相关论文: Internal sets and internal functions in Colombeau …

Pippenger's Galois theory of finite functions and relational constraints is extended to the infinite case. The functions involved are functions of several variables on a set $A$ and taking values in a possibly different set $B$, where any…

A natural connection between rational functions of several real or complex variables, and subspace collections is explored. A new class of function, superfunctions, are introduced which are the counterpart to functions at the level of…

We investigate the foundations of a theory of algebraic data types with variable binding inside classical universal algebra. In the first part, a category-theoretic study of monads over the nominal sets of Gabbay and Pitts leads us to…

We determine the proof-theoretic strength of the principle of countable saturation in the context of the systems for nonstandard arithmetic introduced in our earlier work.

The validity of the Addition Theorem for algebraic entropies $\ent_L$ induced by non-discrete length functions $L$ on the category of locally $L$-finite modules over arbitrary rings is proved. Concrete examples of non-discrete length…

This thesis concerns embeddings and self-embeddings of foundational structures in both set theory and category theory. The first part of the work on models of set theory consists in establishing a refined version of Friedman's theorem on…

We study universal approximation of continuous functionals on compact subsets of products of Hilbert spaces. We prove that any such functional can be uniformly approximated by models that first take finitely many continuous linear…

Submodular set functions are undoubtedly among the most important building blocks of combinatorial optimization. Somewhat surprisingly, continuous counterparts of such functions have also appeared in an analytic line of research where they…

We develop a number of basic concepts in the theory of categories internal to an $\infty$-topos. We discuss adjunctions, limits and colimits as well as Kan extensions for internal categories, and we use these results to prove the universal…

We show that for smooth manifolds X and Y, any isomorphism between the special algebra of Colombeau generalized functions on X, resp. Y is given by composition with a unique Colombeau generalized function from Y to X. We also identify the…

We present a geometric approach to defining an algebra $\hat{\mathcal G}(M)$ (the Colombeau algebra) of generalized functions on a smooth manifold $M$ containing the space ${\mathcal D}'(M)$ of distributions on $M$. Based on differential…

In this paper we give a method, based on the characteristic function of a set, to solve some difficult problems of set theory in undergraduate research.

We review a few results concerning interpolation of monotone functions on infinite lattices, emphasizing the role of set-theoretic considerations. We also discuss a few open problems.

A new notion of partition-determined functions is introduced, and several basic inequalities are developed for the entropy of such functions of independent random variables, as well as for cardinalities of compound sets obtained using these…

A sharp, distribution free, non-asymptotic result is proved for the concentration of a random function around the mean function, when the randomization is generated by a finite sequence of independent data and the random functions satisfy…

We study generalized inner functions on a large family of Reproducing Kernel Hilbert Spaces. We show that the only inner functions that are entire are the normalized monomials.

We develop the theory of central ideals on commutative rings. We introduce and study the central seminormalization of a ring in another one. This seminormalization is related to the theory of regulous functions on real algebraic varieties.…

We consider a class of functions defined on metric spaces which generalizes the concept of piecewise Lipschitz continuous functions on an interval or on polyhedral structures. The study of such functions requires the investigation of their…

Inner functions play a central role in function theory and operator theory on the Hardy space over the unit disk. Motivated by recent works of C. B\'en\'eteau et al. and of D. Seco, we discuss inner functions on more general weighted Hardy…

We discuss the concept of inner function in reproducing kernel Hilbert spaces with an orthogonal basis of monomials and examine connections between inner functions and optimal polynomial approximants to $1/f$, where $f$ is a function in the…