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,&...

The generalized bull is the graph B(i,j) obtained by attaching endvertices of two disjoint paths of lengths i, j to two vertices of a triangle. We prove that every 3‐connected {K(1,3), X}‐free graph, where X ∈ {B(1,6), B(2,5),B(3,4)}, is Hamilton‐connected. The results are sharp&#x...

Aim: The aim of the presented work was to establish the success rate of spontaneous eruption of teeth (with incomplete roots development) with dentigerous (follicular) cyst into the mouth cavity after completed cystectomy. Further, the position of impacted teeth with obstacles represented&#x...

The weak and strong comparison principles (WCP and SCP, respectively) are investigated for quasilinear elliptic boundary value problems with the p-Laplacian in one space dimension, Δp(u) =d/dx(|u'|p−2u'). We treat the “degenerate” case of 2 <p <∞ and allow also for the non...

In this paper, we characterize all pairs of (possibly disconnected) graphs R, S such that (i) every 2‐connected {R, S}‐free graph of sufficiently large order has a 2‐factor, and (ii) every connected {R, S}‐free graph of sufficiently large order with minimum degree at least two...

We investigate automorphism groups of planar graphs. The main result is a complete recursive description of all abstract groups that can be realized as automorphism groups of planar graphs. The characterization is formulated in terms of inhomogeneous wreath products. In the proof, we&#x...

We derive conditions ensuring that the range of a set-valued mapping with a compact convex domain covers a prescribed set. In Fréchet spaces, we consider approximations by one single-valued mapping such that the inverse of it has convex fbers. Subsequently, in Banach and finite-dim...

We study existence of solutions for a boundary degenerate (or singular) quasilinear equation in a smooth bounded domain under Dirichlet boundary conditions. We consider a weighted p−Laplacian operator with a coefficient that is locally bounded inside the domain and satisfying certain additio...

We derive conditions ensuring that the range of a given continuous mapping with a compact convex domain covers a prescribed set. In Fréchet spaces, we consider approximations by one single-valued mapping such that the inverse of it has either convex fibers or admits a continuo...

We formulate a simple algorithm for computing global exact symmetries of closed discrete curves in the plane. The method is based on a suitable trigonometric interpolation of vertices of the given polyline and consequent computation of the symmetry group of the obtained trigonometric&#x...