Related papers: A Dynamical approach to Quasi-Analytic type Proble…
We consider the asymptotic behavior of the surface quasi-geostrophic equation, subject to a small external force. Under suitable assumptions on the forcing, we first construct the steady states and we provide a number of useful a posteriori…
We offer an alternative and shorter proof to a result by Jan J.Ub{\o}e about monotonicity properties of a one-dimensional function that appeared in the Mathematical Intelligencer in 2015. Our proof is based on reducing the problem to…
We prove dynamical stability and instability theorems for asymptotically hyperbolic static solutions of Einstein's equation with $\Lambda<0$, viewed as self-similar solutions of the Ricci-harmonic flow. More precisely, we show that static…
We show global existence backwards from scattering data at infinity for semilinear wave equations satisfying the null condition or the weak null condition. Semilinear terms satisfying the weak null condition appear in many equations in…
In a recent paper, Hod has proven no-go theorem for asymptotically flat static regular boson stars. In the present work, we extend discussions to the gravity with a negative cosmological constant. We consider a scalar field vanishing at…
General methods of solving equations deal with solving N equations in N variables and the solutions are usually a set of discrete values. However, for problems with a softly broken symmetry these methods often first find a point which would…
A one-to-one continuous function from a triangle to itself is defined that has both interesting number theoretic and analytic properties. This function is shown to be a natural generalization of the classical Minkowski ?(x) function. It is…
In this paper we prove the existence of a large class of periodic solutions of the Vlasov-Poisson in one space dimension that decay exponentially as t goes to infinity. The exponential decay is well known for the linearized version of the…
In this paper, we study the existence of solutions of the equation $(-\Delta)_1^s u=f$ in a bounded open set with Lipschitz boundary $\Omega\subset \Rn$, vanishing on $\Co \Omega$, for some given $s\in (0,1)$, and asymptotics as $p\to 1$ of…
Let's consider a control system described by the implicit equation $F(x,\dot x) = 0$. If this system is differentially flat, then the following criterion is satisfied : For some integer $r$, there exists a function $\varphi(y_0, y_1,…
In this paper, we contribute to the study of the class $(\Sigma)$. In the first part of the paper, we provide new ways to characterize stochastic processes of the above mentioned class and we derive some new properties. For instance, we…
Let $F$ be a function from $\mathbb{F}_{p^n}$ to itself and $\delta$ a positive integer. $F$ is called zero-difference $\delta$-balanced if the equation $F(x+a)-F(x)=0$ has exactly $\delta$ solutions for all non-zero $a\in\mathbb{F}_{p^n}$.…
We show that a viscosity solution of a uniformly elliptic, fully nonlinear equation which vanishes on an open set must be identically zero, provided that the equation is $C^{1,1}$. We do not assume that the nonlinearity is convex or…
The normal form and zero dynamics are powerful tools useful in analysis and control of both linear and nonlinear systems. There are no simple closed form solutions to the general zero dynamics problem for nonlinear systems. A few algorithms…
In recent years there has been intense interest in the vanishing discount problem for Hamilton-Jacobi equations. In the case of the scalar equation, B. Ziliotto has recently given an example of the Hamilton-Jacobi equation having non-convex…
We study the Ricci flatness condition on generic supermanifolds. It has been found recently that when the fermionic complex dimension of the supermanifold is one the vanishing of the super-Ricci curvature implies the bosonic submanifold has…
The first part of the present article consists in a survey about the dynamical constructive method designed using dynamical theories and dynamical algebraic structures. Dynamical methods uncovers a hidden computational content for numerous…
We study the hole probability of Gaussian random entire functions. More specifically, we work with the flat model (the zero set of this function has a distribution which is invariant with respect to the plane isometries). A hole is the…
Let $F^{+}$ be a mock modular form associated to a normalized newform $g$. K. Bringmann et. al. obtained a $p$-adic modular form starting from $F^{+}$ by adding a suitable linear combination of Eichler integrals of $g(q)$ and $g(q^{p})$. We…
A positive cosmological constant simplifies the asymptotics of forever expanding cosmological solutions of the Einstein equations. In this paper a general mathematical analysis on the level of formal power series is carried out for vacuum…