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Kleene's computability theory based on the S1-S9 computation schemes constitutes a model for computing with objects of any finite type and extends Turing's 'machine model' which formalises computing with real numbers. A fundamental…

Logic · Mathematics 2024-01-17 Sam Sanders

Kleene's computability theory based on his S1-S9 computation schemes constitutes a model for computing with objects of any finite type and extends Turing's `machine model' which formalises computing with real numbers. A fundamental…

Logic · Mathematics 2023-02-15 Sam Sanders

Let $K$ be a prime knot in $S^3$ and $G(K)=\pi_1(S^3-K)$ the knot group. We write $K_1 \geq K_2$ if there exists a surjective homomorphism from $G(K_1)$ onto $G(K_2)$. In this paper, we determine this partial order on the set of prime knots…

Geometric Topology · Mathematics 2009-06-23 Keiichi Horie , Teruaki Kitano , Mineko Matsumoto , Masaaki Suzuki

Baker's conjecture states that a transcendental entire function of order less than $1/2$ has no unbounded Fatou components. It is known that, for such functions, there are no unbounded periodic Fatou components and so it remains to show…

Complex Variables · Mathematics 2015-02-10 D. A. Nicks , P. J. Rippon , G. M. Stallard

We consider the Lambek calculus, or non-commutative multiplicative intuitionistic linear logic, extended with iteration, or Kleene star, axiomatised by means of an $\omega$-rule, and prove that the derivability problem in this calculus is…

Logic · Mathematics 2023-06-22 Stepan Kuznetsov

We classify the possible ramification data and etale local structure of orders over surfaces with canonical singularities.

Rings and Algebras · Mathematics 2014-02-26 Daniel Chan , Paul Hacking , Colin Ingalls

In this article, we investigate the existence and uniqueness of weak solutions to the continuous coagulation equation with collisional breakage for a class of unbounded collision kernels and distribution function. The collision kernels and…

Analysis of PDEs · Mathematics 2018-06-12 Prasanta Kumar Barik , Ankik Kumar Giri

In this paper we study the existence of radially symmetric solitary waves in R^N for the nonlinear Klein-Gordon equations coupled with the Maxwell's equations when the nonlinearity exhibits critical growth. The main feature of this kind of…

Analysis of PDEs · Mathematics 2013-10-11 Paulo C. Carriao , Patricia L. Cunha , Olimpio H. Miyagaki

We prove that a non-affine latin quandle (also known as left distributive quasigroup) of order $2^k$ exists if and only if $k = 6$ or $k \geq 8$. The construction is expressed in terms of central extensions of affine quandles.

Group Theory · Mathematics 2020-02-28 Tomáš Nagy

We prove that, unless assuming additional set theoretical axioms, there are no reflexive space without unconditional sequences of density the continuum. We give for every integer $n$ there are normalized weakly-null sequences of length…

Functional Analysis · Mathematics 2011-11-23 J. Lopez-Abad , S. Todorcevic

We study a nonlinear equation with an elliptic operator having degenerate coercivity. We prove the existence of a W^{1,1}_0 solution which is distributional or entropic, according to the growth assumptions on a lower order term in…

Analysis of PDEs · Mathematics 2012-06-19 Lucio Boccardo , Gisella Croce , Luigi Orsina

This article is devoted to studying individual ergodic theorems for subsequential weighted ergodic averages on the noncommutative Lp-spaces associated to a semifinite von Neumann algebra M. In particular, we establish the convergence of…

Operator Algebras · Mathematics 2022-11-01 Morgan O'Brien

We formulate and verify a non-Archimedean analogue of Chase's lemma. Following the framework by K.\ Eda removing restriction of cardinality from analogy on direct product between countability and non-$\omega_1$-measurability, we extend the…

Logic · Mathematics 2026-04-07 Tomoki Mihara

We study the one-dimensional nonlinear Klein-Gordon (NLKG) equation with a convolution potential, and we prove that solutions with small $H^s$ norm remain small for long times. The result is uniform with respect to $c \geq 1$, which however…

Analysis of PDEs · Mathematics 2018-02-14 Stefano Pasquali

We introduce the idea of a weakly entangled linear order, and show that it is consistent for a Suslin line to be weakly entangled. We generalize the notion of entangled linear orders to $\omega_1$-trees, and prove that an $\omega_1$-tree is…

Logic · Mathematics 2020-04-28 John Krueger

Revisiting and completing a work due to A. I. Ba\v{s}kirov, we construct compact sequential spaces of any sequential order up to and including $\omega_1$ as quotient spaces of $\beta\omega$ under CH.

General Topology · Mathematics 2010-01-07 Chiara Baldovino

Turing's famous 'machine' model constitutes the first intuitively convincing framework for computing with real numbers. Kleene's computation schemes S1-S9 extend Turing's approach and provide a framework for computing with objects of any…

Logic · Mathematics 2021-10-20 Dag Normann , Sam Sanders

We focus on formulae $\exists X.\, \varphi(\vec{Y}, X)$ of monadic second-order logic over the full binary tree, such that the witness $X$ is a well-founded set. The ordinal rank $\mathrm{rank}(X) < \omega_1$ of such a set $X$ measures its…

Logic in Computer Science · Computer Science 2025-12-16 Damian Niwiński , Paweł Parys , Michał Skrzypczak

A longstanding open problem is whether there exists a non syntactical model of the untyped lambda-calculus whose theory is exactly the least lambda-theory (l-beta). In this paper we investigate the more general question of whether the…

Logic · Mathematics 2008-12-18 Chantal Berline , Giulio Manzonetto , Antonio Salibra

Ordinary differential equation (ODE) is widely used in modeling biological and physical processes in science. In this article, we propose a new reproducing kernel-based approach for estimation and inference of ODE given noisy observations.…

Methodology · Statistics 2021-10-26 Xiaowu Dai , Lexin Li