Non-disturbance criteria of quantum measurements

Using the general sequential product proposed by Shen and Wu in [J. Phys. A: Math. Theor. 42, 345203, 2009], we derive three criteria for describing non-disturbance between quantum measurements that may be unsharp with such new sequential products, which generalizes Gudder's results

The Drazin inverse of the linear combinations of two idempotents in the Banach algebra

AbstractIn this paper, some Drazin inverse representations of the linear combinations of two idempotents in a Banach algebra are obtained. Moreover, we present counter-examples to and establish the corrected versions of two theorems by Cvetković-Ilić and Deng

A note on Browder spectrum of operator matrices

AbstractWhen A∈B(H) and B∈B(K) are given, we denote by MC the operator acting on the Hilbert space H⊕K of the form MC=(AC0B). In this note, it is shown that the following results in [Hai-Yan Zhang, Hong-Ke Du, Browder spectra of upper-triangular operator matrices, J. Math. Anal. Appl. 323 (2006) 700–707]W3(A,B,C)=W1(A,B,C)(in line 17 on p. 705) and⋂C∈B(K,H)σb(MC)=(⋂C∈B(K,H)σ(MC))∖[ρb(A)∩ρb(B)] are not always true, although the authors tried to fill the gap in their proofs by proposing an additional condition in [H.-Y. Zhang, H.-K Du, Corrigendum to “Browder spectra of upper-triangular operator matrices” [J. Math. Anal. Appl. 323 (2006) 700–707], J. Math. Anal. Appl. 337 (2007) 751–752]. A counterexample is given and then we show that under one of the following conditions:(i)σsu(B)=σ(B);(ii)intσp(B)=ϕ;(iii)σ(A)∩σ(B)=ϕ;(iv)σa(A)=σ(A), we have⋂C∈B(K,H)σb(MC)=σle(A)∪σre(B)∪W(A,B)∪σD(A)∪σD(B), where W(A,B)={λ∈C:N(B−λ)andH/R(A−λ)¯are not isomorphic up to a finitedimensional subspace}

Recent progress in the study of brown adipose tissue

Brown adipose tissue in mammals plays a critical role in maintaining energy balance by thermogenesis, which means dissipating energy in the form of heat. It is held that in mammals, long-term surplus food intake results in energy storage in the form of triglyceride and may eventually lead to obesity. Stimulating energy-dissipating function of brown adipose tissue in human body may counteract fat accumulation. In order to utilize brown adipose tissue as a therapeutic target, the mechanisms underlying brown adipocyte differentiation and function should be better elucidated. Here we review the molecular mechanisms involved in brown adipose tissue development and thermogenesis, and share our thoughts on current challenges and possible future therapeutic approaches

Optimization of a Decellularization/Recellularization Strategy for Transplantable Bioengineered Liver

The liver is a complex organ that requires constant perfusion for the delivery of nutrients and oxygen and the removal of waste in order to survive. Efforts to recreate or mimic the liver microstructure via a ground-up approach are essential for liver tissue engineering. A decellularization/recellularization strategy is one of the approaches aiming at the possibility of producing a fully functional organ with in vitro-developed construction for clinical applications to replace failed livers, such as end-stage liver disease (ESLD). However, the complexity of the liver microarchitecture along with the limited suitable hepatic component, such as the optimization of the extracellular matrix (ECM) of the biomaterials, the selection of the seed cells, and development of the liver-specific three-dimensional (3D) niche settings, pose numerous challenges. In this chapter, we have provided a comprehensive outlook on how the physiological, pathological, and spatiotemporal aspects of these drawbacks can be turned into the current challenges in the field, and put forward a few techniques with the potential to address these challenges, mainly focusing on a decellularization-based liver regeneration strategy. We hypothesize the primary concepts necessary for constructing tissue-engineered liver organs based on either an intact (from a naïve liver) or a partial (from a pretreated liver) structure via simulating the natural development and regenerative processes