相关论文: Creating Strong Total Commutative Associative Comp…
We present an algorithmic approach to the verification of identities on multiple theta functions in the form of products of theta functions $[(-1)^{\delta}a_1^{\alpha_1}a_2^{\alpha_2}\cdots a_r^{\alpha_r}q^{s}; q^{t}]_\infty$, where…
Pattern matching is a powerful tool which is part of many functional programming languages as well as computer algebra systems such as Mathematica. Among the existing systems, Mathematica offers the most expressive pattern matching.…
We establish global universal approximation theorems on spaces of piecewise linear paths, stating that linear functionals of the corresponding signatures are dense with respect to $L^p$- and weighted norms, under an integrability condition…
We exhibit a way of "forcing a functional to be an effective operation" for arbitrary partial combinatory algebras (pcas). This gives a method of defining new pcas from old ones for some fixed functional, where the new partial functions can…
Choice correspondences are crucial in decision-making, especially when faced with indifferences or ties. While tie-breaking can transform a choice correspondence into a choice function, it often introduces inefficiencies. This paper…
In this paper we consider Positive Definite functions on products $\Omega_{2q}\times\Omega_{2p}$ of complex spheres, and we obtain a condition, in terms of the coefficients in their disc polynomial expansions, which is necessary and…
The existence of pseudorandom unitaries (PRUs) -- efficient quantum circuits that are computationally indistinguishable from Haar-random unitaries -- has been a central open question, with significant implications for cryptography,…
In this paper, we study some properties of a certain kind of permutation $\sigma$ over $\mathbb{F}_{2}^{n}$, where $n$ is a positive integer. The desired properties for $\sigma$ are: (1) the algebraic degree of each component function is…
It is important that practical data-flow analyzers are backed by reliably proven theoretical results. Abstract interpretation provides a sound mathematical framework and necessary generic properties for an abstract domain to be well-defined…
On a smooth closed manifold $M$, we introduce a novel theory of maximal slope curves for any pair $(\phi,H)$ with $\phi$ a semiconcave function and $H$ a Hamiltonian. By using the notion of maximal slope curve from gradient flow theory, the…
We present an approach which is based on the one-particle irreducible (1PI) generating functional formalism and includes electronic correlations on all length-scales beyond the local correlations of dynamical mean field theory (DMFT). This…
We prove the existence of explicit linear multistep methods of any order with positive coefficients. Our approach is based on formulating a linear programming problem and establishing infeasibility of the dual problem. This yields a number…
This study introduces a procedure to obtain general expressions, $y = f(x)$, subject to linear constraints on the function and its derivatives defined at specified values. These constrained expressions can be used describe functions with…
In this paper, we prove common fixed point results for a self-mappings satisfying an implicit function which is general enough to cover a multitude of known as well as unknown contractions. Our results modify, unify, extend and generalize…
Let $K$ be a finite field of characteristic $p$. We study a certain class of functions $K\rightarrow K$ that agree with an $\mathbb{F}_p$-affine function $K\rightarrow K$ on each coset of a given additive subgroup $W$ of $K$ - we call them…
Consider a countable amenable group acting by homeomorphisms on a compact metrizable space. Chung and Li asked if expansiveness and positive entropy of the action imply existence of an off-diagonal asymptotic pair. For algebraic actions of…
We prove several conjectures made by Z.-W. Sun on the existence of permutations conditioned by certain rational functions. Furthermore, we fully characterize all integer values of the "inverse difference" rational function. Our proofs…
The dependency pair (DP) framework is one of the most powerful techniques for automatic termination and complexity analysis of term rewrite systems. While DPs were extended to prove almost-sure termination of probabilistic term rewrite…
Our main result is a generalized Dillon-type theorem, giving graph-theoretic conditions which guarantee that a $p$-ary function in an even number of variables is bent, for $p$ a prime number greater than 2. The key condition is that the…
Cohn and Umans proposed a framework for developing fast matrix multiplication algorithms based on the embedding computation in certain groups algebras. In subsequent work with Kleinberg and Szegedy, they connected this to the search for…