On the regularity condition for decomposable communication channels
On the relation between the multidimensional moment problem and the one-dimensional moment problem.
On the Relations Between 2D and 3D Fractal Dimensions: Theoretical Approach and Clinical Application in Bone Imaging
The inner knowledge of volumes from images is an ancient problem. This question becomes complicated when it concerns quantization, as the case of any measurement and in particular the calculation of fractal dimensions. Trabecular bone tissues have, like many natural elements, an architecture which shows a fractal aspect. Many studies have already been developed according to this approach. The question which arises however is to know to which extent it is possible to get an exact determination of the...
On the rigidity of one-dimensional systems of contraction similitudes.
On the Rockafellar theorem for -monotone multifunctions
Let X be an arbitrary set, and γ: X × X → ℝ any function. Let Φ be a family of real-valued functions defined on X. Let be a cyclic -monotone multifunction with non-empty values. It is shown that the following generalization of the Rockafellar theorem holds. There is a function f: X → ℝ such that Γ is contained in the -subdifferential of f, .
On the scooping property of measures by means of disjoint balls
On the search for Borel selections
On the selector problems for the partitions of Polish spaces and for the compact-valued mappings
On the self-similar Jordan arcs admitting structure parametrization.
On the sequence of integer parts of a good sequence for the ergodic theorem
If is a sequence of real numbers which is good for the ergodic theorem, is the sequence of the integer parts good for the ergodic theorem ? The answer is negative for the mean ergodic theorem and affirmative for the pointwise ergodic theorem.
On the setwise convergence of sequences of measures.
On the singlevaluedness and differentiation of metric projections
On the singularities of convex functions.
On the space of vector-valued functions integrable with respect to the white noise
On the Spectra of Certain Semi-Groups.
On the Speed of Convergence in the Ergodic Theorem.
On the strong maximal function and rearrangements
On the strong McShane integral of functions with values in a Banach space
The classical Bochner integral is compared with the McShane concept of integration based on Riemann type integral sums. It turns out that the Bochner integrable functions form a proper subclass of the set of functions which are McShane integrable provided the Banach space to which the values of functions belong is infinite-dimensional. The Bochner integrable functions are characterized by using gauge techniques. The situation is different in the case of finite-dimensional valued vector functions....
On the structure of a vector measure.
On the structure of the intersection of two middle third Cantor sets.
Motivated by the study of planar homoclinic bifurcations, in this paper we describe how the intersection of two middle third Cantor sets changes as the sets are translated across each other. The resulting description shows that the intersection is never empty; in fact, the intersection can be either finite or infinite in size. We show that when the intersection is finite then the number of points in the intersection will be either 2n or 3 · 2n. We also explore the Hausdorff dimension of the intersection...