Approximation algorithms for dynamic resource allocation

We consider a problem of allocating limited quantities of M types of resources among N independent activities that evolve over T epochs. In each epoch, we assign to each activity a task which consumes resources, generates utility, and determines the subsequent state of the activity. We study the complexity of, and approximation algorithms for, maximizing average utility.     

On a New Non-Geometric Element in Gravity

In this essay a generalized notion of flavor-oscillation clocks is introduced. The generalization contains the element that various superimposed mass eigenstates may have different relative orientation of the component of their spin with respect to the rotational axis of the gravitational source. It is found that these quantum mechanical clocks do not always redshift identically when moved from the gravitational environment of a non-rotating source to the field of a rotating source. The non-geometric contributions to the redshifts may be interpreted as quantum mechanically induced fluctuations over a geometric structure of space-time.     

Dislocation unpinning model of acoustic emission from alkali halide crystals

The present paper reports the dislocation unpinning model of acoustic emission (AE) from alkali halide crystals. Equations are derived for the strain dependence of the transient AE pulse rate, peak value of the AE pulse rate and the total number of AE pulse emitted. It is found that the AE pulse rate should be maximum for a particular strain of the crystals. The peak value of the AE pulse rate should depend on the volume and strain rate of the crystals, and also on the pinning time of dislocations. Since the pinning time of dislocations decreases with increasing strain rate, the AE pulse rate should be weakly dependent on the strain rate of the crystals. The total number of AE should increase linearly with deformation and then it should attain a saturation value for the large deformation. By measuring the strain dependence of the AE pulse rate at a fixed strain rate, the time constantτ _s for surface annihilation of dislocations and the pinning timeτ _p of the dislocations can be determined. A good agreement is found between the theoretical and experimental results related to the AE from alkali halide crystals.     

Asymmetric synthesis of 6-(2′,3′,4′,5′,6′-pentafluorophenyl)-δ-lactones via “allyl”boranes: application for the synthesis of fluorinated analog of key pharmacophore of statin drugs

Asymmetric “allyl”boration of pentafluorobenzaldehyde with various α-pinene based “allyl”boranes provides homoallylic alcohols in high de and ee; the alcohols have been converted into δ-lactones via acryloylation, ring-closing metathesis and hydrogenation. Pentafluorophenyl analog of key pharmacophore of statin drugs has been synthesized using diastereoselective epoxidation and regioselective reduction as key steps.     

A convenient synthesis of linear pyranocoumarins. Xanthyletin and 3-Phenylxanthyletin

A convenient synthesis of linear pyranocoumarins, viz., 8,8-dimethyl-2H,8H-benzo[1,2-b; 5,4-b]dipyran-2-one (xanthyletin,1) and 8,8-dimethyl-3-phenyl-2H,8H-benzo[1,2-b; 5,4-b]dipyran-2-one (3-phenylxanthyletin,2) is described. The key steps are blocking the 8-position of appropriate 7-hydroxy-2H-1-benzopyran-2-one derivatives with iodine and 1,1-dimethyl-2-propynylation followed by cyclisation.

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Ein einfacher Syntheseweg zu linearen Pyranocumarinen. Xanthyletin und 3-Phenylxanthyletin

Zusammenfassung Es wird ein vorteilhafter Weg zur Synthese von linearen Pyranocumarinen am Beispiel von Xanthyletin und 3-Phenylxanthyletin gezeigt. Das Syntheseprinzip besteht in einer Blockierung der 8-Position des entsprechenden 7-Hydroxy-2H-1-benzopyran-2-ons mit Jod und einer 1,1-Dimethyl-2-propinylierung mit nachfolgender Cyclisierung.

     

Heats of solution and neutralization ofLewis acids and bases in acetic anhydride

Heats solution of someLewis acids and bases in acetic anhydride have been determined and the following order of their relative strengths is proposed: SbCl₅>SO₃>SnCl₄>TiCl₄>AsCl₃ and piperidine> n-butylamine>potassium acetate>sodium acetate -picoline>quinoline. Heats neutralization of theseLewis acids and bases in acetic anhydride suggest that the major enthalpy change in these neutralization reactions is due to the combination of a proton and the (CH₂COOCOCH₃)-ion, resulting in the formation of acetic anhydride.

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Lösungs- und Neutralisationswärmen von Lewis-Säuren und-Basen in Essigsäureanhydrid

Zusammenfassung Es wurden die Lösungswärmen einigerLewis-Säuren in Essigsäureanhydrid bestimmt und folgende Reihung nach ihrer relativen Stärke vorgeschlagen: SbCl₅>SO₃>SnCl₄>TiCl₄>AsCl₃ und Piperidin> n-Butylamin>KAc>NaAc-Picolin>Chinolin. Die Neutralisationswärmen dieserLewis-Säuren und-Basen legen nahe, daß der Hauptanteil daran auf die Reaktion eines Protons mit (CH₂–COOCOCH₃)-zurückzuführen ist.

     

A novel transformation of O-methyldalbergin

O-methyldalbergin and related 4-phenylcoumarins are markedly different from ordinary coumarins in their behaviour towards alkali. They are stable in boiling alkali and on addition of mercuric oxide yield coumarilic acids. Phenyl-coumarilic acids undergo decarboxylation readily when boiled with aqueous alcoholic mercuric chloride to yield phenyl substituted coumarones.     

Experimental and theoretical studies of the quenching of Li(3p,4p) by N2

Quenching mechanisms of the Li3p and Li4p states in collision with the nitrogen molecule are studied by laser-induced fluorescence spectroscopy and by a quantum chemical calculation. The Li3p state is observed to be efficiently quenched to the Li3s state detected as intense 3s-->2p emission. The Li4p state is efficiently quenched to the Li4s and Li3d states detected as 4s-2p and 3d-2p emissions, respectively. The potential-energy surfaces for the Li(2s-4p)N2 states show a large number of conical intersections and avoided crossings resulting from the couplings between the ionic [Li+(N2)-] and covalent configurations. There are a large number of stable excited states, and we give here the spectroscopic constants for the lowest two stable isomers correlating to Li2p+N2.     

Biginelli reaction in aqueous medium: a greener and sustainable approach to substituted 3,4-dihydropyrimidin-2(1H)-ones

An environmentally benign aqueous Biginelli protocol for the synthesis of substituted 3,4-dihydropyrimidin-2(1H)-ones using polystyrenesulfonic acid (PSSA) as a catalyst has been achieved. These microwave-assisted reactions proceed efficiently in water in the absence of organic solvent, with simple filtration as the product isolation step.     

Rapid analysis of 2,4-D in soil samples by modified Soxhlet apparatus using HPLC with UV detection

The 2,4-dichlorophenoxy acetic acid (2,4-D) is used as a systemic herbicide to control broadleaf weeds in wheat, corn, range land/pasture land, sorghum, and barley. In this study, a fast and efficient method is developed by selection of modified extraction apparatus and high-performance liquid chromatography (HPLC)-UV conditions for the determination of 2,4-D in soil samples. The method is applied to the study of soil samples collected from the agricultural field. The herbicide is extracted from soil samples by acetonitrile in a modified Soxhlet apparatus. The advantages of the apparatus are that it uses small volume of organic solvent, reduced time of extraction, and better recovery of the analyte. The extract is filtered using a very fine microfiber paper. The total extract is concentrated in a rotatory evaporator, dried under ultrahigh pure N2, and finally reconstituted in 1 mL of acetonitrile. HPLC-UV at 228 nm is used for analysis. The herbicide is identified and quantitated using the HPLC system. The method is validated by the analysis of spiked soil samples. Recoveries obtained varied from 85% to 100% for spiked soil samples. The limit of quantitation (LOQ) and the limit of detection (LOD) are 0.010 and 0.005 parts per million (ppm), respectively, for spiked soil samples. The LOQ and LOD are 0.006 and 0.003 ppm for unspiked soil samples. The measured concentrations of 2,4-D in spiked soil samples are between 0.010 and 0.020 ppm with an average of 0.016 +/- 0.003 ppm. For unspiked soil samples it is between 0.006 ppm and 0.012 ppm with an average of 0.009 +/- 0.002 ppm. The measured concentrations of 2,4-D in soil samples are generally low and do not exceed the regulatory agencies guidelines.