Additive Spanners and (alpha, beta)-Spanners

An (alpha, beta)-spanner of an unweighted graph G is a subgraph H that distorts distances in G up to a multiplicative factor of a and an additive term beta. It is well known that any graph contains a (multiplicative) (2k - 1, 0)-spanner of size O(n(1+1/k)) and an (additive) (1, 2)-spanner of size O(n(3/2)). However no other additive spanners are known to exist. In this article we develop a couple of new techniques for constructing (alpha, beta)-spanners. Our first result is an additive (1, 6)-spanner of size O(n(4/3)). The construction algorithm can be understood as an economical agent that assigns costs and values to paths in the graph, purchasing affordable paths and ignoring expensive ones, which are intuitively well approximated by paths already purchased. We show that this path buying algorithm can be parameterized in different ways to yield other sparseness-distortion tradeoffs. Our second result addresses the problem of which (alpha, beta)-spanners can be computed efficiently, ideally in linear time. We show that, for any k, a (k, k - 1)-spanner with size O(kn(1+1/k)) can be found in linear time, and, further, that in a distributed network the algorithm terminates in a constant number of rounds. Previous spanner constructions with similar performance had roughly twice the multiplicative distortion.

Stabilized alpha-Ni(OH)2 as electrode material for for alkaline secondary cells

Hydrotalcite-like compounds of formula Ni1-xAl(x)(OH)2(CO3)x/2 . nH2O (x = 0.1 to 0.25), having the same structure as that of alpha-Ni(OH)2, have been synthesized by substituting nickel hydroxide with aluminum. Of these, the compounds of compositions x greater-than-or-equal-to 0.2 are found to have prolonged stability in strong alkaline medium. The electrodes comprising stabilized alpha-Ni(OH)2 of x = 0.2 composition are rechargeable with discharge-capacity values of 240 (+/- 15) mAh-g-1 and are attractive for applications in various alkaline secondary cells employing nickel-positive electrodes.

Analysis of a conformation-specific epitope of the alpha subunit of human chorionic gonadotropin: Study using monoclonal antibody probes

Monoclonal antibodies (MAbs) have been used extensively for identification of sequence-specific epitopes using either the ELISA or/and IRMA methods, However, attempts to use MAbs for identification of conformation-specific epitopes have been very few as they are considered very labile. We have investigated the stability of conformation-specific epitopes of human chorionic gonadotropin (hCG) using a quantitative solid-phase radioimmnunoassay (SPRIA) technique. Several epitopes are stable to mild modification (chemical and proteolytic) conditions, and epitopes show differential stability for these modifications. Based on these observations, a monoclonal antibody (MAb 16) for an a-subunit-specific epitope of hCG has been used to monitor changes at the epitopic site (identified as epitope 16) on modification of hCG, using SPRIA with immobilized MAb 16. Modifications of amino groups, hydroxyl group of tyrosine as well as carboxyl group of Asp/Glu all bring about sufficient changes in the epitope integrity. Peptide bond hydrolysis at lysine residues damages the epitope, but not at arginine residues, Hydrolysis at tyrosine does not affect the epitope, though modification of the side-chain of tyrosine inactivates the epitope. Destruction of the epitope occurs on reduction of the disulphide bonds. Partial retention of the epitope activity is seen on modification of carboxyl or the epsilon-amino groups of lysine. Based on these results four to six amino acids have been identified to be at the epitopic site, and the data suggest that two peptide segments are brought together by the disulphide bond Cys10-Cys60 to form the epitope.

Vinyl Monomer Based Polyperoxides as Potential Initiators for Radical Polymerization: An Exploratory Investigation with Poly(.alpha.-methylstyrene peroxide)

We describe the use of poly(alpha-methylstyrene peroxide) (P alpha MSP), an alternating copolymer of alpha-methylstyrene and oxygen, as initiator for the radical polymerization of vinyl monomers. Thermal decomposition of P alpha MSP in 1,4-dioxane follows first-order kinetics with an activation energy (E(a)) of 34.6 kcal/mol. Polymerization of methyl methacrylate (MMA) and styrene using P alpha MSP as an initiator was carried out in the temperature range 60-90 degrees C. The kinetic order with respect to the initiator and the monomer was close to 0.5 and 1.0, respectively, for both monomers. The E(a) for the polymerization was 20.6 and 22.9 kcal/mol for MMA and styrene, respectively. The efficiency of P alpha MSP was found to be in the range 0.02-0.04. The low efficiency of P alpha MSP was explained in terms of the unimolecular decomposition of the alkoxy radicals which competes with primary radical initiation. The presence of peroxy segments in the main chain of PMMA and polystyrene was confirmed from spectroscopic and DSC studies. R(i)'/2I values for P alpha MSP compared to that of BPO at 80 degrees C indicate that P alpha MSP can be used as an effective high-temperature initiator.

A large conductance Ca2+-activated K+ channel in alpha T3-1 pituitary gonadotrophs

The Ca2+-activated K+ channel in endocrine cells is responsible for membrane hyperpolarization and rhythmic firing of action potentials. The probability of opening of this channel is sensitive to intracellular-free Ca2+ concentration. In this study we have identified one such large conductance Ca2+-activated K+ channel in alpha T3-1 pituitary gonadotroph cell. This channel is ohmic with a unit conductance of 170 pS in symmetrical KCl (135 mM) and its current reverses near zero millivolts. When more than one channel is present in the patch membrane they open and close independent of each other, exhibiting no cooperativity between them as expected of a binomial distribution. The regulatory mechanism of this channel in modulating hormone secretion from alpha T3-1 gonadotroph cells is indicated.

A novel (main chain) (side chain) polymeric peroxide: Synthesis and initiating characteristics of poly(alpha-(tert-butylperoxymethyl)styrene peroxide)

A novel (main chain)-(side chain) vinyl polyperoxide, poly(alpha-(tert-butylperoxymethyl)styrene peroxide) (MCSCPP), an alternating copolymer of alpha-(tert-butylperoxymethyl)styrene (TPMS) and oxygen, has been synthesized by the oxidative polymerization of TPMS. The MCSCPP was characterized by H-1 NMR, C-13 NMR, IR, DSC, EI-MS, and GC-MS studies. The overall activation energy (E(a)) for the degradation of MCSCPP was found to be 27 kcal/mol. Formaldehyde and alpha-(tert-butylperoxy)acetophenone (TPAP) were identified as the primary degradation products of MCSCPP; TPAP was found to undergo further degradation. The side chain peroxy groups were found to be thermally more stable than those in the main chain. Polymerization of styrene in the presence of MCSCPP as initiator, at 80 degrees C, follows classical kinetics. The presence of peroxy segments in the polystyrene chain was confirmed by both H-1 NMR and thermal decomposition studies. Interestingly, unlike other vinyl polyperoxides, the MCSCPP initiator shows an increase in molecular weight with conversion.

Chemo- and stereoselective reduction of alpha,beta-epoxyketones with diisopropoxytitanium(III) tetrahydroborate

Reduction of alpha,beta-epoxyketones with diisopropoxytitanium(III) tetrahydroborate in dichloromethane under mild conditions (-78 degrees--> -20 degrees C) provides anti- (or erythro-) alpha,beta-epoxy alcohols in high yields with high degree of chemo- and stereoselectivity. Copyright (C) 1996 Elsevier Science Ltd

Structure of N-tert-butyloxycarbonyl-[alpha]-aminoisobutyryl-DL-pipecolyl-[alpha]-aminoisobutyric acid methyl ester

C20H35N3O6 (Boc-Aib-DL-Pip-Aib-OMe, Boc = tert-butyloxycarbonyl, Aib = alpha-aminoisobutyric acid, Pip = pipecolic acid, OMe = methoxy), M(r) = 413.5, monoclinic, P2(1)/c, a = 18.055 (3), b = 15.048 (3), c = 17.173 (3) angstrom, beta = 91.7 (1)-degrees, V = 4663.8 (9) angstrom3, Z = 8, D(m) = 1.16, D(x) = 1.178 Mg m-3, lambda(Mo Kalpha) = 0.71069 angstrom, mu = 0.081 mm-1, F(000) = 1792, T = 297 K. The final R value for 4925 [I greater-than-or-equal-to 3sigma(I)] reflections is 0.065 (wR = 0.067). The peptide backbone of the two independent molecules in the asymmetric unit is folded at the -Aib-Pip- sequence to form a type-I (I') beta-bend stabilized by a 1 <-- 4 intramolecular N-H...O=C hydrogen bond between the Aib(3) peptide N-H and Boc urethane C=O groups.

Helix termination and chain reversal: Crystal and molecular structure of the alpha,beta-dehydrooctapeptide Boc-Val Delta Phe-Phe-Ala-Leu-Ala-Delta Phe-Leu-OH

The crystal structure of the dehydro octapeptide Boc-Val-Delta Phe-Phe-Ala-Leu-Ala-Delta Phe-Leu-OH has been determined to atomic resolution by X-ray crystallographic methods. The crystals grown by slow evaporation of peptide solution in methanol/water are orthorhombic, space group P2(1)2(1)2(1). The unit cell parameters are a = 8.404(3), b = 25.598(2) and c = 27.946(3) Angstrom, Z = 4. The agreement factor is R = 7.58% for 3636 reflections having (\F-o\) greater than or equal to 3 sigma (\F-o\). The peptide molecule is characterised by a 3(10)-helix at the N-terminus and a pi-turn at the C-terminus. This conformation is exactly similar to the helix termination features observed in proteins. The pi-turn conformation observed in the octapeptide is in good agreement with the conformational features of pi-turns seen in some proteins. The alpha(L)-position in the pi-turn of the octapeptide is occupied by Delta Phe(7), which shows that even bulky residues can be accommodated in this position of the pi-turns. In proteins, it is generally seen that alpha(L)-position is occupied by glycine residue. No intermolecular head-to-tail hydrogen bonds are observed in solid state structure of the octapeptide. A water molecule located in the unit cell of the peptide molecule is mainly used to hold the peptide molecule together in the crystal. The conformation observed for the octapeptide might be useful to understand the helix termination and chain reversal in proteins and to construct helix terminators for denovo protein design.

Insertion of nickel nanoparticles in the interlayers of alpha-zirconium phosphate by the decomposition of the intercalated nickel acetate

By employing EXAFS and magnetic measurements, it is shown that nanoparticles of nickel along with those of NiO are incorporated between the layers of a-zirconium phosphate (ZrP) by the thermal decomposition of nickel acetate intercalated in ZrP. The nickel nanoparticles are superparamagnetic. Hydrogen reduction produces small ferromagnetic nickel particles, most of which appear to be outside the interlayer space of ZrP.

Microstructure of copolyperoxides of alpha-methylstyrene with styrene and methyl methacrylate

This paper reports a study on the microstructure of two series of copolyperoxides of alpha-methylstyrene, with styrene and with methylmethacrylate. The copolyperoxides were synthesized by the free radical-initiated oxidative copolymerization of the vinyl monomer pairs. The copolyperoxide compositions obtained from the H-1 and C-13 NMR spectra led to the determination of the reactivity ratios. The product of the reactivity ratios indicates that alpha-methylstyrene forms a block copolyperoxide with styrene and a random copolyperoxide with methylmethacrylate. Microstructural parameters like average sequence length, run number, etc. have been determined for the latter copolyperoxide from analysis of its C-13 NMR spectrum. The aromatic quaternary and carbonyl carbons were found to be sensitive to triad sequences. The end groups of the copolyperoxides have been identified by H-1 NMR as well as FTIR spectroscopic techniques. The thermal degradation of the copolyperoxides has been studied by differential scanning calorimetry, which confirms the alternating peroxide units in the copolyperoxide chain.

Synthesis and characterization of tetrapolymers of styrene, methyl methacrylate, alpha-methylstyrene, and oxygen

This paper presents the first report on a terpolyperoxide (TPPE) synthesized by the oxidative terpolymerization of styrene, methyl methacrylate, and a-methylstyrene. TPPEs of different compositions were synthesized by varying the vinyl monomers feed, and they were then characterized by spectroscopic and thermal studies. The conventional terpolymer equation has been used to predict the composition of TPPEs. The H-1 NMR chemical shift values of TPPEs were found to vary with the composition. The shape of the backbone methylene protons (4.00-4.50 ppm) was found to be sensitive to the sequence distribution of vinyl monomers in the polymer chain. Formaldehyde, benzaldehyde, acetophenone, and methyl pyruvate were identified as the primary degradation products. The overall thermal stability and the average enthalpy of degradation (Delta H-d), as obtained by thermogravimetric analysis and differential scanning calorimetry, respectively, do not vary much with the composition of TPPEs.

Synthesis of epoxy-terminated polymers by radical polymerization using alpha-(t-butylperoxymethyl)styrene as chain transfer agent

Epoxy-terminated polystyrene has been synthesized by radical polymerization using alpha-(t-butylperoxymethyl) styrene (TPMS) as the chain transfer agent. The chain transfer constants were found to be 0.66 and 0.80 at 60 and 70 degrees C, respectively. The presence of epoxy end groups was confirmed by functional group modification of epoxide to aldehyde by treatment with BF3.Et(2)O. Thermal stability of TPMS was followed by differential scanning calorimetry and iodimetry. Thermal decomposition of TPMS in toluene follows first order kinetics with an activation energy of 23 kcal/mol. (C) 1996 John Wiley & Sons, Inc.