Transformation formula for exponential sums involving fourier coefficients of modular forms

In 1984 Jutila [5] obtained a transformation formula for certain exponential sums involving the Fourier coefficients of a holomorphic cusp form for the full modular group SL(2, Z). With the help of the transformation formula he obtained good estimates for the distance between consecutive zeros on the critical line of the Dirichlet series associated with the cusp form and for the order of the Dirichlet series on the critical line, [7]. In this paper we follow Jutila to obtain a transformation formula for exponential sums involving the Fourier coefficients of either holomorphic cusp forms or certain Maass forms for congruence subgroups of SL(2, Z) and prove similar estimates for the corresponding Dirichlet series.

An Approach Toward Homocalystegines and Silyl-homocalystegines. Acid-Mediated Migrations of Acetates in Seven-Membered Ring Systems

A short access to homocalystegine analogues silylated at C7 is described. The synthesis involves the desymmetrization of a (phenyldimethylsilyl)methylcycloheptatriene using osmium-mediated dihydroxylation, followed by the diol protection and a cycloaddition involving the remaining diene moiety and an acylnitroso reagent. Additions of the osmium and acylnitroso reagents were shown, through X-ray diffraction studies of the resulting major isomers, to occur anti and syn, respectively, relative to the SiCH2 substituent. N-O bond cleavage on the resulting cycloadduct then produces the aminopolyol having a silylmethyl substituent. Oxidation of the C-Si bond also afforded an access to unusual amino-heptitols having five contiguous stereogenic centers. In the course of this work, we finally observed a unusual rearrangement taking place on cycloheptanone 18 substituted by two acetyl groups and a neighboring Boc-protected amine. A profound reorganization of the substituents on the seven-membered ring effectively took place under acidic conditions (TFA) leading to the thermodynamically more stable homocalystegine-type compound., DFT calculations of the conformational energy of isomeric silyl homocalystegines indicated that the product observed upon the acid-mediated rearrangement was the most stable of a series of analogues with various distributions of substituents along the seven-membered ring backbone. A tentative mechanism is proposed to rationalize the acetate migrations and inversions of the stereochemistry at various stereocenters.

Grain size effect on the phase transformation temperature of nanostructured CuFe2O4

We report a large decrease in tetragonal to cubic phase transformation temperature when grain size of bulk CuFe2O4 is reduced by mechanical ball milling. The change in phase transformation temperature was inferred from in situ high temperature conductivity and x-ray diffraction measurements. The decrease in conductivity with grain size suggests that ball milling has not induced any oxygen vacancy while the role of cation distribution in the observed decrease in phase transformation temperature is ruled out from in-field Fe-57 Mossbauer and extended x-ray absorption fine structure measurements. The reduction in the phase transformation temperature is attributed to the stability of structures with higher crystal symmetry at lower grain sizes due to negative pressure effect. (C) 2011 American Institute of Physics. doi: 10.1063/1.3493244]

Analysis of serpentine folded-waveguide slow-wave structure using elliptical conformal transformation

Elliptical conformal transformation was used to derive closed form expressions for the equivalent circuit series inductance and shunt capacitance per period of a serpentine folded-waveguide slow-wave structure including the effects of the beam-hole. The lumped parameters were subsequently interpreted for the dispersion and interaction impedance characteristics of the structure. The analysis was benchmarked for two typical millimeter-wave structures operating in Ka- and W-bands, against measurement, 3D electromagnetic modeling using CST Microwave Studio, parametric analysis and equivalent circuit analysis. (C) 2010 Elsevier GmbH. All rights reserved.

Composition Driven Monolayer to Bilayer Transformation in a Surfactant Intercalated Mg-Al Layered Double Hydroxide

The structure and organization of dodecyl sulfate (DDS) surfactant chains intercalated in an Mg-Al layered double hydroxide (LDH), Mg(1-x)Alx(OH)(2), with differing Al/Mg ratios has been investigated. The Mg-Al LDHs can be prepared over a range of compositions with x varying from 0.167 to 0.37 and therefore provides a simple system to study how the organization of the alkyl chains of the intercalated DDS anions change with packing density; the Al/Mg ratio or x providing a convenient handle to do so. Powder X-ray diffraction measurements showed that at high packing densities (x >= 0.3) the alkyl chains of the intercalated dodecyl sulfate ions are anchored on opposing LDH sheets and arranged as bilayers with an interlayer spacing of similar to 27 angstrom. At lower packing densities (x < 0.2) the surfactant chains form a monolayer with the alkyl chains oriented flat in the galleries with an interlayer spacing of similar to 8 angstrom. For the in between compositions, 0.2 <= x < 0.3, the material is biphasic. MD simulations were performed to understand how the anchoring density of the intercalated surfactant chains in the Mg-Al LDH-DDS affects the organization of the chains and the interlayer spacing. The simulations are able to reproduce the composition driven monolayer to bilayer transformation in the arrangement of the intercalated surfactant chains and in addition provide insights into the factors that decide the arrangement of the surfactant chains in the two situations. In the bilayer arrangement, it is the dispersive van der Waals interactions between chains in opposing layers of the anchored bilayer that is responsible for the cohesive energy of the solid whereas at lower packing densities, where a monolayer arrangement is favored, Coulomb interactions between the positively charged Mg-Al LDH sheets and the negatively charged headgroup of the DDS anion dominate.

Evolution of Transformation Texture in a Metastable B - Titanium Alloy

Texture evolution in h. c. p. (alpha) phase derived from aging of a differently processed metastable b.c.c. (beta) titanium alloy was investigated. The study was aimed at examining (i) the effect of different b. c. c. cold rolling textures and (ii) the effect of different defect structures on the h. c. p transformation texture. The alloy metastable beta alloy Ti-10V-4.5Fe-1.5Al was rolled at room temperature by unidirectional (UDR) and multi-step cross rolling (MSCR). A piece of the as-rolled materials were subjected to aging in order to derive the h. c. p. (alpha) phase. In the other route, the as-rolled materials were recrystallized and then aged. Textures were measured using X-ray as well as Electron Back Scatter Diffraction. Rolling texture of beta phase, as characterized by the presence of a strong gamma fibre, was found stronger in M S C R compared to UDR, although they were qualitatively similar. The stronger texture of MSCR sample could be attributed to the inhomogeneous deformation taking place in the sample that might contribute to weakening of texture. Upon recrystallization in beta phase field close to beta-transus. the textures qualitatively resembled the corresponding beta deformation textures; however, they got strengthed. The aging of differently beta rolled samples resulted in the product alpha-phase with different textures. The (UDR + Aged) sample had a stronger texture than (MSCR + Aged) sample, which could be due to continuation of defect accumulation in UDR sample, thus providing more potential sites for the nucleation of alpha phase. The trend was reversed in samples recrystallized prior to aging. The (MSCR + Recrystallized + Aged) sample showed stronger texture of alpha phase than the (UDR + Recrystallized + Aged) sample. This could be attributed to extensive defect annihilation in the UDR sample on recrystallization prior to aging. The (MSCR + Aged) sample exhibited more alpha variants when compared to (MSCR + Recrystallized + Aged) sample. This has been attributed to the availability of more potential sites for nucleation of alpha phase in the former. It could be concluded that alpha transformation texture depends mainly on the defect structure of the parent phase.

Transformation of 16-dehydroprogesterone and 17?-hydroxyprogesterone by Mucor piriformis

Mucor piriformis was used to study the mode of transformation of 16-dehydroprogesterone (I, pregna-4, 16-diene-3, 20-dione) and 17 alpha-hydroxyprogesterone (II, 17 alpha-hydroxypregn-4-ene-3, 20-dione). Biotransformation products formed from I were 14 alpha-hydroxypregna-4, 16-diene-3, 20-dione (Ia), 7 alpha, 14 alpha-dihydroxypregna-4 16-diene-3, 20-dione (Ib), 3 beta, 7 alpha, 14 alpha-trihydroxy-5 alpha-pregn-16-en-20-one (Ic), and 3 alpha, 7 alpha, 14 alpha-trihydroxy-5 alpha-pregn-16-en-20-one (Id). Metabolites Ic and Id appear to be hitherto unknown. Timecourse studies suggested that the transformation is initiated by hydroxylation at the 14 alpha-position (Ia) followed by hydroxylation at the 7 alpha-position (Ib). Microsomes (105,000 g sediment) prepared from 16-dehydroprogesterone-induced cells hydroxylate I to its 14 alpha-hydroxy derivative (Ia) in the presence of NADPH. Incubation of Ia with the organism resulted in the formation of Ib, Ic and Id. Biotransformation products formed from compound II were 17 alpha, 20 alpha-dihydroxypregn-4-en-3-one (IIa), 7 alpha, 17 alpha-dihydroxypregn-4-ene-3, 20-dione (IIb), 6 beta, 17 alpha, 20 alpha-trihydroxypregn-4-en-3-one (IIc) and 11 alpha, 17 alpha, 20 alpha-trihydroxypregn-4-en-3-one (IId). Time-course studies indicated that IIa is the initial product formed, which is further hydroxylated either at the 6 beta or 11 alpha position. Incubation of IIa with the organism resulted in the formation of IIc and IId. Reduction of the 4-en-3-one system and 20-keto group has not been observed before in organisms of the order Mucorales. In addition, M. piriformis has been shown to carry out hydroxylation at the C-6, C-7, C-11 and C-14 positions in the steroid molecules tested.

Tri-n-butylin hydride mediated dehalogenation in water

A new methodology has been developed to reduce water soluble and water insoluble organohalides in aqueous medium in high yields using TBTH.

Thickness-dependent fcc-hcp phase transformation in polycrystalline titanium thin films

Polycrystalline Ti thin films are shown to gradually transform from face-centered cubic (fcc) to hexagonal close-packed structure (hcp) with increasing film thickness. Diffraction stress analysis revealed that the fcc phase is formed in a highly compressive hcp matrix (>= 2 GPa), the magnitude of which decreases with increasing film thickness. A correlation between stress and crystallographic texture vis-a-vis the fcc-hcp phase transformation has been established. The total free energy change of the system upon phase transformation calculated using the experimental results shows that the fcc-hcp transformation is theoretically possible in the investigated film thickness regime (144-720 nm) and the hcp structure is stable for films thicker than 720 nm, whereas the fcc structure can be stabilized in Ti films much thinner than 144 nm. (C) 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Antigenic determinants at the carboxy terminus of chicken egg white riboflavin carrier protein (RCP): Epitope mapping and antibody-mediated pregnancy curtailment in rodents

The epitopic core sequences recognized by three monoclonal antibodies raised to chicken riboflavin carrier protein (RCP) were mapped to the C-terminal tail-end of the protein using the pepscan method A 21-residue synthetic peptide corresponding to residues 200-219 of the protein and comprising the regions corresponding to the antibodies was synthesized. Administration of polyclonal antibodies specific to this peptide led to termination of early pregnancy in mice. Also, active immunization of rats with the peptide-purified protein derivative conjugate inhibited establishment of pregnancy. These results demonstrate the functional importance of the C-terminal 200-219 region of chicken RCP. Copyright (C) 1996 Elsevier Science Ltd.

Design of some 2-D filters through the transformation technique

The transformation technique is a tool FIR designing 2-D filters, useful for the design of specially shaped filters with passband/stopband regions not centred around the origin. The authors extend this technique to design two types or filters. A notch filter has a stopband centred about a small region in the 2-D frequency plane. The authors propose an extension to the transformation technique with the windowing concept to achieve the design of notch filters. A directional filter has a passband extending fully along: a straight line pacing through the origin. The transformation technique is: further extended to yield such directional filters. Design and application examples for both these fillers are also presented.

Baculovirus mediated high-level expression of luciferase in silkworm cells and larvae

Bombyx mori nuclear polyhedrosis virus (BmNPV)-based baculovirus expression system exploits silkworm larvae as an economical alternative to large-scale cell cultures for production of biomolecules. To generate recombinant BmNPV at high efficiency, we have achieved high efficiency transfection of B. mori cells, BmN, through lipofection. Optimal conditions for lipofection were standardized by quantification of the transient expression level of firefly luciferase (luc) reporter gene under control of an immediate early gene promoter of BmNPV Lipofection was 50-fold and 100-fold more efficient than the calcium phosphate method for transfecting BmN and Sf9 cells, respectively. Lipofection enabled us to generate a recombinant BmNPV (vBmluc), harboring luc under control of the strong polyhedrin promoter On infection with vBmluc, luciferase was expressed at very high levels, 170 mu g/10(6) BmN cells or 13 mg/larva. Expression of luciferase in vBmluc-infected larvae was visualized by luminescence emission instantaneously following luciferin injection generating ''glowing silkworms''.

Realtime kinetic analysis of antigen-antibody interaction using solid phase binding: Transformation of hCG-monoclonal antibody complex

Kinetic constants of MAb-hCG interactions have been determined using solid phase binding of I-125[hCG] to immobilized MAb. While association has been shown to follow the expected pattern, dissociation consists of at least two reversible steps, one with a rate constant of 0.0025 min(-1), and a second with a rate constant of 0.00023 min(-1). Validity of affinity constant measurements in the light of the complex reaction kinetics is discussed, A comparison between the method of surface plasmon resonance technology (BIAcore) and solid phase binding (SPB) for determination of kinetic parameters shows that SPB provides not only a cost-effective approach for determination of realtime kinetic parameters of macromolecular ligand-ligate interaction but also a method with several advantages over the BIAcore system in investigating the mechanism of antigen-antibody interaction.

Effect of beta-lactamase-catalyzed hydrolysis of cephalosporins on peroxynitrite-mediated nitration of serum albumin and cytochrome c

The hydrolysis of beta-lactam antibiotics by beta-lactamases is one of the major bacterial defense systems. These enzymes generally hydrolyze a variety of antibiotics including the latest generation of cephalosporins, cephamycins and imipenem. In this paper, the effect of cephalosporins-based antibiotics on the peroxynitrite-mediated nitration of protein tyrosine is described. Although some of the antibiotics have weak inhibitory effect on the nitration reactions in the absence of beta-lactamase, they exhibit very strong inhibition in the presence of beta-lactamase. This is due to the elimination of heterocyclic thiol/thione moieties from cephalosporins by beta-lactamase-mediated hydrolysis. After the elimination, the thiols/thiones effectively scavenge peroxynitrite, leading to the inhibition of the nitration reactions.

Observation of Water-Mediated Helix-Terminating Conformation in a Dehydrophenylalanine Peptide: Crystal and Solution Structure of the Octapeptide Ac-.DELTA.Phe-Val-.DELTA.Phe-Phe-Ala-Val-.DELTA.Phe-Gly-OMe

We have synthesised and determined the solution conformation and X-ray crystal structure of the octapeptide Ac-Delta Phe(1)-Val(2)-Delta Phe(3)-Phe(4)-Ala(5)-Val(6)-Delta Phe(7)-Gly(8)-OCH3 (Delta Phe = alpha,beta-dehydrophenylalanine) containing three Delta Phe residues as conformation constraining residues. In the solid state, the peptide folds into (i) an N-terminal (3)10(R)-helical pentapeptide segment, (ii) a middle non-helical segment, and (iii) a C-terminal incipient (3)10(L)-helical segment. The results of H-1 NMR data also suggest that a similar multiple-turn conformation for the peptide is largely maintained in solution. Though the C-terminal helix is incipient, the overall conformation of the octapeptide matches well with the conformation of the hairpins reported. Comparison of the pi-turn seen in the octapeptide molecule with those observed in proteins at the C-terminal end of helixes shows the structural similarity among them. A water molecule mediates the 5 --> 2 hydrogen bond in the pi-turn region. This is the first example of a water-inserted pi-turn in oligopeptides reported so far. Comparison between the present octapeptide and another (3)10(R)-helical dehydro nonapeptide Boc-Val-Delta Phe-Phe-Ala-Phe-Delta Phe-Val-Delta Phe-Gly-OCH3 solved by us recently, demonstrates the possible sequence-dependent conformational variations in alpha,beta-dehydrophenylalanine-containing oligopeptides.