相关论文: Algebraic estimates, stability of local zeta funct…

In 1970s, a method was developed for integration of nonlinear equations by means of algebraic geometry. Starting from a Lax representation with spectral parameter, the algebro-geometric method allows to solve the system explicitly in terms…

We establish square function estimates for integral operators on uniformly rectifiable sets by proving a local $T(b)$ theorem and applying it to show that such estimates are stable under the so-called big pieces functor. More generally, we…

For a hyperbolic map f on a saddle type fractal Lambda with self-intersections, the number of f- preimages of a point x in Lambda may depend on x. This makes estimates of the stable dimensions more difficult than for diffeomorphisms or for…

Oscillatory integrals arise in many situations where it is important to obtain decay estimates which are stable under certain perturbations of the phase. Examining the structural problems underpinning these estimates leads one to consider…

We carry out a stability analysis for the real space split operator method for the propagation of the time-dependent Klein-Gordon equation that has been proposed Ruf et al. [M. Ruf, H. Bauke, C.H. Keitel, A real space split operator method…

We study pairs $(f, \Gamma)$ consisting of a non-Archimedean rational function $f$ and a finite set of vertices $\Gamma$ in the Berkovich projective line, under a certain stability hypothesis. We prove that stability can always be attained…

We establish two new estimates which control a function (after subtracting its average) in $L^1$ by only the $L^1$ norm of its radial derivative. While the interior estimate holds for all superharmonic functions, the boundary version is…

This paper contains two main contributions. First, it provides optimal stability estimates for advection-diffusion equations in a setting in which the velocity field is Sobolev regular in the spatial variable. This estimate is formulated…

As is known, every finite-dimensional algebra over a field is isomorphic to the centralizer algebra of \textbf{two} matrices. So it is fundamental to study first the centralizer algebra of a single matrix, called a centralizer matrix…

It is shown that for $A_\R(\D)$ functions $f_1$ and $f_2$ with $$ \inf_{z\in\bar{\D}}(\abs{f_1(z)}+\abs{f_2(z)})\geq\delta>0 $$ and $f_1$ being positive on real zeros of $f_2$ then there exists $A_\R(\D)$ functions $g_2$ and $g_1,g_1^{-1}$…

In this article we discuss the role of stability functions in geometric invariant theory and apply stability function techniques to problems in toric geometry. In particular we show how one can use these techniques to recover results of…

An easy-to-use and effective formula for stability testing of a system with fractional-delay characteristic equation in the general form of $\Delta(s)=P_0(s)+\sum_{i=1}^N P_i(s)\exp(-\zeta_i s^{\beta_i}) =0$, where $P_i(s)$ ($i=0,..., N$)…

An integro-differential equation, modeling dynamic fractional order viscoelasticity, with a Mittag-Leffler type convolution kernel is considered. A discontinuous Galerkin method, based on piecewise constant polynomials is formulated for…

We present a new stability and error analysis of fully discrete approximation schemes for the transient Stokes equation. For the spatial discretization, we consider a wide class of Galerkin finite element methods which includes both inf-sup…

In earlier work we developed the theory of signatures of hermitian forms over algebras with involution with respect to orderings on the base field of the algebra and obtained in particular that the total signature of a hermitian form is a…

Petr Novotn\'y and Ji\v{r}\'l Hrivn\'ak \cite{Nov} investigated generalize the concept of Lie derivations via certain complex parameters and obtained various Lie and Jordan operator algebras as well as two one- parametric sets of linear…

The algebraic stability theorem for $\mathbb{R}$-persistence modules is a fundamental result in topological data analysis. We present a stability theorem for $n$-dimensional rectangle decomposable persistence modules up to a constant…

We first study geometrically oriented truncation associated with stability along the line of Arthur's analytic truncation. Then, we give a detailed discussion on the so-called Abelian Parts of non-abelian L functions, using an advanced…

A short intrinsic proof is given for the Bourgain-Brezis-Mironescu theorem with an extension for higher-order gradient forms. This argument illustrates the role of functional geometry and Fourier analysis for obtaining embedding estimates.…

We prove H\"{o}lder-logarithmic stability estimates for the problem of finding an integrable function $v$ on $\mathbb{R}^d$ with a super-exponential decay at infinity from its Fourier transform $\mathcal{F} v$ given on the ball $B_r$. These…