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An interesting family of geometric integrators for Lagrangian systems can be defined using discretizations of the Hamilton's principle of critical action. This family of geometric integrators is called variational integrators. In this…

We analyze two reduction methods for nonholonomic systems that are invariant under the action of a Lie group on the configuration space. Our approach for obtaining the reduced equations is entirely based on the observation that the dynamics…

This work proposes a novel convex-non-convex formulation of the image segmentation and the image completion problems. The proposed approach is based on the minimization of a functional involving two distinct regularization terms: one…

We construct the most general supersymmetric two boson system that is integrable. We obtain the Lax operator and the nonstandard Lax representation for this system. We show that, under appropriate redefinition of variables, this reduces to…

Homogenization of a spectral problem in a bounded domain with a high contrast in both stiffness and density is considered. For a special critical scaling, two-scale asymptotic expansions for eigenvalues and eigenfunctions are constructed.…

Proximal operators with affine constraints arise in numerous models in nonconvex projection, composite optimization, and structured regularization. However, their efficient computation remains challenging due to the simultaneous presence of…

Second order nonlinear eigenvalue problems are considered for which the spectrum is an interval. The boundary conditions are of Robin and Dirichlet type. The shape and the number of solutions are discussed by means of a phase plane…

Utilizing some conservation laws of (1+1)-dimensional integrable local evolution systems, it is conjectured that higher dimensional integrable equations may be regularly constructed by a deformation algorithm. The algorithm can be applied…

A nonlinear optimization method is proposed for the solution of inverse medium problems with spatially varying properties. To avoid the prohibitively large number of unknown control variables resulting from standard grid-based…

For an integrable Hamiltonian system we construct a representation of the phase space symmetry algebra over the space of functions on a Lagrangian manifold. The representation is a result of the canonical quantization of the integrable…

This thesis presents our results on Liouville integrable systems of Calogero-Ruijsenaars type: 1. We prove an explicit formula providing canonical spectral coordinates for the rational Calogero-Moser system. 2. We explore action-angle…

Quantum superintegrable systems are solvable eigenvalue problems. Their solvability is due to symmetry, but the symmetry is often "hidden". The symmetry generators of 2nd order superintegrable systems in 2 dimensions close under commutation…

The higher order symmetries are investigated in a covariant Hamiltonian formulation. The covariant phase-space approach is extended to include the presence of external gauge fields and scalar potentials. The special role of the Killing-Yano…

This paper addresses the problem of blind and fully constrained unmixing of hyperspectral images. Unmixing is performed without the use of any dictionary, and assumes that the number of constituent materials in the scene and their spectral…

An integrable extension of the well known nonlinear Schroedinger (NLS) equation to a higher space-dimension, recently proposed by us, is investigated, exploring its various important aspects. Focusing on the idea of construction its…

Hybrid inverse problems are mathematical descriptions of coupled-physics (also called multi-waves) imaging modalities that aim to combine high resolution with high contrast. The solution of a high-resolution inverse problem, a first step…

We study a class of convex-concave min-max problems in which the coupled component of the objective is linear in at least one of the two decision vectors. We identify such problem structure as interpolating between the bilinearly and…

We show that a large class of non-degenerate second-order (maximally) superintegrable systems gives rise to Hessian structures, which admit natural (Hessian) coordinates adapted to the superintegrable system. In particular, abundant…

The solution of systems of non-autonomous linear ordinary differential equations is crucial in a variety of applications, such us nuclear magnetic resonance spectroscopy. A new method with spectral accuracy has been recently introduced in…

Boundary value problems for integrable nonlinear evolution PDEs formulated on the finite interval can be analyzed by the unified method introduced by one of the authors and used extensively in the literature. The implementation of this…