A transform method for linear evolution PDEs on a finite interval

We study initial boundary value problems for linear scalar evolutionpartial differential equations, with spatial derivatives ofarbitrary order, posed on the domain {t > 0, 0 < x <L}. We show that the solution can be expressed as an integralin the complex k-plane. This integral is defined in terms ofan x-transform of the initial condition and a t-transform ofthe boundary conditions. The derivation of this integral representationrelies on the analysis of the global relation, which is an algebraicrelation defined in the complex k-plane coupling all boundaryvalues of the solution. For particular cases, such as the case of periodic boundaryconditions, or the case of boundary value problems for even-orderPDEs, it is possible to obtain directly from the global relationan alternative representation for the solution, in the formof an infinite series. We stress, however, that there existinitial boundary value problems for which the only representationis an integral which cannot be written as an infinite series.An example of such a problem is provided by the linearized versionof the KdV equation. Similarly, in general the solution of odd-orderlinear initial boundary value problems on a finite intervalcannot be expressed in terms of an infinite series.     

Inner-sphere oxidation of iron(II) by tris(malonato)cobaltate(III)

The kinetics of oxidation of Fe²⁺ by [Co(C₃H₂O₄)₃]^3? in acidic solutions at 605 nm showed a simple first-order dependence in each reactant concentration. The second-order rate constant dependence on [H⁺] is in accordance with eqn (i) k₂ = k′₂ + k₃[H⁺] (i) where k′₂ and k₃ have values of 73.4 ± 14.0 M ^?1 s^?1 and 353 ± 41 M^?2 s^?1, respectively, at 1.0 M ionic strength (NaClO₄) and 25°C. At 310 nm the formation and decomposition of an intermediate, believed to be [FeC₃H₂O₄]⁺, was observed. The increase in the rate of oxidation with increasing [H⁺] was interpreted in terms of a “one-ended” dissociation mechanism which facilitates chelation of Fe₂₊ by the carbonyl oxygens of malonate in the transition state.     

The response of microstructure to processing in a series of poly(siloxaneimide) copolymers

Poly(siloxaneimide) (PSI) segmented copolymers exhibit organized microdomains if the blocks are sufficiently incompatible. As with neat diblock and triblock copolymers, the processing route employed to prepare films of PSI materials is expected to influence the dimensions and/or morphology of the resultant microstructure. In this work, small-angle neutron scattering (SANS) is utilized to characterize the disordered microstructure found in films of a series of PSI copolymers which are subjected to solvent casting and various thermal treatments. Microstructural dimensions such as the periodicity and correlation length are deduced from the Teubner-Strey (TS) model for disordered microemulsions. The scattering intensity of each copolymer up to q = 5.0 nm^?1, where q is the scattering vector, is found to scale as q^?2.8+?0.1. Results indicate that processing the materials as cast films or as melt-pressed films allowed to cool slowly has a small, but discernible, effect on microstructural characteristics. SANS profiles of films quenched from elevated temperatures reveal a clear transition in microdomain periodicity, which correlates well with the glass transition temperature of the imide microphase in these and other materials of similar chemical structure. © 1993 John Wiley & Sons, Inc.     

检测实验室如何开展管理评审工作

详细论述了管理评审的基本概念、如何开展管理评审工作以及中国实验室国家认可委员会的有关政策。     

η-Allylpentacarbonylvanadium

The preparation of η-C₃H₅V(CO)₅ from allyl chloride and sodium hexacarbonylvanadate (–I) is reported. Composition, IR and NMR spectra are in accordance with a π-bonded C₃H₅-moiety; the preparation has been extended to give complexes with substituted allyl groups. Furthermore (1-3-η-2-butenyl)pentacarbonylvanadium can be obtained by the addition of butadiene to HV (CO)₆.     

The phase diagram for the binary system K2CrO4CaCrO4

The phase diagram for the binary system K₂CrO₄CaCrO₄ has been determined for CaCrO₄ concentrations up to 60 mole%, using the techniques of differential thermal analysis, X-ray diffraction, and drop calorimetry. Essential features of the phase diagram are: the solid-solid phase transition for pure K₂CrO₄ at 670°C, β-K₂CrO₄ ? α-K₂CrO₄; a eutectoid reaction at 14 mole% CaCrO₄ and 548°C, β-K₂CrO₄ ? α-K₂CrO₄ + K₂CrO₄ · CaCrO₄; a peritectoid event at 50 mole% CaCrO₄ and 640°C, β-K₂CrO₄ + CaCrO₄ ? K₂CrO₄ · CaCrO₄; and a eutectic reaction at 51 mole% CaCrO₄ and 678°C, L ? β-K₂CrO₄ + CaCrO₄. X-ray diffraction studies lead to the determination of the unit cell dimensions for the K₂CrO₄ · CaCrO₄ double salt, a C-centered monoclinic form with a₀ = 7.615(6) Å, b₀ = 22.797(15) Å, c₀ = 9.777(9) Å, β = 115.45(5)°.     

The crystal structure of CuVo3(II), a high-pressure ilmenite phase

The crystal structure of a second high-pressure copper vanadate phase, CuVO₃(II), has been determined and refined by full-matrix least-squares procedures using automatic diffractometer data to a residual R = 0.042 (R_w = 0.051). The space group is rhombohedral, $\text{R}\text{3}$, with hexagonal unit cell a = 4.966(2) and c = 14.084(5) Å [a_R = 5.501(2) Å and α = 53.66(3)°]. The structure is the fully ordered ilmenite-type and, on the basis of published magnetic data and the interatomic distances, the valence distribution Cu⁺V⁵⁺O₃ is proposed. This represents a unique example of Cu⁺ in an octahedral environment.     

Electrode processes in the oxidation of tetrahydroisoquinoline derivatives

The electrochemical oxidation of the alkaloid laudanosine (Ia) to O-methylflavinantine (II) has been studied in acetonitrile solvent. Using cyclic voltammetry, rotating disc voltammetry and preparative electrolyses on several alkaloids, simple aliphatic amines and aromatic compounds, some aspects of the mechanism of this coupling reaction are elucidated. The first anodic wave for laudanosine at platinum has E_p=0.55 V vs. Ag/Ag⁺. The electrode rapidly becomes partially passivated at potentials above 0.5 V. This is due to a film which “dissolves” below 0.5 V, at a rate independent of the potential. It is shown that the reaction (Ia)→(II) proceeds at 0.5 V by initial oxidation of the amine moiety. If acids such as sodium bicarbonate are added to the anolyte the amine is protonated causing the first wave to disappear. Oxidation at 1.1 V under these acidic conditions produces the same product, but more rapidly and in significantly higher yield because electrode filming and side reactions resulting from the amine oxidation are abrogated.     

Double asymmetric induction in benchrotrene derivatives

Attachment of a Cr(CO)₃ moiety to one of the aromatic rings in rigid diaryl ketones of very low prochirality followed by addition of a chiral and optically pure reagent leads to satisfactory asymmetric induction ~40%. Asymmetric induction is smaller in the case of acyclic systems.     

The pyrolysis of trimethylgermane and trimethylsilane

The number of products and the H₂/CH₄ ratio obtained from the flow pyrolyses of (CH₃)₃GeH and (CH₃)₃SiH were very different. The (CH₃)₃GeH decomposition is consistent with the following mechanism:

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The pyrolysis of (CH₃)₃SiH was found to be much more complex, presumably due to the formation of silicon-carbon double bonded intermediates and the (CH₃)₂Si(H)CH₂ radical. We also present data which supports the presence of a H atom chain sequence during this pyrolysis.