We study a nonlinear eigenvalue problem on the exterior to a simply connected bounded domain inRN containing the origin.We consider positive weak solutions satisfying Dirichlet boundary conditions on the compact boundary and decaying to zero at infinity. We discuss multiplicity and uniquenes...

A signed circuit is a minimal signed graph (with respect to inclusion) that admits a nowhere-zero flow. We show that each flow-admissible signed graph on m edges can be covered by signed circuits of total length at most (3+2/3)m, improving a recent result of Cheng et...

We obtain Caccioppoli-type estimates for nontrivial and nonnegative solutions to anticoercive partial differential inequalities of elliptic type involving weighted p-Laplacian. Using Caccioppoli-type estimates, we obtain several variants of Hardy-type inequalities in weighted Sobolev spaces.

Methods using Pythagorean hodographs both in Euclidean plane and Minkowski space are often used in geometric modelling when necessary to solve the problem of rationality of offsets of planar domains. A main justification for studying and formulating approximation and interpolation algorithms ...

In this paper we study quasilinear homogeneous eigenvalue problem with the p-Laplacian involving singular weights. We work on a bounded domain with Lipschitzian boundary and the weights are negative powers of the distance from the boundary. We generalize results concerning the existence ...

Aims: The retrospective study assessed outcomes of orthodontic treatment using fixed appliance and clear plastic aligner with PAR index, and compared effectiveness of the therapy with TEI (treatment efficiency index). Another aim was to compare the number of occlusal contacts and assess ...

In this study, the combination of metabolomics and standard biochemical and biometric parameters was used to describe the metabolic effects of diet-induced obesity and its treatment with the novel antiobesity compound palm11-PrRP31 (palmitoylated prolactin-releasing peptide) in spontaneously hypertensive r...

Diet is a major factor determining gut microbiota composition and perturbances in this complex ecosystem are associated with the inflammatory bowel disease (IBD). Here, we used gnotobiotic approach to analyze, how interaction between diet rich in proteins and gut microbiota influences the&#x...

We show that the elliptic equation with non-Lipschitz right-hand side, considered on a smooth star-shaped domain Ω subject to zero Dirichlet boundary conditions, might possess a nonnegative ground state solution which violates Hopf’s maximum principle only on a nonempty subset Γ of the&...

A digraph in which, for every pair of vertices u and v (not necessarily distinct), there is at most one walk of length at most k from u to v is called a k-geodetic digraph. The order N(d,k) of a k-geodetic digraph of minimum out-degree d is at least th...

Analysis of bioactive lipids in adipose tissue could lead to better understanding of the pathogenesis of obesity and its complications. However, current MS methods are limited by a high content of triacylglycerols (TAGs), which markedly surpasses the amount of other lipids and suppresse...

There are two basic ways of weakening the definition of the well-known metric regularity property by fixing one of the points involved in the definition. The first resulting property is called metric subregularity and has attracted a lot of attention during the last decades. O...

We consider the implicit discretization of Nagumo equation on finite lattices and show that its variational formulation corresponds in various parameter settings to convex, mountain-pass or saddle-point geometries. Consequently, we are able to derive conditions under which the implicit discretization&...

The long-term fiscal outlook of most high-income countries is grim. Should independent central bankers be afraid of an unpleasant monetarist arithmetic, i.e., fiscal imbalances spilling over to monetary policy and jeopardizing price stability? To provide some insights, this paper tracks the ...

We study {K(1,3),Y}-free graphs, and show that the following three statements are equivalent: (1) every connected {K(1,3),Y}-free graph which is distinct from an odd cycle and which has independence number at least 3 is perfect; (2) every connected {K(1,3),Y}-free graph which is distinc...

Elastic thickness (Te) is a parameter representing the lithospheric strength with respect to the loading. Those places, having large values of elastic thickness, flexes less. In this paper, the on-orbit measured gravitational gradients of the Gravity field and steady-state Ocean Circulation ...

We estimate the elastic thickness of a continental lithosphere by using two approaches that combine the Vening Meinesz-Moritz (VMM) regional isostatic principle with isostatic flexure models formulated based on solving flexural differential equations for a thin elastic shell with and without ...

In this paper we consider the classification of uniquelly regular Grothendick dessins with nilpotent automorphism groups. The problem is reduced to the classification of finite maximally automorphic p-groups.

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...

Existence, uniqueness and continuous dependence results together with maximum principles represent key tools in the analysis of lattice reaction-diffusion equations. In this paper, we study these questions in full generality by considering nonautonomous reaction functions, possibly nonsymmetric diffusion a...