Unusual Reactivity Mode of Coordinated Oximes: Platinum(IV)-Assisted Ring Closure by Reaction with Acetone

The platinum(II) complexes trans-[PtCl(2)(RR'C=NOH)(2)], where R = R' = Me, RR' = (CH(2))(4) and (CH(2))(5), react with m-chloroperoxybenzoic acid in Me(2)CO to give the platinum(IV) complexes [PtCl(2)(OCMe(2)ON=CRR')(2)] in 50-60% yields. The complexes [PtCl(2)(OCMe(2)ON=CRR')(2)] were characterized by elemental analysis, EI-MS, and IR and Raman spectroscopies; X-ray structure analyses were performed for both trans-[PtCl(2)(OCMe(2)ON=CC(4)H(8))(2)] and trans-[PtCl(2)(OCMe(2)ON=CC(5)H(10))(2)]. The former compound crystallizes in the triclinic space group P&onemacr; with a = 8.088(2) ?, b = 8.327(2) ?, c = 8.475(2) ?, alpha = 103.54(3) degrees, beta = 102.15(3) degrees, gamma = 108.37(3) degrees, V = 501.0(2) ?(3), Z = 1, and rho(calcd) = 1.917 g cm(-)(3). The latter complex crystallizes in the monoclinic space group C2/c with a = 12.5260(10) ?, b = 9.3360(10) ?, c = 18.699(2) ?, beta = 98.320(10) degrees, V = 2163.7(4) ?(3), Z = 4, and rho(calcd) = 1.862 g cm(-)(3). The structures of [PtCl(2)(OCMe(2)ON=CC(4)H(8))(2)] and [PtCl(2)(OCMe(2)ON=CC(5)H(10))(2)] show an octahedron of Pt where two Cl atoms and two chelate ligands are mutually trans, respectively.     

Iterated Spectra of Numbers---Elementary, Dynamical, and Algebraic Approaches

sets and central sets are subsets of which arise out of applications of topological dynamics to number theory and are known to have rich combinatorial structure. Spectra of numbers are often studied sets of the form . Iterated spectra are similarly defined with coming from another spectrum. Using elementary, dynamical, and algebraic approaches we show that iterated spectra have significantly richer combinatorial structure than was previously known. For example we show that if and , then is an set and consequently contains an infinite sequence together with all finite sums and products of terms from that sequence without repetition.

     

Reactivity of trans-[PtX(2)(ketoxime)(2)] Complexes toward m-Chloroperoxybenzoic Acid: An Efficient Route to Coordinated Nitrosoalkanes and Solvent Dependence of the Reaction

The platinum(II) compounds trans-[PtX(2)(RR'C=NOH)(2)] [X = Cl, R = R' = Me, RR' = (CH(2))(4), (CH(2))(5); X = Br, R = R' = Me] react with m-chloroperoxybenzoic acid (MCPBA) in dimethylformamide to give the platinum(II) complexes [PtX(2){N(=O)CRR'ONCRR'}] containing coordinated nitrosoalkane ligands. The complexes [PtX(2){N(=O)CRR'ONCRR'}] were characterized by elemental analysis, EI-MS, IR, electronic absorption, and (1)H NMR spectroscopy; X-ray structure analysis was performed for [PtCl(2){N(=O)CC(5)H(10)ONCC(5)H(10)}]. The latter compound crystallizes in the triclinic P&onemacr; space group with a = 9.214(2) ?, b = 9.577(2) ?, c = 10.367(2) ?, alpha = 109.14(2) degrees, beta = 91.87(2) degrees, gamma = 115.62(2) degrees, V = 762.8(3) ?(3), Z = 2, and rho(calcd) = 2.135 g cm(-)(3). The reaction between trans-[PtX(2)(RR'C=NOH)(2)] and MCPBA displays a solvent dependence: interaction of these reagents in ketones, R(1)R(2)C=O, yields the platinum(IV) chelates [PtX(2)(OCR(1)R(2)ON=CRR')(2)], while the oxidation state of the oxime N atom remains unchanged. Heating [PtCl(2)(OCR(1)R(2)ON=CRR')(2)] in DMF or in DMF-d(7) at 100 degrees C leads to the extrusion of R(1)R(2)C=O and the formation of [PtCl(2){N(=O)CRR'ONCRR'}].     

The symmetric quadratic knapsack problem: approximation and scheduling applications

This paper reviews two problems of Boolean non-linear programming: the Symmetric Quadratic Knapsack Problem and the Half-Product Problem. The problems are related since they have a similar quadratic non-separable objective function. For these problems, we focus on the development of fully polynomial-time approximation schemes, especially of those with strongly polynomial time, and on their applications to various scheduling problems.     

Two-machine flow shop no-wait scheduling with machine maintenance

We study a two-machine flow shop scheduling problem with no-wait in process, in which one of the machines is subject to mandatory maintenance. The length of the maintenance period is defined by a non-decreasing function that depends on the starting time of that maintenance. The objective is to minimize the completion time of all activities. We present a polynomial-time approximation scheme for this problem. Received: November 2004 / Received version: March 2005 AMS classification: 90B35, 90B30, 90C59 The research was partly supported by INTAS (Project 03-51-5501) All correspondence to: Vitali A. Strusevich     

On iterates of fully closed absolutes

In this article we give a sufficient condition for a space X to have the fully closed absolute faX with the property fa(faX)=faX. An example of a compact space X such that the canonical mapping fa(α+1)X→fa(α)X (where α is a given ordinal) is not a homeomorphism is constructed. Also we give an example of a compact space X such that the canonical mapping faX→X is not a homeomorphism but for which there exists a homeomorphism faX→X.     

Models of G time variations in diverse dimensions

A review of different cosmological models in diverse dimensions leading to a relatively small time variation in the effective gravitational constant G is presented. Among them: the 4-dimensional (4-D) general scalar-tensor model, the multidimensional vacuum model with two curved Einstein spaces, the multidimensional model with the multicomponent anisotropic “perfect fluid”, the S-brane model with scalar fields and two form fields, etc. It is shown that there exist different possible ways of explaining relatively small time variations of the effective gravitational constant G compatible with present cosmological data (e.g. acceleration): 4-dimensional scalar-tensor theories or multidimensional cosmological models with different matter sources. The experimental bounds on ? may be satisfied either in some restricted interval or for all allowed values of the synchronous time variable.     

The definition of core electrons

The traditional separation of electrons in molecules into core and valence types is often based on molecular orbital energies. This method is known to lead in some cases to large relative errors in correlated calculations. Instead, we propose a method based on the definition of molecular core character using separation of basis functions into core and valence types. This gives size-consistency to separation of electrons in molecules into core and valence types.     

Unexpected photochemical transformation of imidazole derivatives containing the 5-hydroxy-2-methyl-4H-pyran-4-one moiety. Environmentally friendly method for the synthesis of substituted imidazo[1,5-a]pyridine-5,8-diones

An unexpected photochemical transformation of imidazole derivatives containing the 5-hydroxy-2-methyl-4H-pyran-4-one moiety was discovered, which led to the synthesis of previously unknown imidazo[1,5-a]pyridine-5,8-dione derivatives. The structures of imidazole and imidazo[1,5-a]pyridine-5,8-dione derivatives were unambiguously determined by X-ray diffraction analysis.     

Turbulent Flow Produced by Piston Motion in a Spark-ignition Engine

Turbulence produced by the piston motion in spark-ignition engines is studied by 2D axisymmetric numerical simulations in the cylindrical geometry as in the theoretical and experimental work by Breuer et al. (Flow Turbul Combust 74:145, 2005). The simulations are based on the Navier–Stokes gas-dynamic equations including viscosity, thermal conduction and non-slip at the walls. Piston motion is taken into account as a boundary condition. The turbulent flow is investigated for a wide range of the engine speed, 1,000–4,000 rpm, assuming both zero and non-zero initial turbulence. The turbulent rms-velocity and the integral length scale are investigated in axial and radial directions. The rms-turbulent velocity is typically an order-of-magnitude smaller than the piston speed. In the case of zero initial turbulence, the flow at the top-dead-center may be described as a combination of two large-scale vortex rings of a size determined by the engine geometry. When initial turbulence is strong, then the integral turbulent length demonstrates self-similar properties in a large range of crank angles. The results obtained agree with the experimental observations of Breuer et al. (Flow Turbul Combust 74:145, 2005).