Related papers: On normalized Horn systems
We introduce a universally applicable method, based on the bond-algebraic theory of dualities, to search for generalized order parameters in disparate systems including non-Landau systems with topological order. A key notion that we advance…
We establish a theorem concerning the normal forms by examining the newly presented concept of $\mu$-dichotomy. This work establishes the nonresonance condition based on the associated spectrum of this general nonautonomous hyperbolicity.
We clarify what it means for two full dualities based on the same algebra to be different. Our main theorem gives conditions on two different alter egos of a finite algebra under which, if one yields a full duality, then the other does too.…
We discuss a general procedure to generate a class of (everywhere regular) solutions of Einstein equations that can have an (a-priori fixed) arbitrary number of horizons. We then report on work currently in progress i) to find a suitable…
We formalize the concept of a centralizer-respecting homomorphism, surjective homomorphisms which are equivariant with respect to taking the centralizer of a subgroup. There is a functor from the category of centralizer-respecting…
A generalized complex manifold which satisfies the $\partial \overline{\partial}$-lemma admits a Hodge decomposition in twisted cohomology. Using a Courant algebroid theoretic approach we study the behavior of the Hodge decomposition in…
The randomised Horn problem, in both its additive and multiplicative version, has recently drawn increasing interest. Especially, closed analytical results have been found for the rank-1 perturbation of sums of Hermitian matrices and…
The differential systems satisfied by orthogonal polynomials with arbitrary semiclassical measures supported on contours in the complex plane are derived, as well as the compatible systems of deformation equations obtained from varying such…
Neural networks have provided powerful approaches to solve various scientific problems. Many of them are even difficult for human experts who are good at accessing the physical laws from experimental data. We investigate whether neural…
We survey and analyze different ways in which bornologies, coarse structures and uniformities on a group agree with the group operations.
We consider random dynamical systems such as groups of conformal transformations with a probability measure, or transversaly conformal foliations with a Laplace operator along the leaves, in which case we consider the holonomy pseudo-group.…
We discuss the quantization of mechanical systems for which the Hamiltonian vector fields of observables form the deformation of $n$-dimensional oscilator algebra. Because of this fact these systems can be considered as "deformations" of…
Quantized orbital structures are typical for many aspects of classical gravity (Newton's as well as Einstein's). The astronomical phenomenon of orbital resonances is a well-known example. Recently, Rothman, Ellis and Murugan (2001)…
We demonstrate that a system of bi-orthogonal polynomials and their associated functions corresponding to a regular semi-classical weight on the unit circle constitute a class of general classical solutions to the Garnier systems by…
We review recent progress on Horn's problem, which asks for a description of the possible eigenspectra of the sum of two matrices with known eigenvalues. After revisiting the classical case, we consider several generalizations in which the…
We present here some conjectures on the diagonalizability of uniform principal bundles on rational homogeneous spaces, that are natural extensions of classical theorems on uniform vector bundles on the projective space, and study the…
This paper studies hamiltonization of nonholonomic systems using geometric tools. By making use of symmetries and suitable first integrals of the system, we explicitly define a global 2-form for which the gauge transformed nonholonomic…
Constrained Hamiltonian description of the classical limit is utilized in order to derive consistent dynamical equations for hybrid quantum-classical systems. Starting with a compound quantum system in the Hamiltonian formulation conditions…
We generalize the Weinstein-Moser theorem on the existence of nonlinear normal modes near an equilibrium in a Hamiltonian system to a theorem on the existence of relative perodic orbits near a relative equilibrium in a Hamiltonian system…
Normal and composition series of modules enumerated by ordinal numbers are studied. The Jordan-Holder theorem for them is discussed.