudryashov, Kudryashov, Kudryashov, Kudryashov, Kudryashov, Kudryashov, Kudryashov, Kudryashov, Liu, Lou, Musette, Newell, Nikolai A. Kudryashov, Olver, Weiss, Weiss, Yan   +31 more
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Liouvillian first integrals of quadratic–linear polynomial differential systems

Journal of Mathematical Analysis and Applications, 2011
Agraïments: The second author has been partially supported by FCT through CAMGSD, Lisbon. For a large class of quadratic-linear polynomial differential systems with a unique singular point at the origin having non-zero eigenvalues, we classify the ones which have a Liouvillian first integral, and we provide the explicit expression of them.
Llibre, Jaume, Valls, Clàudia
openaire   +2 more sources

On fully discrete collocation methods for solving weakly singular integral equations

Mathematical Modelling and Analysis, 2009
A popular class of methods for solving weakly singular integral equations is the class of piecewise polynomial collocation methods. In order to implement those methods one has to compute exactly certain integrals that determine the linear system to be ...
Raul Kangro, Inga Kangro
doaj   +1 more source

Integration with respect to the Haar measure on unitary, orthogonal and symplectic group

, 2004
We revisit the work of the first named author and using simpler algebraic arguments we calculate integrals of polynomial functions with respect to the Haar measure on the unitary group U(d).
Collins, Benoit, Sniady, Piotr
core   +1 more source

Rota-Baxter operators on the polynomial algebras, integration and averaging operators [PDF]

, 2014
The concept of a Rota–Baxter operator is an algebraic abstraction of integration. Following this classical connection, we study the relationship between Rota–Baxter operators and integrals in the case of the polynomial algebra k[x] k[x] .
Birkhoff, Guo, Guo, Li Guo, Markus Rosenkranz, Rota, Shanghua Zheng   +6 more
core   +3 more sources