We formulate some term rewriting systems in which the number of computation steps is finite for each output, but this number cannot be bounded by a provably total computable function in Peano arithmetic PA. Thus, the termination of such systems is unprovable in PA. These systems are derived from an independent combinatorial result known as the Worm principle; they can also be viewed as versions of the well-known Hercules-Hydra game introduced by Paris and Kirby.
We study the dynamics of Smale-Vietoris diffeomorphisms
We construct a full exceptional collection of vector bundles in the bounded derived category of coherent sheaves on the Grassmannian IGr(3,8) of isotropic 3-dimensional subspaces in an 8-dimensional symplectic vector space.
Homology groups of spaces of nonsingular polynomial embeddings R1→Rn of degrees ≤4 are calculated. A general algebraic technique of such calculations for spaces of polynomial knots of arbitrary degrees is described.
We consider the Paley--Wiener spaces of L2 -functions whose Fourier transform has a bounded support. We show that every continuous mapping that generates a superposition operator acting on these spaces is affine and injective.
New lower bounds are obtained for the number N_B(x) of Novák numbers not exceeding the given quantity x. In addition, conditioned on the generalized Riemann Hypothesis, upper bounds are found for the number of prime factors of Novák numbers and a description of the prime factors of Novák numbers N such that 2N is a Novák-Carmichael number is presented.
We solve a technical problem related to adeles on an algebraic surface. Given a finite set of natural numbers up to two, one associates an adelic group. We show that this operation commutes with taking intersections if the surface is defined over an uncountable field and we provide a counterexample otherwise.
We study regular global attractors of dissipative dynamical semigroups with discrete and continuous time and we investigate attractors for non-autonomous perturbations of such semigroups. The main theorem states that regularity of global attractors preserves under small non-autonomous perturbations. Besides, non-autonomous regular global attractors remain exponential and robust. We apply these general results to model non-autonomous reaction-diffu\-sion systems in a bounded domain of R^3 with time-dependent external forces.