Zero-Sets of Quaternionic and Octonionic Analytic Functions with Central Coefficients

We prove that the zero set of any quaternionic (or octonionic)analytic function f with central (that is, real) coefficientsis the disjoint union of codimension two spheres in R⁴ or R⁸(respectively) and certain purely real points. In particular,for polynomials with real coefficients, the complete root-setis geometrically characterisable from the lay-out of the rootsin the complex plane. The root-set becomes the union of a finitenumber of codimension 2 Euclidean spheres together with a finitenumber of real points. We also find the preimages f^–1for any quaternion (or octonion) A. We demonstrate that this surprising phenomenon of complete spheresbeing part of the solution set is very markedly a special ‘real’phenomenon. For example, the quaternionic or octonionic Nthroots of any non-real quaternion (respectively octonion) turnout to be precisely N distinct points. All this allows us todo some interesting topology for self-maps of spheres.     

Quantumchromodynamic corrections for ΔF=2 processes in the presence of a heavy top quark

We calculate the QCD corrections to the ΔS=2 and ΔB=2 transition amplitudes for the casem _t ?m _w and extrapolate the results tom _t ?m _w , where they join smoothly with the low mass calculations,m _t ?m _w . We present explicit formulas for the corrections with numerical results summarized in tables and figures and compare them with earlier calculations. We arrive at a QCD corrected effective Hamiltonian which must hold for all ranges ofm _t .     

Synthesis of highly functionalized indeno[1,2-b]furans

Some novel functionalized indeno[1,2-b]furans were synthesized from the reaction of indandione/indanone and aldehydes at room temperature followed by the reaction of the Knoevenagel condendensed intermediate with 4-hydroxycoumarins in the presence of iodine as catalyst in dimethyl sulfoxide (DMSO) under thermal conditions. The reaction involved in a condensation and Michael addition followed by lactone ring opening and intramolecular cyclization process to afford the product in high yield in easy work-up procedure.     

Die langsame Strömung einer einfachen viskoelastischen Flüssigkeit durch einen endlich breiten Spalt

Zusammenfassung Es wird die zweidimensionale schleichende Strömung einer einfachen viskoelastischen Flüssigkeit durch einen endlich breiten Spalt mit Hilfe einer Störungsrechnung untersucht. Dabei wird vorausgesetzt, daß die Relaxationslänge klein gegen die Spaltbreite ist.Für einige Werte der Strömungsparameter werden Ergebnisse für die Geschwindigkeitsverteilung im Spalt, den Stromlinienverlauf und die Reibungsspannungen graphisch dargestellt und diskutiert. Obwohl wegen der Beschränkung der Lösungsmethode die bei Experimenten beobachteten Zirkulationsströmungen nicht beschrieben werden können, zeigen die Ergebnisse, daß die Tendenz der Abweichung vom newtonschen Verhalten in die gleiche Richtung geht.

---

Summary The two-dimensional creeping flow of a simple viscoelastic fluid through a finite gap located in an infinitely wide plate is analysed by using a perturbation method.Solutions for the streamline pattern, the velocity distribution in the gap and the stress components are derived and discussed. Because of the restrictions of the perturbation method no circular flow, as observed in some experiments, is predicted, but the results indicate at least some tendencies into this direction.

---

---

Mit 8 Abbildungen     

Controlled buckling and crumpling of nanoparticle-coated droplets

We introduce a new experimental approach to study the structural transitions of large numbers of nanoparticle-coated droplets as their volume is reduced. We use an emulsion system where the dispersed phase is slightly soluble in the continuous phase. By adding a fixed amount of unsaturated continuous phase, the volume of the droplets can be controllably reduced, causing them to buckle or crumple, thereby becoming nonspherical. The resultant morphologies depend both on the extent of volume reduction and the average droplet size. The buckling and crumpling behavior implies that the droplet surfaces are solid.     

Polyaniline/Single‐Walled Carbon Nanotubes Composite Based Triglyceride Biosensor

Nanocomposite film comprising of polyaniline (PANI) and single walled carbon nanotubes (SWCNT) has been fabricated onto indium‐tin‐oxide (ITO) coated glass plate using electrophoretic technique. Co‐immobilization of glycerol dehydrogenase (GDH) and lipase (LIP) has been done via N‐ethyl‐N′‐(3‐dimethylaminopropyl) carbodiimide and N‐hydroxysuccinimide chemistry to explore its application for triglyceride (tributyrin) sensing. Response studies have been done using linear sweep voltammetry revealing that LIP‐GDH/PANI‐SWCNT‐TB/ITO bioelectrode can detect tributyrin in the range of 50 to 400 mg dL^?1 with low Michaelis–Menten constant of 1.138 mM, improved response time of 12 s, high sensitivity as 4.28×10^?4 mA mg^?1 dL and storage stability of about 13 weeks.     

A Thermostable Alkaline Lipase from a Local Isolate Bacillus subtilis EH 37: Characterization, Partial Purification, and Application in Organic Synthesis

A mesophilic bacterial culture producing a novel thermostable alkaline lipase was isolated from oil rich soil sample and identified as Bacillus subtilis EH 37. The lipase was partially purified by ammonium sulfate precipitation and hydrophobic interaction chromatography with 17.8-fold purification and 41.9 U/ml specific activity. The partially purified enzyme exhibited maximum activity at pH 8.0 and at 60 °C. It retained 100% of activity at 50 °C and 60 °C for 60 min. The presence of Ca⁺², Mg⁺², and Zn²⁺ exhibited stimulatory effect on lipase activity, whereas Fe⁺³ and Co⁺² reduced its activity. The enzyme retained more than 80% of its initial activity upon exposure to organic solvents, exhibited 107% and 115% activity in the presence of 15% isopropyl alcohol and 30% n-hexane, respectively. The EH 37 lipase also proved to be an efficient catalyst in synthesis of ethyl caprylate in organic solvent, thus providing a concept of application of B. subtilis lipase in non-aqueous catalysis.     

Biosynthesis of Indigo Dye by Newly Isolated Naphthalene-Degrading Strain <Emphasis Type="Italic">Pseudomonas s</Emphasis>p. HOB1 and its Application in Dyeing Cotton Fabric

Indigo is one of the oldest dyes manufactured chemically and is mostly used in textile, food, and pharmaceutical industries. However, owing to the environmental hazards posed by the chemical production, the present scenario in the field stipulates a biosynthesis alternative for indigo production. The present study describes an indigenously isolated naphthalene-degrading strain Pseudomonas sp. HOB1 producing a blue pigment when indole was added in the growth medium. This blue pigment was analyzed by high-pressure thin-layer chromatography and other spectroscopic techniques which revealed it to be the indigo dye. Pseudomonas sp. HOB1 showed ability to produce 246 mg indigo liter⁻¹ of the medium. The K _m for the enzyme naphthalene dioxygenase which is involved in indigo formation is 0.3 mM, and V _max was as high as 50 nmol min⁻¹ mg dry biomass⁻¹. The bacterial indigo dye was further successfully applied for dyeing cotton fabrics. The high indigo productivity of Pseudomonas sp. HOB1 using naphthalene as growth substrate and its applicability on cotton fabrics, therefore, stems the probability of using this culture for commercial indigo production.     

Electrophoretically deposited polyaniline nanotubes based film for cholesterol detection

Polyaniline nanotube (PANI-NT) based films have been fabricated onto indium-tin-oxide (ITO) coated glass plates via electrophoretic technique. These PANI-NT/ITO electrodes have been utilized for covalent immobilization of cholesterol oxidase (ChOx) using glutaraldehyde (Glu) as cross-linker. Structural, morphological and electrochemical characterization of PANI-NT/ITO electrode and ChOx/Glu/PANI-NT/ITO bioelectrode have been done using FT-IR spectroscopy, SEM, electrochemical impedance spectroscopy and cyclic voltammetry techniques. Response studies of the ChOx/Glu/PANI-NT/ITO bioelectrode have been carried out using both linear sweep voltammetry and UV-Visible spectrophotometry. The results of the biosensing studies reveal that this bioelectrode can be used to detect cholesterol in wide detection range of 25-500 mg/dL with high sensitivity of 3.36 mA mg(-1) dL and fast response time of 30 s at pH 7.4. This bioelectrode exhibits very low value of Michaelis-Menten constant of 1.18 mM indicating enhanced interactions between cholesterol and ChOx immobilized onto this nanostructured PANI matrix.     

Gamma irradiation route to synthesis of highly re-dispersible natural polymer capped silver nanoparticles

Aqueous dispersions of highly stable, redispersible silver nanoparticles (Ag NPs) were synthesized using gamma radiolysis with gum acacia as a protecting agent. The formation of nanosized silver was confirmed by its characteristic surface plasmon absorption peak at around 405 nm in UV–vis spectra. The size of the silver nanoparticles can be tuned by controlling the radiation dose, ratio of gum acacia to silver ions and also the ionic strength of the medium. Dynamic light scattering (DLS) measurement of the as-synthesized nanoparticles indicated the size less than 3 nm at higher dose of radiation and this also corroborated the size measurement from the width of the corresponding X-ray diffraction (XRD) peak. The face centered cubic (fcc) crystallinity of the nanoparticles was evident from XRD and high resolution transmission electron microscopic (HRTEM) measurements. Fourier transform infra-red (FTIR) spectroscopic data indicate a bonding of Ag NPs with COO^? group of acacia through bridging bidentate linkage.