Essential,Weyl and Browder spectra of unbounded upper triangular operator matrices

This paper is concerned with the spectral properties of the unbounded upper triangular operator matrix with diagonal domain. Some sufficient and necessary conditions are given under which the essential spectrum, the Weyl spectrum and the Browder spectrum of such operator matrix, respectively, coincide with the union of the essential spectrum, the Weyl spectrum and the Browder spectrum of its diagonal entries.     

Directed neural stem cell differentiation on polyaniline-coated high strength hydrogels

Stem-cell-based neural regeneration has received significant attention, as it has potential to restore functionality to diseased or damaged neural tissues that have a limited ability to self-repair or regenerate. Culturing neural stem cells (NSCs) on hydrogel substrates has been shown to facilitate differentiation to neural progenitors, but this has only been achieved on very soft hydrogels, greatly increasing the difficulty of manufacture and limiting their wide applications. Here, we realized the differentiation of NSCs to neural and glial progenitors on high-strength hydrogels. Hydrogen-bonding-strengthened conductive hydrogels (PVV-PANI) were synthesized through one-pot copolymerization of 2-vinyl-4,6-diamino-1,3,5-triazine, 1-vinylimidazole and polyethylene glycol diacrylate, followed by post-coating with polyaniline (PANI). Diaminotriazine-diaminotriazine hydrogen bonding dramatically increases their mechanical strength, while copolymerization with VI pronouncedly promotes the adsorption of PANI particles, endowing the hydrogels with electrical conductivity. These hydrogels exhibit tensile strengths up to 1.16 MPa, a 559% breaking strain, a 9.9 MPa compressive strength and up to 16.7 mS/cm conductivity. Importantly, PVV-PANI hydrogels support the attachment, proliferation, and differentiation of NSCs, and allow the efficient induction of neural and glial differentiation via electrical stimulation. This work demonstrates high-strength conductive hydrogels can serve as an electroactive soft-wet platform for modulating the specific differentiation of NSCs, a significant step towards cell-based therapies for neurological diseases.     

On the Semicircular Law of Large-Dimensional Random Quaternion Matrices

It is well known that the Gaussian symplectic ensemble is defined on the space of \(n\times n\) quaternion self-dual Hermitian matrices with Gaussian random elements. There is a huge body of literature regarding this kind of matrices based on the exact known form of the density function of the eigenvalues (see Erd?s in Russ Math Surv 66(3):507–626, 2011; Erd?s in Probab Theory Relat Fields 154(1–2):341–407, 2012; Erd?s et al. in Adv Math 229(3):1435–1515, 2012; Knowles and Yin in Probab Theory Relat Fields, 155(3–4):543–582, 2013; Tao and Vu in Acta Math 206(1):127–204, 2011; Tao and Vu in Electron J Probab 16(77):2104–2121, 2011). Due to the fact that multiplication of quaternions is not commutative, few works about large-dimensional quaternion self-dual Hermitian matrices are seen without normality assumptions. As in natural, we shall get more universal results by removing the Gaussian condition. For the first step, in this paper, we prove that the empirical spectral distribution of the common quaternion self-dual Hermitian matrices tends to the semicircular law. The main tool to establish the universal result is given as a lemma in this paper as well.     

Escape rate of Brownian particles from a metastable potential well under time derivative Ornstein-Uhlenbeck noise

We investigate the escape rate of Brownian particles that move in a cubic metastablepotential subjected to an internal time derivative Ornstein-Uhlenbeck noise (DOUN). Thisnoise can induce the ballistic diffusion of force-free Brownian particles. Some newfeatures are found. The escape rate for DOUN shows qualitative different dependence onpotential well width compared with OUN which induces normal diffusion. As the potentialbarrier height decreases, the escape rate of DOUN deviates from Arrhenius law considerablyearlier than that of Ornstein-Uhlenbeck noise (OUN). The Brownian particles escape fasterunder DOUN than that under OUN. A quasi-periodic oscillation occurs in transient state. Asolvable case is presented to demonstrate the significant cancellation behavior in thebarrier region that governs most of these phenomena. The physical mechanism of thefindings can be clarified by the noise features. These characteristics should be commonfor internal noises that induce superdiffusion, especially the ballistic diffusion.     

Effect of pressure on the selectivity for the esterification of ethylene glycol with propionic acid in supercritical CO2

The esterification of ethylene glycol with propionic acid was investigated in supercritical CO2 at 50.0 degrees C. The effect of pressure on equilibrium conversion and selectivity of ethylene glycol monopropionate (monoester) and ethylene glycol dipropinonate (diester) was studied systematically. It was shown that the equilibrium conversion and selectivity was nearly independent of pressure as pressure was lower than 9 MPa. At higher pressure, however, the yield and selectivity of the diester increased considerably, while those of the monoester decreased with increasing pressure. The main reason was that reactants and products distributed between the vapor phase and liquid phase at higher pressures. The solvent power of CO2 for the diester is stronger than that for the monoester. More diester molecules in the liquid phase were extracted into the vapor at higher pressures, which shifted equilibrium of the consecutive reversible reactions.     

Identification and analysis of alpha1,6-fucosylated proteins in human normal liver tissues by a target glycoproteomic approach

alpha1,6-Fucose residues within the N-glycan core structures were commonly observed in many glycoproteins. Our previous studies showed that aberrantly alpha1,6-fucosylated glycoproteins might be associated with metastasis of hepatocellular carcinoma (HCC). Little is known about human normal liver tissues (HNLTs) in the literatures. In this study, a target glycoproteomic approach which consists of lectin-affinity chromatography, 2-DE, protein immunoprecipitation and lectin blot, and MALDI-MS/MS, was utilized to screen physiologically alpha1,6-fucosylated glycoproteins. Lens culinaris agglutinin (LCA)-affinity glycoprotein profiles of HNLT were established and analyzed, which allowed identification of 53 proteins by MS analysis, including haptoglobin precursor, alpha-enolase, etc. Gene ontology (GO) annotation proved that these proteins distribute predominately in organelle and play crucial roles in binding and catalytic reactions. The present methodology enabled the identification of all the specific subsets of glycoprotein, and the corresponding data could contribute to the finding of more aberrantly alpha1,6-fucosylated glycoproteins related to liver diseases.