Determinantal point processes in the plane from products of random matrices

We show that the density of eigenvalues for three classes of random matrix ensembles is determinantal. First we derive the density of eigenvalues of product of k independent n x n matrices with i.i.d. complex Gaussian entries with a few of matrices being inverted. In second example we calculate the same for (compatible) product of rectangular matrices with i.i.d. Gaussian entries and in last example we calculate for product of independent truncated unitary random matrices. We derive exact expressions for limiting expected empirical spectral distributions of above mentioned ensembles.

Time-temperature histories of spherical food products during bulk forced-air precooling

A general mathematical model for forced air precooling of spherical food products in bulk is developed. The food products are arranged inline to form a rectangular parallelepiped. Chilled air is blown along the height of the package. The governing equations for the transient two-dimensional conduction with internal heat generation in the product, simultaneous heat and mass transfer at the product-air interface and one-dimensional transient energy and species conservation equations for the moist air are solved numerically using finite difference methods. Results are presented in the form of time-temperature histories. Experiments are conducted with model foods in a laboratory scale air precooling tunnel. The agreement between the theoretical and experimental results is found to be good. In general, a single product analysis fails to predict the precooling characteristics of bulk loads of food products. In the range of values investigated, the respiration heat is found to have a negligible effect.

On optimum stratification with proportional allocation for a class of pareto distributions

Cum ./LSTA_A_8828879_O_XML_IMAGES/LSTA_A_8828879_O_ILM0001.gif rule [Singh (1975)] has been suggested in the literature for finding approximately optimum strata boundaries for proportional allocation, when the stratification is done on the study variable. This paper shows that for the class of density functions arising from the Wang and Aggarwal (1984) representation of the Lorenz Curve (or DBV curves in case of inventory theory), the cum ./LSTA_A_8828879_O_XML_IMAGES/LSTA_A_8828879_O_ILM0002.gif rule in place of giving approximately optimum strata boundaries, yields exactly optimum boundaries. It is also shown that the conjecture of Mahalanobis (1952) “. . .an optimum or nearly optimum solutions will be obtained when the expected contribution of each stratum to the total aggregate value of Y is made equal for all strata” yields exactly optimum strata boundaries for the case considered in the paper.

Acid-catalysed cyclisations: structures of novel products isolated in the reaction of 2-[3-(2,6-dimethoxyphenyl)but-2-enyl]-2-methylcyclopentane-1,3-dione with MeOH-HCl

Reaction of the title compound (1a) with anhydrous MeOH-HCl gave 2-endo-(2,6-dimethoxyphenyl)-2-exo-methyl-5-methylbicyclo[3.2.1]octane-6,8-dione (3a), 1,5,14-timethoxy-5,8-seco-6,7-dinorestra-1,3,5(10),9(11)-tetraen-17-one (4), 1,5-dimethoxy-5,8-seco-6,7-dinorestra-1,3,5(10),8,14-pentaen-17-one (5), and 3,4,5,6-tetrahydro-2,7-dimethoxy-3,6-dimethyl-3,2,6-(13-oxopropan[1]yI[3]ylidene)-2H-1-benzoxocin (6). Structures assigned to compounds (3a), (4), and (6) are based on spectral data. The exo-tricyclic acetal structure (6) was further confirmed by the analysis of the 1H n.m.r. spectra of the isomeric alcohols (11) and (12), obtained by sodium borohydride reduction of (6).

Mössbauer studies of the corrosion products of iron formed in aqueous ammonium nitrate solution

The products of corrosion reaction of electrolytic iron in 45% ammonium nitrate solution formed under various conditions of time, temperature and pH have been analysed mainly by Mössbauer spectroscopy, in combination with X-ray diffraction, infrared absorption and electron microscopy techniques. γ-Fe00H is found to be the major product of hydrolytic precipitation at pH > 5.6 while only α-FeOOH is formed at pH < 3.0. In the pH range 3.0 < pH < 5.0, α-Fe00H and ferrihydrite are both formed. However, once the nuclei of α-Fe00H are formed under low pH conditions, their growth is favoured even in the otherwise unfavourable slightly acidic medium, resulting in a hydrous α-Fe00H which has two distinct hyperfine fields at the 57Fe nucleus. Magnetite is always formed in the vicinity of the metal and its rate of formation on the surface increases with temperature. α-Fe203 is the major product of hydrolytic precipitation at temperatures >80C. The possible mechanisms for the formation of each of the corrosion products are discussed.

Reactivity of Cationic Terminal Borylene Complexes: Novel Mechanisms for Insertion and Metathesis Chemistry Involving Strongly Lewis Acidic Ligand Systems

The reactions of terminal borylene complexes of the type [CpFe(CO)(2)(BNR2)](+) (R = `Pr, Cy) with heteroallenes have been investigated by quantum-chemical methods, in an attempt to explain the experimentally observed product distributions. Reaction with dicyclohexylcarbodiimide (CyNCNCy) gives a bis-insertion product, in which 1 equiv of carbodiimide is assimilated into each of the Fe=B and B=N double bonds to form a spirocyclic boronium system. In contrast, isocyanates (R'NCO, R' = Ph, 2,6-wXy1, CY; XYl = C6H3Me2) react to give isonitrile complexes of the type [CpFe(CO)(2)(CNR')]+, via a net oxygen abstraction (or formal metathesis) process. Both carbodiimide and socyanate substrates are shown to prefer initial attack at the Fe=B bond rather than the B=N bond of the borylene complex. Further mechanistic studies reveal that the carbodiimide reaction ultimately leads to the bis-insertion compounds [CpFe(CO)(2)C(NCy)(2)B(NCY)(2)CNR2](+), rather than to the isonitrile system [CpFe(CO)(2)(CNCy)](+), on the basis of both thermodynamic (product stability) and kinetic considerations (barrier heights). The mechanism of the initial carbodiimide insertion process is unusual in that it involves coordination of the substrate at the (borylene) ligand followed by migration of the metal fragment, rather than a more conventional process: i.e., coordination of the unsaturated substrate at the metal followed by ligand migration. In the case of isocyanate substrates, metathesis products are competitive with those from the insertion pathway. Direct, single-step metathesis reactivity to give products containing a coordinated isonitrile ligand (i.e. [CpFe(CO)(2)(CNR')](+)) is facile if initial coordination of the isocyanate at boron occurs via the oxygen donor (which is kinetically favored); insertion chemistry is feasible when the isocyanate attacks initially via the nitrogen atom. However, even in the latter case, further reaction of the monoinsertion product so formed with excess isocyanate offers a number of facile (low energetic barrier) routes which also generate ['CpFe(CO)(2)(CNR')](+), rather than the bis-insertion product [CpFe(CO)(2)C(NR')(O)B(NR')(O)CNR2](+) (i.e., the direct analogue of the observed products in the carbodiimide reaction).

Microbial susceptibility of condensation products of carboxy-terminated polybutadiene and glycerol

Keeping in view the prospects of biodegradable polymers, a polymer was synthesized by the condensation of carboxy-terminated polybutadiene (CTPB) of Mnsim-5000 with glycerol and tested for its microbial susceptibility. The results of end group estimations and viscosity measurements indicated a quantitative reaction between the two reactants under experimental conditions. The clear-zone method was employed in this investigation to test biodegradability. Two strains of Serratia and three strains of Staphylococcus did show a clear zone surrounding the colony. However, the microbial growth was found to diminish after 4 or 5 days.

Novel Oxidation of Pyridoxal in Ternary Metal Complexes. An X-Ray Study of the Products

Attempts to prepare ternary metal complexes of pyridoxylidene-amino acid Schiff bases culminated in the oxidation of pyridoxal to pyridoxic acid or to its lactone and their complex formation, as evidenced from an X-ray study.

Dynamics of dense sheared granular flows. Part II. The relative velocity distributions

The distribution of relative velocities between colliding particles in shear flows of inelastic spheres is analysed in the Volume fraction range 0.4-0.64. Particle interactions are considered to be due to instantaneous binary collisions, and the collision model has a normal coefficient of restitution e(n) (negative of the ratio of the post- and pre-collisional relative velocities of the particles along the line joining the centres) and a tangential coefficient of restitution e(t) (negative of the ratio of post- and pre-collisional velocities perpendicular to line joining the centres). The distribution or pre-collisional normal relative velocities (along the line Joining the centres of the particles) is Found to be an exponential distribution for particles with low normal coefficient of restitution in the range 0.6-0.7. This is in contrast to the Gaussian distribution for the normal relative velocity in all elastic fluid in the absence of shear. A composite distribution function, which consists of an exponential and a Gaussian component, is proposed to span the range of inelasticities considered here. In the case of roughd particles, the relative velocity tangential to the surfaces at contact is also evaluated, and it is found to be close to a Gaussian distribution even for highly inelastic particles.Empirical relations are formulated for the relative velocity distribution. These are used to calculate the collisional contributions to the pressure, shear stress and the energy dissipation rate in a shear flow. The results of the calculation were round to be in quantitative agreement with simulation results, even for low coefficients of restitution for which the predictions obtained using the Enskog approximation are in error by an order of magnitude. The results are also applied to the flow down an inclined plane, to predict the angle of repose and the variation of the volume fraction with angle of inclination. These results are also found to be in quantitative agreement with previous simulations.

Unusual products of oxidation with Cr(VI) of methyl 5-methyl-7-methoxy-8-isopropyl-3,4-2-naphthoate

Abstract is not available.

Electron energy distributions and transport coefficients in N2 in E times B fields

Using the concept of energy-dependent effective field intensity, electron transport coefficients in nitrogen have been determined in E times B fields (E = electric field intensity, B = magnetic flux density) by the numerical solution of the Boltzmann transport equation for the energy distribution of electrons. It has been observed that as the value of B/p (p = gas pressure) is increased from zero, the perpendicular drift velocity increased linearly at first, reaches a maximum value, and then decreases with increasing B/p. In general, the electron mean energy is found to be a function of Eavet/p( Eavet = averaged effective electric field intensity) only, but the other transport coefficients, such as transverse drift velocity, perpendicular drift velocity, and the Townsend ionization coefficient, are functions of both E/p and B/p.

An extragenic suppressor of prp24-1 defines genetic interaction between PRP24 and PRP21 gene products of Saccharomyces cerevisiae

The temperature-sensitive prp24-1 mutation defines a gene product required for the first step in pre-mRNA splicing. PRP24 is probably a component of the U6 snRNP particle. We have applied genetic reversion analysis to identify proteins that interact with PRP24. Spontaneous revertants of the temperature-sensitive (ts) prp24-1 phenotype were analyzed for those that are due to extragenic suppression. We then extended our analysis to screen for suppressors that confer a distinct conditional phenotype. We have identified a temperature-sensitive extragenic suppressor, which was shown by genetic complementation analysis to be allelic to prp21-1. This suppressor, prp21-2, accumulates pre-mRNA at the non-permissive temperature, a phenotype similar to that of prp21-1. prp21-2 completely suppresses the splicing defect and restores in vivo levels of the U6 snRNA in the prp24-1 strain. Genetic analysis of the suppressor showed that prp21-2 is not a bypass suppressor of prp24-1. The suppression of prp24-1 by prp21-2 is gene specific and also allele specific with respect to both the loci. Genetic interactions with other components of the pre-spliceosome have also been studied. Our results indicate an interaction between PRP21, a component of the U2 snRNP, and PRP24, a component of the U6 snRNP. These results substantiate other data showing U2-U6 snRNA interactions.

Wigner distributions for finite-state systems without redundant phase-point operators

We set up Wigner distributions for N-state quantum systems following a Dirac-inspired approach. In contrast to much of the work in this study, requiring a 2N x 2N phase space, particularly when N is even, our approach is uniformly based on an N x N phase-space grid and thereby avoids the necessity of having to invoke a `quadrupled' phase space and hence the attendant redundance. Both N odd and even cases are analysed in detail and it is found that there are striking differences between the two. While the N odd case permits full implementation of the marginal property, the even case does so only in a restricted sense. This has the consequence that in the even case one is led to several equally good definitions of the Wigner distributions as opposed to the odd case where the choice turns out to be unique.

Convective heat-transfer rate distributions over a missile shaped body flying at hypersonic speeds

Experiments are carried out with air as the test gas to obtain the surface convective heating rate on a missile shaped body flying at hypersonic speeds. The effect of fins on the surface heating rates of missile frustum is also investigated. The tests are performed in a hypersonic shock tunnel at stagnation enthalpy of 2 MJ/kg and zero degree angle of attack. The experiments are conducted at flow Mach number of 5.75 and 8 with an effective test time of 1 ms. The measured stagnation-point heat-transfer data compares well with the theoretical value estimated using Fay and Riddell expression. The measured heat-transfer rate with fin configuration is slightly higher than that of model without fin. The normalized values of experimentally measured heat transfer rate and Stanton number compare well with the numerically estimated results. (C) 2009 Elsevier Inc. All rights reserved.