Related papers: Trace theorems: critical cases and best constants
In these notes, we present versions of trace theorems for Sobolev spaces over an interval in the real line, and also a one-dimensional version of the well-known Poincare inequality.
We study the behaviour of functions of dissipative operators under relatively bounded and relatively trace class perturbation. We introduce and study the class of analytic relatively operator Lipschitz functions. An essential role is played…
Contraction theory is an analytical tool to study differential dynamics of a non-autonomous (i.e., time-varying) nonlinear system under a contraction metric defined with a uniformly positive definite matrix, the existence of which results…
When using graphs and graph transformations to model systems, consistency is an important concern. While consistency has primarily been viewed as a binary property, i.e., a graph is consistent or inconsistent with respect to a set of…
Optimality Theory is a constraint-based theory of phonology which allows constraints to be violated. Consequently, implementing the theory presents problems for declarative constraint-based processing frameworks. On the basis of two…
Formalisms based on temporal logics interpreted over finite strict linear orders, known in the literature as finite traces, have been used for temporal specification in automated planning, process modelling, (runtime) verification and…
Approximate dynamic programming has been investigated and used as a method to approximately solve optimal regulation problems. However, the extension of this technique to optimal tracking problems for continuous time nonlinear systems has…
Trace formulae for d-regular graphs are derived and used to express the spectral density in terms of the periodic walks on the graphs under consideration. The trace formulae depend on a parameter w which can be tuned continuously to assign…
An algorithm for solving nonconvex smooth optimization problems is proposed, analyzed, and tested. The algorithm is an extension of the Trust Region Algorithm with Contractions and Expansions (TRACE) [Math. Prog. 162(1):132, 2017]. In…
The class of closed graphs by a linear ordering on their sets of vertices is investigated. A recent characterization of such a class of graphs is analyzed by using tools from the proper interval graph theory.
We consider the problem of decomposing a piecewise constant function on the circle into a sum of indicator functions of closed circular disks in the plane, whose number and location are not a priori known. This represents a situation where…
We study trace functions on the form $ t\to\tr f(A+tB) $ where $ f $ is a real function defined on the positive half-line, and $ A $ and $ B $ are matrices such that $ A $ is positive definite and $ B $ is positive semi-definite. If $ f $…
This paper presents a consistent approach to prescribe traction boundary conditions in atomistic models. Due to the typical multiple-neighbor interactions, finding an appropriate boundary condition that models a desired traction is a…
The concept of fixed point plays a crucial role in various fields of applied mathematics. The aim of this paper is to establish the existence of a unique fixed point of some type of functions which satisfy a new contraction principle,…
We obtain a simple formula for the first-order trace of a regular differential operator on a segment perturbated by a multiplication operator. The main analytic ingredient of the proof is an improvement of the Tamarkin equiconvergence…
Here we obtain the exact asymptotics for large and moderate deviations, strong law of large numbers and central limit theorem for chains with unbounded variable length memory.
We establish higher order trace formulas for pairs of contractions along a multiplicative path generated by a self-adjoint operator in a Schatten-von Neumann ideal, removing earlier stringent restrictions on the kernel and defect operator…
A two-dimensional or quasi-two-dimensional nematic liquid crystal refers to a surface confined system. When such a system is further confined by external line boundaries or excluded from internal line boundaries, the nematic directors form…
Finding optimal trajectories for multiple traffic demands in a congested network is a challenging task. Optimal transport theory is a principled approach that has been used successfully to study various transportation problems. Its usage is…
Properties of local and global slope of a function and its approximate critical points sets are studied in relation to determination of the function.