相关论文: Generalizations of the Recursion Theorem

We present a closed-form solution for n-th term of a general three-term recurrence relation with arbitrary given n-dependent coefficients. The derivation and corresponding proof are based on two approaches, which we develop and describe in…

This paper provides a uniform explanation of different extensions and generalizations of the butterfly theorem based on the Desargues involution theorem.

This paper explores the proof by J. Bourgain, H. Furstenberg, Y. Katznelson and D.S. Ornstein of their return times theorem [2] and lights a corner in it regarding the role of auto-correlation. As for pointwise convergence, this was already…

The problem of when the vanishing of a (generalized) Schur complement of a block matrix (corresponding to the leading principal subblock) implies that the other (generalized) Schur complement (corresponding to the trailing principal…

We give an abstract approach to the results of Adams and Nobel, [1]. It allows to exhibit a new property of VC classes. It should be stressed that the basic ideas of proofs can be found in [1].

We extend the criterion on the existence of telescopers for hypergeometric terms to the case of P-recursive sequences. This criterion is based on the concept of integral bases and the generalized Abramov-Petkovsek reduction for P-recursive…

We present two possible generalisations of Roth's approximation theorem on proper adelic curves, assuming some technical conditions on the behavior of the logarithmic absolute values. We illustrate how tightening such assumptions makes our…

We present a dual of a family of partition identities of Andrews involving partitions with no repeated odd parts (among other conditions), along with an overpartition generalization that encapsulates both families. These were discovered…

The scaling theory of irreversible aggregation is discussed in some detail. First, we review the general theory in the simplest case of binary reactions. We then extend consideration to ternary reactions, multispecies aggregation,…

We study compressible types in the context of (local and global) NIP. By extending a result in machine learning theory (the existence of a bound on the recursive teaching dimension), we prove density of compressible types. Using this, we…

This work is, in part, a generalization of the article by A.A. Bruen ,T.C Bruen and J.M.McQuillan on Desargues Theorem in arXiv:2007.09175[mathCO]July 17,2020. We prove the extension of Desargues theorem in all dimensions, using 4 different…

We show that varieties of dimension at least 2 over infinite fields are determined as abstract schemes by their Zariski topological spaces together with the rational equivalence relation on the set of effective divisors. This gives a…

We consider pseudo-Riemannian generalizations of Osserman, Clifford, and the duality principle properties for algebraic curvature tensors and investigate relations between them. We introduce quasi-Clifford curvature tensors using a…

We introduce a GP generalization of ResNets (including ResNets as a particular case). We show that ResNets (and their GP generalization) converge, in the infinite depth limit, to a generalization of image registration variational…

We define a generalization of the Turing machine that computes on general sets. Our main theorem states that the class of generalized Turing machine computable functions and the class of Set Recursive functions coincide.

It is shown that a 4-recollement of derived categories of CM-finite algebras induces a 2-recollement of the corresponding Cohen-Macaulay Auslander algebras, which generalises the main theorem of Pan [S. Y. Pan, Derived equivalences for…

The aim of this article is to introduce Vogel's localization theorem for classes of D-complexes: this generalization of Waldhausen's localization theorem is especially useful and powerful in that it gives an explicit and computable…

Kolmogorov's axioms of probability theory are extended to conditional probabilities among distinct (and sometimes intertwining) contexts. Formally, this amounts to row stochastic matrices whose entries characterize the conditional…

We present new generalized Cline's formula and Jacobson's lemma for the g-Drazin inverse in a ring. These extend many known results, e.g., Chen and Abdolyousefi (Generalized Jacobson's Lemma in a Banach algebra, Comm. Algebra, {\bf…

Next-to-leading logarithmic final-state resummed predictions have traditionally been calculated, manually, separately for each observable. In this article we derive NLL resummed results for generic observables. We highlight and discuss the…