Related papers: Monotonicity results and bounds for the inverse hy…
Some inequalities for different types of convexity are established.
In this paper, we use the inverse curvature flow to prove a sharp geometric inequality on star-shaped and two-convex hypersurface in hyperbolic space.
In the paper, the authors review origins, motivations, and generalizations of a series of inequalities involving several exponential functions and sums, establish three new inequalities involving finite exponential functions and sums by…
This note remarks that small-gain results for a negative feedback loop around a monotone system can be seen as consequences of results concerning an extended monotone system.
The {\it curvature} and the {\it reduced curvature} are basic differential invariants of the pair: (Hamiltonian system, Lagrange distribution) on the symplectic manifold. We show that negativity of the curvature implies that any bounded…
We consider nonlinear perturbations of the hyperbolic equation in the Hilbert space. Necessary and sufficient conditions for the existence of solutions of boundary-value problem for the corresponding equation and iterative procedures for…
The vector form of a Lorentz transformation which is separated with time and space parts is studied. It is necessary to introduce a new definition of the relative velocity in this transformation, which plays an important role for the…
Systems of orthogonal polynomials whose recurrence coefficients tend to infinity are considered. A summability condition is imposed on the coefficients and the consequences for the measure of orthogonality are discussed. Also discussed are…
In this paper we present an overview of results for discrete trigonometric and hyperbolic systems. These systems are discrete analogues of trigonometric and hyperbolic linear Hamiltonian systems. We show results which can be viewed as…
We prove the isodiametric inequality in the spherical and in the hyperbolic space
We discuss a time-harmonic inverse scattering problem for the Helmholtz equation with compactly supported penetrable and possibly inhomogeneous scattering objects in an unbounded homogeneous background medium, and we develop a monotonicity…
In this paper, we prove the short-time existence of hyperbolic inverse (mean) curvature flow (with or without the specified forcing term) under the assumption that the initial compact smooth hypersurface of $\mathbb{R}^{n+1}$…
A dimension reduction for the hyperbolic space is established. When points are far apart an embedding with bounded distortion into the hyperbolic plane is achieved.
We introduce in this document a direct method allowing to solve numerically inverse type problems for linear parabolic equations. We consider the reconstruction of the full solution of the parabolic equation posed in $\Omega\times (0,T)$ -…
In this paper, we study the monotonicity of parabolic frequency motivated by \cite{frequency on RF} under the Ricci flow and the Ricci-harmonic flow on manifolds. Here we consider two cases: one is the monotonicity of parabolic frequency…
We consider invertible discrete-time dynamical systems having a hyperbolic product structure in some region of the phase space with infinitely many branches and variable recurrence time. We show that the decay of correlations of the SRB…
In this article we are interested in the boundary stabilization in finite time of one-dimensional linear hyperbolic balance laws with coefficients depending on time and space. We extend the so called "backstepping method" by introducing…
We review some old and new results about strict and non strict hyperbolic formulations of the Einstein equations.
We define finite-time hyperbolic coordinates, describe their geometry, and prove various results on both their convergence as the time scale increases, and on their variation in the state space. Hyperbolic coordinates reframe the classical…
We introduce the theory of operator monotone functions and employ it to derive a new inequality relating the quantum relative entropy and the quantum conditional entropy. We present applications of this new inequality and in particular we…