The weak chromatic number, or clique chromatic number (CCHN) of a graph is the minimum number of colors in a vertex coloring, such that every maximal clique gets at least two colors. The weak chromatic index, or clique chromatic index (CCHI) of a graph is the CCHN&#x...

We study the Nagumo reaction–diffusion equation on graphs and its dependence on the underlying graph structure and reaction–diffusion parameters. We provide necessary and sufficient conditions for the existence and nonexistence of spatially heterogeneous stationary solutions. Furthermore, we observe that&#...

IA sum graph G is a graph with a mapping of the vertex set of G onto a set of positive integers S in such a way that two vertices of G are adjacent if and only if the sum of their labels is an element of S. In an exclusive sum graph ...

Say that a class of ultrafilters exists generically if every filter base of size < c can be extended to an ultrafilter in that class. We investigate generic existence of ultrafilters defined in terms of ideals on the natural numbers, like the summable ultrafilters and ...

This paper brings a revision of the so far known uniqueness result for a onedimensional damped model of a suspension bridge. Using standard techniques, however with finer arguments, we provide a significant improvement and extension of the allowed interval for the stiffness parameter.

Liraglutide is the glucagon-like peptide-1 receptor agonist widely used for the treatment of type 2 diabetes mellitus. Recently, it has been demonstrated to decrease cardiovascular morbidity and mortality in patients with type 2 diabetes and high cardiovascular risk. Although the major modes...

We study the regularity criteria for the incompressible Navier-Stokes equations in the whole space $\mathbb{R}^3$ based on one velocity component, namely $u_3$, $\nabla u_3$ and $\nabla^2 u_3$. We use a generalization of the Troisi inequality and anisotropic Lebesgue spaces and pro...

We study snarks whose edges cannot be covered by fewer than five perfect matchings. Esperet and Mazzuoccolo found an infinite family of such snarks, generalising an example provided by Hägglund. We construct another infinite family, arising from a generalisation in a different direction...

In this paper, we introduce a unifying approach to option pricing under continuous-time stochastic volatility models with jumps. For European style options, a new semi-closed pricing formula is derived using the generalized complex Fourier transform of the corresponding partial integro-differential&#x...

The article is devoted to the simulation of viscous incompressible turbulent fluid flow based on solving the Reynolds averaged Navier–Stokes (RANS) equations with different k−omega models. The isogeometrical approach is used for the discretization based on the Galerkin method. Primary goal o...

We prove the existence and uniqueness result for positone problem in the exterior domain with the singular term near zero. The method of sub and supersolutions is applied.

In this paper, we investigate the local stability of critical points with energy that is higher than the ground-state energy of the functional associated with the bistable equation. We assume that a double-well potential lacks C^2 regularity at the global minimizers. Previous work ...

Aims: The study focused on the evaluation of changes in upper and lower dental arch following rapid palatal expansion (RPE) in mixed dentition and the expansion stability into the permanent dentition. Material: The first sample (HYRAX group) included 31 patients with RPE in mixed&#...

We discuss several properties of eigenvalues and eigenfunctions of the p-Laplacian on a ball subject to zero Dirichlet boundary conditions. Among main results, in two dimensions, we show the existence of nonradial eigenfunctions which correspond to the radial eigenvalues.

We present the existence of positive solutions for a degenerate (or singular) quasilinear equation in a ball or in the entire space. As differential operator we consider a weighted p-Laplacian with a continuous cofficient satisfying a mild integrability condition towards the boundary of...

In a paper of 1950 Graves proved that for a function f acting between Banach spaces and an interior point x in its domain, if there exists a continuous linear mapping A which is surjective and the Lipschitz modulus of the difference f-A at x is sufficiently smal...

We prove a necessary and sufficient conditions for discreteness of the set of all eigenvalues of half–linear eigenvalue problem with locally integrable weights. Our conditions appear to be equivalent to the compact embedding of certain weighted Sobolev and Lebesgue spaces.

In this article, we study a long memory stochastic volatility model (LSV), under which stock prices follow a jump-diffusion stochastic process and its stochastic volatility is driven by a continuous-time fractional process that attains a long memory. LSV model should take into account&#...

Pentagonal tiling is a tiling or tessellation of the plane where each piece (tile) is a pentagon. We describe classification, history and some properties of pentagonal tiling.

Metformin, vildagliptin and their combination are widely used for the treatment of diabetes, but little is known about the metabolic responses to these treatments. In the present study, NMR-based metabolomics was applied to detect changes in the urinary metabolomic profile of a mouse&#x...