for all x, y ∈ X. Kannan [] proved that if X is complete, then a Kannan mapping has a fixed point. It is interesting that Kannan’s theorem is independent of the Banach contraction principle []. Also, Kannan’s fixed point theorem is very important because Subrahmanyam [] proved that Kannan’s theorem characterizes the metric completeness. That is, a metric space X is complete if and only if ev...

Let G be a simple, simply connected algebraic group over an algebraically closed field k of characteristic p>0. σ:G→G surjective endomorphism such that the fixed point set G(σ) is Suzuki or Ree group. Then, let Gσ denote scheme-theoretic kernel σ. Using methods Jantzen and Bendel–Nakano–Pillen, we compute 1-cohomology for Frobenius kernels with coefficients in induced modules, H1(Gσ,H0(λ)), ext...

Since metal nanoparticles have a high surface-to-volume ratio and very active surface atoms, they are very attractive catalysts for a wide variety of organic and inorganic reactions, compared to bulk catalysts. Metal nanoparticles suspended in colloidal solutions and those adsorbed onto bulk supports have been used as catalysts for a wide variety of carbon-carbon bond formation reactions such a...

rule learning in human and non-human animals . . . . . . . 73 Reiko Hoshi-Shiba, Fang Sun, Kenta Suzuki, Dilshat Abla, Kazuo Okanoya Combinational vocal usage for emotional expression in common marmoset (Callithrix jacchus) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 Yoko Kato, Hayato Gokan, Arata Oh-Nishi, Takafumi Minamimoto Vocal deviance detection in auditory cortex of a so...

Air and moisture stable homoleptic bis(diimidazolylidine)nickel(II) complexes, ([(diNHC)(2)Ni](2+)) 3a,b and their corresponding silver(I) 4a,b and palladium(II) 5a,b complexes were synthesized and characterized by NMR and single crystal X-ray analysis. The catalytic potential of complex 3a was assessed in Mizoroki-Heck and Suzuki-Miyaura coupling reactions. In the Suzuki-Miyaura coupling react...

We classify $N{=}1$ SVOAs with no free fermions and bosonic subalgebra a simply connected WZW algebra which is not of type $\mathrm{E}$. The latter restriction makes the classification tractable; former implies that automorphism groups resulting are finite. discover two infinite families nine exceptional examples. exceptions all related to Leech lattice: their larger in Suzuki chain ($\mathrm{C...

The third effect of electrodes of a polarizing current applied on a nerve denotes, as described by Suzuki (1) and Suzuki, Ando and Miyata (2), the effect of a longer or stronger polarization, which causes changes in the threshold of stimulation under both electrodes in direction opposite to those due to the electrotonus. The changes in the threshold by the electrotonus, which appear soon after ...

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 ...