We develop a new and uniform approach to the three families of simple groups of Lie type discovered by Suzuki and Ree, without using Lie algebras. A novel type of algebraic structure is defined, whose automorphism groups are the groups in question. This leads to elementary proofs of the group orders and simplicity, as well as much information on subgroup structure and geometry.

Marinomycins A-C (1-3), and their monomeric analogues monomarinomycin A (m-1) and iso-monomarinomycin A (m-2), were synthesized by a convergent strategy from key building blocks ketophosphonate 5, aldehyde 6, and dienyl bromide carboxylic acid 7. The first attempt to construct marinomycin A [1, convertible to marinomycins B (2) and C (3) by light] by direct Suzuki-type dimerization/cyclization ...

Optical recording methods were used to characterize the intrinsic movements of squid stellate ganglia. Ganglionic contractions were rhythmic and occurred at a mean frequency of 8 min-1. Contractions were eliminated when Na+ in the external saline were replaced by Tris, but were only slowed when Na+ was replaced by sucrose. This suggests that Na+ plays some role in generating the contractions, b...

The regiocontrolled preparation of triarylisothiazoles is presented. 3-Halo-5-phenylisothiazole-4-carbonitriles, 1 (hal=Cl) and 18 (hal=I), are converted into the corresponding 4-bromo derivatives 5 (3-hal=Cl) and 24 (3-hal=I) via a Hunsdiecker strategy while the 4-iodo analogues 7 (3-hal=Cl) and 22 (3-hal=I) are prepared via a Hoffmann and Sandmeyer strategy. Regioselective Suzuki, Stille and ...

This paper extends the Suzuki and Shimodora method [Suzuki R, H. Pvclust: an R package for assessing uncertainty in hierarchical clustering. Bioinformatics. 2006;22:1540–1542] cluster analysis to multivariate datasets examines reliability of simulated probabilities relation simulation adopted. The extension is applied squared Euclidean Mahalanobis-type distances employs three methods, Monte-Car...

Samet et al. in [S. Samet, C. Vetro, H. Yazidi, J. Nonlinear Sci. Appl., 6 (2013), 162–169] proved some fixed point theorem for contractions of rational type. In order to clarify the mathematical structure of contractions of rational type, we generalize this theorem in a general setting.

recently, choudhury and metiya [fixed points of weak contractions in cone metric spaces, nonlinear analysis 72 (2010) 1589-1593] proved some fixed point theorems for weak contractions in cone metric spaces. weak contractions are generalizations of the banach's contraction mapping, which have been studied by several authors. in this paper, we introduce the notion of $f$-weak contractions and als...

A new type of public key cryptosystem, called MST3, has been recently developed on the basis of logarithmic signatures and covers of finite groups. The Suzuki 2-groups have been suggested for a possible realization of the generic version of MST3. On one hand, due to their structure, the Suzuki 2-groups allow one to study the security complexity of the system, on the other hand they possess a si...

This paper considers Q-Fano 3-folds X with ρ = 1. The aim is to determine the maximal Fano index f of X. We prove that f ≤ 19, and that in case of equality, the Hilbert series of X equals that of weighted projective space P(3, 4, 5, 7). We also consider all possibility of X for f ≥ 9. 0. Introduction We say that X is a Q-Fano variety if it has only terminal singularities, the anticanonical Weil...