Estimation of Multinomial Probabilities under a Model Constraint

In this paper estimation of the probabilities of a multinomial distribution has been studied. The five estimators considered are: unrestricted estimator (UE), restricted estimator (RE) (under model ), preliminary test estimator (PTE) based on a test of the model , shrinkage estimator (SE) and the positive-rule shrinkage estimator (PRSE). Asymptotic distributions of these estimators are given under Pitman alternatives and the asymptotic risk under a quadratic loss has been evaluated. The relative performance of the five estimators is then studied with respect to their asymptotic distributional risks (ADR). It is seen that neither of the preliminary test and shrinkage estimators dominates the other, though each fares well relative to the other estimators. However, the positive rule estimator is recommended for use for dimension 3 or more while the PTE is recommended for dimension less than 3.     

STUDY ON THE DUCTILE DEFORMATION DOMAIN OF THE SIMPLE SHEAR IN ROCKS——TAKING BRITTLE FAULTS OF THE COVERING STRATA IN THE SOUTHERN JIANGSU AREA AS AN EXAMPLE

A study on the ductile deformation domain of the brittle fault in the shallow level ofthe crust is a new probe field for the modern structural geology. Taking the southern Jiang-su Province area as an example the orientation measurement of quartz crystals, the com-positional texture observation of three pressure sensitive minerals and the rheological param-eter determination of dislocation densities, etc. have been demonstrated and analysed basedon typical samples in the present paper. In addition, their generation mechanisms arealso discussed from the cataclastic rheology, the dynamic differentiation and the simpleshearing, specially, from the Ode strength theory. Finally, a generative relationship betweenthe ductile deformation domain of the brittle fault system, in the regional layer--slip andthe formation of the stratabound ore deposit is shown as well.     

Darstellung und Kristallstruktur von LnAl3Br12 (Ln = La,Ce, Pr,Nd, Sm,Gd) und thermischer Abbau zu LnBr3

Preparation and Crystal Structure of LnAl₃Br₁₂ (Ln = La, Ce, Pr, Nd, Sm, Gd) and Thermal Decomposition to LnBr₃ LnAl₃Br₁₂ (Ln = La, Ce, Pr, Nd, Sm, Gd) was prepared in crystalline form for the first time. The crystal structures of LaAl₃Br₁₂, PrAl₃Br₁₂, and NdAl₃Br₁₂ were determined on single crystals by X-ray methods. The isotypic compounds crystallize with trigonal symmetry, space group P 3₁12, Z = 3. A structural comparison to lanthanoide chloroaluminates of equal composition is given and thermal decomposition of LnAl₃Br₁₂ (Ln = Nd) to the corresponding lanthanoide tribromide is described.     

Glucomannan from Narcissus poeticus Studied by PMR and 13C NMR Spectroscopy

Native acetylated glucomannan of molecular weight (MW) 32000 with a glucose:mannose ratio 1:30 was isolated from bulbs of Narcissus poeticus. Glucomannan was depolymerized to a fragment of MW 15000 with an unchanged primary structure and was studied using PMR and ¹³C NMR spectroscopy. It was found that the linear chain of the biopolymer consists of 1-4-bound D-gluco- and D-mannopyranose units and the O-Ac groups are localized on C-2, C-3, and C-6 hydroxyls in certain anhydromannose units.     

Effect of Hydration–Dehydration Processes on the Structure and Porosity of Detemplated Silica Fibers

A study was carried out on the conditions of template removal (calcination or extraction by solvents) and hydration–dehydration processes on the hexagonal structure and porosity of detemplated fibers. The hydration–dehydration cycle leads to a decrease in fiber porosity, especially in fiber detemplation by extraction with surfactant solvents such as ethanol and acetic acid.     

Synthesis and magnetic properties of liquid crystalline lanthanide complexes with alkylsulfate counterions

The reaction of Schiff"s base L with lanthanide alkylsulfates affords liquid crystalline complexes with the general formula L₃Ln(C_nH_2n+1OSO₃)₃. The liquid crystalline structure and magnetic properties are studied by polarization thermal microscopy, differential scanning calorimetry, X-ray diffraction, and measurement of magnetic susceptibility. The temperatures of the existence of the mesophase and magnetic anisotropy of the complexes with the same lanthanide depend on the chain length of the alkyl fragment in the sulfate anion.     

Network theory of the nonlinear behaviour of polymer melts. Simple shear flow

Summary The network model developed in a previous paper is applied to the simple shear flow of polymer melts. The constitutive equation obtained consists of two terms. One of them describes the stress due to the network strands which exist at the onset of the deformation, dissociate during the deformation and result in a single integral constitutive equation with a strain dependent damping function. The formulation of the damping function in invariant form seems to be almost impossible.The second normal stress differenceN ₂ of the model is not zero,but has negative values. According to our model this is a consequence of the deformation dependence of the disentanglement process. The theory is compared with experimental data for a LDPE melt. It is found that the model explains the main features of the shear flow behaviour of the LDPE melt investigated preciously.

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Zusammenfassung Das Netzwerk-Modell, das in einer vorangegangenen Arbeit entwickelt wurde, wird für die einfache Scherströmung von Polymerschelzen angewendet. Die abgeleitete rheologische Zustandsgleichung besteht aus zwei Gliedern. Das erste beschreibt die Spannung-Dehnung-Beziehung der Kettensegmente, die zu Beginn der Deformation existieren und während der Deformation aufgelöst werden. Es hat die Form der einfachen Integralbeziehung mit einer Gedächtnisfunktion. Es ist kaum möglich, die dabei erhaltene Gedächtnisfunktion als Funktion der Invarianten der der Tensoren darzustellen. Die zweite Normal-SpannungsdifferenzN ₂ des Modells ist nicht Null und hat einen negativen Wert. Dies ist nach unserem Modell eine Folge der Deformationsabhängigkeit des Entschlaufungsprozesses. Die Theorie wird mit dem experimentellen Daten für eine LDPE-Schmelze verglichen, wobei sich zeigt, daß das Modell die wesentlichen Merkmale des Scherverhaltens der LDPE-Schmelze gut erklärt.

     

Synthesis and structural studies of polynuclear ruthenium clusters derived from reactions of 1,2,3,4-tetraphenyl-1,2,3,4-tetraphospholane with [Ru3(CO)12]

Reactions of 1,2,3,4-tetraphenyl-1,2,3,4-tetraphospholane (I) with triruthenium dodecacarbonyl at different temperatures result in the cleavage of P-P bonds and even P-C bond(s) in I to afford a series of new ruthenium cluster derivatives containing phosphido and phosphinidene ligands: a penta-ruthenium wing-tip bridged butterfly cluster [Ru₅(CO)₁₁(μ₄-PPh)(μ₃-PPh){(μ₄-η²-(PPh)₂CH₂}] (1), a hepta-ruthenium polyhedral (consisting of two fused square pyramids with a co-apex) cluster [Ru₇(CO)₁₅(μ₄-PPh)₂{(μ₂-PPh)₂CH₂}](2), a linked penta-ruthenium cluster [Ru₄(CO)₁₀(μ₄-PPh)(μ₃-PPh)₂(μ₃-η²-PPhCH₂)Ru(CO)₃] (3), and a hepta-nuclear polyhedral (consisting of two fused square pyramids with different apexes) cluster [Ru₇(CO)₁₅(μ₄-PPh)₂{(μ₂-PPh)₂CH₂}](4). Clusters 2 and 4 are isomeric and differ only in the connection of the two square pyramids in the Ru₇ polyhedron. All the newly obtained clusters have been fully characterized by spectroscopic (IR, FABMS, ¹H- and ³¹P-NMR spectroscopy) and analytical techniques, and their molecular structures are established by single crystal X-ray diffraction analysis.     

Molecular Structure of Samarium Dibromide

The molecular structure of samarium dibromide has been studied by electron diffraction at T _exp = 1250(50) K. The molecule has C_2v symmetry; the internuclear distance R_g(Sm–Br) = 274.5(5) pm; _g =131(6)°. The vibration frequencies were estimated from the experimental values of the mean square vibration amplitudes.     

Structure and Dynamics of Methyl-substituted Beryllocene: [Be(C5Me5)2]

In this paper we study theoretically the molecular structure of [Be(C₅Me₅)₂], with special interest in similarities and differences found in the computed geometric parameters, depending on the treatment of the electron correlation used. Given the low energy differences found between the different configurations studied (less than 4 kcal mol⁻¹), and the high fluxionality found in experimental studies for this compound, we analyzed the dynamics of the system by means of first principles molecular dynamics calculations. A complex dynamics is found and analyzed in terms of two molecular rearrangement processes: 1,2-sigmatropic intraring rearrangement and a ring inversion mechanism that interchanges the roles (with regard to their coordination to the central Be atom) of the two rings.Dedicated to Dr. Jeal Paul Malrieu on occasion of his 65th birthday.