Phase diagram and exotic spin-spin correlations of anisotropic Ising model on the Sierpi\'nski gasket

The anisotropic antiferromagnetic Ising model on the fractal Sierpi\'{n}ski gasket is intensively studied, and a number of exotic properties are disclosed. The ground state phase diagram in the plane of magnetic field-interaction of the system is obtained. The thermodynamic properties of the three plateau phases are probed by exploring the temperature-dependence of magnetization, specific heat, susceptibility and spin-spin correlations. No phase transitions are observed in this model. In the absence of a magnetic field, the unusual temperature dependence of the spin correlation length is obtained with $0 \leq$J$_b/$J$_a<1$, and an interesting crossover behavior between different phases at J$_b/$J$_a=1$ is unveiled, whose dynamics can be described by the J$_b/$J$_a$-dependence of the specific heat, susceptibility and spin correlation functions. The exotic spin-spin correlation patterns that share the same special rotational symmetry as that of the Sierpi\'{n}ski gasket are obtained in both the $1/3$ plateau disordered phase and the $5/9$ plateau partially ordered ferrimagnetic phase. Moreover, a quantum scheme is formulated to study the thermodynamics of the fractal Sierpi\'{n}ski gasket with Heisenberg interactions. We find that the unusual temperature dependence of the correlation length remains intact in a small quantum fluctuation.Comment: 9 pages, 12 figure

N′-(2-Methoxy­benzyl­idene)nicotinohydrazide

The title compound, C14H13N3O2, was prepared by the reaction of 2-methoxy­benzyaldehyde with nicotinic acid hydrazide in methanol. The dihedral angle between the benzene and pyridine rings is 5.9 (3)°. In the crystal structure, mol­ecules are linked by inter­molecular N—H⋯O hydrogen bonds, leading to the formation of chains along the c axis; adjacent chains are linked via C—H⋯O and C—H⋯N hydrogen bonds

Tetra­kis(3,5-dimethyl-1H-pyrazole-κN 2)(nitrato-κ2 O,O′)cadmium(II) nitrate

The title compound, [Cd(NO3)(C5H8N2)4]NO3, was prepared by reaction of cadmium nitrate and 3,5-dimethyl­pyrazole in ethanol solution. The Cd atom adopts a distorted cis-CdO2N4 octa­hedral geometry involving four dimethylpyrazole molecules and one bidentate nitrate anion. The mol­ecular structure and packing are stabilized by N—H⋯O and C—H⋯O inter- and intra­molecular hydrogen-bonding inter­actions

N-(1H-1,2,3-Benzotriazol-1-ylmeth­yl)phthalimide

The title compound [systematic name: 2-(1H-1,2,3-benzotriazol-1-ylmeth­yl)isoindole-1,3-dione], C15H10N4O2, was prepared by the reaction of 1H-benzotriazole and 2-bromo­methyl­isoindole-1,3-dione. The benzotriazole and isoindole units are almost planar and make a dihedral angle of 70.2 (1)° (mean planes include C and N atoms). A weak C—H⋯O intra­molecular hydrogen bond involving a carbonyl O atom as acceptor stabilizes the observed mol­ecular conformation

HIF-1α Contributes to Hypoxia-induced Invasion and Metastasis of Esophageal Carcinoma via Inhibiting E-cadherin and Promoting MMP-2 Expression

Hypoxia-inducible factor-1α (HIF-1α) has been found to enhance tumor invasion and metastasis, but no study has reported its action in esophageal carcinoma. The goal of this study was to explore the probable mechanism of HIF-1α in the invasion and metastasis of esophageal carcinoma Eca109 cells in vitro and in vivo. mRNA and protein expression of HIF-1α, E-cadherin and matrix metalloproteinase-2 (MMP-2) under hypoxia were detected by RT-PCR and Western blotting. The effects of silencing HIF-1α on E-cadherin, MMP-2 mRNA and protein expression under hypoxia or normoxia were detected by RT-PCR and Western blotting, respectively. The invasive ability of Eca109 cells was tested using a transwell chambers. We established an Eca109-implanted tumor model and observed tumor growth and lymph node metastasis. The expression of HIF-1α, E-cadherin and MMP-2 in xenograft tumors was detected by Western blotting. After exposure to hypoxia, HIF-1α protein was up-regulated, both mRNA and protein levels of E-cadherin were down-regulated and MMP-2 was up-regulated, while HIF-1α mRNA showed no significant change. SiRNA could block HIF-1α effectively, increase E-cadherin expression and inhibit MMP-2 expression. The number of invading cells decreased after HIF-1α was silenced. Meanwhile, the tumor volume was much smaller, and the metastatic rate of lymph nodes and the positive rate were lower in vivo. Our observations suggest that HIF-1α inhibition might be an effective strategy to weaken invasion and metastasis in the esophageal carcinoma Eca109 cell line