The Lang–Trotter conjecture for products of non-CM elliptic curves

The Ramanujan Journal - Inspired by the work of Lang–Trotter on the densities of primes with fixed Frobenius traces for elliptic curves defined over $${\mathbb {Q}}$$ and by the subsequent...     

The Effect of a Substrate on the Current-vs-Voltage Characteristics of Thin-Film Sandwich Structures Based on Buckminsterfullerene

We analyze the current-vs-voltage (J-V) characteristics of ITO/C₆₀/Al sandwich cells, where ITO is the double indium tin oxide, C₆₀ is the buckminsterfullerene and Al is the thermally evaporated top aluminum electrode. These cells were obtained on either glass/ITO or polyethyleneterephthalate/ITO substrates (or, optionally, on glass/ZnO substrates) in a parallel process under identical conditions. However, the J-V dependences in each series behave very differently. The results are discussed in terms of the migration of admixtures from a bulk substrate material toward the top metallic electrode, thus modifying the photovoltaic properties of cells.     

Absence of Anomalous Dissipation of Energy in Forced Two Dimensional Fluid Equations

We prove the absence of anomalous dissipation of energy for long time averaged solutions of the forced critical surface quasi-geostrophic equation in two spatial dimensions.     

Metallaphotoredox Difluoromethylation of Aryl Bromides

Herein, we report a convenient and broadly applicable strategy for the difluoromethylation of aryl bromides by metallaphotoredox catalysis. Bromodifluoromethane, a simple and commercially available alkyl halide, is harnessed as an effective source of difluoromethyl radical by silyl‐radical‐mediated halogen abstraction. The merger of this fluoroalkyl electrophile activation pathway with a dual nickel/photoredox catalytic platform enables the difluoromethylation of a diverse array of aryl and heteroaryl bromides under mild conditions. The utility of this procedure is showcased in the late‐stage functionalization of several drug analogues.     

Adsorption process of phenothiazine solution in dimethyl sulfoxide on graphite electrodes

In this paper, an original solution for the modeling and simulation of the adsorption process of a phenothiazine derivative on graphite electrodes is presented. The adsorption process is considered a distributed parameter one, due to the fact that the adsorbed phenothiazine quantity is a function depending on two independent variables. The structure parameters of the adsorption process, which define the influence of both independent variables, are determined using an experimental identification method. The experimental data are obtained through an experiment which is based on the process step response. In order to simulate the adsorption process, the approximate analytical solution, representing the process model, is determined. The simulation results prove the model generality; it is being simulated in relation to both independent variables.     

Crystal and molecular structures of 11,12-epoxydrim-8(9)-en-11β-ol-7-one

The crystal structure of 11,12-epoxydrim-8(9)-en-11β-ol-7-one is determined by X-ray diffraction. The crystal data for the C₁₅H₂₂O₃ composition are as follows: a = 6.646(1) Å, b = 7.242(1) Å, c = 7.635(2) Å, α = 84.34(3)°, β = 84.50(3)°, γ = 69.84(3)°, space group P1, and Z = 1. The structure is solved by the direct method and refined in the anisotropic approximation to R = 0.043 and R _w = 0.110. The stereochemical formula of the compound is determined. It is shown that the hydroxyl group at the C(11) atom is situated at the β position. In the crystal, the molecules related by the translation along the a-b direction of the unit cell are linked into infinite chains by intermolecular hydrogen bonds between the hydrohyl group and the carbonyl oxygen atom [O-H?O, 2.867(4) Å].     

Characterization of nano-composite oxide ceramics and monitoring of oxide thin film growth by laser-induced breakdown spectroscopy

Multi-component oxide ceramics and epitaxial oxide thin films are analyzed by laser-induced breakdown spectroscopy (LIBS). Furthermore, pulsed-laser deposition (PLD) of thin films is investigated by long-term monitoring of the optical plasma emission. Both nano-composite high-temperature superconductors (HTS) consisting of YBa₂Cu₃O_7 − δ bulk and Y₂Ba₄MCuO_x (M-2411, M = Ag, Nb) nano-particles, and semiconducting ZnO doped with Aluminum and Lithium are ablated by nano-second laser pulses. The plasma emission is recorded using grating spectrometers with intensified gated detectors. The LIBS signals of nano-particles correlate with the nominal content of the M-2411 phase (0–15 mol%) and reveal a strong signal of Ytterbium impurity (3–35 ppm). In situ monitoring of the PLD process shows element signals that are stable for more than 10,000 laser pulses for both HTS and ZnO ceramics. The relative concentration of elements in thin films and ceramics as determined by LIBS is almost the same.     

Fundaments of Hermitean Clifford Analysis Part I: Complex Structure

Hermitean Clifford analysis focusses on h–monogenic functions taking values in a complex Clifford algebra or in a complex spinor space. Monogenicity is expressed here by means of two complex mutually adjoint Dirac operators, which are invariant under the action of a Clifford realisation of the unitary group. In this contribution we present a deeper insight in the transition from the orthogonal setting to the Hermitean one. Starting from the orthogonal Clifford setting, by simply introducing a so-called complex structure J ∈ SO(2n; ), the fundamental elements of the Hermitean setting arise in a quite natural way. Indeed, the corresponding projection operators 1/2 (1 ± iJ) project the initial basis (e_α, α = 1, . . . , 2n) onto the Witt basis and moreover give rise to a direct sum decomposition of into two components, where the SO(2n; )-elements leaving those two subspaces invariant, commute with the complex structure J. They generate a subgroup which is doubly covered by a subgroup of Spin(2n; ), denoted Spin _J (2n; ), being isomorphic with the unitary group U(n; ). Finally the two Hermitean Dirac operators are shown to originate as generalized gradients when projecting the gradient on the invariant subspaces mentioned, which actually implies their invariance under the action of Spin _J (2n; ). The eventual goal is to extend the complex structure J to the whole Clifford algebra , in order to conceptually unravel the true meaning of Hermitean monogenicity and its connections to orthogonal monogenicity. During the final redaction of this paper, we received the sad news that our friend, colleague and co-author Jarolím Bureš died on October 1, 2006 Submitted: October 16, 2006. Accepted: December 29, 2006.     

Functional polymers based on acrylamide crosslinked copolymers

Crosslinked copolymers of acrylamide were obtained by the aqueous suspension polymerization method. Divinylbenzene and N,N-methylene-bis-acrylamide were used as crosslinking agents. Ethylacrylate was used as a third comonomer. The real acrylamide content in the crosslinked copolymers was calculated taking into account the found nitrogen content after the removal of the soluble fractions. The water uptake in dependence on the copolymer structure gave information on the hydrophilicity of these copolymers. Hofmann degradation of the amide groups led to copolymers containing vinylamine functional groups, which were characterized by IR spectroscopy and by anion exchange capacity. Carboxylic groups were generated by the alkaline hydrolysis of the ester groups.     

Synthesis of 11-aminodrim-7-ene from drimenol

11-Aminodrim-7-ene was synthesized from drimenol in four steps. Drimenol was oxidized into drimenal and its oxime was dehydrated by p-tosylchloride or acetic anhydride in pyridine to form 9-cyano-11-nordrim-7-ene, reduction of which by LiAlH₄ in the presence of anhydrous AlCl₃ produced 11-aminodrim-7-ene. The reaction of 9-cyano-11-nordrim-7-ene, NaBH₄, and CoCl₂·6H₂O produced a mixture of drimenylamine and 7,8-dihydrodrimenylamine in a 2:1 ratio. Translated from Khimiya Prirodnykh Soedinenii, No. 3, pp. 311–314, May–June, 2009.