A General Duality Scheme for Nonconvex Minimization Problems with a Strict Inequality Constraint

We establish a duality formula for the problem Minimize f(x)+g(x) for h(x)+k(x)<0 where g, k are extended-real-valued convex functions and f, h belong to the class of functions that can be written as the lower envelope of an arbitrary family of convex functions. Applications in d.c. and Lipschitzian optimization are given.     

Sensitivity of risk measures with respect to the normal approximation of total claim distributions

A simple and commonly used method to approximate the total claim distribution of a (possibly weakly dependent) insurance collective is the normal approximation. In this article, we investigate the error made when the normal approximation is plugged in a fairly general distribution-invariant risk measure. We focus on the rate of convergence of the error relative to the number of clients, we specify the relative error’s asymptotic distribution, and we illustrate our results by means of a numerical example. Regarding the risk measure, we take into account distortion risk measures as well as distribution-invariant coherent risk measures.     

Newton-Leibniz integration for ket-bra operators (II)—application in deriving density operator and generalized partition function formula

Via the route of applying Newton-Leibniz integration rule to Dirac’s symbolic operators, we show that the density operator e^−βH, where H is multi-mode quadratic interacting boson operators, is a mapping of symplectic transformation in the coherent state representation appearing in the form of non-symmetric ket-bra operator integration. By virtue of the technique of integration within an ordered product (IWOP) of operators, we deduce its normally ordered form which directly leads to the generalized partition function formula and the Wigner function. Some new representations, such as displacement-squeezing correlated squeezed coherent states, constructed by the IWOP technique, also bring convenience in deriving partition functions.     

A method for thin foil thickness determination by transmission electron microscopy

With the intention of determining the local thickness within a crystalline thin foil specimen, by means of transmission electron microscopy (TEM), a method previously proposed by Zuo and Shi [J.M. Zuo, Y.F. Shi, Microsc. Microanal. 7 (Suppl. 2) (2001) 224-225] was applied. Using the convergent beam technique, with the incident beam parallel to a zone axis with low indices, diffraction patterns were obtained for some aluminum alloys with low solute content. These patterns were contrasted with those obtained from simulations based on the dynamic theory with Bloch's waves formalism. The local thickness of the thin foil was then obtained by visually comparing the simulated patterns with the experimental one.Comparison of the proposed method with that based on the analysis of two-beam convergent beam patterns [P.M. Kelly, A. Jostsons, R.G. Blake, J.G. Napier, Phys. Stat. Solidi (a) 31 (1975) 771-780] and with that based on the ratio of intensity of the zero loss peak to the total intensity in an electron energy loss spectrum [R.F. Egerton, Electron Energy Loss Spectroscopy in the Electron Microscope, second ed., Plenum Press, New York, 1996] was carried out. A very good agreement between thicknesses determined using the different methods was found. The sensitivity of the method of Zuo et al. was found to be about 1 or 2 nm. The advantages and limitations of the different methods are discussed. The method of Zuo et al. can provide fast and reliable results and can be applied in all modern instruments.     

Damping of the domain walls motion in Co-based amorphous ribbons with helical magnetic anisotropy: Part III

The damping of the motion of domain walls of a sandwich domain structure by the eddy currents magnetic fields, the stray fields and the hysteresis friction fields is investigated. The blocking of the motion of domain walls by the eddy currents magnetic fields is discovered.