Reaction-diffusion equations serve as a basic framework for numerous dynamic phenomena like pattern formation and travelling waves. Spatially discrete analogues of Nagumo reaction-diffusion equation on lattices and graphs provide insights how these phenomena are strongly influenced by the discrete and...

Dynamics of populations with logistic growth leads to global persistence on arbitrary networks, whereas bistable dynamics is always associated with local extinction. In this paper we study a reaction-diffusion model on networks with a combination of both logistic and bistable reactions. We&#...

Existing flank milling path-planning methods typically lead to tiny gaps or overlaps between neighbor-ing paths, which causes artifacts and imperfections in the workpiece. We propose a new multi-strip path-planning method for 5-axis flank milling of free-form surfaces which targets G1 (tangent-pl...

We study the existence of travelling wave solutions of a nonlinear fourth–order partial differential equation which can be considered as a model of an asymmetrically supported beam. We use a variational approach and show that there exist infinitely many travelling wave solutions under&#...

A graph is said to be distance-hereditary if the distance function in every connected induced subgraph is the same as in the graph itself. We prove that the ordinary Weisfeiler-Leman algorithm tests the isomorphism of any two graphs if one of them is distance-hereditary; more&...

For a non-decreasing sequence of positive integers S = (s_1, s_2 , ...), the S-packing chromatic number x_S(G) of a graph G is the smallest integer k such that the vertex set of G can be partitioned into subsets X_i, i \in {1, 2, ... , k}, where vertic...

We are concerned with the existence and qualitative properties of traveling wave solutions for a quasilinear reaction-diffusion equation on the real line. We consider a non-Lipschitz reaction term of Fisher-KPP type and a discontinuous diffusion coefficient that allows for degenerations and ...

Design: A cross-sectional study conducted between September 2016 and September 2019. Settings and participants: A total of 241 undergraduate midwifery students in a convenience sample participated in this study at a Faculty of Health Care Studies (in the Czech Republic). Methods: Data w...

In the first one in this series of two papers, we have proved that every 3‐connected {K(1,3), N(1,3,3)}‐free graph is Hamilton‐connected. In this paper, we continue in this direction by proving that every 3‐connected {K(1,3), X}‐free graph, where X ∈ {N(1,1,5), N(2,2,3)}, is Hamilt...

In several recent publications B-spline functions appeared with control points from abstract algebras, e.g. complex numbers, quaternions or Clifford algebras. In the context of constructions of Pythagorean hodograph curves, computations with these B-splines occur, mixing the components of the control&...

Anorexia nervosa (AN), a pathological restriction of food intake, leads to metabolic dysregulation. We conducted a metabolomics study to reveal changes caused by AN and the effect of hospital realimentation on metabolism. Both stool and serum from patients with AN and healthy controls&#...

A permutation is layered if it contains neither 231 nor 312 as a pattern. It is known that, if σ is a layered permutation, then the density of σ in a permutation of order n is maximized by a layered permutation. Albert, Atkinson, Handley, Holtonand Stromquist [Electr...

We discuss the existence of a continuum of positive weak solutions to a fractional Laplacian problem involving superlinear reaction term when a bifurcation parameter is small. We employ degree theory combined with a re-scaling argument, boundary analysis, and a continuation theorem to o...

An independent transversal of a graph G with a vertex partition P is an independent set of G intersecting each block of P in a single vertex. Wanless and Wood proved that if each block of P has size at least t and the average degree of vertices in each...

We investigate the existence of solutions to the nonlinear problem u′′(x) + λ_+u^+(x) − λ_−u^−(x) + g(x, u(x)) = f (x) , x ∈ (0, 2π) , u(0) = u(2π) , u′(0) = u′(2π) ,where the point [λ_+, λ_−] is a point of the Fučík spectru...

We give a new proof of the Skeletal Lemma, which is the main technical tool in our paper on Hamilton cycles in line graphs (Kaiser and Vrána, 2012). It generalises results on disjoint spanning trees in graphs to the context of 3-hypergraphs. The lemma is proved in&#x...

Nonlinear energy functionals appearing in the calculus of variations can be discretized by the finite element (FE) method and formulated as a sum of energy contributions from local elements. A fast evaluation of energy functionals containing the first order gradient terms is a cent...

Using symmetrization techniques, we show that, for every N>=2, any second eigenfunction of the fractional Laplacian in the N-dimensional unit ball with homogeneous Dirichlet conditions is nonradial, and hence its nodal set is an equatorial section of the ball.

In this paper, we deal with the optimal choice of the parameter gamma for augmented Lagrangian preconditioning of GMRES method for efficient solution of linear systems obtained from discretization of the incompressible Navier-Stokes equations. We consider discretization of the equations using...

This is the first one in a series of two papers, in which we complete the characterization of forbidden generalized nets implying Hamilton‐connectedness of a 3‐connected claw‐free graph. In this paper, we first develop the necessary techniques that allow one to handle the problem,&...