All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 7 Next

Displaying 121 – 140 of 171

Showing per page

Expansions of the real line by open sets: o-minimality and open cores

Chris Miller, Patrick Speissegger (1999)

Fundamenta Mathematicae

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...

Explicit Construction of Piecewise Affine Mappings with Constraints

Waldemar Pompe (2010)

Bulletin of the Polish Academy of Sciences. Mathematics

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 extension maps in intersections of non-quasi-analytic classes

Jean Schmets, Manuel Valdivia (2005)

Annales Polonici Mathematici

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 ( ) ( [ - 1 , 1 ] r ) ; (b) there is no continuous linear extension map from Λ ( ) ( r ) into ( ) ( ℝ r ) ; (c) under some additional assumption on , there is an explicit extension map from ( ) ( [ - 1 , 1 ] r ) into ( ) ( [ - 2 , 2 ] r ) by use of a modification of the Chebyshev polynomials. These results extend the corresponding ones obtained by Beaugendre in [1] and [2].

Extending analyticK-subanalytic functions

Artur Piękosz (2004)

Open Mathematics

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

Krzysztof Grelowski (2008)

Annales Polonici Mathematici

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 n times differentiable functions of several variables

Hajrudin Fejzić, Dan Rinne, Clifford E. Weil (1999)

Czechoslovak Mathematical Journal

It is shown that n times Peano differentiable functions defined on a closed subset of ℝ m and satisfying a certain condition on that set can be extended to n times Peano differentiable functions defined on ℝ m if and only if the n th order Peano derivatives are Baire class one functions.

Extending n-convex functions

Allan Pinkus, Dan Wulbert (2005)

Studia Mathematica

We are given data α₁,..., αₘ and a set of points E = x₁,...,xₘ. We address the question of conditions ensuring the existence of a function f satisfying the interpolation conditions f ( x i ) = α i , i = 1,...,m, that is also n-convex on a set properly containing E. We consider both one-point extensions of E, and extensions to all of ℝ. We also determine bounds on the n-convex functions satisfying the above interpolation conditions.

Currently displaying 121 – 140 of 171