On derivatives of functions defined on disconnected sets, I
On derivatives of functions defined on disconnected sets, II
On derivo-periodic multifunctions
The problem of linearity of a multivalued derivative and consequently the problem of necessary and sufficient conditions for derivo-periodic multifunctions are investigated. The notion of a derivative of multivalued functions is understood in various ways. Advantages and disadvantages of these approaches are discussed.
On determining sets for the class of somewhat continuous functions
On differentiability of Peano type functions
On differentiability of Peano type functions
On differentiability of Peano type functions. II
On differentiability with respect to parameters of the Lebesgue integral.
On Dini Derivatives and on a Property of Denjoy.
On Dini derivatives and on certain classes of Zahorski
On embedding of the class .
On entropy of patterns given by interval maps
Defining the complexity of a green pattern exhibited by an interval map, we give the best bounds of the topological entropy of a pattern with a given complexity. Moreover, we show that the topological entropy attains its strict minimum on the set of patterns with fixed eccentricity m/n at a unimodal X-minimal case. Using a different method, the last result was independently proved in[11].
On equations and properties concerning some classes of chordal polygons.
On equivalence of coefficient conditions.
On equivalence of coefficient conditions. II.
On equivalence of super log Sobolev and Nash type inequalities
We prove the equivalence of Nash type and super log Sobolev inequalities for Dirichlet forms. We also show that both inequalities are equivalent to Orlicz-Sobolev type inequalities. No ultracontractivity of the semigroup is assumed. It is known that there is no equivalence between super log Sobolev or Nash type inequalities and ultracontractivity. We discuss Davies-Simon's counterexample as the borderline case of this equivalence and related open problems.
On error bounds for Gauss-Legendre and Lobatto quadrature rules.
On essential cluster sets
On essential -variation.
On Euler methods for Caputo fractional differential equations
Numerical methods for fractional differential equations have specific properties with respect to the ones for ordinary differential equations. The paper discusses Euler methods for Caputo differential equation initial value problem. The common properties of the methods are stated and demonstrated by several numerical experiments. Python codes are available to researchers for numerical simulations.