Sampling with a String

Kramer's sampling theorem forms a bridge between the Whittaker-Shannon-Kotel'nikov sampling theorem and boundary-value problems. It has been shown that sampling expansions associated with Sturm-Liouville boundary-value problems are Lagrange-type sampling series, i.e., Lagrange series with infinitely many terms converging to entire functions. String theory as developed by Feller, Kac, and Krein, is a generalization of the Sturm-Liouville theory. We investigate sampling series associated with strings and compare them with those associated with Sturm-Liouville problems. We show that unlike sampling series associated with Sturm-Liouville problems, those associated with strings include not only Lagrange-type sampling series, but also Lagrange polynomial interpolation.     

Growth of InP/InGaAs multiple quantum well structures by chemical beam epitaxy

InP/InGaAs multiple quantum well structures with up to 200 periods have been grown by CBE. These structures exhibit exceptional lateral uniformity, measured as ±1 Å in period, ±13 ppm in lattice mismatch and ±0.5 nm in wavelength across a 2 inch wafer. Good surface morphology, sharp interfaces and excellent growth control have all been demonstrated.     

Symmetrical and Asymmetrical Bisphosphonate Esters. Synthesis, Selective Hydrolysis, and Isomerization

Two simple and efficient one-pot procedures for the synthesis of a series of α-branched N-heterocycle-substituted methane-1,1-bisphosphonates are outlined. In the first method, the parent halosubstrates were reacted with cyanomethylphosphonate followed by reaction with dialkyl phosphonates to give asymmetrical or symmetrical bisphosphonates (BPs). In the second approach, the same halocompounds were reacted with tetraethyl methyl-1,1-bisphosphonate to give the requisite BPs. Partial and complete hydrolysis of the prepared BPs were also investigated. The products contain functional groups advantageous for further synthetic modification as structural units for coupling with the drug.     

An electrolytic device for preparation of hydrogen and oxygen from water for isotopic analysis

An electrolytic device for decomposition of water has been developed which readily gives hydrogen and oxygen for isotopic measurement with a mass spectrometer. A 20-mul sample can be decomposed quantitatively in 10 min with good reproducibility. The results produced are comparable with those obtained by reduction with uranium.     

Palladium(0)-catalyzed regioselective synthesis of alpha-dehydro-beta-amino esters from amines and allyl acetates: synthesis of a alpha-dehydro-beta-amino acid derived cyclic peptide as a constrained beta-turn mimic

Acetates derived from the adducts of the Baylis-Hillman reaction can be reacted in a regioselective manner with amines in the presence of palladium(0) catalyst to afford alpha-dehydro-beta-amino esters (2 and 3) in good yields. The regioselectivity of the reaction can be controlled by temperature and reaction medium leading to the synthesis of regioisomers 2 or 3. The alpha-dehydro-beta-amino acid 3 is a turn inducer, and the dipeptides 6 derived from it show the presence of an eight-membered intramolecular hydrogen bond. Also, cobalt(II) chloride catalyzes the cleavage of epoxy peptides with alpha-dehydro-beta-amino acid derivative 3b to afford the corresponding dipeptide derivatives 8, which exhibit an intramolecular hydrogen bond and thus mimic a beta-turn. This intramolecular hydrogen bonding preorganizes the corresponding diallylated peptide 8c for cyclization via ring-closing metathesis to afford the cyclic peptide 9 as a constrained mimic of a beta-turn.     

Dithiolate complexes of manganese and rhenium: X-ray structure and properties of an unusual mixed valence cluster Mn3(CO)6(mu-eta2-SCH2CH2CH2S)3

Treatment of Mn(2)(CO)(10) with 3,4-toluenedithiol and 1,2-ethanedithiol in the presence of Me(3)NO.2H(2)O in CH(2)Cl(2) at room temperature afforded the dinuclear complexes Mn(2)(CO)(6)(mu-eta(4)-SC(6)H(3)(CH(3))S-SC(6)H(3)(CH(3))S) (1), and Mn(2)(CO)(6)(mu-eta(4)-SCH(2)CH(2)S-SCH(2)CH(2)S) (2), respectively. Similar reactions of Re(2)(CO)(10) with 3,4-toluenedithiol, 1,2-benzenedithiol, and 1,2-ethanedithiol yielded the dirhenium complexes Re(2)(CO)(6)(mu-eta(4)-SC(6)H(3)(CH(3))S-SC(6)H(3)(CH(3))S) (3), Re(2)(CO)(6)(mu-eta(4)-SC(6)H(4)S-SC(6)H(4)S) (4), and Re(2)(CO)(6)(SCH(2)CH(2)S-SCH(2)CH(2)S) (5), respectively. In contrast, treatment of Mn(2)(CO)(10) with 1,3-propanedithiol afforded the trimanganese compound Mn(3)(CO)(6)(mu-eta(2)-SCH(2)CH(2)CH(2)S)(3) (6), whereas Re(2)(CO)(10) gave only intractable materials. The molecular structures of 1, 3, and 6 have been determined by single-crystal X-ray diffraction studies. The dimanganese and dirhenium carbonyl compounds 1-5contain a binucleating disulfide ligand, formed by interligand disulfide bond formation between two dithiolate ligands identical in structure to that of the previously reported dimanganese complex Mn(2)(CO)(6)(mu-eta(4)-SC(6)H(4)S-SC(6)H(4)S). Complex 6, on the other hand, forms a unique example of a mixed-valence trimangenese carbonyl compound containing three bridging 1,3-propanedithiolate ligands. The solution properties of 6 have been investigated by UV-vis and EPR spectroscopies as well as electrochemical techniques.     

Experimental study of effect of void volume fraction on neutron diffusion parameters in water

The dependence of the diffusion parameters including slowing down area, neutron diffusion length and migration length on the voided volume fraction in water has been studied experimentally. For this purpose, the PIEAS Neutron Transport Facility (PNTF) comprised of a 10 Ci Am–Be neutron source and a water filled aluminum tank with Perspex voided tubes has been designed and fabricated. A BF₃ detector was used for the neutron counting. The slowing down area was determined at the cadmium cutoff level. The diffusion parameters were determined first in the absence of voids. The experimentally measured values of the slowing down area, the diffusion length and the migration length have been found in good agreement with the corresponding values determined by other workers. By varying void volume fraction from 0% to 7.5%, the experimental measurements show a monotonic increase in the slowing down area from 58.71±2.6 to 71.28±3.2 cm², in the diffusion length from 2.95±0.13 to 3.11±0.13 cm and in the migration length from 8.21±0.165 to 8.99±0.169 cm. Our measurements show that the diffusion parameters exhibit a quadratic dependence on the void volume fraction.