Constructing Invariant Fairness Measures for Surfaces

The paper proposes a rational method to derive fairness measures for surfaces. It works in cases where isophotes, reflection lines, planar intersection curves, or other curves are used to judge the fairness of the surface. The surface fairness measure is derived by demanding that all the given curves should be fair with respect to an appropriate curve fairness measure. The method is applied to the field of ship hull design where the curves are plane intersections. The method is extended to the case where one considers, not the fairness of one curve, but the fairness of a one parameter family of curves. Six basic third order invariants by which the fairing measures can be expressed are defined. Furthermore, the geometry of a plane intersection curve is studied, and the variation of the total, the normal, and the geodesic curvature and the geodesic torsion is determined.     

Duality Theory in Fuzzy Linear Programming Problems with Fuzzy Coefficients

The concept of fuzzy scalar (inner) product that will be used in the fuzzy objective and inequality constraints of the fuzzy primal and dual linear programming problems with fuzzy coefficients is proposed in this paper. We also introduce a solution concept that is essentially similar to the notion of Pareto optimal solution in the multiobjective programming problems by imposing a partial ordering on the set of all fuzzy numbers. We then prove the weak and strong duality theorems for fuzzy linear programming problems with fuzzy coefficients.     

High resolution electronic study of ONO, ONO and ONO: A rovibronic survey covering 11 800-14 380 cm

The 11 800-14 380 cm⁻¹ frequency range has been scanned for rotationally resolved rovibronic transitions in the A²B₂-X²A₁ electronic band system of the symmetric (C_2v) ¹⁶O¹⁴N¹⁶O and ¹⁸O¹⁴N¹⁸O isotopologues and in the corresponding electronic band system of the asymmetric (C_s) ¹⁸O¹⁴N¹⁶O isotopologue. The rotational analysis—reflecting minor differences in mass—in combination with symmetry induced spectral differences allows an identification of 68 ¹⁶O¹⁴N¹⁶O vibronic levels, 26 ¹⁸O¹⁴N¹⁸O vibronic levels and 51 ¹⁸O¹⁴N¹⁶O vibronic levels. The bands are recorded using near infrared fluorescence spectroscopy and a piezo valve based pulsed molecular beam expansion of premixed ¹⁸O₂ and ¹⁴N¹⁶O in Ar. The majority of the observed bands is rotationally assigned and can be identified as transitions starting from the vibrational ground state of one of the isotopologues. Numerous hot bands have also been identified. A comparison of the overall spectroscopic features of C_2v vs. C_s symmetric species provides qualitative information on symmetry dependence of vibronic couplings.     

Moderate and Small Deviations for the Ranges of One-Dimensional Random Walks

We establish moderate and small deviations for the ranges of integer valued random walks. Our theorems apply to the limsup and the liminf laws of the iterated logarithm. We establish moderate and small deviations for the ranges of integer valued random walks. Our theorems apply to the limsup and the liminf laws of the iterated logarithm.     

奇点理论浅引

本文是奇点理论的非正式的介绍。主要内容包括奇点分类与奇点拓扑的基本问题与结果。特别突出了简单奇点的券的性质及其与Ｌｉｅ代数的关系。本文的目的在于引起读者对一分支的兴趣。     

H-空间与拟向量变分不等式

本在Hausdorff locally convex H-空间上建立了一个新的不动点定理；利用局部交性质，在Hausdorff locally convex H-空间上建立了相应的拟向量变分不等式．     

截面体与凸体的包含测度

本文建立了E^n中的凸体与其位似体的包含测度的相等关系，同时给出了凸体Minkowski和的包含测度的估计。最后证明了E^3中的关于原点对称的旋转椭球与其截面体相似的充要条件是K为以原点为心的球。     

Photochemical reaction mechanism of cyclobutanone: CASSCF study

The photochemical reaction channels of cyclobutanone have been studied at the CASSCF level with a 6‐31G* basis set. Starting from the n‐π* excited‐state (S₁) cyclobutanone, the three reactions can take place: decarbonylation (produce CO and cyclopropane or propylene), cycloelimination (produce ketene and ethylene), and ring expansion (produce oxacarbene). Our computation indicates that decarbonylation products CO and triplet trimethylene are formed on the triplet n‐π* excited state (T₁) in a stepwise way via a biradical intermediate after intersystem crossing (ISC) to T₁ from S₁. And, then, the triplet trimethylene undergoes a second ISC to the ground state (S₀) to produce the singlet trimethylene from which cyclopropane can be produced rapidly only overcoming a 1 to 2‐kcal/mol barrier while propylene can be formed as a secondary product. The cycloelimination products ketene and ethylene are formed on the S₀ in a concerted mechanism after internal conversion (IC) to S₀ from S₁ via a biradical conical intersection. The reaction channels corresponding to ring expansion on the S₀, T₁, and S₁ states have also been discussed, and the likeliest reaction path is that oxacarbene is formed on the ground state following S₁/S₀ internal conversion. The surface topology of cyclobutanone on the S₁ surface is characterized by a transition state separating the minimum from the S₁/S₀ conical intersection, which is consistent with the previous computations and can explain the wavelength dependence of the fluorescence emission yield. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

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.