A unification of the existence theorems of the nonlinear complementarity problem

The nonlinear complementarity problem is the problem of finding a point x in the n-dimensional Euclidean space,R ⁿ , such that x ? 0, f(x) ? 0 and 〈x,f(x)～ = 0, where f is a nonlinear continuous function fromR ⁿ into itself. Many existence theorems for the problem have been established in various ways. The aim of the present paper is to treat them in a unified manner. Eaves's basic theorem of complementarity is generalized, and the generalized theorem is used as a unified framework for several typical existence theorems.     

Cubic phases of 4′-n-alkoxy-3′-nitrobiphenyl-4-carboxylic acids (ANBC-n)

The structure of the thermotropic cubic phases of 4′- ⁿ -alkoxy-3′-nitrobiphenyl-4-carboxylic acids (ANBC- ⁿ , where ⁿ indicates the number of carbon atoms in the alkoxy group) was studied by X-ray diffraction. For the homologues with ⁿ = 15, 16, 17, and 18, the cubic phase was of an ^Ia 3 ^d type, whereas the homologues with ⁿ = 19, 20, and 21 exhibited an ^Im 3 ^m cubic structure; for these seven homologues the same type of cubic structure was observed both on heating and cooling. Further lengthening of the alkoxy chain to ⁿ = 22 and 26, however, gave two types of cubic structure in the cubic phase region on heating, one with ^Im 3 ^m symmetry in the low temperature region and the other with ^Ia 3 ^d symmetry in the high temperature region. On cooling, the two homologues exhibited the ^Ia 3 ^d cubic structure only. This is the first example in the cubic phase region of a series of homologues containing two types of structure, dependent on temperature and ⁿ . Such a complicated phase diagram in the cubic region is clearly understood qualitatively in terms of Gibbs free energy-temperature diagrams. The dependence of structural parameters such as the cubic lattice constant on the alkoxy chain length ⁿ are also presented and discussed.     

Permutation Cellular Automata

Permutation cellular automata are cellular automata defined by using finite maximal prefix codes. The overall dynamics of onesided and twosided permutation cellular automata is studied. For some classes of permutation cellular automata including the class of those defined by using finite maximal bifix codes, the overall dynamics is completely or partially described in terms of the codes used to define them.     

Intra-abdominal fat area is a predictor for new onset of individual components of metabolic syndrome: MEtabolic syndRome and abdominaL ObesiTy (MERLOT study)

Objective: To investigate the significance of intra-abdominal fat area (IAFA) on new onset of individual components of the metabolic syndrome: high blood pressure, dyslipidemia, or hyperglycemia. Methods: We conducted a longitudinal study using checkup data of a hospital from 1994 to 2010. Of 25,255 subjects, we examined 1,380 Japanese, who underwent computed tomography to measure IAFA and had no metabolic syndrome components at baseline. Results: During 3.6 years of the mean follow-up period, one of metabolic syndrome components occurred in 752 subjects. Of three components, high blood pressure was more prevalent. The multiple Cox regression analysis disclosed that IAFA is significantly associated with onset of metabolic syndrome components (HR: 1.05 per 10 cm², 95%CI: 1.03–1.07). This finding was independent of BMI, and significant even in non-obese individuals with body mass index <25 kg/m². Conclusions: MERLOT study demonstrates that IAFA is an independent predictor for new onset of individual components of the metabolic syndrome, even in non-obese healthy Japanese.     

Synthesis of All Stereoisomers of Monomeric Spectomycin A1/A2 and Evaluation of Their Protein SUMOylation-Inhibitory Activity

A synthetic methodology to access all possible stereoisomers of spectomycin A1 (SMA1) and A2 (SMA2) has been established through late-stage diversification. The key reaction for the construction of all four diastereomers is an intramolecular cyclization based on the umpolung of π-allyl palladium species with bis(pinacolato)diborane (B₂(pin)₂). Silyl group assisted direct benzylic oxidation of each isomer enabled construction of the fragile β-hydroxytetralone skeleton to provide the SMAs. The relative and absolute stereochemistry of SMA2 was also determined, and the absolute stereochemistry of SMA1 was extrapolated based on the optical rotation of SMA2. The axial chirality of SMAs is discussed based on circular dichroism spectra and DFT calculations, and it is concluded that the M isomer is predominant in solution. Biochemical assessment of all isomers in vitro revealed that the C9 hydroxyl group and dimeric structure were both important for protein SUMOylation-inhibitory activity.