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pro vyhledávání: '"Bihun, Oksana"'
Publikováno v:
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Title from PDF of title page (University of Missouri--Columbia, viewed on Feb. 11, 2010). The entire thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file; a non-technical public abstract appears in the
Externí odkaz:
http://hdl.handle.net/10355/6129
Autor:
Bihun, Oksana, Driver, Kathy
Let $\displaystyle \{x_{k,n-1}\} _{k=1}^{n-1}$ and $\displaystyle \{x_{k,n}\} _{k=1}^{n},$ $n \in \mathbb{N}$, be two sets of real, distinct points satisfying the interlacing property $ x_{i,n}
Externí odkaz:
http://arxiv.org/abs/1905.04276
Autor:
Bihun, Oksana
Publikováno v:
Nonlinear Systems and Their Remarkable Mathematical Structures, N. Euler (ed), CRC Press, Boca Raton FL, 2018
Several recently discovered properties of multiple families of special polynomials (some orthogonal and some not) that satisfy certain differential, difference or q-difference equations are reviewed. A general method of construction of isospectral ma
Externí odkaz:
http://arxiv.org/abs/1808.00550
Autor:
Bihun, Oksana
A time-dependent monic polynomial in the z variable with N distinct roots such that exactly one root has multiplicity m>=2 is considered. For k=1,2, the k-th derivatives of the N roots are expressed in terms of the derivatives of order j<= k of the f
Externí odkaz:
http://arxiv.org/abs/1808.00512
Autor:
Bihun, Oksana, Calogero, Francesco
Recently new solvable systems of nonlinear evolution equations -- including ODEs, PDEs and systems with discrete time -- have been introduced. These findings are based on certain convenient formulas expressing the $k$-th time-derivative of a root of
Externí odkaz:
http://arxiv.org/abs/1806.07502
Autor:
Bihun, Oksana, Chakravarty, Sarbarish
Publikováno v:
SIGMA 13 (2017), 095, 24 pages
Dubrovin [Lecture Notes in Math., Vol. 1620, Springer, Berlin, 1996, 120-348] showed that the Chazy XII equation $y'''- 2yy''+3y'^2 = K(6y'-y^2)^2$, $K \in \mathbb{C}$, is equivalent to a projective-invariant equation for an affine connection on a on
Externí odkaz:
http://arxiv.org/abs/1712.09033
Autor:
Bihun, Oksana, Fulghesu, Damiano
Publikováno v:
Aequat. Math. 92 (2018), 453-470
In this paper we consider monic polynomials such that their coefficients coincide with their zeros. These polynomials were first introduced by S. Ulam. We combine methods of algebraic geometry and dynamical systems to prove several results. We obtain
Externí odkaz:
http://arxiv.org/abs/1705.02057
Autor:
Bihun, Oksana, Mourning, Clark
Publikováno v:
Adv. Math. Phys., Volume 2018 (2018), Article ID 4710754, 10 pages
Via a generalization of the pseudospectral method for numerical solution of differential equations, a family of nonlinear algebraic identities satisfied by the zeros of a wide class of orthogonal polynomials is derived. The generalization is based on
Externí odkaz:
http://arxiv.org/abs/1701.05542
Autor:
Bihun, Oksana
We identify a class of remarkable algebraic relations satisfied by the zeros of the Krall orthogonal polynomials that are eigenfunctions of linear differential operators of order higher than two. Given an orthogonal polynomial family {p_n(x)}, we rel
Externí odkaz:
http://arxiv.org/abs/1608.03873
Autor:
Bihun, Oksana, Calogero, Francesco
A technique is introduced which allows to generate -- starting from any solvable discrete-time dynamical system involving N time-dependent variables -- new, generally nonlinear, generations of discrete-time dynamical systems, also involving N time-de
Externí odkaz:
http://arxiv.org/abs/1606.07278