Related papers: Linearly Ordered Families of Baire 1 Functions
We introduce sequences of functions orthogonal on a finite interval: proper orthogonal rational functions, orthogonal exponential functions, orthogonal logarithmic functions, and transmuted orthogonal polynomials
A polynomial algorithm is obtained for the NP-complete linear ordering problem.
We prove the following classification theorem of the ``Glimm -- Effros'' type for Borel order relations: a Borel partial order on the reals either is Borel linearizable or includes a copy of a certain Borel partial order $\meo$ which is not…
In this paper, we extend Busy Beaver function to a class of higher order Busy Beaver functions based on Turing oracle machine. We prove some results about the relation between decidability of number theoretical formula and higher order Busy…
In this paper, we study uniqueness problems for an entire function that shares small functions of finite order with their difference operators. In particular, we give a generalization of results in [2,3,13].
We give an algebraic characterization of half-factorial orders in algebraic number fields. This generalizes prior results for seminormal orders and for orders in quadratic number fields.
Most of the special functions of mathematical physics are connected with the representation of Lie groups. The action of elements $D$ of the associated Lie algebras as linear differential operators gives relations among the functions in a…
We give a complete description of all order 1 invariants of planar curves.
This chapter is divided into two parts. The first part is a survey of some recent results on nests and the orderability problem. The second part consists of results, partial results and open questions, all viewed in the light of nests. From…
It is proved the existence of large algebraic structures \break --including large vector subspaces or infinitely generated free algebras-- inside, among others, the family of Lebesgue measurable functions that are surjective in a strong…
In this paper we study the subdifferential set of an operator. We give possible relation of the subdifferential set of an operator to that of its value, at a point where the operator attains its norm.
It was recently shown that arbitrary first-order models canonically extend to models (of the same language) consisting of ultrafilters. The main precursor of this construction was the extension of semigroups to semigroups of ultrafilters, a…
Collective versions of order convergences and corresponding types of collectively qualified sets of operators in vector lattices are investigated. It is proved that collectively order to norm bounded sets are bounded in the operator norm…
A method of reducing general quaternion functions of first degree, i.e., linear quaternion functions, to quaternary canonical form is given. Linear quaternion functions, once reduced to canonical form, can be maintained in this form under…
The set of linear structures of most known balanced Boolean functions is nontrivial. In this paper, some balanced Boolean functions whose set of linear structures is trivial are constructed. We show that any APN function in even dimension…
In this paper we propose a procedure which allows the construction of a large family of FIR d x d matrix wavelet filters by exploiting the one-to-one correspondence between QMF systems and orthogonal operators which commute with the shifts…
The structure functions of the Lagrangian gauge algebra are given explicitly in terms of the hamiltonian constraints and the first order Hamiltonian structure functions and their derivatives.
Let $\mathcal{H}$ be a complex infinite dimensional Hilbert space and $\mathcal{B}(\mathcal{H})$ the algebra of all bounded linear operators on $\mathcal H$. The star partial order is defined by $A\overset{*}{\leq}B$ if and only if…
In this paper, we give necessary and sufficient conditions for the space B_1(X) of first Baire class functions on a Tychonoff space X, with pointwise topology, to be (strongly) sequentially separable.
We introduce the concept of a prenormed model of a particular kind of finitary single-sorted first-order theories, interpreted over a category with finite products. These are referred to as prealgebraic theories, for the fact that their…