scholarly journals The double noncommutative spacetime and the double complex symmetric gravitational theory

2004 ◽  
Vol 53 (9) ◽  
pp. 2846
Author(s):  
Wu Ya-Bo ◽  
Shao Ying ◽  
Dong Peng
Keyword(s):  
Gravitational Theory ◽  
Double Complex ◽  
Noncommutative Spacetime ◽  
Complex Symmetric

A COMINRES-QLP Method for Solving Complex Symmetric Linear Systems

2020 ◽  
Vol 140 (12) ◽  
pp. 832-841
Author(s):  
Lijun Liu ◽  
Kazuaki Sekiya ◽  
Masao Ogino ◽  
Koki Masui
Keyword(s):  
Linear Systems ◽  
Complex Symmetric Linear Systems ◽  
Complex Symmetric

Cobaloxime-Based Double Complex Salts as Efficient and Versatile Catalysts for the Light-Driven Hydrogen Evolution Reaction

2020 ◽  
Author(s):  
Elisabeth Hofmeister ◽  
Jisoo Woo ◽  
Tobias Ullrich ◽  
Lydia Petermann ◽  
Kevin Hanus ◽  
...  
Keyword(s):  
Hydrogen Evolution ◽  
Hydrogen Evolution Reaction ◽  
Systematic Study ◽  
Cobalt Complexes ◽  
Spectroscopic Studies ◽  
Double Complex ◽  
Double Complex Salts ◽  
Noble Metal Catalysts ◽  
Reduction Potentials ◽  
Complex Salts

Cobaloximes and their BF<sub>2</sub>-bridged analogues have emerged as promising non-noble metal catalysts for the photocatalytic hydrogen evolution reaction (HER). Herein we report the serendipitous discovery that double complex salts such as [Co(dmgh)<sub>2</sub>py<sub>2</sub>]<sup>+</sup>[Co(dmgBPh<sub>2</sub>)<sub>2</sub>Cl<sub>2</sub>]<sup>-</sup> can be obtained in good yields by treatment of commercially available [Co(dmgh)<sub>2</sub>pyCl] with triarylboranes. A systematic study on the use of such double complex salts and their single salts with simple counterions as photocatalysts revealed HER activities comparable or superior to existing cobaloxime catalysts and suggests ample opportunities for this compound class in catalyst/photosensitizer dyads and immobilized architectures. Preliminary electrochemical and spectroscopic studies indicate that one key advantage of these charged cobalt complexes is that the reduction potentials as well as the electrostatic interaction with charged photosensitizers can be tuned.

scholarly journals Local Spectral Properties Under Conjugations

2021 ◽  
Vol 18 (3) ◽  
Author(s):  
Pietro Aiena ◽  
Fabio Burderi ◽  
Salvatore Triolo
Keyword(s):  
Hilbert Space ◽  
Spectral Properties ◽  
Operator Matrices ◽  
Weyl Type Theorems ◽  
Triangular Operator ◽  
Analytic Core ◽  
Complex Symmetric ◽  
Symmetric Operators ◽  
The Relationship

AbstractIn this paper, we study some local spectral properties of operators having form JTJ, where J is a conjugation on a Hilbert space H and $$T\in L(H)$$ T ∈ L ( H ) . We also study the relationship between the quasi-nilpotent part of the adjoint $$T^*$$ T ∗ and the analytic core K(T) in the case of decomposable complex symmetric operators. In the last part we consider Weyl type theorems for triangular operator matrices for which one of the entries has form JTJ, or has form $$JT^*J$$ J T ∗ J . The theory is exemplified in some concrete cases.

Generalized Riemann spaces

1956 ◽  
Vol 52 (4) ◽  
pp. 623-625 ◽  
Author(s):  
John Moffat
Keyword(s):  
Curvature Tensor ◽  
Physical Theory ◽  
Dimensional Space ◽  
Riemann Space ◽  
Recent Attempt ◽  
Fundamental Tensor ◽  
Fundamental Properties ◽  
Complex Symmetric ◽  
Definition Of ◽  
Generalized Curvature Tensor

ABSTRACTThe recent attempt at a physical interpretation of non-Riemannian spaces by Einstein (1, 2) has stimulated a study of these spaces (3–8). The usual definition of a non-Riemannian space is one of n dimensions with which is associated an asymmetric fundamental tensor, an asymmetric linear affine connexion and a generalized curvature tensor. We can also consider an n-dimensional space with which is associated a complex symmetric fundamental tensor, a complex symmetric affine connexion and a generalized curvature tensor based on these. Some aspects of this space can be compared with those of a Riemann space endowed with two metrics (9). In the following the fundamental properties of this non-Riemannian manifold will be developed, so that the relation between the geometry and physical theory may be studied.

scholarly journals Entanglement entropy in cubic gravitational theories

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Elena Cáceres ◽  
Rodrigo Castillo Vásquez ◽  
Alejandro Vilar López
Keyword(s):  
Entanglement Entropy ◽  
Gravitational Theory ◽  
Riemann Tensor ◽  
Holographic Entanglement Entropy ◽  
Gravitational Theories ◽  
Entropy Functional ◽  
Wide Range ◽  
Splitting Problem ◽  
Range Of Values

Abstract We derive the holographic entanglement entropy functional for a generic gravitational theory whose action contains terms up to cubic order in the Riemann tensor, and in any dimension. This is the simplest case for which the so-called splitting problem manifests itself, and we explicitly show that the two common splittings present in the literature — minimal and non-minimal — produce different functionals. We apply our results to the particular examples of a boundary disk and a boundary strip in a state dual to 4- dimensional Poincaré AdS in Einsteinian Cubic Gravity, obtaining the bulk entanglement surface for both functionals and finding that causal wedge inclusion is respected for both splittings and a wide range of values of the cubic coupling.

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