相关论文: The Kobayashi metric in the normal direction and t…
We prove the Yamada-Watanabe Theorem for semilinear stochastic partial differential equations with path-dependent coefficients. The so-called "method of the moving frame" allows us to reduce the proof to the Yamada-Watanabe Theorem for…
We consider an inverse problem for the linear one-dimensional wave equation with variable coefficients consisting in determining an unknown source term from a boundary observation. A method to obtain approximations of this inverse problem…
In this paper, we introduce a new combinatorial curvature on two and three dimensional triangulated manifolds, which transforms in the same way as that of the smooth scalar curvature under scaling of the metric and could be used to…
In indirect measurements, the measurand is determined by solving an inverse problem which requires a model of the measurement process. Such models are often approximations and introduce systematic errors leading to a bias of the posterior…
The main objective of this paper is to introduce a new method for qualitative analysis of various designs of robot arms. To this end we define the complexity of a map, examine its main properties and develop some methods of computation. In…
This book aims to provide a brief overview of recent advancements in the theory of inverse problems for stochastic partial differential equations. In order to keep the content concise, we will only discuss the inverse problems of two…
We survey the recent developments in the theory of quasireg- ular mappings in metric spaces. In particular, we study the geometric porosity of the branch set of quasiregular mappings in general metric measure spaces, and then, introduce the…
We study directions along which the norms of vectors are preserved under a linear map. In particular, we find families of matrices for which these directions are determined by integer vectors. We consider the two-dimensional case in detail,…
Giving a new form of the vortex mode equation by a proper change of parameter, our aim is to analyze the point and contact symmetries of the new equation. Fundamental invariants and a form of general solutions of point transformations along…
We formulate on a half-strip an initial boundary value problem for the two-dmensional Kawahara equation. Existence and uniqueness of a regular solution as well as the exponential decay rate for the elevated norm of small solutions are…
The properties of the normal distribution under linear transformation, as well the easy way to compute the covariance matrix of marginals and conditionals, offer a unique opportunity to get an insight about several aspects of uncertainties…
A problem of a wave identification is formulated. An example is considered in conditions of one-dimensional Cauchy problem for conventional string equation in matrix form and its inhomogeneous two-component version. The acoustic and…
In this paper, we consider the travel time tomography problem for conformal metrics on a bounded domain, which seeks to determine the conformal factor of the metric from the lengths of geodesics joining boundary points. We establish forward…
A common task in experimental sciences is to fit mathematical models to real-world measurements to improve understanding of natural phenomenon (reverse-engineering or inverse modeling). When complex dynamical systems are considered, such as…
In this essay we give an introduction to conformal symmetry, based on the example of the Yamabe operator and its use in conformal differential geometry, and in representation theory.
It is shown that the contraction mapping principle with the involvement of a Carleman Weight Function works for a Coefficient Inverse Problem for a 1D hyperbolic equation. Using a Carleman estimate, the global convergence of the…
The interest in a system often resides in the interplay among different parameters governing its evolution. It is thus often required to access many of them at once for a complete description. Assessing how quantum enhancement in such…
The solution of a fine tuning problem is one of the principal motivations of Supersymmetry. However experimental constraints indicate that many Supersymmetric models are also fine tuned (although to a much lesser extent). We review the…
Univariate and multivariate normal probability distributions are widely used when modeling decisions under uncertainty. Computing the performance of such models requires integrating these distributions over specific domains, which can vary…
Axiomatic approach to measurement theory is developed. All the possible statistical properties of apparatuses measuring an observable with nondegenerate spectrum allowed in standard quantum mechanics are characterized.