Related papers: Continuous Craig Interpolation
A new proof of the Wulff-Gage isoperimetric inequality for origin-symmetric convex bodies is provided. As its applications, we prove the uniqueness of log-Minkowski problem and a new proof of the log-Minkowski inequality of curvature…
In this paper, we show the new fixed point theorem in metric spaces. Furthermore, for this fixed point theorem, we apply to the Collatz conjecture.
Software model checking is a challenging problem, and generating relevant invariants is a key factor in proving the safety properties of a program. Program invariants can be obtained by various approaches, including lightweight procedures…
An abstract Pick interpolation theorem for a family of positive semi-definite kernels on a set $X$ is formulated. The result complements those in \cite{Ag} and \cite{AMbook} and will subsequently be applied to Pick interpolation on…
In this note, we outline the general development of a theory of symmetric homology of algebras, an analog of cyclic homology where the cyclic groups are replaced by symmetric groups. This theory is developed using the framework of crossed…
We prove a differential analog of a theorem of Chevalley on extending homomorphisms for rings with commuting derivations, generalizing a theorem of Kac. As a corollary, we establish that, under suitable hypotheses, the image of a…
Using Easton collapses, we give a simplified construction of a model in which Chang's Conjecture for triples holds.
This paper is a study of first-order coherent logic from the point of view of duality and categorical logic. We prove a duality theorem between coherent hyperdoctrines and open polyadic Priestley spaces, which we subsequently apply to prove…
In this paper we study nonlinear interpolation problems for interpolation and peak-interpolation sets of function algebras. The subject goes back to the classical Rudin-Carleson interpolation theorem. In particular, we prove the following…
We provide a general and syntactically-defined family of sequent calculi, called \emph{semi-analytic}, to formalize the informal notion of a "nice" sequent calculus. We show that any sufficiently strong (multimodal) substructural logic with…
In this paper, we propose an interpolation formula for periodic functions. This formula can be regarded as an analog of the Sinc approximation, which is an interpolation formula for functions defined on the entire infinite interval.…
We prove a new q-analogue of Nicomachus's Theorem about the sum of cubes and some related results.
We show the equivalence of several notions in the theory of taut foliations and the theory of tight contact structures. We prove equivalence, in certain cases, of existence of tight contact structures and taut foliations.
In this paper, we present an interpolation framework for structure-preserving model order reduction of parametric bilinear dynamical systems. We introduce a general setting, covering a broad variety of different structures for parametric…
Using Morse theory and a new relative homological linking of pairs, we prove a ``homological linking principle'', thereby generalizing many well known results in critical point theory.
We prove an analog of Siegel's theorem for integral points in the context of Drinfeld modules. The result holds for finitely generated submodules of the additive group over a function field of transcendence dimension 1.
We study continuous homomorphisms between algebras of iterated Laurent series over a commutative ring. We give a full description of such homomorphisms in terms of a discrete data determined by the images of parameters. In similar terms, we…
In this paper we prove FG-coupled fixed point theorems for different contractive mappings and generalized quasi- contractive mappings in partially ordered complete metric spaces. We prove the existence of FG-coupled fixed points of…
Using an alternate description of support varieties of pairs of modules over a complete intersection, we give several new applications of such varieties, including results for support varieties of intermediate complete intersections.…
We prove that direct limits of finite dimensional Lie algebroids and their prolongations can be endowed with structures of convenient spaces.