Related papers: Trace does not preserve Reflexivity
In this paper, we propose an extension of trace ratio based Manifold learning methods to deal with multidimensional data sets. Based on recent progress on the tensor-tensor product, we present a generalization of the trace ratio criterion…
The purpose of this paper is to present the critical cases of the trace theorems for the restriction of functions to closed surfaces, and to give the asymptotics for the norms of the traces under dilations of the surface. We also discuss…
Approximate expressions for X-ray resonant and M\"ossbauer reflectivity in the total external reflection region are developed for the limiting cases of a semiinfinite mirror with a small resonant addition to the total susceptibility and for…
A notion of rigidity with respect to an arbitrary semidualizing complex C over a commutative noetherian ring R is introduced and studied. One of the main result characterizes C-rigid complexes. Specialized to the case when C is the relative…
The aim of this article is twofold: give a short proof of the existence of real spectral shift function and the associated trace formula for a pair of contractions, the difference of which is trace-class and one of the two a strict…
We study a relative trace formula for a compact Riemann surface with respect to a closed geodesic $C$. This can be expressed as a relation between the period spectrum and the ortholength spectrum of $C$. This provides a new proof of…
A comparative study of thawing and tracking models of dark energy is carried out with the help of a dynamical systems analysis. It is found that both of them have stable solutions which are consistent with the requirement of a dark energy.…
Temporal causal representation learning methods assume that causal mechanisms switch instantaneously between discrete domains, yet real-world systems often exhibit continuous mechanism transitions. For example, a vehicle's dynamics evolve…
Recently, we have constructed the conformal gravity with metric and torsion, finding the gravitational field equations that give the conservation laws and trace condition; in the present paper we apply this theory to the case of the Dirac…
We introduce a notion of weak definability of first order structures, show that various classification-theoretic properties are or are not preserved under it, and that the properties which are preserved can also be characterized in terms of…
In this paper we discuss trace properties of $d^+$-summable $K$-cycles considered by A.Connes in [\rfr(Conn4)]. More precisely we give a proof of a trace theorem on the algebra $\A$ of a $K$--cycle stated in [\rfr(Conn4)], namely we show…
A uniform dimensional result for normally reflected Brownian motion (RBM) in a large class of non-smooth domains is established. Exact Hausdorff dimensions for the boundary occupation time and the boundary trace of RBM are given. Extensions…
Here I present an overview of recent studies of the phenomenon of negative refraction and left-handed materials. I will discuss some basic questions pertinent to the problem. It is pointed out that the current claims of negative refraction…
The question of building a local diff-invariant effective gravitational action for the trace anomaly is reconsidered. General Relativity (GR) combined with the existing action for the trace anomaly is an inconsistent low energy effective…
The authors claim that they "strictly" closed locality loophole, but their work does not close the locality loophole. there are at least two local transinformation explanations. The two explanations are the counter-examples of their claim.…
The celebrated Auslander-Reiten Conjecture, on the vanishing of self extensions of a module, is one of the long-standing conjectures in ring theory. Although it is still open, there are several results in the literature that establish the…
A simple condition is given that is sufficient to determine whether a measure that is absolutely continuous with respect to a Gau{\ss}ian measure on the space of distributions is reflection positive. It readily generalises conventional…
The trace of a Markov process is the time changed process of the original process on the support of the Revuz measure used in the time change. In this paper, we will concentrate on the reflecting Brownian motions on certain closed strips.…
The uniform tracial completion of a C*-algebra A with compact non-empty trace space T(A) is obtained by completing the unit ball with respect to the uniform 2-seminorm $\|a\|_{2,T(A)}=\sup_{\tau \in T(A)} \tau(a^*a)^{1/2}$. The trace…
From the fundamental requirement of causality, we derive a rigorous criterion of negative refraction (left-handedness). This criterion imposes the lower limits on the electric and magnetic losses in the region of the negative refraction. If…