相关论文: Quantifying the ill-conditioning of analytic conti…
This review article aims to stress and reunite some of the analytic formalism of the anomalous diffusive processes that have succeeded in their description. Also, it has the objective to discuss which of the new directions they have taken…
Most clinical prediction studies are developed from retrospective cohorts and reported as if all patient information were observed at once. In practice, clinicians face a more consequential question: \emph{when is there already enough…
The boundary conditions prescribing the constant traction or the so-called do-nothing conditions are frequently taken on artificial boundaries in the numerical simulations of steady flow of incompressible fluids, despite the fact that they…
A strictly truncated (weak-coupling) perturbation theory is applied to the attractive Holstein and Hubbard models in infinite dimensions. These results are qualified by comparison with essentially exact Monte Carlo results. The second order…
We consider a dynamical system generated by an analytic perturbation $A_\varepsilon$ of an analytic Anosov diffeomorphism $A_0$ of $\TTT^d$. We show that, if $A_0$ admit a splitting of $\mathrm T\mathds T^d$ in $k$ invariant subspaces,…
We study asymptotic properties of conditional least squares estimators for the drift parameters of two-factor affine diffusions based on continuous time observations. We distinguish three cases: subcritical, critical and supercritical. For…
We consider a dynamical system subjected to weak but adiabatically slow fluctuations of external origin. Based on the ``adiabatic following'' approximation we carry out an expansion in \alpha/|\mu|, where \alpha is the strength of…
Analytic functions in the Hardy class $H^2$ over the upper half-plane $\mathbb{H}_+$ are uniquely determined by their values on any curve $\Gamma$ lying in the interior or on the boundary of $\mathbb{H}_+$. The goal of this paper is to…
In studying the complexity of iterative processes it is usually assumed that the arithmetic operations of addition, multiplication, and division can be performed in certain constant times. This assumption is invalid if the precision…
We completely describe a new domain for abstract interpretation of numerical programs. Fixpoint iteration in this domain is proved to converge to finite precise invariants for (at least) the class of stable linear recursive filters of any…
The long time effect of nonlinear perturbation to oscillatory linear systems can be characterized by the averaging method, and we consider first-order averaging for its simplest applicability to high-dimensional problems. Instead of the…
We consider a lattice of weakly coupled expanding circle maps. We construct, via a cluster expansion of the Perron-Frobenius operator, an invariant measure for these infinite dimensional dynamical systems which exhibits space-time-chaos.
The problems of optimally estimating a phase, a direction, and the orientation of a Cartesian frame (or trihedron) with general pure states are addressed. Special emphasis is put on estimation schemes that allow for inconclusive answers or…
The Maxwell-Dirac system describes the interaction of an electron with its self-induced electromagnetic field. In space dimension $d=3$ the system is charge-critical, that is, $L^2$-critical for the spinor with respect to scaling, and local…
A linear equation Au=f (1) with a bounded, injective, but not boundedly invertible linear operator in a Hilbert space H is studied. A new approach to solving linear ill-posed problems is proposed. The approach consists of solving a Cauchy…
One of the main objectives of science is the recognition of a general pattern in a particular phenomenon in some particular regime. In this work, this is achieved with the analytical expression for the optimal protocol that minimizes the…
The conductance of disordered wires with symplectic symmetry is studied by numerical simulations on the basis of a tight-binding model on a square lattice consisting of M lattice sites in the transverse direction. If the potential range of…
In this paper we consider a fragment of the first-order theory of the real numbers that includes systems of equations of continuous functions in bounded domains, and for which all functions are computable in the sense that it is possible to…
The Hodge equations for 1-forms are studied on Beltrami's projective disc model for hyperbolic space. Ideal points lying beyond projective infinity arise naturally in both the geometric and analytic arguments. An existence theorem for…
Systems of wave equations may fail to be globally well posed, even for small initial data. Attempts to classify systems into well and ill-posed categories work by identifying structural properties of the equations that can work as…