We characterise the pairs of graphs {X, Y} such that all {X, Y}-free graphs(distinct from C5) are perfect. Similarly, we characterise pairs {X, Y} such that all {X, Y}-free graphs (distinct from C5) are ω-colourable (that is, their chromatic number is equal to their clique...

For every graph X, we consider the class of all connected {K(1,3), X}-free graphs which are distinct from an odd cycle and have independence number at least 4, and we show that all graphs in the class are perfect if and only if X is an induced subgraph of&#...

In this paper, we perform robustness and sensitivity analysis of several continuous-time stochastic volatility (SV) models with respect to the process of market calibration. The analyses should validate the hypothesis on importance of the jump part in the underlying model dynamics. Also ...

This paper is devoted to a problem from geometric modelling and related applications when exact symbolic computations are sometimes used also on objects given inexactly, i.e., when it is not adequately respected that numerical or input errors may significantly influence fundamental propertie...

We investigate some strong comparison principles for nonnegative solutions to several parabolic problems with the p-Laplace operator in one space dimension. We focus on the special case of comparing a stationary (i.e., time-independent) solution with a time-dependent solution. We take advantage&#...

A reaction–diffusion system exhibiting Turing’s diffusion driven instability is considered. The equation for an activator is supplemented by unilateral terms of the type $s_{−}(x)u^{−}, s_{+}(x)u^{+}$ describing sources and sinks active only if the concentration decreases below and increases above, re...

A periodic behavior is a well observed phenomena in biological and economical systems. We show that evolutionary games on graphs with imitation dynamics can display periodic behavior for an arbitrary choice of game theoretical parameters describing social-dilemma games. We construct graphs a...

We show that every k-tree of toughness greater than k/3 is Hamilton-connected for k >= 3. (In particular, chordal planar graphs of toughness greater than 1 are Hamilton-connected.) This improves the result of Broersma et al. (2007) and generalizes the result of Böhme et...

Using the variational structure of the second order periodic problems we find an optimal impulsive control which forces the conservative system into a periodic motion. In particular, our main results concern the system of charged planar pendulums with external disturbances and neglected ...

This article presents a new family of solutions to the singularly perturbed Allen-Cahn equation α2Δu + u(1 − u2) = 0 in a smooth bounded domain Ω ⊂ R3, with Neumann boundary condition and α > 0 a small parameter. These solutions have the property that as α&#x...

This paper deals with the problem of nonparametric kernel estimation, particularly nonparametric kernel estimation of regression function in real life situations. There are many fields of application (Gross Domestic Product, Unemployment, Stock Market, etc.) and therefore this paper is focused on...

We study the existence of steady states to the Keller–Segel system with linear chemotactical sensitivity function on a smooth bounded domain in RN,N≥3, having rotational symmetry. We find three different types of chemoattractant concentration which concentrate along suitable (N−2)-dimensional minimal&...

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.

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...