On the p-drop theorem, 1 ≤ p ≤∞.
On the penalty approximation of quadratic programming problem
On the performance of the particle swarm optimization algorithm with various inertia weight variants for computing optimal control of a class of hybrid systems.
On the perturbations in a time-optimal closed-loop system
On the points of non-differentiability of convex functions
We characterize sets of non-differentiability points of convex functions on . This completes (in ) the result by Zajíček [2] which gives a characterization of the magnitude of these sets.
On the Principle of Linearized Stability for Varitional Inequalities.
On the projective Finsler metrizability and the integrability of Rapcsák equation
A. Rapcsák obtained necessary and sufficient conditions for the projective Finsler metrizability in terms of a second order partial differential system. In this paper we investigate the integrability of the Rapcsák system and the extended Rapcsák system, by using the Spencer version of the Cartan-Kähler theorem. We also consider the extended Rapcsák system completed with the curvature condition. We prove that in the non-isotropic case there is a nontrivial Spencer cohomology group in the sequences...
On the propagation of singularities of semi-convex functions
On the properties of the Aumann integral with applications to differential inclusions and control systems
On the quadratic optimal control problem for Volterra integro-differential equations
On the quasiconvex exposed points
The notion of quasiconvex exposed points is introduced for compact sets of matrices, motivated from the variational approach to material microstructures. We apply the notion to give geometric descriptions of the quasiconvex extreme points for a compact set. A weak version of Straszewicz type density theorem in convex analysis is established for quasiconvex extreme points. Some examples are examined by using known explicit quasiconvex functions.
On the quasiconvex exposed points
The notion of quasiconvex exposed points is introduced for compact sets of matrices, motivated from the variational approach to material microstructures. We apply the notion to give geometric descriptions of the quasiconvex extreme points for a compact set. A weak version of Straszewicz type density theorem in convex analysis is established for quasiconvex extreme points. Some examples are examined by using known explicit quasiconvex functions.
On the real-time emission control - case study application
On the rectifiability of domains with finite perimeter
On the reduction of pairs of bounded closed convex sets
Let X be a Hausdorff topological vector space. For nonempty bounded closed convex sets A,B,C,D ⊂ X we denote by A ∔ B the closure of the algebraic sum A + B, and call the pairs (A,B) and (C,D) equivalent if A ∔ D = B ∔ C. We prove two main theorems on reduction of equivalent pairs. The first theorem implies that, in a finite-dimensional space, a pair of nonempty compact convex sets with a piecewise smooth boundary and parallel tangent spaces at some boundary points is not minimal. The second theorem...
On the regularity of edges in image segmentation
On the regularity of local minimizers of decomposable variational integrals on domains in
We consider local minimizers of variational integrals like or its degenerate variant with exponents which do not fall completely in the category studied in Bildhauer M., Fuchs M., Calc. Var. 16 (2003), 177–186. We prove interior - respectively -regularity of under the condition that . For decomposable variational integrals of arbitrary order a similar result is established by the way extending the work Bildhauer M., Fuchs M., Ann. Acad. Sci. Fenn. Math. 31 (2006), 349–362.
On the Regularity of Minimal Surfaces with Free Boundaries in Riemannian Manifolds.
On the Regularity of Solutions to Variational Problems in BV (...).
On the regularity of the minimizer of a functional with exponential growth
Minimizers of a functional with exponential growth are shown to be smooth. The techniques developed for power growth are not applicable to the exponential case.