Related papers: On an optimal problem of bilinear forms
As an application of the theory of linear parabolic differential equations on noncompact Riemannian manifolds, developed in earlier papers, we prove a maximal regularity theorem for nonuniformly parabolic boundary value problems in…
The paper addresses questions of existence and regularity of solutions to linear partial differential equations whose coefficients are generalized functions or generalized constants in the sense of Colombeau. We introduce various new…
In this paper, by using the Brunovsky normal form, we provide a reformulation of the problem consisting in finding the actuator design which minimizes the controllability cost for finite-dimensional linear systems with scalar controls. Such…
Spectral estimation can be preformed using the so called THREE-like approach. Such method leads to a convex optimization problem whose solution is characterized through its dual problem. In this paper, we show that the dual problem can be…
A linear stochastic transport equation with non-regular coefficients is considered. Under the same assumption of the deterministic theory, all weak $L^\infty$-solutions are renormalized. But then, if the noise is nondegenerate, uniqueness…
We analyze fast diagonal methods for simple bilevel programs. Guided by the analysis of the corresponding continuous-time dynamics, we provide a unified convergence analysis under general geometric conditions, including H\"olderian growth…
In this paper we study a mixed problem for the nonlinear Schr\"odinger equation globally that have a nonlinear adding, in which the coefficient is a generalized function. Here is proved a global solvability theorem of the considered problem…
Here is investigated the bilinear optimal control problem of quantum mechanical systems with final observation governed by a stochastic nonlinear Schr\"odinger equation perturbed by a linear multiplicative Wiener process. The existence of…
A method is given for solving an optimal H2 approximation problem for SISO linear time-invariant stable systems. The method, based on constructive algebra, guarantees that the global optimum is found; it does not involve any gradient-based…
Numerous tasks in imaging and vision can be formulated as variational problems over vector-valued maps. We approach the relaxation and convexification of such vectorial variational problems via a lifting to the space of currents. To that…
As part of the search for the value of the smallest upper bound of the best constant for the famous Grothendieck inequality, the so-called Grothendieck constant (a hard open problem - unsolved since 1953), we provide a further approach,…
We presented here a refinement of Hermite-Hadamard inequality as a linear combination of its end-points. The problem of best possible constants is closely connected with well known Simpson's rule in numerical integration. It is solved here…
A generalization of the Bowen-York initial data to the case with a positive cosmological constant is investigated. We follow the construction presented recently by Bizo\'n, Pletka and Simon, and solve numerically the Lichnerowicz equation…
The general solution of the one-dimensional stationary Schroedinger equation in the form of a formal power series is considered. Its efficiency for numerical analysis of initial value and boundary value problems is discussed.
The normality equations for the Newtonian dynamical systems on an arbitrary Riemannian manifold of the dimension $n \geq 3$ are considered. Locally the solution of such equations reduces to three possible cases: in two of them the solution…
In this article we give, for the fist time the solution of the general difference equation of 2-degree. We also give as application the expansion of a continued fraction into series, which was first proved, found in the past by the author.
The integrability in quadratures of normality equation for spatially homogeneous dynamical systems in two-dimensional space is shown. The classical symmetries of this equation are calculated and the corresponding self-similar solutions are…
We define new geometric constants for normed planes, determine their optimal values, and characterize types of planes for which these optimal values are attained. Relations of these constants to several topics, such as areas and distances…
We study the evolution equations for a regularized version of Dirac-harmonic maps from closed Riemannian surfaces. We establish the existence of a global weak solution for the regularized problem, which is smooth away from finitely many…
The generalized Gaussian distribution that stems from information theory is studied. The log-Minkowski problem associated with generalized Gaussian distribution shall be introduced and solved.