Second Quantization of the Stueckelberg Relativistic Quantum Theory and Associated Gauge Fields

The gauge compensation fields induced by the differential operators of the Stueckelberg-Schrödinger equation are discussed, as well as the relation between these fields and the standard Maxwell fields; An action is constructed and the second quantization of the fields carried out using a constraint procedure. The properties of the second quantized matter fields are discussed.     

Quality assurance for the analytical data of micro elements in food

The micro element content of food is an important quality index due to the action of these elements on human health. In this article, we discuss how to ensure the reliability of analytical data on micro elements in order to truly represent the condition of food. Sampling, treatment of the analytical sample, selection of the analytical method, standard solution, and certified reference material, blank test, calibration of the instrument and equipment, application of the quality control chart, assessment of the final analytical result, and quality assurance system are briefly described. Received: 5 July 2001 Accepted: 19 November 2001     

Magnetic resonance imaging: a new window into industrial processing.

Although the most important use of nuclear magnetic resonance imaging (MRI) continues to be for diagnostic medicine, recognition is being gained for many nonmedical applications. Examples include the following areas: petrogeology, food, agriculture, polymers and polymer-composites, and pharmaceuticals. These areas all involve studies of species that have short spin-spin relaxation times, and consequently need far fast gradient switching. These technical details are discussed and typical applications given.     

A Primitive Non-symmetric 3-Class Association Scheme on 36 Elements with p11 = 0 Exists and is Unique

In this paper we construct a primitive, non-symmetric 3-class association scheme with parameters v = 36, v₁ = 7, p¹₁₁ = 0 and p²₁₁ = 4 and show that such a scheme is determined by its parameters.     

Expression of theSU(2) rotation matrices D( j ) in terms of normalized irreducible tensorial matrices

TheSU(2) rotation matricesD ^(j), specified in terms of axis and angle of rotation, are expressed as linear combination of normalized irreducible tensorial matricces (NITM) of rankl = 0 to 2j rotated to the polar angles of the axis. The rotated NITM are constructed from spherical harmonics of the same rank. Since this formulation requires no matrix products, it may be computationally more efficient than Euler angle formulas, particularly for largej. Rotated NITM and formulas for theD ^(j) withj = 1/2 andj = 1 are written out explicitly. A formula for the structure constants of the products of conformable NITM is also given in terms of 3-j and 6-j symbols.     

Silver nitrate-acetonitrile and iodine-benzene complexes as studied by NMR in thermotropic liquid crystals

Silver nitrate-acetonitrile and π iodine-benzene complexes in thermotropic liquid crystals have been studied by ¹H, ²H, and ¹³C NMR spectroscopy and by optical microscopy. Evidence for at least two silver complexes in each liquid crystal is presented.     

The star chromatic number of a graph

We study a generalization of the notion of the chromatic number of a graph in which the colors assigned to adjacent vertices are required to be, in a certain sense, far apart. © 1993 John Wiley & Sons, Inc.     

Chemical synthesis and electric properties of the conducting copolymer of aniline and o‐aminophenol

A copolymer, poly(aniline‐co‐o‐aminophenol), was prepared chemically by using ammonium peroxydisulfate as an oxidant. The monomer concentration ratio of o‐aminophenol to aniline strongly influences the copolymerization rate and properties of the copolymer. The optimum composition of a mixture for the chemical copolymerization consisted of 0.3 M aniline, 0.021 M o‐aminophenol, 0.42 M ammonium peroxydisulfate, and 2 M H₂SO₄. The result of cyclic voltammograms in a potential region of ?0.20 to 0.80 V (vs.SCE) indicates that the electrochemical activity of the copolymer prepared under the optimum condition is similar to that of polyaniline in more acid solutions. However, the copolymer still holds the good electrochemical activity until pH 11.0. Therefore, the pH dependence of the electrochemical property of the copolymer is improved, compared with poly(aniline‐co‐o‐aminophenol) prepared electrochemically, and is much better than that of polyaniline. The spectra of IR and ¹H NMR confirm that o‐aminophenol units are included in the copolymer chain, which play a key role in extending the usable pH region of the copolymer. The visible spectra of the copolymers show that a high concentration ratio of o‐aminophenol to aniline in a mixture inhibits the chain growth. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 5573–5582, 2007