We investigate the Fredholm alternative for the p-Laplacian in an exterior domain which is the complement of the closed unit ball in R^N (N ≥ 2). By employing techniques of Calculus of Variations we obtain the multiplicity of solutions. The striking difference between our case...

We show that some sufficient conditions for hamiltonian properties of claw-free graphs can be substantially strengthened under an additional assumption that G is hourglass-free (where hourglass is the graph with degree sequence 4, 2, 2, 2, 2).

It is easy to see that in a connected graph any 2 longest paths have a vertex in common. For k >= 7, Skupień in 1966 obtained a connected graph in which some longest paths have no common vertex, but every k - 1 longest paths have a common vertex.&#x...

We describe the historical process of derivation of the p-Laplace operator from a nonlinear Darcy law and the continuity equation. The story begins with nonlinear flows in channels and ditches. As the nonlinear Darcy law we use the power law discovered by Smreker and verified&...

Invasive pulmonary aspergillosis results in 450,000 deaths per year and complicates cancer chemotherapy, transplantations and the treatment of other immunosuppressed patients. Using a rat model of experimental aspergillosis, the fungal siderophores ferricrocin and triacetylfusarinine C were identified as m...

The square of a graph G, denoted G^2, is the graph obtained from G by joining by an edge any two nonadjacent vertices which have a common neighbor. A graph G is said to have F_k property if for any set of k distinct vertices {x_1,x_2,...,x_k} in G, there&#x...

Given a triangle-free planar graph G and a 9-cycle C in G, we characterize situations where a 3-coloring of C does not extend to a proper 3-coloring of G. This extends previous results when C is a cycle of length at most 8.

Aim: The aim of the study was to compare digital and plaster orthodontic models with the emphasis on the reliability of measurements performed in digital and physical form. Another aim was to evaluate the way of how digital and plaster models are made and to assess p...

We provide global variational characterization of the Fucik spectrum for the Laplace operator and the results apply to nonresonance and resonance problems.

A d-interval is a union of at most d disjoint closed intervals on a fixed line. Tardos [Combinatorica 15 (1995), 123-134] and the second author [Disc. Comput. Geom. 18 (1997), 195-203] used topological tools to bound the transversal number τ of a family H of d-intervals&#...

It is shown that a 3-edge connected cubic graph has a dominating even subgraph in which every component contains at least six vertices.

Nešetřil and Ossona de Mendez introduced the notion of first order convergence as an attempt to unify the notions of convergence for sparse and dense graphs. It is known that there exist first order convergent sequences of graphs with no limit modeling (an analytic representat...

We study a class of semipositone elliptic systems depending on a parameter using bifurcation theory. We show that there are two disjoint unbounded connected components of the solution set and discuss the nodal properties of solutions on these components. Finally, as a consequence o...

Although the property of strong metric subregularity of set-valued mappings has been present in the literature under various names and with various (equivalent) definitions for more than two decades, it has attracted much less attention than its older “siblings”, the metric regularity a...

In this note, after a review of results about abstract doubly nonlinear evolution equations ddtBu+Au=f with non-potential operators B, we consider systems of doubly nonlinear reaction–diffusion equations ∂v∂t−div(a(∇u))=f and concentrate on the one hand on static relations v = b(u) between u...

This paper is focused on numerical solving of RANS (Reynolds-Averaged Navier-Stokes) equation with k-omega model for simulation of turbulent flows in 3D. The solver which is based on a recently proposed approach called isogeometric analysis is presented. This numerical method is based o...

An essentially k-edge connected graph G is a connected graph such that deleting less than k edges from G cannot result in two nontrivial components. In this paper we prove that if an essentially 2-edge-connected graph G satisfies that for any pair of leaves at distance&#x...

Let G be a regular bipartite graph and X ⊆ E (G). We show that there exist perfect matchings of G containing both, an odd and an even number of edges from X if and only if the signed graph (G, X ) is not equivalent to (G, ∅). In fact, we ...

We survey known results related to nowhere-zero flows and related topics, such as circuit covers and the structure of circuits of signed graphs. We include an overview of several di↵erent definitions of signed graph colouring.

The popularity and business impact of major sports have been growing globally over time. This paper focuses on ice hockey, specifically the National Hockey League in North America. It reports a striking irregularity in ice hockey’s scoring dynamics relative to comparable sports such...