Results 11 to 20 of about 40,856 (184)

Classification of cubic differential systems with invariant straight lines of total multiplicity eight and two distinct infinite singularities

Electronic Journal of Qualitative Theory of Differential Equations, 2015
In this article we prove a classification theorem (Main theorem) of real planar cubic vector fields which possess two distinct infinite singularities (real or complex) and eight invariant straight lines, including the line at infinity and including ...
Cristina Bujac, Nicolae Vulpe
doaj   +1 more source

Connection coefficients for basic Harish-Chandra series [PDF]

, 2014
Basic Harish-Chandra series are asymptotically free meromorphic solutions of the system of basic hypergeometric difference equations associated to root systems.
Askey, Avan, Batchelor, Behrend, Birkhoff, Chalykh, Chalykh, Chalykh, Cherednik, Cherednik, Cherednik, Cherednik, Cherednik, Cherednik, Cherednik, Cherednik, Cherednik, de Moura, Etingof, Etingof, Etingof, Felder, Filali, Frenkel, Gasper, Gervais, Haiman, Heckman, Heckman, Ismail, Jasper V. Stokman, Jimbo, Jimbo, Jimbo, Kato, Kazarnovski-Krol, Koelink, Konno, Koornwinder, Kulish, Letzter, Macdonald, Macdonald, Matsuo, Noumi, Noumi, Noumi, Opdam, Ruijsenaars, Ruijsenaars, Ruijsenaars, Sahi, Smirnov, Spiridonov, Stokman, Stokman, Stokman, Stokman, Tarasov, van Diejen, van Meer, van Meer, Whittaker   +62 more
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First integrals and phase portraits of planar polynomial differential cubic systems with invariant straight lines of total multiplicity eight

Electronic Journal of Qualitative Theory of Differential Equations, 2017
In the article [C. Bujac, J. Llibre, N. Vulpe, Qual. Theory Dyn. Syst. 15(2016), 327–348] for the family of cubic differential systems with the maximum number of invariant straight lines, i.e.
Cristina Bujac, Nicolae Vulpe
doaj   +1 more source

Whittaker limits of difference spherical functions [PDF]

, 2009
We introduce the (global) q-Whittaker function as the limit at t=0 of the q,t-spherical function extending the symmetric Macdonald polynomials to arbitrary eigenvalues. The construction heavily depends on the technique of the q-Gaussians developed by the
Cherednik, Ivan
core   +8 more sources

Image Local Features Description Through Polynomial Approximation

IEEE Access, 2019
This work introduces a novel local patch descriptor that remains invariant under varying conditions of orientation, viewpoint, scale, and illumination.
Fawad, Muhibur Rahman, Muhammad Jamil Khan, Muhammad Adeel Asghar, Yasar Amin, Salman Badnava, Seyed Sajad Mirjavadi   +6 more
doaj   +1 more source

Invariants of the vacuum module associated with the Lie superalgebra gl(1|1) [PDF]

, 2015
We describe the algebra of invariants of the vacuum module associated with the affinization of the Lie superalgebra $\mathfrak{gl}(1|1)$. We give a formula for its Hilbert--Poincar\'{e} series in a fermionic (cancellation-free) form which turns out to ...
Molev, A. I., Mukhin, E. E.
core   +2 more sources

Inverse Harish-Chandra Transform and Difference Operators [PDF]

, 1997
We apply a new technique based on double affine Hecke algebras to the Harish-Chandra theory of spherical zonal functions. The formulas for the Fourier transforms of the multiplications by the coordinates are obtained as well as a simple proof of the ...
Cherednik, Ivan
core   +5 more sources

Rational Parking Functions and LLT Polynomials [PDF]

, 2015
We prove that the combinatorial side of the "Rational Shuffle Conjecture" provides a Schur-positive symmetric polynomial. Furthermore, we prove that the contribution of a given rational Dyck path can be computed as a certain skew LLT polynomial, thus ...
Gorsky, Eugene, Mazin, Mikhail
core   +3 more sources

An exactly solvable quantum four-body problem associated with the symmetries of an octacube

New Journal of Physics, 2015
In this article, we show that eigenenergies and eigenstates of a system consisting of four one-dimensional hard-core particles with masses 6 m , 2 m , m , and 3 m in a hard-wall box can be found exactly using Bethe Ansatz.
Maxim Olshanii, Steven G Jackson
doaj   +1 more source

Global configurations of singularities for quadratic differential systems with exactly three finite singularities of total multiplicity four

Electronic Journal of Qualitative Theory of Differential Equations, 2015
In this article we obtain the geometric classification of singularities, finite and infinite, for the two subclasses of quadratic differential systems with total finite multiplicity $m_f=4$ possessing exactly three finite singularities, namely: systems ...
Joan Artés, Jaume Llibre, Dana Schlomiuk, Nicolae Vulpe   +3 more
doaj   +1 more source