On a family of elliptic curves of rank at least 2

Let C_m:y² = x³ ? m²x + p²q² be a family of elliptic curves over ?, where m is a positive integer and p, q are distinct odd primes. We study the torsion part and the rank of C_m(?). More specifically, we prove that the torsion subgroup of C_m(?) is trivial and the ?-rank of this family is at least 2, whenever m ? 0 (mod 3), m ? 0 (mod 4) and m ≡ 2 (mod 64) with neither p nor q dividing m.

     

Fast Algorithms for Finding O(Congestion + Dilation) Packet Routing Schedules

O (c+d) steps using constant-size queues, where c is the congestion of the paths in the network, and d is the length of the longest path. The proof, however, used the Lovász Local Lemma and was not constructive. In this paper, we show how to find such a schedule in time, with probability , for any positive constant β, where is the sum of the lengths of the paths taken by the packets in the network, and m is the number of edges used by some packet in the network. We also show how to parallelize the algorithm so that it runs in NC. The method that we use to construct the schedules is based on the algorithmic form of the Lovász Local Lemma discovered by Beck. Received: July 8, 1996     

Surface modification of polyacrylonitrile fiber for immobilization of antibodies and detection of analyte

Pendent nitrile groups of multifilamentous polyacrylonitrile (PAN) fibers were reduced to amino groups using lithium aluminum hydride for different time of reduction and amine content was estimated by performing acid-base titrations. Attenuated total reflection-fourier transform infrared spectroscopy (ATR-FTIR) and Differential Scanning Calorimetry (DSC) were used for the characterization of the generated amino groups and thermal properties of the reduced fibers, respectively. The surface morphology of the fibers after reduction and immobilization was characterized using Scanning Electron Microscope (SEM). The newly formed amino groups of the fibers were activated by using glutaraldehyde for the covalent linking of Goat anti-Rabbit IgG-HRP (GAR-HRP) antibody enzyme conjugate. Modified PAN fibers were evaluated as a matrix for sandwich ELISA by using Goat anti-Rabbit antibody (GAR-IgG), Rabbit anti-Goat (RAG-IgG) as analyte and enzyme conjugate GAR-HRP. The fibers reduced for 24 h were able to detect the analyte RAG-IgG at a concentration as low as 3.75 ng mL⁻¹ with 12% skimmed milk as blocking reagent for the optimized concentration of primary antibody GAR-IgG 3 μg mL⁻¹ and peroxidase conjugate GAR-HRP dilution of 8000 fold. The sensitivity, specificity and reproducibility of the developed immunoassay was further established with antibodies present in human blood using Rabbit anti-Human (RAH-IgG) antibody and the corresponding HRP enzyme conjugate. As low as 0.1 μL of human blood was sufficient to perform the assay with the modified fibers.     

Quality-augmented fusion of level-2 and level-3 fingerprint information using DSm theory

Existing algorithms that fuse level-2 and level-3 fingerprint match scores perform well when the number of features are adequate and the quality of images are acceptable. In practice, fingerprints collected under unconstrained environment neither guarantee the requisite image quality nor the minimum number of features required. This paper presents a novel fusion algorithm that combines fingerprint match scores to provide high accuracy under non-ideal conditions. The match scores obtained from level-2 and level-3 classifiers are first augmented with a quality score that is quantitatively determined by applying redundant discrete wavelet transform to a fingerprint image. We next apply the generalized belief functions of Dezert–Smarandache theory to effectively fuse the quality-augmented match scores obtained from level-2 and level-3 classifiers. Unlike statistical and learning based fusion techniques, the proposed plausible and paradoxical reasoning approach effectively mitigates conflicting decisions obtained from classifiers especially when the evidences are imprecise due to poor image quality or limited fingerprint features. The proposed quality-augmented fusion algorithm is validated using a comprehensive database which comprises of rolled and partial fingerprint images of varying quality with arbitrary number of features. The performance is compared with existing fusion approaches for different challenging realistic scenarios.     

Ag-based bimetallic clusters as catalysts for p-nitrophenol reduction by glycerol: A DFT investigation

Reducing p-nitrophenol (PNP) to p-aminophenol is an industrially relevant synthesis. Nevertheless, only a few heterogeneous catalysts have been evaluated for the reduction of PNP by glycerol. Appropriate quantum computational studies can screen potential catalysts for this crucial green reaction. The present research investigates the catalytic activities of Pd@Ag and Ni@Ag core-shell nanogeometries toward PNP reduction by glycerol through density functional theory (DFT) calculations. The central atom of a geometry-optimized 13-atom Ag cluster was replaced by Pd and Ni atoms to create the core-shell morphologies. The interaction energies of PNP and glycerol with each of the (metal/bimetallic) clusters were evaluated by DFT calculations to find the best PNP and glycerol molecule orientation with the respective bimetallic cluster. Electrostatic potential surface and natural bond orbital analyses were performed to study the charge distribution and transfer between atomic orbitals. The frequencies of vibrational modes in isolated PNP/glycerol structures were compared to those when these molecules were in the presence of the different metal clusters to infer the effect of the interactions. All performed analyses indicated improved catalytic activity toward PNP reduction by glycerol upon Ni-doping of the Ag₁₃ cluster.     

Understanding the pH-dependent behavior of graphene oxide aqueous solutions: a comparative experimental and molecular dynamics simulation study

Understanding the pH-dependent behavior of graphene oxide (GO) aqueous solutions is important to the production of assembled GO or reduced GO films for electronic, optical, and biological applications. We have carried out a comparative experimental and molecular dynamics (MD) simulation study to uncover the mechanisms behind the aggregation and the surface activity of GO at different pH values. At low pH, the carboxyl groups are protonated such that the GO sheets become less hydrophilic and form aggregates. MD simulations further suggest that the aggregates exhibit a GO-water-GO sandwichlike structure and as a result are stable in water instead of precipitating. However, at high pH, the deprotonated carboxyl groups are very hydrophilic such that individual GO sheets prefer to dissolve in bulk water like a regular salt. The GO aggregates formed at low pH are found to be surface-active and do not exhibit characteristic features of surfactant micelles. Our findings suggest that GO does not behave like conventional surfactants in pH 1 and 14 aqueous solutions. The molecular-level understanding of the solution behavior of GO presented here can facilitate and improve the experimental techniques used to synthesize and sort large, uniform GO dispersions in a solution phase.     

Metal exchange kinetics: uncatalyzed replacement of Ni(II) from tetramethylenediaminetetraacetatonickel(II) complex by Cu(II)

The kinetics of metal exchange between copper(II) and tetramethylenediaminetetraacetatonickel(II), [Ni(TMDTA)] has been studied between pH 3.4 and 4.8 at an ionic strength of 1.25 M (NaClO₄) and a temperature of 25.0 ± 0.1 °C. The reaction is first order in [Ni(TMDTA)]. The reaction order in [Cu²⁺] varies from first to zero and then back to first as [Cu²⁺] is increased. At low copper concentration, the first-order rate constant is pH independent and represents the attack of copper on the nickel complex through a pathway in which TMDTA is partially uncoordinated before reaction with copper. Evidence is presented for a stepwise dechelation mechanism followed by attack of copper to give a dinuclear intermediate. The zero-order rate is pH dependent. At higher [Cu²⁺], the swing back to first order is due to the formation of a weak copper-tetramethylenediaminetetraacetatonickelate complex which then converts to products through a dinuclear intermediate. A plausible mechanism, consistent with all the kinetic data, is presented.     

Extraction and Purification of Purple Membrane for Photochromic Thin Film Development: Application in Photoelectrochemical Investigation

Purple membrane (PM) has been extracted and purified from archaebacteria for thin film development. The purified purple membrane is isolated in 1?% polyvinyl alcohol solution for making thin film within gelatin and organically modified silicate matrices. For thin film within gelatin matrix, homogenized purple membrane suspension is mixed with 8?% gelatin and poured into a specially designed block with desired thickness of spacer having hydrophobicity followed by gelatinization of the same over home-made thermostatic control unit at 38?°C. The gelatinized matrix is then allowed to dry under controlled conditions of humidity and temperature. The films of varying thicknesses ranging between 40, 50, and 60??? are used for photo-electrochemical measurements. The results on photo-electrochemistry of non-oriented purple membrane film provides valuable information on the generation of forward (light on) and backward (light off) photocurrent as a function of: (a) applied potential and (b) film thickness. An increase in applied negative potential increases the amplitude of photocurrent whereas decrease in film thickness facilitates the reversibility of photocurrent response.     

Cationic organoaluminum compounds as intramolecular hydroamination catalysts

Cationic dialkylaluminum and m-terphenylalkylaluminum compounds catalyze the intramolecular hydroamination of primary and secondary aminopentenes. The reaction rates are strongly dependent on the substrate and the catalyst substituents. The bulky species [Dipp1AlEt][CHB₁₁H₅I₆] (Dipp1 = 2,6-Dipp₂C₆H₃–, Dipp = 2,6-iPr₂C₆H₃–), 4, was the most active catalyst. Although the neutral species DcpAlEt₂ (Dcp = 2,6-(2,6-Cl₂C₆H₃)₂C₆H₃–), 7, and Dipp1AlEt₂, 8, showed some catalytic activity, they were more than 25 times less reactive than their cationic counterparts [DcpAlEt][CHB₁₁H₅Cl₆], 3, and 4. The cyclization of secondary benzylaminopentenes with [Et₂Al][CHB₁₁H₅I₆], 1, was strongly dependent on the substitution of the C-2 olefinic carbon.