Related papers: Residual pathologies
In this paper, we study a general Syracuse problem. We give some necessary conditions concerning the existence of eventual non trivial cycles. Some properties based on linear logarithmic forms are established. New general conjectures are…
The phase transitions and critical properties of two types of inhomogeneous systems are reviewed. In one case, the local critical behaviour results from the particular shape of the system. Here scale-invariant forms like wedges or cones are…
Models of contagion arise broadly both in the biological and social sciences, with applications ranging from the transmission of infectious diseases to the diffusion of innovations and the spread of cultural fads. In this Letter, we…
An old problem in mathematical physics deals with the structure of the dispersion relation of the Schr\"odinger operator $-\Delta+V(x)$ in $R^n$ with periodic potential near the edges of the spectrum. A well known conjecture says that…
We study the limit behaviour of solutions of a class of solutions of nonlinear parabolic equations with a degenerate strong absorption. We prove that two types of phenomena can occur: the pointwise singularity or the formation of razor…
We study an inverse problem for fractional elasticity. In analogy to the classical problem of linear elasticity, we consider the unique recovery of the Lam\'e parameters associated to a linear, isotropic fractional elasticity operator from…
We consider a renewal-like recursion and prove that the solution is polynomially decaying asymptotically under suitable conditions. We prove similar results for the corresponding integral equation. In both cases coefficients and functions…
The subject of the article is linear systems of wave equations on cosmological backgrounds with convergent asymptotics. The condition of convergence corresponds to the requirement that the second fundamental form, when suitably normalised,…
The purpose of this paper is to study a class of ill-posed differential equations. In some settings, these differential equations exhibit uniqueness but not existence, while in others they exhibit existence but not uniqueness. An example of…
Standard regression approaches assume that some finite number of the response distribution characteristics, such as location and scale, change as a (parametric or nonparametric) function of predictors. However, it is not always appropriate…
We describe traveling waves in a basic model for three-dimensional water-wave dynamics in the weakly nonlinear long-wave regime. Small solutions that are periodic in the direction of translation (or orthogonal to it) form an…
The qualitative analysis of the initial value problem P related to a non linear third order parabolic equation typical of diffusive models is discussed. Some basic properties of the the fundamental solution of a related linear operator are…
There are many problems that lead to analysis of dynamical systems in which one can distinguish motions of two types: slow one and fast one. An averaging over fast motion is used for approximate description of the slow motion. First…
We consider high-dimensional estimation problems where the number of parameters diverges with the sample size. General conditions are established for consistency, uniqueness, and asymptotic normality in both unpenalized and penalized…
It is shown that the phenomenon of irreversibility in many-body and few-body systems can be explained and described within the framework of the concept of direct (not instantaneous) interaction of particles without using probabilistic…
On infinitesimally short time interval various processes contributing to population change tend to operate independently so that we can simply add their contributions (Metz and Diekmann (1986)). This is one of the cornerstones for…
The kinematics of particles refer to events and tangent vectors, while that of waves refer to dual gradient planes. Special relativity [1-3] applies to both objects alike. Here we show that spacetime exchange symmetry [7] implicit in the…
We consider three distinct discrete-time models of learning and evolution in games: a biological model based on intra-species selective pressure, the dynamics induced by pairwise proportional imitation, and the exponential / multiplicative…
We view a conic optimization problem that has a unique solution as a map from its data to its solution. If sufficient regularity conditions hold at a solution point, namely that the implicit function theorem applies to the normalized…
We show that for a large class of evolutionary nonlinear and nonlocal partial differential equations, symmetry of solutions implies very restrictive properties of the solutions and symmetry axes. These restrictions are formulated in terms…