Existence theory for integrodifferential equations and Henstock-Kurzweil integral in Banach spaces.
Expansions of the real line by open sets: o-minimality and open cores
The open core of a structure ℜ := (ℝ,<,...) is defined to be the reduct (in the sense of definability) of ℜ generated by all of its definable open sets. If the open core of ℜ is o-minimal, then the topological closure of any definable set has finitely many connected components. We show that if every definable subset of ℝ is finite or uncountable, or if ℜ defines addition and multiplication and every definable open subset of ℝ has finitely many connected components, then the open core of ℜ is...
Expected values in the alternative set theory and their applications to some limit theorems
This article presents an alternative approach to statistical moments within non-standard models and by the help of these moments some limit theorems are reformulated and proved.
Explicit bounds on some nonlinear integral inequalities.
Explicit bounds on some nonlinear retarded integral inequalities.
Explicit Construction of Piecewise Affine Mappings with Constraints
We construct explicitly piecewise affine mappings u:ℝ ⁿ → ℝ ⁿ with affine boundary data satisfying the constraint div u = 0. As an application of the construction we give short and direct proofs of the main approximation lemmas with constraints in convex integration theory. Our approach provides direct proofs avoiding approximation by smooth mappings and works in all dimensions n ≥ 2. After a slight modification of our construction, the constraint div u = 0 can be turned into det Du = 1, giving...
Explicit estimates for some mixed integral inequalities.
Explicit estimates on integral inequalities with time scale.
Explicit extension maps in intersections of non-quasi-analytic classes
We deal with projective limits of classes of functions and prove that: (a) the Chebyshev polynomials constitute an absolute Schauder basis of the nuclear Fréchet spaces ; (b) there is no continuous linear extension map from into ; (c) under some additional assumption on , there is an explicit extension map from into by use of a modification of the Chebyshev polynomials. These results extend the corresponding ones obtained by Beaugendre in [1] and [2].
Explicit solutions of some fractional partial differential equations via stable subordinators.
Exploded and compressed numbers.
Exploded and compressed spaces.
Exponential inequalities for a class of operators.
Exponential stability for the wave equation with weak nonmonotone damping.
Expressing as a difference of two positive functions
Extended fractional calculus of variations, complexified geodesics and Wong's fractional equations on complex plane and on Lie algebroids
In this work, we communicate the topic of complex Lie algebroids based on the extended fractional calculus of variations in the complex plane. The complexified Euler-Lagrange geodesics and Wong's fractional equations are derived. Many interesting consequences are explored.
Extending analyticK-subanalytic functions
Letg:U→ℝ (U open in ℝn) be an analytic and K-subanalytic (i. e. definable in ℝanK, whereK, the field of exponents, is any subfield ofℝ) function. Then the set of points, denoted Σ, whereg does not admit an analytic extension is K-subanalytic andg can be extended analytically to a neighbourhood of Ū.
Extending Hardy fields by non--germs
For a large class of Hardy fields their extensions containing non--germs are constructed. Hardy fields composed of only non--germs, apart from constants, are also considered.
Extending means of two variables to several variables.
Extending times differentiable functions of several variables
It is shown that times Peano differentiable functions defined on a closed subset of and satisfying a certain condition on that set can be extended to times Peano differentiable functions defined on if and only if the th order Peano derivatives are Baire class one functions.