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There are two basic ways of weakening the definition of the well-known metric regularity property by fixing one of the points involved in the definition. The first resulting property is called metric subregularity and has attracted a lot of…
The Cauchy problem for first-order PDE with the initial data which have a piecewise discontinuities localized in different spatial points is completely solved. The interactions between discontinuities arising after breakup of initial…
We consider a fixed angle inverse scattering problem in the presence of a known Riemannian metric. First, assuming a no caustics condition, we study the direct problem by utilizing the progressing wave expansion. Under a symmetry assumption…
We solve a problem of singular stochastic control with discretionary stopping, suggested as an interesting open problem by Karatzas, Ocone, Wang and Zervos (2000), by providing suitable candidates for the moving boundaries in an unsolved…
A new algorithm to determine the position of the crack (discontinuity set) of certain minimizers of Mumford-Shah functional in situations when a crack-tip occurs is introduced. The conformal mapping $w=\sqrt{z}$ in the complex plane is used…
We axiomatize and generalize Markov's approach to the continuity problem for Type 1 computable functions, i.e. the problem of finding sufficient conditions on a computable topological space to obtain a theorem of the form "computable…
We present two algorithms for large-scale low-rank Euclidean distance matrix completion problems, based on semidefinite optimization. Our first method works by relating cliques in the graph of the known distances to faces of the positive…
This paper aims to solve the equations of geometrically exact 3D nonlinear Cosserat static rods under large displacements with a mesh free alternative method to finite elements: the shooting method. One of the main goal of the work…
The fixed-point theory and its applications to various areas of science are well known. In this paper we present some existence and uniqueness theorems for fixed circles of self-mappings on metric spaces with geometric interpretation. We…
Our main aim in this paper is to introduce a general concept of multidimensional fixed point of a mapping in spaces with distance and establish various multidimensional fixed point results. This new concept simplifies the similar notion…
This paper is devoted to the investigation of an important issue recently brought into attention by a recent paper of Arutyunov: the relation between openness of composition of set-valued maps and fixed point results. More precisely, we…
A recent open problem was stated on the geometric properties of $\varphi $-fixed points of self-mappings of a metric space in the non-unique fixed point cases. In this paper, we deal with the solutions of this open problem and present some…
This paper investigates the existence of localised axisymmetric (radial) patterns on the surface of a ferrofluid in the presence of a uniform vertical magnetic field. We formally investigate all possible small-amplitude solutions which…
We study the scattering rigidity problem for standard stationary manifolds using timelike geodesics with a fixed momentum. Taking advantage of the symmetry of this manifolds, we use Hamiltonian reduction to show that this problem is related…
The basic tool for solving problems in metric geometry and isotonic regression is the metric projection onto closed convex cones. Isotonicity of these projections with respect to a given order relation can facilitate finding the solutions…
The paper concerns a new method to obtain a direct proof of the openness at linear rate/metric regularity of composite set-valued maps on metric spaces by the unification and refinement of several methods developed somehow separately in…
The concept of fixed point plays a crucial role in various fields of applied mathematics. The aim of this paper is to establish the existence of a unique fixed point of some type of functions which satisfy a new contraction principle,…
This paper investigates the disturbance decoupling problem by dynamic output feedback in the general case of systems with possible input-output feedthrough matrices. In particular, we aim to extend the geometric condition based on…
A recent trend in Non-Rigid Structure-from-Motion (NRSfM) is to express local, differential constraints between pairs of images, from which the surface normal at any point can be obtained by solving a system of polynomial equations. The…
We consider Hamilton--Jacobi equations, where the Hamiltonian depends discontinuously on both the spatial and temporal location. Our main results are the existence and well--posedness of a viscosity solution to the Cauchy problem. We define…