Processes of flats induced by higher dimensional processes III

Stationary processes of k-flats in ^d can be thought of as point processes on the Grassmannian _k ^d of k-dimensional subspaces of ^d . If such a process is sampled by a (d–k+ j)-dimensional space F, it induces a process of j-flats in F. In this work we will investigate the possibility of determining the original k-process from knowledge of the intensity measures of the induced j-processes. We will see that this is impossible precisely when 1<k<d–1 and j=0,...,2[r/2]–1, where r is the rank of the manifold _k ^d . We will show how the problem is equivalent to the study of the kernel of various integral transforms, these will then be investigated using harmonic analysis on Grassmannian manifolds.The research of the first and third authors was supported in part by NSF grants DMS-9207019 and DMS-9304284. The research of the second author was supported in part by NFR contract number R-RA 4873-306 and the Swedish Academy of Sciences.     

Nitrato- and fluoroboracites M3B7O13NO3 and M3B7O13F

New boracites containing nitrato- or fluoroanions that appear to be true low-pressure phases have been synthesized at superatmospheric pressures. The M₃B₇O₁₃NO₃ compounds (M = Co, Ni, Cu, Zn, Cd) transform rapidly and reversibly in the temperature region 300–500°C between probable orthorhombic and face centered cubic symmetry, while the M₃B₇O₁₃F compounds (M = Mg, Mn, Fe, Co, Zn) appear to maintain rhombohedral symmetry up to their decomposition temperatures of 800–900°C. True high-pressure boracite-like phases containing F and Cr, Mn, Fe, or Co that decompose upon heating to M₃B₇O₁₃F have also been isolated.     

Obtaining partial widths from siegert wavefunctions

It is shown that a simple expression for the partial widths in a multichannel decay problem can be readily obtained from a Siegert wavefunction.     

Characterizing dominates on a family of triangular norms

Dominates is a relation which can be defined on any collection of operations which (1) are defined on the same partially ordered set and (2) have the same identity. In this paper the family considered is a family {T _p } _p=?∞ ^∞ of triangular norms given, for any real numberp ≠ 0, by $$T_p (a,b) = \left[ {Max(a^p + b^p - 1,0} \right]^{{1 \mathord{\left/ {\vphantom {1 p}} \right. \kern-\nulldelimiterspace} p}} $$ and, forp=?∞, 0 or ∞, by taking appropriate limits of those already defined. We sayT _q dominatesT _p provided $$T_q (T_p (a,b),T_p (c,d)) \geqq T_p (T_q (a,c),T_q (b,d))$$ for alla,b,c,d in [0, 1]. The main result of this paper is that dominates is transitive on this family, in fact,T _q dominatesT _p if and only ifq ≦p.     

Synthetic thermally reversible gel systems. IV

The polymerization kinetics in water of acrylylglycinamide (AG) initiated by K₂S₂O₈ was studied over the temperature range 40.0 to 60.0°C. Monomer concentration was varied from 7.8 × 10^?3 to 31.2 × 10^?3M and catalyst from 1.85 × to 11.10 × 10^?5M. The rate expression is ?d[M]/dt = R_p, = k_1.22[K₂S₂O₈]^0.5[M]^1.22, and the overall empirical rate constant, k_1.22 = 1.14 × 10¹¹e^?15,800/RT 1.^0.72 mole^?0.72 min^?1. To explain the dependence on monomer, a kinetic scheme which includes a bimolecular reaction (k₂) between monomer and initiator is suggested. The simplified expression which describes the initial rate of polymerization is: ?d[M]/dt = R_p, = k₄(2[I]/k₅)^1/2[M](k₁ + k₂[M])^1/2, where k₁, k₂, k₄ and k₅ are rate constants for S₂O₈ = decomposition, a bimolecular reaction between monomer and initiator, propagation, and termination, respectively. Individual bimolecular rate constants are expressed in liter/mole-min. The equation predicts a dependence on monomer concentration between 1.0 and 1.5 with 1.5 being approached a t high monomer concentrations. Plots of R_P²/[M]² versus [M] are linear, as predicted by the postulated reaction route and values for k₂ and k₄/k₅^1/2 were obtained from the slopes and intercepts of these plots. The temperature dependence of the bimolecular monomer-initiator reaction is k₂ = 5.19 × 10²¹e^?36,000/RT. Instead of the usual behavior, the k₄/k₅^1/2 ratio was found to decrease with temperature and the difference of activation energies, (E₄ ? E₅/2), is ?1.50 kcal. The temperature dependence of the propagation to square root of the termination rate constant ratio is k₄/k₅^1/2 = 6.16e^1500/RT. These rather unusual results may be related to the ability of AG polymers in water to form thermally reversible gels; even above the gel melting points, the polymers are considerably aggregated in solution. This would tend to make the bimolecular termination reaction more temperature dependent and also account for the high values (59–69) for the k₄/k₅^1/2 ratios. For similar temperatures, the overall rate constants for AG are approximately four times those for acrylamide.     

Chemical studies on the anobiidae: Sex pheromone of the drugstore beetle, stegobium paniceum (L.) (coleoptera)

Chemical an spectroscopic evidence is presented to show that 2,3-dihydro-2,3,5-trimethyl-6-(1-methyl-2-oxobutyl)-4H-pyran-4-one (10) is the sex pheromone produced by the female drugstore beetle, Stegobium paniceum L.     

A self-assembling protein template for constrained synthesis and patterning of nanoparticle arrays

Self-assembling biomolecules that form highly ordered structures have attracted interest as potential alternatives to conventional lithographic processes for patterning materials. Here, we introduce a general technique for patterning nanoparticle arrays using two-dimensional crystals of genetically modified hollow protein structures called chaperonins. Constrained chemical synthesis of transition metal nanoparticles is initiated using templates functionalized with polyhistidine sequences. These nanoparticles are ordered into arrays because the template-driven synthesis is constrained by the nanoscale structure of the crystallized protein. We anticipate that this system may be used to pattern different classes of nanoparticles based on the growing library of sequences shown to specifically bind or direct the growth of materials.