A new type of stable generalized convex functions.
A non absolutely convergent integral which admits transformation and can be used for integration on manifolds
A non-absolutely convergent integral which admits -transformations
A non-archimedean “curve integral” and its application to the construction of potentials and solutions of differential equations
A non-commutative sewing lemma.
A note about the almost continuity
A note on a property of the Gini coefficient
The scope of this note is a self-contained presentation of a mathematical method that enables us to give an absolute upper bound for the difference of the Gini coefficients where represents the vector of the gross wages and represents the vector of the corresponding super-gross wages that is used in the Czech Republic for calculating the net wage. Since (as of June 2019) , the study of the above difference seems to be somewhat inaccessible for many economists. However, our estimate based...
A note on certain functional determinants.
A note on certain functional determinants. (Summary).
A note on convex functions.
A note on fractional integration
A note on global implicit function theorem.
A note on Hölder's inequality
A note on martingale transforms and -weights
A note on partial derivatives of convex functions
A note on propagation of singularities of semiconcave functions of two variables
P. Albano and P. Cannarsa proved in 1999 that, under some applicable conditions, singularities of semiconcave functions in propagate along Lipschitz arcs. Further regularity properties of these arcs were proved by P. Cannarsa and Y. Yu in 2009. We prove that, for , these arcs are very regular: they can be found in the form (in a suitable Cartesian coordinate system) , , where , are convex and Lipschitz on . In other words: singularities propagate along arcs with finite turn.
A note on quasiconvex functions that are pseudoconvex.
In the present note we consider the definitions and properties of locally pseudo- and quasiconvex functions and give a sufficient condition for a locally quasiconvex function at a point x ∈ Rn, to be also locally pseudoconvex at the same point.
A note on strong pseudoconvexity
A strongly pseudoconvex function is generalized to non-smooth settings. A complete characterization of the strongly pseudoconvex radially lower semicontinuous functions is obtained.
A note on the scalar Haffian.
In this note a uniform transparent presentation of the scalar Haffian will be given. Some well-known results will be generalized. A link will be established between the scalar Haffian and the derivative matrix as developed by Magnus and Neudecker.
A note on the three-segment problem
We improve a theorem of C. L. Belna (1972) which concerns boundary behaviour of complex-valued functions in the open upper half-plane and gives a partial answer to the (still open) three-segment problem.