A highly efficient method for the direct synthesis of α-iodoketals from methyl ketones has been developed via sustainable integration of orthogonal tandem catalytic reactions: copper(II) oxide catalyzed iodination reaction and the subsequent excess or regenerated iodine catalyzed regioselective ketalization reaction.

This paper,based on the “knowledge,ability and quality”,establishes knowledge integration modular curriculum system. For the first time in Henan Province,this paper creates a professional ability standard module for tourism management,establishes the diversified teaching method which possesses the characteristics of teaching process integration. To enhance the learning assessment method of stud...

This paper considers computation of fitted values and marginal effects in the Box–Cox regression model. Two methods, (1) the ‘‘smearing’’ technique suggested by Duan (see Ref. 10) and (2) direct numerical integration, are examined and compared with the ‘‘naive’’ method often used in econometrics.

A direct method for solving variational problems using Legendre wavelets is presented. An operational matrix of integration is first introduced and is utilized to reduce a variational problem to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique. © 2000 IMACS. Published by Elsevier Science B.V. All rights reserved.

The analytic expression of the momentum representation in terms of the associated Legendre function is determined by a direct integration of Fourier transform of the wave function of coordinates using the Levi-Civita transformation and 2 2 R R → the generating function method. A new generating function for the associated Legendre functions are obtained.

A new computational method based on Wilson wavelets is proposed for solving a class of nonlinear stochastic It^{o}-Volterra integral equations. To do this a new stochastic operational matrix of It^{o} integration for Wilson wavelets is obtained. Block pulse functions (BPFs) and collocation method are used to generate a process to forming this matrix. Using these basis functions and their operat...

The Tauberian theorem of Wiener and Ikehara provides the most direct way to the prime number theorem. Here it is shown how Newman’s contour integration method can be adapted to establish the Wiener–Ikehara theorem. A simple special case suffices for the PNT. But what about the twin-prime problem?

We present an algorithm for determining quadrature rules for computing the direct illumination of predominantly diffuse objects by high dynamic range images. The new method precisely reproduces fine shadow detail, is much more efficient as compared to Monte Carlo integration, and does not require any manual intervention.

The best and most detailed structural information is obtained when the diffraction pattern of a single crystal a few tenths of a millimetre in each dimension is analyzed, but growing high-quality crystals of this size is often difficult, sometimes impossible. However, many crystallization experiments that do not yield single crystals do yield showers of randomly oriented microcrystals that can ...