The lonely runner problem for lacunary sequences

The paper contains a new proof with a small improvement of a theorem of A. Dubickas on The Lonely Runner Conjecture and lacunary sequences. The proof is an adaptation of the Bernshteyn’s proof of the Lopsided Local lemma from his Local Cut Lemma (Bernshteyn, 2017).     

New Poincaré-type inequalities

We present some Poincaré-type inequalities for quadratic matrix fields with applications e.g. in gradient plasticity or fluid dynamics. In particular, applications to the pseudostress–velocity formulation of the stationary Stokes problem and to infinitesimal gradient plasticity are discussed.     

Quasi-steady state in the Michaelis–Menten system

We discuss the differential equations derived from the Michaelis–Menten model of an enzyme-catalyzed reaction, with no a priori conditions on parameters or initial concentrations. Using an elementary approach, we derive and investigate inequalities and conditions for the validity of the quasi-stationary approximation, confirming results by Segel and Slemrod, and determine new estimates for the pre-steady state period.     

Modeling of a vehicle seat suspension system with pneumatic spring and viscous dampers

The paper contains physical and mathematical model of the passive system of seat suspension, used in trucks and buses. Spring force in this system is performed by air spring, whereas damping force is generated by two viscous dampers. Based on the experimental research of characteristic parts of the suspension system, the parameters of mathematical model are determined. Both results of computer simulations and experiments are presented as power spectral density of acceleration courses, measured on seat, in comparison with courses measured on excitation platform in laboratory. Transmissibility of real system and its model are also presented in the paper. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A feasible theory of truth over combinatory algebra

We define an applicative theory of truth _TPT${\mathsf{T}}_{\mathsf{PT}}$ which proves totality exactly for the polynomial time computable functions. _TPT${\mathsf{T}}_{\mathsf{PT}}$ has natural and simple axioms since nearly all its truth axioms are standard for truth theories over an applicative framework. The only exception is the axiom dealing with the word predicate. The truth predicate can only reflect elementhood in the words for terms that have smaller length than a given word. This makes it possible to achieve the very low proof-theoretic strength. Truth induction can be allowed without any constraints. For these reasons the system _TPT${\mathsf{T}}_{\mathsf{PT}}$ has the high expressive power one expects from truth theories. It allows embeddings of feasible systems of explicit mathematics and bounded arithmetic.     

Lawson’s genus two surface and meromorphic connections

We investigate the Lawson genus 2 surface by methods from integrable system theory. To this surface we derive a globally defined meromorphic DPW potential, which is determined up to two unknown functions depending only on the spectral parameter.