Interchange Technique Research Articles

Berg's Technique for Pseudo-Actions With Applications to af Embeddings

AbstractBerg's interchange technique is generalized to the context of certain new objects called pseudo-actions. This is used to find a more geometric proof of the Pimsner-Voiculescu theorem on the AF embedding of the irrational rotation algebras. Connections with Berg's original results are briefly examined.Embedding diagrams are introduced to provide a uniform way of describing embeddings of transformation group C*-algebras C(X) ⋊ ℤ into AF algebras. Pimsner has classified the transformation group C* -algebras which can be AF embedded. We present a new proof of this result using embedding diagrams and pseudo-actions. The need to calculate the join of an open cover with its iterates under the transformation has been eliminated.

On Minimizing Flow Time on Processors with Variable Unit Processing Time

This paper uses the interchange technique to prove a result of Meilijson and Tamir that the shortest processing time (SPT) schedule minimizes total flow time on parallel identical processors that have unequal starting times and nonincreasing unit processing time. The SPT schedule remains optimal for a special case when the unit processing time is increasing.

A class of sorting algorithms based on Quicksort

Bsort, a variation of Quicksort, combines the interchange technique used in Bubble sort with the Quicksort algorithm to improve the average behavior of Quicksort and eliminate the worst case situation of O(n 2 ) comparisons for sorted or nearly sorted lists. Bsort works best for nearly sorted lists or nearly sorted in reverse.

Synthesls and Pnopeaties of 4-Penten-2-oxide Denlvatives of Some Elements

Abstract The alcohol interchange technique has been successfully applied for the synthesis of 4-penten-2-oxide derivatives of boron, aluminium, germanium, titanium, niobium, tantalum and butyitin derivatives. Germanium tetra-4-penten-2-oxide and 4-penten-2-yl borate could also be synthesized by the reactions of 4-pente-2-ol with (i)germanium tetrachloride in the presence in the presence of ammonia and (ii) boric oxide respectively. These derivatives were characterized by elemental analyses, molecular weight determinations, IR and PMR spectral studies.

Synthesis and Properties of Bimetallic Alkoxides and Mixed Acetylacetonates of Tin(II) with Aluminium (III)

Abstract Evidence for the formation of a bimetallic isopropoxide of tin(II) with aluminium (III) has been obtained by conductance studies. The compound (I), Sn [Al(OPr1)4]2, has been synthesised, purified and characterized. Chemical evidence for the formation of compound (I) was obtained by reacting Sn[Al(OPr1)4]2 with acetylacatone. A number of other bimetallic derivatives, Sn[Al(OR)4]2 and Sn[Al(OPr1)(oBut)3]2 (where R = Me, Et, CF3CH2 and (CH2Cl)2CH) have also been synthesised by the alcohol interchange technique. All these compounds were characterisad by i.r. and p.m.r. spectral studies. The molecular weights of these compounds in boiling benzene have also been determined.

Alkyl Thioglycolates of Aluminium, Titanium and Zirconium

Abstract Alkyl thioglycolates of the type Al(OR)G (R = Pri, But); M(OR)2G (M = Ti, Zr; R = Pri, But); MG2 (M = Ti, Zr), Al2G3 and Al(GH)G where GH2 is methyl or ethyl thioglycolate have been prepared. The isopropoxy derivatives were obtained by carrying out the reaction between the isopropoxide of the corresponding metal with methyl or ethyl thioglycolate in anhydrous benzene in different molar ratios, whereas the tertiary butoxy derivatives were prepared from the respective isopropoxy derivatives by alcohol interchange technique. Molecular weights of soluble titanium and zirconium derivatives show them to be dimeric in nature. Structures have been suggested on the basis of infrared spectral and molecular weight studies.

Aluminium Derivatives of Tridentate Bifunctional Schiff Bases Derived from Salicylaldehyde and Benzoylacetone

S = salicylaldehyde and benzoylacetone and B = (CH2-)2, -CH2-CH -CH3 and C6H5) in different stoichiometric ratios have been synthesised. The products Al (OPri) (SB) are soluble in benzene. The tertiary butoxy products have been prepared by the alcohol interchange technique. Infrared spectra of the new derivatives are reported. Thermogravimetric analyses have also been carried out.

Organic compounds of lanthanide elements—III: alcoholates of lanthanum and cerium (III) chlorides

The reactions of alcohols (methanol, ethanol, propanols, butanols etc.) with anhydrous lanthanum and cerium (III) chlorides have been investigated and a large number of new compounds with the general formula MCl 3·3ROH have been isolated. When lanthanum and cerium (III) chloride monohydrates were allowed to react with alcohols, dialcoholates with the formula MCl 3·H 2O·2ROH were isolated. The synthesis of higher alcoholates from the lower derivatives was also successfully achieved by the use of alcohol interchange technique. Some physico-chemical properties (pyrolysis, molecular weight, conductivity and spectra) of these alcoholate derivatives were also studied.

Alkoxides of Vanadium. I. Synthesis of Trialkylorthovanadates by Alcohol Interchange Technique

AbstractA number of alkoxides of vanadium have been prepared more conveniently in higher yields by alcohol interchange technique.

Cluster Analyses of Skin Resistance and Heart Rate at Rest and Under Stress

Cluster Analyses of Skin Resistance and Heart Rate at Rest and Under Stress

Organic Derivatives of Boron. Part I. Synthesis by Alcohol Interchange Technique

Organic Derivatives of Boron. Part I. Synthesis by Alcohol Interchange Technique