On the embedding Waterman, Chanturia and generalized Wiener classes in the classes .
On the entropy of Darboux functions
We prove some results concerning the entropy of Darboux (and almost continuous) functions. We first generalize some theorems valid for continuous functions, and then we study properties which are specific to Darboux functions. Finally, we give theorems on approximating almost continuous functions by functions with infinite entropy.
On the equality condition in Hölder's and Minkowski inequalities.
On the equality condition in Hölder's and Minkowski's inequalities. (Summary).
On the equation
On the Equivalence of the Riemann-Liouville and the Caputo Fractional Order Derivatives in Modeling of Linear Viscoelastic Materials
Mathematics Subject Classification: 26A33In the process of constructing empirical mathematical models of physical phenomena using the fractional calculus, investigators are usually faced with the choice of which definition of the fractional derivative to use, the Riemann-Liouville definition or the Caputo definition. This investigation presents the case that, with some minimal restrictions, the two definitions produce completely equivalent mathematical models of the linear viscoelastic phenomenon....
On the Erdös-Debrunner inequality.
On the estension of Lipschitz functions with respect to two Hilbert norms and two Lipschitz conditions
On the estimation of averages over infinite intervals with an application to average persistence in population models.
On the Euler characteristic of the links of a set determined by smooth definable functions
The purpose of this paper is to carry over to the o-minimal settings some results about the Euler characteristic of algebraic and analytic sets. Consider a polynomially bounded o-minimal structure on the field ℝ of reals. A () smooth definable function φ: U → ℝ on an open set U in ℝⁿ determines two closed subsets W := u ∈ U: φ(u) ≤ 0, Z := u ∈ U: φ(u) = 0. We shall investigate the links of the sets W and Z at the points u ∈ U, which are well defined up to a definable homeomorphism. It is proven...
On the exact location of the non-trivial zeros of Riemann's zeta function
We introduce the real valued real analytic function κ(t) implicitly defined by (κ(0) = -1/2). By studying the equation κ(t) = n (without making any unproved hypotheses), we show that (and how) this function is closely related to the (exact) position of the zeros of Riemann’s ζ(s) and ζ’(s). Assuming the Riemann hypothesis and the simplicity of the zeros of ζ(s), it follows that the ordinate of the zero 1/2 + iγₙ of ζ(s) is the unique solution to the equation κ(t) = n.
On the existence of a fuzzy integral equation of Urysohn-Volterra type
We present an existence theorem for integral equations of Urysohn-Volterra type involving fuzzy set valued mappings. A fixed point theorem due to Schauder is the main tool in our analysis.
On the existence of functions with perfect level sets.
On the existence of positive solutions for certain difference equations and inequalities.
On the existence of -primitives on arbitrary metric spaces
On the extended Hardy's inequality.
On the extended Hilbert's integral inequality.
On the extension and generation of set-valued mappings of bounded variation
We study set-valued mappings of bounded variation of one real variable. First we prove the existence of an extension of a metric space valued mapping from a subset of the reals to the whole set of reals with preservation of properties of the initial mapping: total variation, Lipschitz constant or absolute continuity. Then we show that a set-valued mapping of bounded variation defined on an arbitrary subset of the reals admits a regular selection of bounded variation. We introduce a notion of generated...
On the failure of a decomposition
On the family of functions with a closure of its graph of measure zero