Maximum order-index of matrices over commutative inclines: an answer to an open problem

AbstractThis paper proves that the maximum order-index of n×n matrices over an arbitrary commutative incline equals (n−1)2+1. This is an answer to an open problem “Compute the maximum order-index of a member of Mn(L)”, proposed by Cao, Kim and Roush in a monograph Incline Algebra and Applications, 1984, where Mn(L) is the set of all n×n matrices over an incline L

Resolution of finite fuzzy relation equations based on strong pseudo-t-norms

AbstractThis work studies the problem of solving a sup-T composite finite fuzzy relation equation, where T is an infinitely distributive strong pseudo-t-norm. A criterion for the equation to have a solution is given. It is proved that if the equation is solvable then its solution set is determined by the greatest solution and a finite number of minimal solutions. A necessary and sufficient condition for the equation to have a unique solution is obtained. Also an algorithm for finding the solution set of the equation is presented

Methyl 4-(4-meth­oxy­phen­yl)-2-methyl-5-oxo-1,4,5,6,7,8-hexa­hydro­quinoline-3-carboxyl­ate

In the title compound, C19H21NO4, the dihydro­pyridine ring adopts a distorted screw-boat conformation. The fused cyclo­hexenone ring forms a slightly distorted envelope conformation. The dihedral angle between the mean planes of the benzene and heterocyclic rings is 86.1 (7)°. An intra­molecular C—H⋯O inter­action occurs. In the crystal, mol­ecules are linked by inter­molecular N—H⋯O hydrogen bonds, forming an infinite chain along the c axis

Enhanced mechanical, thermal and flame retardant properties by combining graphene nanosheets and metal hydroxide nanorods for Acrylonitrile–Butadiene–Styrene copolymer composite

Three metal hydroxide nanorods (MHR) with uniform diameters were synthesized, and then combined with graphene nanosheets (GNS) to prepare acrylonitrile–butadiene–styrene (ABS) copolymer composites. An excellent dispersion of exfoliated two-dimensional (2-D) GNS and 1-D MHR in the ABS matrix was achieved. The effects of combined GNS and MHR on the mechanical, thermal and flame retardant properties of the ABS composites were investigated. With the addition of 2 wt% GNS and 4 wt% Co(OH)2, the tensile strength, bending strength and storage modulus of the ABS composites were increased by 45.1%, 40.5% and 42.3% respectively. The ABS/GNS/Co(OH)2 ternary composite shows the lowest maximum weight loss rate and highest residue yield. Noticeable reduction in the flammability was achieved with the addition of GNS and Co(OH)2, due to the formation of more continuous and compact charred layers that retarded the mass and heat transfer between the flame and the polymer matrix

2,2-Dibromo-1-(4-hydr­oxy-3-methoxy­phen­yl)ethanone

The mol­ecule of the title compound, C9H8Br2O3, is stabilized by an intra­molecular O—H⋯O inter­action. Inter­molecular C—H⋯O inter­actions connect mol­ecules into a two-dimensional array in the bc plane; connections between these are afforded by π–π stacking inter­actions [centroid–centroid distance 3.596 (5) Å]

Cryptopleurine Targets NF-κB Pathway, Leading to Inhibition of Gene Products Associated with Cell Survival, Proliferation, Invasion, and Angiogenesis

Cryptopleurine, a phenanthroquinolizidine alkaloid, was known to exhibit anticancer activity; however, the underlying mechanism is poorly understood. Because the nuclear factor-κB (NF-κB) transcription factors control many physiological processes including inflammation, immunity, and development and progression of cancer, we investigated the effects of cryptopleurine on tumor necrosis factor alpha (TNF-α)-induced NF-κB activation pathway and on the expression of NF-κB-regulated gene products associated with many pathophysiological processes.MDA-MB231, MDA-MB435, MCF-7, HEK293, RAW264.7 and Hep3B cells were used to examine cryptopleurine's effect on the NF-κB activation pathway. Major assays were promoter-reporter gene assay, electrophoretic mobility shift assay (EMSA), in vitro immune complex kinase assay, real-time PCR, Western blot analysis, and Matrigel invasion assay. Experiments documenting cell proliferation and apoptosis were analyzed by MTT method and flow cytometry, respectively. The results indicated that cryptopleurine suppressed the NF-κB activation through the inhibition of IκB kinase (IKK) activation, thereby blocking the phosphorylation and degradation of the inhibitor of NF-κB alpha (IκBα) and the nuclear translocation and DNA-binding activity of p65. The suppression of NF-κB by cryptopleurine led to the down-regulation of gene products involved in inflammation, cell survival, proliferation, invasion, and angiogenesis.Our results show that cryptopleurine inhibited NF-κB activation pathway, which leads to inhibition of inflammation, proliferation, and invasion, as well as potentiation of apoptosis. Our findings provide a new insight into the molecular mechanisms and a potential application of cryptopleurine for inflammatory diseases as well as certain cancers associated with abnormal NF-κB activation