Closed‐form rectangular atomic wave functions of an N‐dimensional atom

A closed‐form expression has been derived to obtain the N‐dimensional rectangular atomic wave functions. The wave functions can be obtained straightforwardly with the knowledge of the angular momentum quantum numbers and the dimension and there is no need to employ recursive methods as in previous works. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem 88: 263–274, 2002     

Compehensive two-dimensional gas chromatography (GC×GC) and its applicability to the characterization of complex (petrochemical) mixtures

In general, petrochemical products contain only a limited number of chemical classes of compounds (sample dimensionality). The enormous number of individual components within these classes, however, soon puts limitations upon a single chromatographic technique when it comes to adequate characterization of these products. Comprehensive two-dimensional gas chromatography (GC×GC) clearly opens the possibility of estimating the composition of hydrocarbon mixtures in a far more detailed fashion than hitherto possible. Although the emphasis of papers of GCxGC thus far almost exclusively applies to the unsurpassed peak-capacity, in the oil industry there is a need for characterization, rather than for analyzing all the individual compounds. In principle a GCxGC system can provide an almost perfect match between its intrinsic properties and the dimensionality of oil samples. To establish the applicability of GCxGC towards petrochemical analytical challenges, a commercially aavailable prototype instrument was subjected to an exhaustive characterization of a typical hydrocarbon precess stream and a fast characterization of a light gas oil. Although there are no fundamental limitations towards the quantitative aspects of a GCxGC system, this paper confines itself to qualitative results only. Quantitative aspects of GCxGC will be published in a forthcoming paper.     

Analysis of Petroleum Distillates from Fire Debris Using Supercritical Fluid Extraction with a Two‐Level Orthogonal Array Experimental Design

A supercritical fluid extraction (SFE) method was developed in the present study as an effective sample pretreatment technique of petroleum distillates from fire debris. Three petroleum distillates were used as target analytes, including 95 unleaded gasoline, kerosene, and premium diesel. An orthogonal array (L16) experimental design was adopted to separately evaluate primary SFE experimental factors. The SFE efficiencies of petroleum distillates at various extraction conditions were examined and the optimized SFE conditions were identified. Experimental results demonstrated that the optimized SFE method not only provided an effective extraction method for the spiked sample, but also successfully recovered residues of petroleum distillates from fire debris.     

The raised-cosine wavelets in computerized tomography

In Computerized Tomography (CT), an image must be recovered from its sampled projections in the form of values of the Radon transform. In this work a method of recovering the image is based on the properties of the raised-cosine wavelet. This wavelet has a closed form which allows for certain precomputations and avoids convolution. The rate of convergence of the resulting algorithm to the image density function is found under suitable hypotheses. This algorithm is then tested on the standard Shepp–Logan     

A formula for the powers of fractional order operators

We derive none some explicit formula for the power of fractional order (differential and integral) operators.     

On the rate of convergence for central limit theorems of sojourn times of Gaussian fields

The aim of this paper is to control the rate of convergence for central limit theorems of sojourn times of Gaussian fields in both cases: the fixed and the moving level. Our main tools are the Malliavin calculus and the Stein method, developed by Nualart, Peccati and Nourdin. We also extend some results of Berman to the multidimensional case.     

Kibble–Slepian formula and generating functions for 2D polynomials

We prove a generalization of the Kibble–Slepian formula (for Hermite polynomials) and its unitary analogue involving the 2D Hermite polynomials recently proved in [16]. We derive integral representations for the 2D Hermite polynomials which are of independent interest. Several new generating functions for 2D q-Hermite polynomials will also be given.     

Bernstein operational matrix of fractional derivatives and its applications

In this paper, Bernstein operational matrix of fractional derivative of order α in the Caputo sense is derived. We also apply this matrix to the collocation method for solving multi-order fractional differential equations. The numerical results obtained by the present method compares favorably with those obtained by various collocation methods earlier in the literature.     

Cohen and multiple Cohen strongly summing multilinear operators

Considering the successful theory of multiple summing multilinear operators as a prototype, we introduce the classes of multiple Cohen strongly p-summing multilinear operators and polynomials. The adequacy of these classes under the viewpoint of the theory of multilinear and polynomial ideals and holomorphy types is discussed in detail.     

New analytical expressions,symmetry relations and numerical solutions for the rotational overlap integrals

In this article, extremely simple analytical formulas are obtained for rotational overlap integrals which occur in integrals over two reduced rotation matrix elements. The analytical derivations are based on the properties of the Jacobi polynomials and beta functions. Numerical results and special values for rotational overlap integrals are obtained by using symmetry properties and recurrence relationships for reduced rotation matrix elements. The final results are of surprisingly simple structures and very useful for practical applications. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012