Discrete Sobolev and Poincaré inequalities for piecewise polynomial functions.
Discretization and anti-discretization of rearrangement-invariant norms.
Discriminant Sets of Families of Hyperbolic Polynomials of Degree 4 and 5
∗ Research partially supported by INTAS grant 97-1644A real polynomial of one real variable is hyperbolic (resp. strictly hyperbolic) if it has only real roots (resp. if its roots are real and distinct). We prove that there are 116 possible non-degenerate configurations between the roots of a degree 5 strictly hyperbolic polynomial and of its derivatives (i.e. configurations without equalities between roots). The standard Rolle theorem allows 286 such configurations. To obtain the result we study...
Distance entre les racines d'un polynôme
Distant bounded variation and products of derivatives
Distortion function and quasisymmetric mappings
We study the relationship between the distortion function and normalized quasisymmetric mappings. This is part of a new method for solving the boundary values problem for an arbitrary K-quasiconformal automorphism of a generalized disc on the extended complex plane.
Distortion theorems for fractional calculus of certain analytic functions with negative coefficients.
Distributed optimization via active disturbance rejection control: A nabla fractional design
This paper studies distributed optimization problems of a class of agents with fractional order dynamics and unknown external disturbances. Motivated by the celebrated active disturbance rejection control (ADRC) method, a fractional order extended state observer (Frac-ESO) is first constructed, and an ADRC-based PI-like protocol is then proposed for the target distributed optimization problem. It is rigorously shown that the decision variables of the agents reach a domain of the optimal solution...
Distribution and rearrangement estimates of the maximal function and interpolation
There are given necessary and sufficient conditions on a measure dμ(x)=w(x)dx under which the key estimates for the distribution and rearrangement of the maximal function due to Riesz, Wiener, Herz and Stein are valid. As a consequence, we obtain the equivalence of the Riesz and Wiener inequalities which seems to be new even for the Lebesgue measure. Our main tools are estimates of the distribution of the averaging function f** and a modified version of the Calderón-Zygmund decomposition. Analogous...
Distribution of terms of a logarithmic sequence.
Distributional derivatives of functions of two variables of finite variation and their application to an impulsive hyperbolic equation
We give characterizations of the distributional derivatives , , of functions of two variables of locally finite variation. Then we use these results to prove the existence theorem for the hyperbolic equation with a nonhomogeneous term containing the distributional derivative determined by an additive function of an interval of finite variation. An application of the above theorem to a hyperbolic equation with an impulse effect is also given.
Distributional fractional powers of the Laplacean. Riesz potentials
For different reasons it is very useful to have at one’s disposal a duality formula for the fractional powers of the Laplacean, namely, , α ∈ ℂ, for ϕ belonging to a suitable function space and u to its topological dual. Unfortunately, this formula makes no sense in the classical spaces of distributions. For this reason we introduce a new space of distributions where the above formula can be established. Finally, we apply this distributional point of view on the fractional powers of the Laplacean...
Disuguaglianze di Sobolev nello spazio iperbolico bidimensionale
Division Problem and Partial Differential Equations with Constant Coefficients in Colombeau's Space of New Generalized Functions.
Division space axiomatics
Dokaz jedne nejednakosti J. Barkes-a
Domaines complets d'existence des fonctions analytiques uniformes dans les corps valués complets
Domination in the families of Frank and Hamacher t-norms
Domination is a relation between general operations defined on a poset. The old open problem is whether domination is transitive on the set of all t-norms. In this paper we contribute partially by inspection of domination in the family of Frank and Hamacher t-norms. We show that between two different t-norms from the same family, the domination occurs iff at least one of the t-norms involved is a maximal or minimal member of the family. The immediate consequence of this observation is the transitivity...
Double exponential integrability, Bessel potentials and embedding theorems
This paper is a continuation of [5] and provides necessary and sufficient conditions for double exponential integrability of the Bessel potential of functions from suitable (generalized) Lorentz-Zygmund spaces. These results are used to establish embedding theorems for Bessel potential spaces which extend Trudinger's result.
Dragomir-Agarwal type inequalities for several families of quadratures.