Regularizations of products of residue and principal value currents

Let f₁ and f₂ be two functions on some complex n-manifold and let φ be a test form of bidegree (n,n−2). Assume that (f₁,f₂) defines a complete intersection. The integral of φ/(f₁f₂) on {²|f₁|=?₁,²|f₂|=?₂} is the residue integral . It is in general discontinuous at the origin. Let χ₁ and χ₂ be smooth functions on [0,∞] such that χj(0)=0 and χj(∞)=1. We prove that the regularized residue integral defined as the integral of , where χj=χj(²|fj|/?j), is Hölder continuous on the closed first quarter and that the value at zero is the Coleff-Herrera residue current acting on φ. In fact, we prove that if φ is a test form of bidegree (n,n−1) then the integral of is Hölder continuous and tends to the -potential of the Coleff-Herrera current, acting on φ. More generally, let f₁ and f₂ be sections of some vector bundles and assume that f₁⊕f₂ defines a complete intersection. There are associated principal value currents Uf and Ug and residue currents Rf and Rg. The residue currents equal the Coleff-Herrera residue currents locally. One can give meaning to formal expressions such as e.g. Uf∧Rg in such a way that formal Leibnitz rules hold. Our results generalize to products of these currents as well.     

Analytic continuation of residue currents

Let X be a complex manifold and let f:X→ℂ ^p be a holomorphic mapping defining a complete intersection. We prove that the iterated Mellin transform of the residue integral associated with f has an analytic continuation to a neighborhood of the origin in ℂ ^p .     

A regularisation of the Coleff–Herrera residue current

We prove that if a holomorphic mapping from some complex manifold to ${\mathbb{C}}^2$ defines a complete intersection then the corresponding Coleff–Herrera residue current can be smoothly regularised by a $(0\text{,}2)$-form depending on two parameters. To cite this article: H. Samuelsson, C. R. Acad. Sci. Paris, Ser. I 339 (2004).     

Chaotic dot-superconductor analog of the Hanbury Brown-Twiss effect

As an electrical analog of the optical Hanbury Brown-Twiss effect, we study current cross correlations in a chaotic quantum dot-superconductor junction. One superconducting and two normal reservoirs are connected via point contacts to a chaotic quantum dot. For a wide range of contact widths and transparencies, we find large positive current correlations. The positive correlations are generally enhanced by normal backscattering in the contacts. Moreover, for normal backscattering in the contacts, the positive correlations survive when suppressing the proximity effect in the dot with a weak magnetic field.     

Synthesis of some 3',5'-dideoxy-5'-C-phosphonomethyl nucleosides.

Ammonium [1-(3',5',6'-trideoxy-beta-D-erythro-hexofuranosyl)thymine]-6'- phosphonate (1), ammonium 3',5'-dideoxycytidine-5'-C-methylphosphonate (2) and 3',5'-dideoxyadenosine-5'-C-methyl phosphonic acid (3) have been synthesized and tested for anti-HIV activity. The key steps involved an Arbuzov reaction between triethyl phosphite and 3,5,6-trideoxy-6-iodo-1,2-O-isopropylidene-alpha-D-erythro- hexofuranose (7), followed by condensation with the appropriate nucleoside bases. The substances 1, 2 and 3 have been tested in vitro against HIV.     

Full counting statistics of multiple Andreev reflection

We derive the full counting statistics of charge transfer through a voltage biased superconducting junction. We find that, for measurement times much longer than the inverse Josephson frequency, the counting statistics describes a correlated transfer of quanta of multiple electron charges, each quantum associated with the transfer of a single quasiparticle. An expression for the counting statistics in terms of the quasiparticle scattering amplitudes is derived.     

Orbital entanglement and violation of Bell inequalities in mesoscopic conductors

We propose a spin-independent scheme to generate and detect two-particle entanglement in a mesoscopic normal-superconductor system. A superconductor, weakly coupled to the normal conductor, generates an orbitally entangled state by injecting pairs of electrons into different leads of the normal conductor. The entanglement is detected via violation of a Bell inequality, formulated in terms of zero-frequency current cross correlators. It is shown that the Bell inequality can be violated for arbitrary strong dephasing in the normal conductor.     

Combining Chemometric Models with Adsorption Isotherm Measurements to Study Omeprazole in RP-LC

The adsorption of the proton-pump inhibitor omeprazole was investigated using RP-LC with chemometric models combined with adsorption isotherm modelling to study the effect of pH and type of organic modifier (i.e., acetonitrile or methanol). The chemometric approach revealed that omeprazole was tailing with methanol and fronting with acetonitrile along with increased fronting at higher pH. The increased fronting with higher pH for acetonitrile was explored using a pH-dependent adsorption isotherm model that was determined using the inverse method and it agreed well with the experimental data. The model indicated that the peaks exhibit more fronting at high pH due to a larger fraction of charged omeprazole molecules. This model could accurately predict the shape of elution profiles at arbitrary pH levels in the studied interval. Using a two-layer adsorption isotherm model, the difference between acetonitrile and methanol was studied at the lowest pH at which almost all omeprazole molecules are neutral. Omeprazole had adsorbate–adsorbate interactions that were similar in strength for the acetonitrile and methanol mobile phases, while the solute–adsorbent interactions were almost twice as strong with methanol. The difference in the relative strengths of these two interactions likely explains the different peak asymmetries (i.e., tailing/fronting) in methanol and acetonitrile. In conclusion, thermodynamic modelling can complement chemometric modeling in HPLC method development and increase the understanding of the separation.

     

Optimizing Column Length and Particle Size in Preparative Batch Chromatography Using Enantiomeric Separations of Omeprazole and Etiracetam as Models: Feasibility of Taguchi Empirical Optimization

The overreaching purpose of this study is to evaluate new approaches for determining the optimal operational and column conditions in chromatography laboratories, i.e., how best to select a packing material of proper particle size and how to determine the proper length of the column bed after selecting particle size. As model compounds, we chose two chiral drugs for preparative separation: omeprazole and etiracetam. In each case, two maximum allowed pressure drops were assumed: 80 and 200 bar. The processes were numerically optimized (mechanistic modeling) with a general rate model using a global optimization method. The numerical predictions were experimentally verified at both analytical and pilot scales. The lower allowed pressure drop represents the use of standard equipment, while the higher allowed drop represents more modern equipment. For both compounds, maximum productivity was achieved using short columns packed with small-particle size packing materials. Increasing the allowed backpressure in the separation leads to an increased productivity and reduced solvent consumption. As advanced numerical calculations might not be available in the laboratory, we also investigated a statistically based approach, i.e., the Taguchi method (empirical modeling), for finding the optimal decision variables and compared it with advanced mechanistic modeling. The Taguchi method predicted that shorter columns packed with smaller particles would be preferred over longer columns packed with larger particles. We conclude that the simpler optimization tool, i.e., the Taguchi method, can be used to obtain “good enough” preparative separations, though for accurate processes, optimization, and to determine optimal operational conditions, classical numerical optimization is still necessary.     

Pulse polarographic determination of nitrosamines: Part 2. Methods for the Determination of N-Nitrosodiphenylamine and N-Nitrosodibutylamine

Differential pulse polarographic methods are reported for the determination of N-nitrosodiphenylamine and N-nitrosodibutylamine in aqueous media. Optimum conditions for analysis were obtained with acetate buffer (pH 3.74) and 0.01 M H₂SO₄, where reduction peak separations were of the order of 300 mV and 200 mV, respectively. Detection limits were approximately 3×10^-8 M for each compound. Methods for the extraction of these nitrosamines from iso-octane to aqueous solutions were quantitatively examined.