Nonparametric Approach for Non-Gaussian Vector Stationary Processes

Suppose that {z(t)} is a non-Gaussian vector stationary process with spectral density matrixf(λ). In this paper we consider the testing problemH: ∫^π_−π K{f(λ)} dλ=cagainstA: ∫^π_−π K{f(λ)} dλ≠c, whereK{·} is an appropriate function andcis a given constant. For this problem we propose a testT_nbased on ∫^π_−π K{f(λ)} dλ=c, wheref(λ) is a nonparametric spectral estimator off(λ), and we define an efficacy ofT_nunder a sequence of nonparametric contiguous alternatives. The efficacy usually depnds on the fourth-order cumulant spectraf₄^Zofz(t). If it does not depend onf₄^Z, we say thatT_nis non-Gaussian robust. We will give sufficient conditions forT_nto be non-Gaussian robust. Since our test setting is very wide we can apply the result to many problems in time series. We discuss interrelation analysis of the components of {z(t)} and eigenvalue analysis off(λ). The essential point of our approach is that we do not assume the parametric form off(λ). Also some numerical studies are given and they confirm the theoretical results.     

Reactions of allylic compounds such as allyl alcohols,allyl ethers,and allylamines using trans-Mo(N2)2(Ph2PCH2CH2PPh2)2

Double-bond migration of allylic alcohols and allylic alkyl ethers was catalytically effected with trans-Mo(N₂)₂(dpe)₂(dpe = Ph₂PCH₂CH₂PPh₂). Decarbonylation occurred simultaneously in the case of allyl alcohol. Diallyl ether and allyl phenol ether gave the fragmentation products presumably through initial oxidative addition of the allylO bond. Allylamine was converted to N-propylideneallylamine and NH₃. N,N-Dimethylallylamine was isomerized to N-trans-propenyldimethylamine, which was further transformed into 4-dimethylamino-1,3-hexadiene and dimethylamine on addition of oxygen. The catalytic allylation of methyl acetoacetate with allylic ethers and amines was achieved by use of trans-Mo(N₂)₂(dpe)₂.     

Chemoselective silylzincation of functionalized terminal alkynes using dianion-type zincate (SiBNOL-Zn-ate): regiocontrolled synthesis of vinylsilanes

A regio- and chemoselective silylzincation reaction of various functionalized alkynes was developed using a newly designed dianion-type zincate. Silylzincation of terminal alkynes, followed by electrophilic trapping, proved to be a powerful tool for the one-pot, regiocontrolled generation of trisubstituted functionalized alkenes. The functionalized vinylzincate intermediate also undergoes copper- and palladium-catalyzed C-C bond-forming reactions in high yields and with high regio- and chemoselectivities.     

The knoevenagel condensation of ethyl acylpyruvates

Extensive studies of the Knoevenagel condensation of aromatic aldehydes and active methyl-lene compounds have been reported (2). In 1894, Knoevenagel reported (3) the reaction of benz-aldehyde with ethyl benzoylpyruvate in the presence of piperidine to give ehtyl benzyl-(bis-benzoyl)pyruvate, m.p. 162°, but no yield of the product was reported. This paper deals with the interesting results of the reactions of ethyl acetylpyruvate ( 2 ) ( 4 ) and ethyl benzoylpyruvate ( 3 ) (5) with some aromatic aldehydes ( 1a-f ).     

Ruthenium-catalyzed propargylation of aromatic compounds with propargylic alcohols

A novel ruthenium-catalyzed propargylation of aromatic compounds with propargylic alcohols has been found to afford the corresponding propargylated aromatic products in good yields with complete regioselectivity. The catalytic reaction provides a potential usefulness for practical application in organic synthesis, because the selective propargylation of aromatic compounds with an aromatic C-H bond cleavage is generally difficult.     

Ruthenium- and platinum-catalyzed sequential reactions: selective synthesis of fused polycyclic compounds from propargylic alcohols and alkenes

A simple method for the preparation of fused polycyclic compounds by an intramolecular cyclization of propargylic alcohols bearing an alkene moiety at a suitable position has been developed, where the presence of both Ru and Pt catalysts promotes a sequence of catalytic cycles in the same medium. This sequential system can be applied to an intermolecular reaction between a propargylic alcohol and an alkene to obtain the corresponding bicyclo[3,1,0]hex-2-ene derivative. These sequential reactions provide a conceptually new type of cycloaddition system between propargylic alcohols and alkenes.     

Differential interactions of cyclodextrins with hydrophobic derivatives of sepharose CL-4B

The partition coefficients K_av between the solution phase and octyl- and phenyl-sepharose CL-4B were determined for three cyclodextrins (CDs), -CD, -CD and -CD in various aqueous solutions, as a measure of their interactions with the two hydrophobic ligands. K_av of the CDs increased in the order of -CD<-CD<-CD for octyl-sepharose CL-4B and -CD<-CD<-CD for phenyl-sepharose CL-4B. In all cases, K_av increased by increasing NaCl concentration in the aqueous solution phase and also by lowering temperature, but in the presence of NaBr and NaSCN, both chaotropic salts, K_av decreased markedly. The spontaneity of the transfer of the CDs from the aqueous solution phases to the gel phases was due to the enthalpy decrease. It was shown that discrete separation of the three CDs can be achieved by the hydrophobic chromatography on a short column (1×25cm) of octyl-sepharose CL-4B by adjusting the NaCl concentration and temperature.     

Development of a catalytic electron transfer system mediated by transition metal ate complexes: applicability and tunability of electron-releasing potential for organic transformations

We have developed a catalytic electron transfer (ET) system composed of a transition metal ate complex (Me3M(II)Li; M = Co(II), Mn(II), Fe(II)) and magnesium. This system (catalytic Me3M(II)Li/Mg) turned out to be effective for various ET reactions, such as the desulfonylation of N-phenylsulfonyl amides, and others (the chemoselective cleavage of O-allyl groups, the reduction of nitro groups, the partial reduction of diketones, and the reductive coupling of diphenyliodonium salt). The ET ability of this system can be tuned by changing the ligands of the ate complexes. This tunability was experimentally and electrochemically demonstrated: alkoxy-ligated and dianion-type ET ate complexes showed attenuated and enhanced reducing abilities, respectively. The modification of the ET abilities was evaluated by means of electrochemical measurements and chemical reactions. These results provide a basis for the design of various tailor-made ET ate complexes.     

Radiation-induced polymerization of 1,2-cyclohexene oxide in the plastic crystalline state

Radiation-induced solid state polymerization of 1,2-cyclohexene oxide has been investigated. By the differential thermal analysis and x-ray diffraction analysis, it was found that this compound has a phase transition point at ?81°C and behaves as a plastic crystal in the temperature range from ?81°C to ?36°C (melting point). The in-source polymerization proceeded not only in the plastic crystalline state but also in the ordinary crystalline state at temperatures below the phase transition point. The overall rate of polymerization and the rate of chain transfer to monomer in the plastic crystalline state were larger than those in the ordinary crystalline state by a factor of about forty, but the kinetic mechanisms were identical, i.e., the termination mechanisms were unimolecular in both solid states. In contrast, the kinetic mechanisms in the plastic crystalline state and in the liquid state were different. From these observations, the effects of molecular motion and molecular arrangement on the polymerizations of 1,2-cyclohexene oxide in the three phases were discussed.