Related papers: Strong Typed B\"ohm Theorem and Functional Complet…
We present a linear functional calculus with both the safety guarantees expressible with linear types and the rich language of combinators and composition provided by functional programming. Unlike previous combinations of linear typing and…
Many different systems with explicit substitutions have been proposed to implement a large class of higher-order languages. Motivations and challenges that guided the development of such calculi in functional frameworks are surveyed in the…
The weak boundedness property associated with a standard alpha-fractional Calderon-Zygmund operator and a weight pair is good-lambda controlled by the testing conditions and the Muckenhoupt and energy side conditions. As a consequence,…
We prove a topological completeness theorem for the modal logic GLP containing operators $\langle\lambda\rangle$ for $\lambda \in$ Ord intended to capture progressively stronger notions of consistency in mathematical theories. We show that,…
This paper first defines operators that are "well-localized" with respect to a pair of accretive functions and establishes a global two-weight Tb theorem for such operators. Then it defines operators that are "well-localized" with respect…
We consider the BGG category $\mathcal{O}$ of a quantized universal enveloping algebra $U_q(\mathfrak{g})$. We call a module $M\in \mathcal{O}$ tensor-closed if $M\otimes N\in\mathcal{O}$ for any $N\in \mathcal{O}$. In this paper we prove…
The $\lambda$-superposition calculus is a successful approach to proving higher-order formulas. However, some parts of the calculus are extremely explosive, notably due to the higher-order unifier enumeration and the functional…
We prove a Tb Theorem that characterizes all Calderon-Zygmund operators that extend compactly on L^p(R^n), 1<p<\infty . The result, whose proof does not require the property of accretivity, can be used to prove compactness of the Double…
A local Tb theorem is an L^2 boundedness criterion by which the question of the global behavior of an operator is reduced to its local behavior, acting on a family of test functions b_Q indexed by the dyadic cubes. We present several…
In the lambda calculus a term is solvable iff it is operationally relevant. Solvable terms are a superset of the terms that convert to a final result called normal form. Unsolvable terms are operationally irrelevant and can be equated…
We prove two completeness results for Kleene algebra with tests and a top element, with respect to guarded string languages and binary relations. While the equational theories of those two classes of models coincide over the signature of…
In the theory of unitary group representations, a group is called type I if all factor representations are of type I, and by a celebrated theorem of James Glimm [Gli61b], the type I groups are precisely those groups for which the…
We propose a complete, new formalism to compute unambiguously B-model open and closed amplitudes in local Calabi-Yau geometries, including the mirrors of toric manifolds. The formalism is based on the recursive solution of matrix models…
A certain class of matrix-valued Borel matrix functions is introduced and it is shown that all functions of that class naturally operate on any operator T in a finite type I von Neumann algebra M in a way such that uniformly bounded…
This document provides a formal proof of Birkhoff's completeness theorem for multi-sorted algebras which states that any equational entailment valid in all models is also provable in the equational theory. More precisely, if a certain…
In this letter we develope an operator formalism for the $b-c$ systems with conformal weight $\lambda=1$ defined on a general closed and orientable Riemann surface. The advantage of our approach is that the Riemann surface is represented as…
The class of Basic Feasible Functionals BFF$_2$ is the type-2 counterpart of the class FP of type-1 functions computable in polynomial time. Several characterizations have been suggested in the literature, but none of these present a…
A finite-time singularity of 2D harmonic map flow will be called "strictly type-II" if the outer energy scale satisfies $\lambda(t) = O(T - t)^{\frac{1 + \alpha}{2}}.$ We prove that the body map at a strict type-II blowup is H\"older…
A uniformly bounded complete orthonormal system of functions $\Theta =\{ \theta_n\}_{n=1}^{\infty},$ $ \|\theta_n\|_{L^\infty_{[0,1]} } \leq M $ is constructed such that $\sum_{n=1}^{\infty} a_{n}\theta_{n}$ converges almost everywhere on…
We prove a generalization of Quillen's Theorem B to strict $\infty$-categories. More generally, we show that under similar hypothesis as for Theorem B, the comma construction for strict $\infty$-categories, that we introduced with…