Results 11 to 20 of about 2,656,443 (77)

λ-Symmetries and integrability by quadratures [PDF]

, 2017
It is investigated how two (standard or generalized) λ-symmetries of a given second-order ordinary differential equation can be used to solve the equation by quadratures. The method is based on the construction of two commuting generalized symmetries for
Muriel Patino, María Concepción, Romero Romero, Juan Luis, Ruiz Serván, Adrián   +2 more
core   +1 more source

Exact polynomial solutions of second order differential equations and their applications

, 2011
We find all polynomials $Z(z)$ such that the differential equation $${X(z)\frac{d^2}{dz^2}+Y(z)\frac{d}{dz}+Z(z)}S(z)=0,$$ where $X(z), Y(z), Z(z)$ are polynomials of degree at most 4, 3, 2 respectively, has polynomial solutions $S(z)=\prod_{i=1}^n(z-z_i)
Zhang, Yao-Zhong
core   +1 more source

Time-warping invariants of multidimensional time series [PDF]

, 2020
In data science, one is often confronted with a time series representing measurements of some quantity of interest. Usually, as a first step, features of the time series need to be extracted. These are numerical quantities that aim to succinctly describe
Diehl, Joscha, Ebrahimi-Fard, Kurusch, Tapia, Nikolas   +2 more
core   +2 more sources

Lectures on Linear Stability of Rotating Black Holes

, 2019
These lecture notes are concerned with linear stability of the non-extreme Kerr geometry under perturbations of general spin. After a brief review of the Kerr black hole and its symmetries, we describe these symmetries by Killing fields and work out the ...
AA Starobinsky, B Carter, BF Whiting, BF Whiting, CW Misner, F Finster, JL Friedman, PR Chernoff, R Adler, R Güven, R Penrose, RM Wald, T Regge, V Alfaro de, WH Press, YB Zel’dovich   +15 more
core   +1 more source

Recombination semigroups on measure spaces

, 2005
The dynamics of recombination in genetics leads to an interesting nonlinear differential equation, which has a natural generalization to a measure valued version. The latter can be solved explicitly under rather general circumstances.
Baake, Michael
core   +2 more sources

Time-warping invariants of multidimensional time series [PDF]

, 2019
In data science, one is often confronted with a time series representing measurements of some quantity of interest. Usually, in a first step, features of the time series need to be extracted. These are numerical quantities that aim to succinctly describe
Diehl, Joscha, Kurusch, Ebrahimi-Fard, Tapia, Nikolas   +2 more
core   +4 more sources

CMV matrices in random matrix theory and integrable systems: a survey

, 2005
We present a survey of recent results concerning a remarkable class of unitary matrices, the CMV matrices. We are particularly interested in the role they play in the theory of random matrices and integrable systems.
Ammar G S, Babelon O, Cantero M J Moral L Velázquez L, Deift P, Dyson F, Faybusovich L, Fermi E, Forrester P J Rains E M, Gekhtman M, Gelfand I M, Geronimus Ya L, Geronimus Ya L, Irina Nenciu, Killip R Nenciu I, Li L-C, Moser J, Olshanetsky M A, Simon B, Simon B, Szegő G, Thiele C Tao T, Toda M   +21 more
core   +2 more sources

Modular forms, Schwarzian conditions, and symmetries of differential equations in physics

, 2017
We give examples of infinite order rational transformations that leave linear differential equations covariant. These examples are non-trivial yet simple enough illustrations of exact representations of the renormalization group.
Abdelaziz, Y., Maillard, J. -M.
core   +1 more source

A problem concerning Riemann sums [PDF]

arXiv, 2020
An open problem concerning Riemann sums, posed by O. Furdui, is considered.
arxiv  

Globally nilpotent differential operators and the square Ising model

, 2008
We recall various multiple integrals related to the isotropic square Ising model, and corresponding, respectively, to the n-particle contributions of the magnetic susceptibility, to the (lattice) form factors, to the two-point correlation functions and ...
Bostan, A., Boukraa, S., Hassani, S., Maillard, J. -M., Weil, J. -A., Zenine, N.   +5 more
core   +3 more sources