On smooth reformulations and direct non-smooth computations for minimax problems

Minimax problems can be approached by reformulating them into smooth problems with constraints or by dealing with the non-smooth objective directly. We focus on verified enclosures of all globally optimal points of such problems. In smooth problems in branch and bound algorithms, interval Newton methods can be used to verify existence and uniqueness of solutions, to be used in eliminating regions containing such solutions, and point Newton methods can be used to obtain approximate solutions for good upper bounds on the global optimum. We analyze smooth reformulation approaches, show weaknesses in them, and compare reformulation to solving the non-smooth problem directly. In addition to analysis and illustrative problems, we exhibit the results of numerical computations on various test problems.     

Unsteady compressible second-order boundary layers at the stagnation point of two-dimensional and axisymmetric bodies

The unsteady laminar compressible boundary-layer flow over two-dimensional and axisymmetric bodies at the stagnation point with mass transfer has been studied for all second-order boundary layer effects when the basic potential flow admits self-similarity. The solutions for the governing equations are obtained by using an implicit finite-difference scheme. Computations have been carried out for different values of the parameters characterizing the unsteadiness in the free stream velocity, wall temperature, mass transfer rate and variable gas properties. The results are found to be strongly affected by the unsteadiness in the free stream velocity. For large injection rates the second-order boundary layer effects may prevail over the first-order boundary layer, but reverse is true for suction. The wall temperature and the variation of the density-viscosity product across the boundary layer appreciably change the skin-friction and heat-transfer rates due to second-order boundary-layer effects.

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Instationäre kompressible Grenzschichten 2. Ordnung am Staupunkt von zweidimensionalen und achsensymmetrischen Körpern

Zusammenfassung Es wurde die instationäre, laminare, kompressible Grenzschichtströmung über einen zweidimensionalen achsensymmetrischen Körper am Staupunkt mit Stoffübergang für alle Grenzschichteffekte 2. Ordnung studiert, wenn die Potentialströmung in sich selbst ähnlich ist. Die Lösung für die grundlegenden Gleichungen wurden unter Anwendung einer impliziten finiten Differenzenmethode erzielt. Es wurden Rechnungen für verschiedene Werte von Parametern durchgeführt, welche die Unstetigkeit in der Freistrahlgeschwindigkeit, die Wandtemperatur, den Stofftransport und die veränderlichen Zustandsgrößen des Gases charakterisieren. Dabei wurde festgestellt, daß die Ergebnisse stark von der Unstetigkeit in der Geschwindigkeit des Freistrahles beeinflußt werden. Für große Zuströmraten können die Effekte 2. Ordnung in der Grenzschicht über die der 1. Ordnung überwiegen, aber das Gegenteil gilt für Absaugung. Die Wandtemperatur und das Dichte-Viskositätsprodukt über die Grenzschicht ändern die Wandreibung und den Wärmeübergang merklich wegen der Grenzschichteffekte 2. Ordnung.

     

Studies on optical absorption and structural properties of Fe doped CdS quantum dots

Fe doped CdS quantum dots have been prepared using simple precursors by chemical precipitation technique. Fe doped CdS quantum dots have been synthesized by mixing cadmium nitrate, sodium sulfide and adding Fe under suitable conditions. X-ray diffraction analysis reveals that undoped and Fe doped CdS crystallizes in hexagonal structure. The lattice constants of Fe doped CdS nanoparticles decreased slightly with incorporation of Fe and no secondary phase was observed. The average grain size of the nanoparticles is found to lie in the range of 2.8–4.2 nm. HRTEM results show that undoped and 3.75% Fe doped CdS nanoparticles exhibit a uniform size distribution and average size of the nanoparticles is about 2–3 nm. Raman spectra show that 1LO and 2LO peaks of the Fe doped CdS samples are slightly red shifted compared with those of undoped CdS. Optical absorption spectra of Fe doped CdS nanoparticles exhibited red shift.     

Ethyl 2‐form­amido‐2‐(4‐iodo­benzyl)‐3‐(4‐iodo­phenyl)­propionate and ethyl 2‐(3‐bromo­benzyl)‐3‐(3‐bromo­phenyl)‐2‐form­amidopropionate

The title compounds, C₁₉H₁₉I₂NO₃ and C₁₉H₁₉Br₂NO₃, are derivatives of α‐amino­isobutyric acid with halogen substituents at the para and meta positions, respectively. The ethoxycarbonyl and formamide side chains attached to the C_α atom of the mol­ecule adopt extended and folded conformations, respectively. The crystal structures are stabilized by N—H⃛O, C—H⃛O, C—Br⃛O and C—I⃛O interactions.     

Precursors to dodecahedrane

The title compounds, (2R,2′′S,3b′S,4a′R,7b′S,8a′R)‐per­hydro­di­spiro­[furan‐2,3′‐di­cyclo­penta­[a,e]­pentalene‐7′,2′′‐furan]‐5,5′′‐dione, C₂₀H₂₆O₄, and (3aR,3bR,4aR,4bS,5aS,8aR,8bR,9aR,9bS,10aS)‐per­hydro­dipentaleno­[2,1‐a:2′,1′‐e]­pentalene‐1,6‐dione, C₂₀H₂₆O₂, are intermediates identified during the synthesis of dodecahedrane. Crystallographic studies have established the ring‐junction stereochemistry for these important intermediates. All the ring junctions are cis‐fused, and the molecular packing is stabilized by van der Waals interactions.     

A fully vectorial effective index method to analyse the propagation properties of microstructured fiber

Based on numerical simulation, we theoretically study the linear and nonlinear properties of microstructured fiber. Using the fully vectorial effective index method, we calculate the effective refractive index for different air hole size. We show how the linear properties such as spot size, numerical aperture, splice loss and bend loss can be controled by changing the air hole size. We also propose the same method for analysing effective area and self-phase modulation of microstructured fiber for different designing parameters. We compare all our results with other numerical methods.     

X-ray diffraction, spectroscopic and thermal studies on a potential semiorganic NLO material: lithium bis-L-malato borate

A semiorganic nonlinear optical material, lithium bis-L-malato borate (LBMB) (molecular formula C8H8BLiO10), has been synthesized, and single crystals grown from an aqueous solution, by the method of slow evaporation at 30 degrees C. Crystals of size up to 7 mm x 3 mm x 2 mm were harvested and characterized by powder and single crystal X-ray diffraction and Fourier transform infrared techniques to confirm the identity of the compound formed. The TG-DTA results establish the good thermal stability of the material. The UV-Vis-NIR spectral study reveals that the material has a wide transparency window (230-1500 nm) with a lower cutoff at 230 nm. Kurtz powder test with a Nd:YAG laser indicates the production of SHG output.     

High speed binary rate multiplier

Binary Rate Multipliers are pulse frequency converting circuits, which perform first degree or linear segment interpolations. Here a scheme for an ideally fast rate Multiplier, different from conventional Binary Rate Multiplier, has been developed and found working satisfactorily. This scheme has been implemented by using standard digital logic modules. Errors in the multiplier and methods employed to eliminate these errors have also been discussed.     

Stereochemistry of benzophenone derivatives: crystal and molecular structure of 3,3′-dibromobenzophenone

The structure of 3,3′-dibromobenzophenone has been reinvestigated using new three-dimensional data. Crystals of 3,3′-dibromobenzophenone are orthorhombic:a = 4·05,b = 11·74,c = 24·80 Å,Z = 4, space groupPbcn. The structure has been refined by three-dimensional methods, including anisotropic full-matrix least squares, to anR index 0·104. The conformation of isolated molecules of benzophenone,pp′-dimethoxy benzophenone and 3,3′-dibromobenzophenone have been calculated by semi-empirical methods, and the results are compared with those obtained from X-ray crystallographic investigations on these compounds. It has been found that the calculated geometries of isolated molecules of benzophenone and its derivatives are different from those observed in the crystal structures of these compounds.     

A sensitive and selective spectrophotometric estimation of catechol derivatives in pharmaceutical preparations

A sensitive and simple spectrophotometric method for the estimation of catechol and its derivatives like dopamine hydrochloride (DPH), levodopa (LDP), methyldopa (MDP) and adrenaline hydrochloride (ADH) in both pure form and in pharmaceutical formulation, is described. The method is based on the interaction of diazotised sulphanilamide (DSA) with catechol derivatives in the presence of molybdate ions in acidic medium. Absorbance of the resulting red coloured product is measured at 490 nm for pyrocatechol (PCL) and at 500 nm for other catechol derivatives. The colour reaction is stable for 24–30 h. Under optimal conditions, Beer's Law range for pyrocatechol was found to be between 0.04 and 2.4 (R.S.D.=0.78%), for DPH was 0.02–2.8 (R.S.D.=0.98%) for LDP was 0.1–2.8 (R.S.D.=1.21%) for MDP was 0.5–7 (R.S.D.=1.41%) and for ADH was 0.5–7 (R.S.D.=1.58%). The method is highly reproducible and specific for these selected catechol derivatives. The common excipients used as additives do not interfere in the proposed method. Analytical data for the determination of the pure compound is presented together with the application of the proposed method to the analysis of some pharmaceutical formulations. The results compare favourably with those of official and reported methods.