Verifying a new identity for Green’s functions of the n=1 supersymmetric non-Abelian Yang-Mills theory with matter fields

We use the higher covariant derivative regularization to investigate a new identity for Green’s functions. It relates certain coefficients of the matter superfield vertex function for which one of the external matter legs is not chiral. Calculations in the first nontrivial order (for the two-loop vertex function) demonstrate that the new identity also holds in the non-Abelian Yang-Mills theory with matter fields. We demonstrate that the new identity follows because the three-loop integrals determining the Gell-Mann-Low function are integrals of total derivatives. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 156, No. 2, pp. 270–281, August, 2008.     

Automorphisms of higher‐dimensional Hadamard matrices

This article derives from first principles a definition of equivalence for higher‐dimensional Hadamard matrices and thereby a definition of the automorphism group for higher‐dimensional Hadamard matrices. Our procedure is quite general and could be applied to other kinds of designs for which there are no established definitions for equivalence or automorphism. Given a two‐dimensional Hadamard matrix H of order ν, there is a Product Construction which gives an order ν proper n‐dimensional Hadamard matrix P⁽ⁿ⁾(H). We apply our ideas to the matrices P⁽ⁿ⁾(H). We prove that there is a constant c > 1 such that any Hadamard matrix H of order ν > 2 gives rise via the Product Construction to cν inequivalent proper three‐dimensional Hadamard matrices of order ν. This corrects an erroneous assertion made in the literature that ”P⁽ⁿ⁾(H) is equivalent to “P⁽ⁿ⁾(H′) whenever H is equivalent to H′.” We also show how the automorphism group of P⁽ⁿ⁾(H) depends on the structure of the automorphism group of H. As an application of the above ideas, we determine the automorphism group of P⁽ⁿ⁾(Hk) when Hk is a Sylvester Hadamard matrix of order 2^k. For ν = 4, we exhibit three distinct families of inequivalent Product Construction matrices P⁽ⁿ⁾(H) where H is equivalent to H₂. These matrices each have large but non‐isomorphic automorphism groups. © 2008 Wiley Periodicals, Inc. J Combin Designs 16: 507–544, 2008     

Charged fluid distribution in higher dimensional spheroidal space-time

A general solution of Einstein field equations corresponding to a charged fluid distribution on the background of higher dimensional spheroidal space-time is obtained. The solution generates several known solutions for superdense star having spheroidal space-time geometry. Formerly V. Regional College of Engineering     

Two-loop Gell-Mann-Low function of the <Emphasis Type="Italic">N</Emphasis>=1 supersymmetric Yang-Mills theory regularized by higher covariant derivatives

We calculate the two-loop Gell-Mann-Low function for the N=1 supersymmetric Yang-Mills theory regularized by higher covariant derivatives. We show that the integrals determining this function reduce to total derivatives and can be easily calculated analytically. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 155, No. 3, pp. 398–414, June, 2008.     

EXISTENCE OF PERIODIC SOLUTIONS TO A KIND OF HIGHER ORDER FUNCTIONAL DIFFERENTIAL EQUATION WITH TWO DEVIATING ARGUMENTS

In this paper, by the theory of Fourier series, Bernoulli number theory and continu-ation theorem of coincidence degree theory, we study a kind of higher order functional differential equation with two deviating arguments. Some new results on the existence of periodic solutions are obtained.     

Hydroformylation of methyl-3-pentenoate over a phosphite ligand modified Rh/SiO2 catalyst

A phosphite ligand modified Rh/SiO2 catalyst has been developed for hydroformylation of internal olefins to linear aldehydes, which showed high activity and regioselectivity and could be separated easily by filtration after reaction in an autoclave. Effects of reaction temperature and syngas pressure on the performances of the catalyst in the reaction were also investigated.     

Polymerization of higher α‐olefins using a Cs‐symmetry hafnium metallocene catalyst. Kinetics of the polymerization and microstructural analysis

The C_s‐symmetry hafnium metallocene [(p‐Et₃Si)C₆H₄]₂C(2,7‐di‐tert‐BuFlu)(C₅H₄)Hf(CH₃)₂ and tetrakis(pentafluorophenyl) borate dimethylanilinium salt ([B(C₆F₅)₄]^?[Me₂NHPh]⁺) were used as the catalytic system for the polymerization of higher α‐olefins (from hexene‐1 to hexadecene‐1) in toluene at 0 °C. The evolution of the polymerization was studied regarding the variation of the molecular weight, molecular weight distribution and yield with time. The effect of the monomer structure on the polymerization kinetics was established. The role of trioctylaluminum in accelerating the polymerization was investigated. ¹³C NMR spectroscopy was used to study the microstructure of the poly(α‐olefins) by the determination of the pentad monomer sequences. The thermal properties of the polymers were obtained by differential scanning calorimetry, DSC. The results were discussed in connection with the polymer microstructure. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 4314–4325, 2009     

Higher order asymptotic solution of mode I crack growth in elastic-perfectly plastic media

A higher order asymptotic solution of near-tip field is studied for plane-atrain Mode-I quasi-static steady crack growth in the incompressible (v=1/2) elastic perfectly-plastic media. The results show that the near-tip stress and strain are fully continuous, and the strain possesses In (A/r) singularity at the crack tip. The expressions of the stress, strain and velocity in each region are also given. The project supported by National Natural Science Foundation of China