An integer arithmetic method to compute generalized matrix inverse and solve linear equations exactly

An algorithm that uses integer arithmetic is suggested. It transforms anm ×n matrix to a diagonal form (of the structure of Smith Normal Form). Then it computes a reflexive generalized inverse of the matrix exactly and hence solves a system of linear equations error-free.

Crystallization characteristics of vitrovac 4040 (Fe39Ni39Mo4Si6B12)

The metallic glass Vitrovac 4040 with the composition Fe39Ni39Mo4Si6B12 crystallizes in the order alpha-Fe, hexagonal Ni5Si2 and gamma-(Fe,Ni,Mo) by primary, secondary and polymorphic modes, respectively. The activation energies determined from the non-isothermal kinetics using Kissinger method turn out to be 490, 550 and 449 kJ.mol-1 for the above crystallization reactions. It has been observed that alpha transforms to gamma during annealing. Further, the bct (Fe1-xNix)3B phase has been identified when the glass is annealed above 1023 K.

The structure of phosphacymantrene

Proton NMR spectra of phosphacymantrene (π-phospholyl manganese tricarbonyl) orientated in the nematic phases of liquid crystals have been investigated. The derived H-H and H-P direct dipolar coupling constants have been used to determine the relative proton-proton and proton-phosphorus distances. A comparison of the geometrical data of various 5-membered aromatic heterocycles shows that the relative distances between the protons closest to the heteroatom increase with the van der Waals radius of the heteroatom. The results suggest that NMR spectroscopy of orientated molecules can be used to determine van der Waals radii.

Photochromism of alkylisophthalaldehydes in the solid state: structure–reactivity correlations

The crystal and molecular structures of the photochromic compounds 2,5-dimethylisophthalaldehyde (I) and 5-isopropyl-2-methylisophthalaldehyde (II) have been determined by single crystal X-ray analyses. The intramolecular gamma-hydrogen abstraction process involved in the photoenolisation of I and II in the solid state has been rationalised in the light of relevant geometrical parameters.

Studies of phosphazenes. Part 33. Thermal rearrangement of alkoxy(p-methylphenoxy)cyclophosphazenes: a synthetic route to oxocyclophosphazanes, phosphazadienes and phosphaz-1-enes

The aryloxy(alkoxy)cyclotriphosphazenes N3P3(OR)6�m(OC6H4Me-p)n(R = Me, n= 1�3; R = Et or CH2Ph, n= 3) rearrange on heating to give trioxocyclotriphosphazanes; the di- and mono-methoxy derivatives, N3P3(OMe)6�n(OC6H4Me-p)n(n= 4 or 5), yield dioxophosphaz-1-enes and an oxophosphazadiene respectively. The 1H, 13C and 31P NMR data for the starting materials and the products are presented. No evidence has been found for partially rearranged products. The geometrical disposition of the aryloxy groups in the starting material is retained in the rearranged products. Some aspects of the mechanism of the thermal rearrangement are discussed.

Study of forging design using slip-line fields

The main purpose of forging design is to ensure cavity filling with minimum material wastage, minimum die load and minimum deformation energy. Given the desired shape of the component and the material to be forged, this goal is achieved by optimising the initial volume of the billet, the geometrical parameters of the die and the process parameters. It is general industrial practise to fix the initial billet volume and the die parameters using empirical relationships derived from practical experience. In this paper a basis for optimising some of the parameters for simple closed-die forging is proposed. Slip-line field solutions are used to predict the flow, the load and the energy in a simple two-dimensional closed-die forging operation. The influence of the design parameters; flash-land width, excess initial workpiece area and forged cross-sectional size; on complete cavity filling and efficient cavity filling are investigated. Using the latter as necessary requirements for forging, the levels of permissable design parameters are determined, the variation of these levels with the size of the cross-section then being examined.

Synthesis Of (+/-)-Beta-Cuparenone Via 3-Oxa-Beta-Cuparenone

Grignard reaction followed by ozonolysis, or ozonolysis followed by Grignard reaction on the pentenoate 8, generates the diol 9. Cyclodehydration of 9 leads to the 3-oxacuparene (6), whereas PCC oxidation furnishes the 3-oxa-beta-cuparenone (7). Methanesulfonic acid-P2O5 transforms 7 into cyclopentenones 4, 5, known precursors to beta-cuparenone (3), and the naphthalenone 14.

The identification of 14 alpha,17 beta-dihydroxyandrost-4-en-3-one monohydrate and 14 alpha,17 beta-dihydroxyandrosta-1,4-dien-3-one monohydrate, metabolites of androstenedione in Mucor piriformis

The microorganism Mucor piriformis transforms androst-4-ene-3,17-dione into a major and several minor metabolites. X-ray crystallographic analysis of two of these metabolites was undertaken to determine unambiguously their composition and chirality. Crystals belong to the orthorhombic space-group P2(1)2(1)2(1), with a = 7.199(4) angstrom and a = 6.023(3) angstrom, b = 11.719(3) angstrom and b = 13.455(4) angstrom, c = 20.409(3) angstrom and c = 20.702(4) angstrom for the two title compounds, respectively. The structures have been refined to final R values of 0.060 and 0.040, respectively.

NMR of bicyclic diazines oriented in a lyotropic mesophase

Restricted Access.. Proton NMR spectra of bicyclic diazines such as phthalazine and quinoxaline have been studied in lyotropic liquid crystalline solvents. Values of the indirect spin-spin couplings which could not be derived from studies in the isotropic medium have been obtained. Geometrical information has been obtained in both the cases. The results are indicative of significant solvcntsolute interactions in phthalazine but not in quinoxaline.

Diffraction of a cylindrical pulse by a half plane under mixed boundary conditions

The general time dependent source problem has been solved by the method of transforms (Laplace, Lebedev–Kontorovich in succession) and the solution is obtained in the form of an infinite series involving Legendre functions. The solutions in the case of harmonic time dependence and the incident plane wave have been derived from the above solution and are presented in the form of an infinite series. In the case of an incident plane wave, the series has been summed and the final solution involves an improper integral which behaves like a complementary error function for large values of the argument. Finally, the far field evaluation has been shown. The results are compared with those of Sommerfeld's half-plane diffraction problem with unmixed boundary conditions.

Structural morphology of acoustically levitated and heated nanosilica droplet

We study the vaporization and precipitation dynamics of a nanosilica encapsulated water droplet by levitating it acoustically and heating it with a CO2 laser. For all concentrations, we observe three phases: solvent evaporation, surface agglomeration, and precipitation leading to bowl or ring shaped structures. At higher concentrations, ring reorientation and rotation are seen consistently. The surface temperature from an infrared camera is seen to be dependent on the final geometrical shape of the droplet and its rotation induced by the acoustic field of the levitator. With nonuniform particle distribution, these structures can experience rupture which modifies the droplet rotational speed. (C) 2010 American Institute of Physics. doi:10.1063/1.3493178]

An in situ electron microscope investigation of the icosahedral-to-decagonal quasicrystalline transformation in Al-20 at.% Mn

The solid-state transformation behaviour of the icosahedral phase in rapidly solidified Al-20 at.% Mn has been investigated by in situ heating experiments in the transmission electron microscope. As-rapidly-solidified Al-20 at.% Mn consists mainly of a dendritic icosahedral phase, with a small amount of interdendritic f.c.c. agr-Al. During subsequent heat treatment at temperatures below about 500°C, the dendritic icosahedral phase grows and consumes the interdendritic agr-Al. At about 500°C the decagonal phase nucleates near icosahedral dendrite and grain boundaries and then grows into the icosahedral matrix by lateral motion of ledges 10-20 nm high across facet planes normal to the twofold symmetry axes. At about 600°C the decagonal phase transforms into a crystalline phase. The present study suggests that solid-state decomposition of the icosahedral phase is the mechanism of decagonal phase formation in as-rapidly-solidified Al-Mn alloys.

A spiral growth model for quasicrystals in two dimensions

Spiral space filling geometrical constructions using rhombuses in two dimensions are considered as plausible mechanisms for quasicrystal growth. These models will show staircase-like features which may be observed experimentally.

Optimal explicit guidance of multistage launch vehicle along three-dimensional trajectory

Details of an efficient optimal closed-loop guidance algorithm for a three-dimensional launch are presented with simulation results. Two types of orbital injections, with either true anomaly or argument of perigee being free at injection, are considered. The resulting steering-angle profile under the assumption of uniform gravity lies in a canted plane which transforms a three-dimensional problem into an equivalent two-dimensional one. Effects of thrust are estimated using a series in a recursive way. Encke's method is used to predict the trajectory during powered flight and then to compute the changes due to actual gravity using two gravity-related vectors. Guidance parameters are evaluated using the linear differential correction method. Optimality of the algorithm is tested against a standard ground-based trajectory optimization package. The performance of the algorithm is tested for accuracy, robustness, and efficiency for a sun-synchronous mission involving guidance for a multistage vehicle that requires large pitch and yaw maneuver. To demonstrate applicability of the algorithm to a range of missions, injection into a geostationary transfer orbit is also considered. The performance of the present algorithm is found to be much better than others.

Effect of substrate temperature on the properties of ZrO2 films prepared by d.c. reactive magnetron sputtering

Studies of ZrO2 films prepared by d.c. reactive magnetron sputtering are described. The effects of substrate temperature on the packing density, refractive index, extinction coefficient and crystallinity phase have been investigated in the temperature range 25–450 °C. The refractive index varied from 1.84 to 1.95 and extinction coefficient from 2 × 10−3 to 9.6 × 10−3. This was explained on the basis of an increase in packing density from 0.686 to 0.813. The change in packing density has been attributed to a decrease in the oxygen condensation at higher temperatures. Annealing results in a decrease in refractive index and increase in extinction coefficient. The films deposited at 150 °C showed a monoclinic phase which transforms to a tetragonal phase at higher substrate temperatures.