THE THEORETICAL COST OF SEQUENTIAL AND PARALLEL ALGORITHMS FOR SOLVING LINEAR SYSTEMS OF EQUATIONS

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Void fraction measurement by X-ray absorption

An X-ray tube and scintillation detectors were mounted on test pipes containing static voids of air–water mixture. Due to fluctuations in the X-ray tube output, void fraction measurements were carried out by using two detectors, one as a reference and the other as a void monitor. The intensity of a narrow (30–100 kV) X-ray beam transmitted through test pipes of different I.D. was measured to obtain the void fraction. The uncertainty in measuring static void fraction, was found to decrease as the void fraction increases, and to increase as X-ray energy increases. It was found that for a certain test-section pipe diameter, there exist an optimum X-ray energy that gives a minimum uncertainty in void fraction measurement.     

Iterative approximation of fixed points of Prešić operators on partial metric spaces

We study the convergence of the Pre?i? type k‐step iterative method for a class of operators satisfying Pre?i? type contractive conditions on the setting of partial metric spaces. Some examples are presented to illustrate our obtained results. As applications of the presented convergence theorems, we derive global attractivity results for a class of matrix difference equations. Numerical experiments are also presented to illustrate the theoretical findings.     

Efficient Solvent‐Free Synthesis of Benzothiazine‐Fused Pyrrolo[3,4‐c]coumarins: Cycloaddition Reactions between Coumarin‐Based Dihydrobenzothiazoles and Isocyanides

A new and unusual synthesis of benzothiazine‐fused pyrrolo[3,4‐c]coumarins, involving the ring‐opening of coumarin‐based dihydrobenzothiazoles and subsequent [4+1] cycloaddition reaction with isocyanides, was described. Thus, simple heating of various 3‐(2,3‐dihydro‐2‐methylbenzo[d]thiazol‐2‐yl)coumarins with isocyanides produced the title compounds in good yields under solvent‐free conditions.     

DFT studies on the tetranuclear cubane complex [Ni4(ampd)4(Cl4)]·MeCN

Density functional theory (DFT) is used to investigate the structural properties of Ni(II) cubane [Ni₄(ampdH)₄Cl₄]·MeCN. The structural features and ground state geometry calculations are computed at the B3LYP/6-31G* (LANL2DZ) level of theory. We shed light on the highest occupied molecular orbital and lowest unoccupied molecular orbital. The absorption spectrum is calculated using time-dependent DFT. The absorption wavelengths are calculated using different functionals, i.e., pw91pw91, B3LYP, BHandHLYP, CAM-B3LYP, LC-BLYP, and M06. The LC-BLYP is in good agreement with the experimental data.     

Synthetic Approaches towards the Sulfonamide Substituted‐1,5‐Diarylimidazole‐2‐thiones as Selective Cyclooxygense‐2 inhibitors

A new series of sulfonamide substituted 1,5‐diarylimidazole, possessing C‐2 alkylthio moiety, were synthesized for their cyclooxygense‐2 (COX‐2) inhibitory activity starting from condensation of N,N‐dibenzylaminosulfonylphenacylamine hydrochloride ( 2 ) and corresponding isothiocyanate in the presence of Et₃N, followed by alkylation in the basic medium. In concomitant with these intermediates, 2‐arylamino‐5‐arylthiazole derivatives 5 were also produced. The ratio of these two products was variable with different isothiocyanates. Final debenzylation was achieved using concentrated sulfuric acid to give the title sulfonamides 8 .     

Rates of intra- and intermolecular electron transfers in hydrogenase deduced from steady-state activity measurements

Electrons are transferred over long distances along chains of FeS clusters in hydrogenases, mitochondrial complexes, and many other respiratory enzymes. It is usually presumed that electron transfer is fast in these systems, despite the fact that there has been no direct measurement of rates of FeS-to-FeS electron transfer in any respiratory enzyme. In this context, we propose and apply to NiFe hydrogenase an original strategy that consists of quantitatively interpreting the variations of steady-state activity that result from changing the nature of the FeS clusters which connect the active site to the redox partner, and/or the nature of the redox partner. Rates of intra- and intermolecular electron transfer are deduced from such large data sets. The mutation-induced variations of electron transfer rates cannot be explained by changes in intercenter distances and reduction potentials. This establishes that FeS-to-FeS rate constants are extremely sensitive to the nature and coordination of the centers.     

Cyclicity of the unramified Iwasawa module

For a number field k and a prime number p, let k _?? be the cyclotomic Z _p -extension of k with finite layers k _n . We study the finiteness of the Galois group X _?? over k _?? of the maximal abelian unramified p-extension of k _?? when it is assumed to be cyclic. We then focus our attention to the case where p?=?2 and k is a real quadratic field and give the rank of the 2-primary part of the class group of k _n . As a consequence, we determine the complete list of real quadratic number fields for which X _?? is cyclic non trivial. We then apply these results to the study of Greenberg??s conjecture for infinite families of real quadratic fields thus generalizing previous results obtained by Ozaki and Taya.     

Stability analysis of graphene based laminated composite sheets under non-uniform inplane loading by nonlocal elasticity

Size dependent buckling of composite laminates made of isotropic graphene layers interlaid with bonding agents is considered. Nonlocal theory of elasticity is used in the buckling analysis to reflect the size scale effects on the critical buckling loads which is discussed in detail. The method is capable of predicting the relative buckling modes for non-uniform inplane loading applied through the thickness of the laminate. All modes of buckling in which the layers may displace together or opposite one another are investigated to study their scale dependent effects. Displacement or load controls are implemented through independent parameters as constraints to form special combination of buckling modes. Each graphene sheet is considered as a Kirchhoff plate model. The interlaid bonding agent is laterally treated as Winkler elastic foundation between graphene layers while neglecting their other load carrying capacities. Various numerical results are obtained reflecting the nonlocality effects. It is observed that in cases of higher load ratios and simpler buckling modes, the effect of nonlocality tends to drastically increase. The results of simpler examples studied are verified by another reference.     

Examination of Template Structural Effects on CEC Chiral Separation Performance of Molecule Imprinted Polymers Made by a Generalized Preparation Protocol

Some acidic chiral templates were used to prepare open tubular (OT) molecule imprinted polymer (MIP) capillary columns to explore the effects of molecular structures of templates on chiral recognition capabilities and to verify the feasibility of the general MIP preparation protocol introduced in the previous study. The templates are phenyl carboxylic acids and their derivatives. Optimization was carried out for chiral separation of template enantiomers for each MIP column through varying pH and composition of eluent. It was found that the preparation protocol can be successfully applied for the appropriate templates with functional groups fulfilling the three-points interaction rule. The chiral separation performances were quite satisfactory for MIPs of such templates although they are yet inferior to the separation performances of the MIP columns fabricated with the templates of profen drugs (2-arylpropionic acids with a large substituent on the phenyl ring). Subtle variations of the template molecular structures have been found to be critical to enhance chiral recognition ability of the resultant MIP column.