Quantum coherence serves as a defining characteristic of quantum mechanics,finding extensive applications in quantum computing and quantum communication processing.This study explores quantum block coherence in the co...Quantum coherence serves as a defining characteristic of quantum mechanics,finding extensive applications in quantum computing and quantum communication processing.This study explores quantum block coherence in the context of projective measurements,focusing on the quantification of such coherence.Firstly,we define the correlation function between the two general projective measurements P and Q,and analyze the connection between sets of block incoherent states related to two compatible projective measurements P and Q.Secondly,we discuss the measure of quantum block coherence with respect to projective measurements.Based on a given measure of quantum block coherence,we characterize the existence of maximal block coherent states through projective measurements.This research integrates the compatibility of projective measurements with the framework of quantum block coherence,contributing to the advancement of block coherence measurement theory.展开更多
Understanding the strength characteristics and deformation behaviour of the tunnel surrounding rock in a fault zone is significant for tunnel stability evaluation.In this study,a series of unconfined compression tests...Understanding the strength characteristics and deformation behaviour of the tunnel surrounding rock in a fault zone is significant for tunnel stability evaluation.In this study,a series of unconfined compression tests were conducted to investigate the mechanical characteristics and failure behaviour of completely weathered granite(CWG)from a fault zone,considering with height-diameter(h/d)ratio,dry densities(ρd)and moisture contents(ω).Based on the experimental results,a regression mathematical model of unconfined compressive strength(UCS)for CWG was developed using the Multiple Nonlinear Regression method(MNLR).The research results indicated that the UCS of the specimen with a h/d ratio of 0.6 decreased with the increase ofω.When the h/d ratio increased to 1.0,the UCS increasedωwith up to 10.5%and then decreased.Increasingρd is conducive to the improvement of the UCS at anyω.The deformation and rupture process as well as final failure modes of the specimen are controlled by h/d ratio,ρd andω,and the h/d ratio is the dominant factor affecting the final failure mode,followed byωandρd.The specimens with different h/d ratio exhibited completely different fracture mode,i.e.,typical splitting failure(h/d=0.6)and shear failure(h/d=1.0).By comparing the experimental results,this regression model for predicting UCS is accurate and reliable,and the h/d ratio is the dominant factor affecting the UCS of CWG,followed byρd and thenω.These findings provide important references for maintenance of the tunnel crossing other fault fractured zones,especially at low confining pressure or unconfined condition.展开更多
Let U be a (B, A)-bimodule, A and B be rings, and be a formal triangular matrix ring. In this paper, we characterize the structure of relative Ding projective modules over T under some conditions. Furthermore, using t...Let U be a (B, A)-bimodule, A and B be rings, and be a formal triangular matrix ring. In this paper, we characterize the structure of relative Ding projective modules over T under some conditions. Furthermore, using the left global relative Ding projective dimensions of A and B, we estimate the relative Ding projective dimension of a left T-module.展开更多
In this paper, we investigate local properties in the system of completely 1-summing mapping spaces. We introduce notions of injectivity, local reflexivity, exactness, nuclearity and finite-representability in the sys...In this paper, we investigate local properties in the system of completely 1-summing mapping spaces. We introduce notions of injectivity, local reflexivity, exactness, nuclearity and finite-representability in the system of completely 1-summing mapping spaces. First we obtain that if V has WEP, V is locally reflexive in the system (Ⅱ<sub>1</sub>(⋅,⋅), π<sub>1</sub>(⋅)) if and only if it is locally reflexive in the system (Ⅰ(⋅,⋅), t(⋅)). Furthermore we prove that an operator space V ⊆ B(H) is exact in the system (Ⅱ<sub>1</sub>(⋅,⋅), π<sub>1</sub>(⋅)) if and only if V is finitely representable in {M<sub>n</sub>}<sub>n∈N</sub> in the system (Ⅱ<sub>1</sub>(⋅,⋅), π<sub>1</sub>(⋅)). At last, we show that an operator space V is finitely representable in {M<sub>n</sub>}<sub>n∈N</sub> in the system (Ⅱ<sub>1</sub>(⋅,⋅), π<sub>1</sub>(⋅)) if and only if V = C.展开更多
基金partially supported by the National Natural Science Foundations of China (Grant No.11901317)the China Postdoctoral Science Foundation (Grant No.2020M680480)+1 种基金the Fundamental Research Funds for the Central Universities (Grant No.2023MS078)the Beijing Natural Science Foundation (Grant No.1232021)。
文摘Quantum coherence serves as a defining characteristic of quantum mechanics,finding extensive applications in quantum computing and quantum communication processing.This study explores quantum block coherence in the context of projective measurements,focusing on the quantification of such coherence.Firstly,we define the correlation function between the two general projective measurements P and Q,and analyze the connection between sets of block incoherent states related to two compatible projective measurements P and Q.Secondly,we discuss the measure of quantum block coherence with respect to projective measurements.Based on a given measure of quantum block coherence,we characterize the existence of maximal block coherent states through projective measurements.This research integrates the compatibility of projective measurements with the framework of quantum block coherence,contributing to the advancement of block coherence measurement theory.
基金supported by the National Natural Science Foundation of China,NSFC(No.42202318).
文摘Understanding the strength characteristics and deformation behaviour of the tunnel surrounding rock in a fault zone is significant for tunnel stability evaluation.In this study,a series of unconfined compression tests were conducted to investigate the mechanical characteristics and failure behaviour of completely weathered granite(CWG)from a fault zone,considering with height-diameter(h/d)ratio,dry densities(ρd)and moisture contents(ω).Based on the experimental results,a regression mathematical model of unconfined compressive strength(UCS)for CWG was developed using the Multiple Nonlinear Regression method(MNLR).The research results indicated that the UCS of the specimen with a h/d ratio of 0.6 decreased with the increase ofω.When the h/d ratio increased to 1.0,the UCS increasedωwith up to 10.5%and then decreased.Increasingρd is conducive to the improvement of the UCS at anyω.The deformation and rupture process as well as final failure modes of the specimen are controlled by h/d ratio,ρd andω,and the h/d ratio is the dominant factor affecting the final failure mode,followed byωandρd.The specimens with different h/d ratio exhibited completely different fracture mode,i.e.,typical splitting failure(h/d=0.6)and shear failure(h/d=1.0).By comparing the experimental results,this regression model for predicting UCS is accurate and reliable,and the h/d ratio is the dominant factor affecting the UCS of CWG,followed byρd and thenω.These findings provide important references for maintenance of the tunnel crossing other fault fractured zones,especially at low confining pressure or unconfined condition.
文摘Let U be a (B, A)-bimodule, A and B be rings, and be a formal triangular matrix ring. In this paper, we characterize the structure of relative Ding projective modules over T under some conditions. Furthermore, using the left global relative Ding projective dimensions of A and B, we estimate the relative Ding projective dimension of a left T-module.
文摘In this paper, we investigate local properties in the system of completely 1-summing mapping spaces. We introduce notions of injectivity, local reflexivity, exactness, nuclearity and finite-representability in the system of completely 1-summing mapping spaces. First we obtain that if V has WEP, V is locally reflexive in the system (Ⅱ<sub>1</sub>(⋅,⋅), π<sub>1</sub>(⋅)) if and only if it is locally reflexive in the system (Ⅰ(⋅,⋅), t(⋅)). Furthermore we prove that an operator space V ⊆ B(H) is exact in the system (Ⅱ<sub>1</sub>(⋅,⋅), π<sub>1</sub>(⋅)) if and only if V is finitely representable in {M<sub>n</sub>}<sub>n∈N</sub> in the system (Ⅱ<sub>1</sub>(⋅,⋅), π<sub>1</sub>(⋅)). At last, we show that an operator space V is finitely representable in {M<sub>n</sub>}<sub>n∈N</sub> in the system (Ⅱ<sub>1</sub>(⋅,⋅), π<sub>1</sub>(⋅)) if and only if V = C.
