相关论文: The tangential cone condition for some coefficient…
This paper addresses the limitations of Physics-Informed Neural Networks for time-dependent problems by introducing a tangent bundle learning framework. Instead of directly approximating the solution, we parameterize its temporal derivative…
We develop a rather general approach to entanglement characterization based on convexity properties and polynomial identities. This approach is applied to obtain simple and efficient entanglement conditions which work equally well in both…
In this article, we investigate inverse source problems for a wide range of PDEs of parabolic and hyperbolic types as well as time-fractional evolution equations by partial interior observation. Restricting the source terms to the form of…
We present several entanglement conditions in order to detect bound entangled states in continuous variable systems. Specifically, Werner and Wolf [Phys. Rev. Lett. 86, 3658 (2001)] and Horodecki and Lewenstein [Phys. Rev. Lett. 85, 2657…
In this paper, it is proved that the continuity of the tangential components of the average electric and magnetic fields is insufficient to describe the reflection of plane waves by a set of thin parallel wires embedded in a dielectric host…
This paper deals with a class of initial-boundary value problems for nonlinear fourth order parabolic systems with time dependent coefficients in a bounded domain $\Omega \subset \mathbb{R}^N, N\geq 2$. Introducing suitable conditions on…
We revisit identification based on timing and information set assumptions in structural models, which have been used in the context of production functions, demand equations, and hedonic pricing models (e.g. Olley and Pakes (1996), Blundell…
This work investigates an inverse problem of determining the radiative coefficient in a degenerate parabolic equation from the final overspecified data. Being different from other inverse coefficient problems in which the principle…
For parameter identification problems the Fr\'echet-derivative of the parameter-to-state map is of particular interest. In many applications, e.g. in seismic tomography, the unknown quantity is modeled as a coefficient in a linear…
In this paper, we introduce the notion of boundary delay equations, establishing a unified framework for analyzing linear time-invariant systems with pure time-delayed boundary conditions. We establish mild sufficient conditions for the…
State-dependent parameter identification, where unknown model parameters depend on one or more state variables in partial differential equations (PDEs) or coupled PDE systems, is fundamental to a wide range of problems in physics,…
A key observation underlying this paper is the fact that the range invariance condition for convergence of regularization methods for nonlinear ill-posed operator equations -- such as coefficient identification in partial differential…
In the present paper, we establish the uniqueness of tangent maps for general weakly holomorphic and locally approximable maps from an arbitrary almost complex manifold into projective algebraic varieties. As a byproduct of the approach and…
We add a time-dependent potential to the inhomogeneous wave equation and consider the task of reconstructing this potential from measurements of the wave field. This dynamic inverse problem becomes more involved compared to static…
We consider two inverse boundary value problems for the time-harmonic Maxwell equations in an infinite slab. Assuming that tangential boundary data for the electric and magnetic fields at a fixed frequency is available either on subsets of…
We address one of the open problems in quantization theory recently listed by Rieffel. By developping in detail Connes' tangent groupoid principle and using previous work by Landsman, we show how to construct a strict, flabby quantization,…
Coefficient inverse problems related to identifying the right-hand side of an equation with use of additional information is of interest among inverse problems for partial differential equations. When considering non-stationary problems,…
The weak formulation of parabolic problems with dynamic boundary conditions is rewritten in form of a partial differential-algebraic equation. More precisely, we consider two dynamic equations with a coupling condition on the boundary. This…
Let ${\mathbf P}^2$ denote the projective plane over a finite field ${\mathbb F}_q$. A pair of nonsingular conics $({\mathcal A}, {\mathcal B})$ in the plane is said to satisfy the Poncelet triangle condition if, considered as conics in…
We present solutions to a set of problems that arise in quantum entanglement theory, whose common trait is the use of algebraic methods. The backbone of the thesis consists of two general theorems, pertaining to specific convex sets of…