弱Hopf代数上的Militaru-Stefan提升定理

本文研究了弱Hopf-Galois扩张的扩张模.利用忠实平坦的弱Hopf-Galois扩张理论,研究了弱Hopf代数上的Militaru-Stefan提升定理,推广了文献[10]中的相应结果.进一步地,通过诱导模的自同态环的cleft扩张刻画了弱稳定模.     

Local regularity criteria of a suitable weak solution to MHD equations

We present a regularity condition of a suitable weak solution to the MHD equations in three dimensional space with slip boundary conditions for a velocity and magnetic vector fields. More precisely, we prove a suitable weak solution are H¨older continuous near boundary provided that the scaled mixed L_(x,t)~(p,q) -norm of the velocity vector field with 3/p + 2/q ≤ 2,2 q ∞ is sufficiently small near the boundary. Also, we will investigate that for this solution u ∈ L_(x,t)~(p,q) with 1≤3/p+2/q≤3/2, 3 p ∞, the Hausdorff dimension of its singular set is no greater than max{p, q}(3/p+2/q-1).     

Analysis of an elasto-piezoelectric system of hemivariational inequalities with thermal effects

In this paper we prove the existence and uniqueness of a weak solution for a dynamic electo-viscoelastic problem that describes a contact between a body and a foundation. We assume the body is made from thermoviscoelastic material and consider nonmonotone boundary conditions for the contact. We use recent results from the theory of hemivariational inequalities and the fixed point theory.     

内蕴平方函数交换子在加权弱Hardy空间上的端点估计

证明了由BMO函数与α阶内蕴面积函数S_α和内蕴g_(λ,α)*函数生成的交换子都是由加权弱Hardy空间WH_(b,ω)~1到加权弱L1空间WL_ω~1上的有界算子.     

Theoretical investigation of the weak interactions of rare gas atoms with silver clusters by resonance Raman spectroscopy modeling

The interactions of rare gas atoms (Rg = Ar, Kr, and Xe) with small neutral and cationic silver clusters have been investigated by density functional methods and the effect of these weak interactions on the resonance Raman spectra of the complexes has been evaluated. The resonance Raman technique that depends on the properties of ground and excited state, seems deeply sensitive to the weak rare gas–metal cluster interactions, and the use of inert gases has been proven to be an excellent approach to recognize the ability of this technique to detect extremely weak interactions. In this work, for , and complexes the IR, normal and resonance Raman spectra have been calculated and the effect of rare gas–cluster stretching vibration ( ) on the pattern and the relative intensities of different spectra have been investigated. The resonance Raman spectra for the weakly interacted complexes (with the interaction energies less than ?2.0 kcal/mol) exhibit the vibration with the detectable intensity that its intensity increases by going from Ag₆–Ar to Ag₆–Xe complex. Moreover, the resonance Raman spectra (based on the excited state gradient approximation) for high intensity nearly degenerate excited states, proved the effect of accumulation of the excited state charge density on the relative intensity of vibration.     

Facile synthesis of aminonaphthoquinone Mannich bases by noncatalytic multicomponent reaction

Mannich bases are formed in a noncatalytic multicomponent reaction, which is promoted by ultrasound irradiation. The procedure avoids the use of toxic solvents, catalyst, and purification, generating the desired compounds in excellent yields and short reaction times.     

In vitro anticancer activity of binuclear Ru(II) complexes with Schiff bases derived from 5-substituted salicylaldehyde and 2-aminopyridine with notably low IC50 values

The binuclear Ru(II) complexes with Schiff bases derived from 5-chlorosalicyladehyde and 2-aminopyridine and its 5-substituted salicylideneimine homologues were tested in vitro against cervical carcinoma (HeLa), metastatic colorectal adenocarcinoma (SW620), lung adenocarcinoma (A549), breast adenocarcinoma (MCF-7), and human lung fibroblast (WI-38) cell lines. All compounds showed strong antiproliferative activity with extremely low IC₅₀ values. The compounds expressed strong activity against gram-positive bacteria, Staphylococcus aureus and Enterococcus faecalis.     

Synthesis,characterization and biological properties of novel ON donor bidentate Schiff bases and their copper(II) complexes

Four novel ON donor Schiff bases (E)-3-((4-phenoxyphenylimino)methyl)benzene-1,2-diol (HL₁),(E)-3-((4-(4-biphenyloxy)phenyliminomethyl)benzene-1,2-diol (HL₂), (E)-3-((4-naphthoxyphenylimino)methyl)benzene-1,2-diol (HL₃), (E)-3-((4-(2-naphthoxy)phenylimino)methyl)benzene-1,2-diol (HL₄) and their copper(II) complexes bis((E)-3-((4-phenoxyphenylimino)methyl)benzene-1,2-diol) copper(II) (Cu(L₁)₂) bis((E)-3-((4-(4-biphenyloxy)phenylimino)methyl)benzene-1,2-diol) copper(II) (Cu(L₂)₂), bis((E)-3-((4-naphthoxyphenylimino)methyl)benzene-1,2-diol) copper(II) (Cu(L₃)₂), bis((E)-3-((4-(2-naphthoxy)phenylimino)methyl)benzene-1,2-diol) copper(II) (Cu(L₄)₂) have been synthesized and characterized by spectroscopic (FTIR, NMR, UV–visible) and elemental analysis. The crystal structures of HL₁, HL₂, HL_3, and HL₄ have been determined, which reveal intramolecular N-H?O (HL₁, HL₂, HL_3, and HL₄) hydrogen bonds in the solid state. Keto-amine and enol-imine tautomerism is exhibited by the Schiff bases in solid and solution states. The Schiff bases and their copper(II) complexes have been screened for their biological activities. In antimicrobial assays (antibacterial and antifungal), HL₄ showed promising results against all strains through dual inhibition property while the rest of the compounds showed activity against selective strains. On the other hand, in cytotoxic, DPPH, and inhibition of hydroxyl (OH) free radical-induced DNA damage assays, the results were found significantly correlated with each other, i.e. the ligands HL₁ and HL₂ showed moderate activity while their complexes Cu(L₁)₂ and Cu(L₂)₂ exhibited prominent increase in activity. As the results of these assays are supporting each other, it represents the strong positive correlation and antioxidant nature of investigated compounds.     

GLOBAL EXISTENCE OF WEAK SOLUTIONS FOR GENERALIZED QUANTUM MHD EQUATION

We prove the existence of a weak solution for a generalized quantum MHD equation in a 2-dimensional periodic box for large initial data. The existence of a global weak solution is established through a three-level approximation,energy estimates, and weak convergence for the adiabatic exponent γ 1.