Maximum likelihood prediction

The principle of maximum likelihood is applied to the joint prediction and estimation of a future random variable and an unknown parameter. We assume dependence between present and future, and the approach is non-Bayesian. Our principal application is to the prediction of higher order statistics from lower ones in Type II censored random samples. Some simple criteria for existence and uniqueness of the predictor are given for this situation and the methods are illustrated with several examples.     

Influence of uniaxial stress on quantum effects in Si inversion layers

We show that the application of a compressional stress to the Si substrate decreases the mobility of electrons in the lowest subband and causes piezoresistance. This effect, together with the electron transfer effect and the existence of localized band-tail states in the subbands at low electron densities, account for the piezoresistance in n-channel (100)Si inversion layer at 4.2 K.     

Dependence of the zero shear-rate viscosity and the viscosity function of linear high-density polyethylenes on the mass-average molar mass and polydispersity

Linear high-density polyethylenes with molar masses M _w between 240 and 1,000,000 g/mol, obtained by metallocene catalysts, were characterized in shear using oscillatory and creep tests. The polydispersities of the molar mass distributions (MMDs) lay between 1 and 16. The resulting zero shear-rate viscosities η₀ covered a range from 2.5×10⁻³ to around 10⁸ Pas. Above a critical molar mass of M _c≈2,900 g/mol, the experimental results can be described by the relation η₀ ∼ M _w^3.6, independently of the MMD. The oscillatory data were fitted with a Carreau–Yasuda equation. The resulting parameters were correlated to molecular structure. The parameter a, being a quantity for the width of the transition between the Newtonian and the non-Newtonian regime, showed a dependence on the molar mass M _w but not on M _w/M _n. The parameter λ of the Carreau-Yasuda equation was found to be the reciprocal crossover frequency for all samples with a log-Gaussian MMD. λ depends on the molar mass M _w and also on M _w/M _n.

Tensor-Nonlinear Constitutive Equations for an Elastic Body with Primary Anisotropy

International Applied Mechanics - A nonlinear elastic body with primary anisotropy is considered. It is assumed that the initial state of the body is equivalent to its natural state, while strains...     

Sigma-borane complexes of iridium: synthesis and structural characterization

Reaction of NaBH4 with (tBuPOCOP)IrHCl affords the previously reported complex (tBuPOCOP)IrH2(BH3) (1) (tBuPOCOP = kappa(3)-C6H3-1,3-[OP(tBu)2]2). The structure of 1 determined from neutron diffraction data contains a B-H sigma-bond to iridium with an elongated B-H bond distance of 1.45(5) A. Compound 1 crystallizes in the space group P1 (Z = 2) with a = 8.262 (5) A, b = 12.264 (5) A, c = 13.394 (4) A, and V = 1256.2 (1) A(3) (30 K). Complex 1 can also be prepared by reaction of BH3 x THF with (tBuPOCOP)IrH2. Reaction of (tBuPOCOP)IrH2 with pinacol borane gave initially complex 2, which is assigned a structure analogous to that of 1 based on spectroscopic measurements. Complex 2 evolves H2 at room temperature leading to the borane complex 3, which is formed cleanly when 2 is subjected to dynamic vacuum. The structure of 3 has been determined by X-ray diffraction and consists of the (tBuPOCOP)Ir core with a sigma-bound pinacol borane ligand in an approximately square planar complex. Compound 3 crystallizes in the space group C2/c (Z = 4) with a = 41.2238 (2) A, b = 11.1233 (2) A, c = 14.6122 (3) A, and V = 6700.21 (19) A(3) (130 K). Reaction of (tBuPOCOP)IrH2 with 9-borobicyclononane (9-BBN) affords complex 4. Complex 4 displays (1)H NMR resonances analogous to 1 and exists in equilibrium with (tBuPOCOP)IrH2 in THF solutions.     

Synthesis and characterization of ruthenium bis(beta-diketonato) pyridine-imidazole complexes for hydrogen atom transfer

Ruthenium bis(beta-diketonato) complexes have been prepared at both the RuII and RuIII oxidation levels and with protonated and deprotonated pyridine-imidazole ligands. RuII(acac)2(py-imH) (1), [RuIII(acac)2(py-imH)]OTf (2), RuIII(acac)2(py-im) (3), RuII(hfac)2(py-imH) (4), and [DBU-H][RuII(hfac)2(py-im)] (5) have been fully characterized, including X-ray crystal structures (acac = 2,4-pentanedionato, hfac = 1,1,1,5,5,5-hexafluoro-2,4-pentanedionato, py-imH = 2-(2'-pyridyl)imidazole, DBU = 1,8-diazabicyclo[5.4.0]undec-7-ene). For the acac-imidazole complexes 1 and 2, cyclic voltammetry in MeCN shows the RuIII/II reduction potential (E1/2) to be -0.64 V versus Cp2Fe+/0. E1/2 for the deprotonated imidazolate complex 3 (-1.00 V) is 0.36 V more negative. The RuII bis-hfac analogues 4 and 5 show the same DeltaE1/2 = 0.36 V but are 0.93 V harder to oxidize than the acac derivatives (0.29 and -0.07 V). The difference in acidity between the acac and hfac derivatives is much smaller, with pKa values of 22.1 and 19.3 in MeCN for 1 and 4, respectively. From the E1/2 and pKa values, the bond dissociation free energies (BDFEs) of the N-H bonds in 1 and 4 are calculated to be 62.0 and 79.6 kcal mol(-1) in MeCN - a remarkable difference of 17.6 kcal mol(-1) for such structurally similar compounds. Consistent with these values, there is a facile net hydrogen atom transfer from 1 to TEMPO* (2,2,6,6-tetramethylpiperidine-1-oxyl radical) to give 3 and TEMPO-H. The DeltaG degrees for this reaction is -4.5 kcal mol(-1). 4 is not oxidized by TEMPO* (DeltaG degrees = +13.1 kcal mol(-1)), but in the reverse direction TEMPO-H readily reduces in situ generated RuIII(hfac)2(py-im) (6). A RuII-imidazoline analogue of 1, RuII(acac)2(py-imnH) (7), reacts with 3 equiv of TEMPO* to give the imidazolate 3 and TEMPO-H, with dehydrogenation of the imidazoline ring.     

Homopolymerization of ω‐Styryl‐Polystyrene Macromonomers in the Presence of CpTiF3/MAO

Summary: ω‐Styryl‐polystyrene macromonomers were synthesized by anionic induced deactivation reactions. Their homopolymerization in the presence of a fluorinated half‐sandwich metallocene catalyst (CpTiF₃/MAO) was investigated. In spite of the intrinsic lower reactivity of these macromonomers with respect to the micromolecular monomer, coordination homopolymerization was possible. The influence of several experimental parameters on the polymerization yield and degree could be demonstrated. In most cases, under identical experimental conditions, higher polymerization yields and degrees were observed with respect to the CpTiCl₃/MAO catalyst.

The synthesis of p‐polystyryl‐substituted styrene derivatives by the homopolymerization of ω‐styryl‐polystyrene macromonomers in the presence of CpTiF₃.     

Synthesis and conformation of 6,8,10-trinitro-1,4-dioxaspiro[4.5]decane

cis, trans-6,8,10-Trinitro-1,4-dioxaspiro[4.5]decane was synthesized by reduction of the corresponding spirocyclic anionic δ-complex with potassium tetrahydroborate. The molecular structure and the conformation of the title compound were established by X-ray diffraction analysis and¹H NMR spectroscopy. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 1713–1717, September, 1999.