Relativistic virial theorem for diatomic molecules. Application to H 2 +

Summary The virial theorem for a molecule in the relativistic clamped-nuclei approximation is derived. The individual energy contributionsA (momentum energy),B (mass energy),T=A+B (kinetic energy) andV (potential energy) are expressed in terms ofE, E/R (derivate w.r.t. the nuclear coordinates) and the relativistic correction E/² (derivative w.r.t. Sommerfield's fine-structure constant ). IfE and E/R are known as functions of , then all individual energy terms are also known as functions of . As an example, numerical results for H ₂ ⁺ are presented. The relativistic and nonrelativistic potential energy curves and the paradoxical behavior of their different contributions are analyzed and interpreted in both the largeR and shortR ranges.Dedicated to Professor W. Kutzelnigg on the occasion of his 60th birthday     

Use of Local Lagrange Interpolation for calculation of retention indices in linear temperature-programmed gas chromatrography

Summary The influence of the isothermal temperature, program rate, initial temperature and flow rate on retention indices was studied. The methods of Kováts, Van Den Dool and Local Lagrange Interpolation are compared. Ten experimental measurements were carried out on a capillary column coated with OV-101 stationary phase.     

Novel aromatic carboxamides from dehydroabietylamine as potential fungicides: Design,synthesis and antifungal evaluation

The present study was carried out to design and synthesize a number of novel aromatic carboxamide derivatives of dehydroabietylamine. The preliminary antifungal assay indicated that most of title compounds displayed moderate to good antifungal activity toward the six fungal strains in vitro. Compounds 3i, 3q, 4b and 4d showed significant antifungal activity against Sclerotinia sclerotiorum, with EC₅₀ values ranging from 0.067 ～ 0.393 mg/L. Compounds 3i, 4b and 4d also showed pronounced mycelial growth inhibition activities against B. cinerea and A. solani. Furthermore, in the in vivo assay, compound 4b exhibited brilliant protective activity against S. sclerotiorum-infected rape leaves. Meanwhile, the in vivo bioassay on tomato plants infected by B. cinerea showed that compound 3i and 4d displayed excellent protective activity at 200 mg/L, which were near to boscalid. Primary mechanistic study revealed that 4b could inhibit sclerotia formation as well as reduce the exopolysaccharide level. SEM and TEM analysis indicated that 4b possessed a strong ability to destroy the surface morphology of mycelia, cell structure and seriously interfere with the growth of the fungal pathogen. In addition, 4b exhibited good inhibitory activity (IC₅₀ = 23.3 ± 1.6 μM) toward succinate dehydrogenase (SDH). Molecular modeling study confirmed the binding modes between compound 4b and SDH. The above antifungal results and fungicidal mechanism study revealed that this class of dehydroabietylamine derivatives could be potential SDH inhibitors and lead compounds for novel fungicides development.     

On the convergence of the LJ search method

The convergence of the Luus-Jaakola search method for unconstrained optimization problems is established.Notation E _n Euclideann-space - f Gradient off(x) - ² f Hessian matrix - (·) ^T Transpose of (·) - I Index set {1, 2, ...,n} - [x _i1 ^*(j) ] Point around which search is made in the (j + 1)th iteration, i.e., [x _1l ^*(j) ,x _2l ^*(j) ,...,x _n1 ^*(j) ] - r _i ⁽ⁱ⁾ Range ofx _il ^*(i) in the (j + 1)th iteration - l ₁ min_i {r _i ⁽⁰⁾ } - l ₂ min_i {r _i ⁽⁰⁾ } - A _j Region of search in thejth iteration, i.e., {x E _n:x _il ^*(j-1) –0.5r _i ^(j-1) x _ix _il ^*(j-1) +0.5r _i ^(j-1) ,i I} - S _j Closed sphere with center origin and radius _j - Reduction factor in each iteration - 1– - (·) Gamma function Many discussions with Dr. S. N. Iyer, Professor of Electrical Engineering, College of Engineering, Trivandrum, India, are gratefully acknowledged. The author has great pleasure to thank Dr. K. Surendran, Professor, Department of Electrical Engineering, P.S.G. College of Technology, Coimbatore, India, for suggesting this work.     

On the ν-dimensional one-component classical plasma: The thermodynamic limit problem revisited

We prove theH-stability property and the existence of the thermodynamic limit of the free energy density of the two-dimensional, one-component classical plasma. We give lower and upper bounds on the free energy density in any dimensionv and draw some consequences.     

An elementary proof of a converse mean-value theorem

We present a new converse mean value theorem, with a rather elementary proof.     

线性不对称损失时非正态分布过程均值优化

针对常见的两种非正态分布———梯形分布和三角分布，研究线性不对称质量损失时其过程均值的优化问题，建立了梯形分布在五种不同情况下线性不对称质量损失的数学模型，基于以上模型给出了线性不对称质量损失时梯形分布最优过程均值的确定方法；研究三角分布在四种不同情况下线性不对称质量损失的数学模型，并给出了线性不对称质量损失时三角分布最优过程均值的确定方法。最后，用实例验证本过程均值优化模型的有效性。实例表明，应用线性不对称损失函数，适当的改变过程均值，可以有效地降低产品的质量损失，通过调整工艺过程将获得最佳经济效益。     

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.     

Evolutionary variational inequalities with a volterra term

The mathematical model of the injection molding process is characterized by evolutionary inequalities with an elliptic principal part and a Volterra term. Existence and uniqueness of the solution of these problems are derived by means of an argument based on the Banach fixed point theorem. Regularity results are obtained by using the penalty and Rothe method. The results can be considered as a starting point for the numerical treatment and for the application to injection molding.     

On statistical properties of the lyapunov exponent of the generalized skew tent map

The statistical properties of the Lyapunov exponent of the chaotic generalized skew tent map is studied. Expressions of the mean and the variance of this Lyapunov exponent at each discrete time index are obtained. A sufficient condition for weakly mixing of the chaotic generalized skew tent map is derived, and the asymptotic distribution of its Lyapunov exponent is provided.