The phase of the Riemann zeta function

We, offer an alternative interpretation of the Riemann zeta functionζ(s) as a scattering amplitude and its nontrivial zeros as the resonances in the scattering amplitude. We also look at several different facets of the phase of theζ function. For example, we show that the smooth part of theζ function along the line of the zeros is related to the quantum density of states of an inverted oscillator. On the other hand, for ℜs>1/2, we show that the memory of the zeros fades only gradually through a Lorentzian smoothing of the delta functions. The corresponding trace formula for ℜs≫1 is shown to be of the same form as generated by a one-dimensional harmonic oscillator in one direction along with an inverted oscillator in the transverse direction. Quite remarkably for this simple model, the Gutzwiller trace formula can be obtained analytically and is found to agree with the quantum result.     

Connecting Jacobi elliptic functions with different modulus parameters

The simplest formulas connecting Jacobi elliptic functions with different modulus parameters were first obtained over two hundred years ago by John Landen. His approach was to change integration variables in elliptic integrals. We show that Landen’s formulas and their subsequent generalizations can also be obtained from a different approach, using which we also obtain several new Landen transformations. Our new method is based on recently obtained periodic solutions of physically interesting non-linear differential equations and remarkable new cyclic identities involving Jacobi elliptic functions.     

Some remarks on the Jacobian question

This revised version of Abhyankar's old lecture notes contains the original proof of the Galois case of then-variable Jacobian problem. They also contain proofs for some cases of the 2-variable Jacobian, including the two characteristic pairs case. In addition, proofs of some of the well-known formulas enunciated by Abhyankar are actually written down. These include the Taylor Resultant Formula and the Semigroup Conductor formula for plane curves. The notes are also meant to provide inspiration for applying the expansion theoretic techniques to the Jacobian problem.     

Enantioselective organocatalytic synthesis of the chiral chromenes by domino oxa-Michael-aldol reaction

The proline based chiral organocatalyst has been found to be an efficient catalyst for enantioselective domino oxa-Michael-aldol reaction. This catalytic system provided the synthesis of substituted 2-aryl-2H-chromenes-3-carbaldehyde in good to high yields (73%–97%) with excellent enantioselectivity (up to 97%) and reasonable reaction times. The atom economy, high yield and mild reaction conditions are some of the important features of this protocol.     

Fluorescence Probes for ALKBH2 Allow the Measurement of DNA Alkylation Repair and Drug Resistance Responses

The DNA repair enzyme ALKBH2 is implicated in both tumorigenesis as well as resistance to chemotherapy in certain cancers. It is currently under study as a potential diagnostic marker and has been proposed as a therapeutic target. To date, however, there exist no direct methods for measuring the repair activity of ALKBH2 in vitro or in biological samples. Herein, we report a highly specific, fluorogenic probe design based on an oligonucleotide scaffold that reports directly on ALKBH2 activity both in vitro and in cell lysates. Importantly, the probe enables the monitoring of cellular regulation of ALKBH2 activity in response to treatment with the chemotherapy drug temozolomide through a simple fluorescence assay, which has only previously been observed through indirect means such as qPCR and western blots. Furthermore, the probe provides a viable high‐throughput assay for drug discovery.     

Determination of cefadroxil by three simple spectrophotometric methods using oxidative coupling reactions

Three simple and sensitive visible spectrophotometric methods for the assay of cefadroxil have been developed. MethodA (_max 410 nm) is based on the reaction of cefadroxil with 3-methyl-2-benzothiazolinone hydrazone hydrochloride in the presence of eeric ammonium sulphate. MethodB (_max, 510 nm) involves the reaction with 4-aminophenazone in the presence of potassium hexacyanoferrate(III). MethodC (_max, 620 nm) involves reaction with 2, 6-dichloroquinone-4-chlorimide (Gibb's reagent). All variables have been optimised and the reaction mechanisms presented. Regression analysis of the Beer's plots showed good correlation in the concentration ranges 1.0–6.0, 2.0–24.0 and 1.0–6.0 g/ml for methodsA, B andC, respectively. No interferences were observed from excipients and the validity of the methods was tested by analysing pharmaceutical dosage forms. Recoveries were 98.0–100.3%. The concentration measurements were reproducible within a relative standard deviation of 1.0%.     

Capillary electrophoretic protein separations in polyacrylamide-coated silica capillaries and buffers containing ionic surfactants

Capillary electrophoretic protein separations of high efficiency and resolution were obtained using polyacrylamide-coated silica capillaries and buffers containing ionic surfactants. The presence of micellar concentrations of sodium dodecyl sulfate or cetyltrimethyl- ammonium chloride minimized protein-capillary wall interactions, and facilitated concurrent separations of a mixture of both acidic and basic proteins, while the polyacrylamide coating provided increased resolution and migration time reproducibility via a reduction in electroosmotic flow. Attempts to obtain size-based protein separations via sieving through buffers containing the hydrophilic polymers methylcellulose and polyethylene glycol were unsuccessful.     

Spectrophotometric procedures for the determination of roxithromycin in pharmaceutical formulations

Four simple and sensitive visible spectrophotometric procedures for the assay of roxithromycin (RXT) have been developed. Procedures A and B are based on the formation of ion-pairs of roxithromycin with the dyes supracen violet 3B and tropaeolin 000, which are extracted into chloroform and have absorption maxima at 590 nm (SV 3B) and 490 nm (TP 000). Procedures C and D are based on condensation between the hydrolysis product of RXT in the presence of 3.6M hydrochloric acid in acetic acid medium and vanillin orp-dimethylaminobenzaldehyde (PDAB) to form coloured products with _max at 500 nm. Regression analysis of the Beer's plot showed good correlation in the concentration ranges 5–60 (A), 5–40 (B) and 5–50 (C & D) g/ml. No interference was observed from excipients and the validity of the procedures was tested by analysing pharmaceutical formulations. Recoveries were 99.0–102.0%. The concentration measurements are reproducible within a relative standard deviation of 1.0%.     

Chemoselective hydrogenation of substituted nitroaromatics using novel water-soluble iron complex catalysts

Chemoselective hydrogenation of substituted nitroaromatic compounds by water-soluble iron complex catalysts with molecular hydrogen has been reported for the first time. This biphasic catalyst presents an opportunity for a solvent-free hydrogenation. This catalyst system provides a low-cost, efficient alternative to the selective but environmentally unacceptable stoichiometric reductions as well as the supported noble metal catalysts used for hydrogenation. An efficient recycling strategy has resulted in a cumulative turnover number above 6000.