Simultaneous determination of acidic,basic and alcoholic substances relating to monoamine hormones and metabolites in biological material by mass fragmentography (GC/MF)

A method is described for the simultaneous quantitative determination of monoamines and related compounds from urine and brain tissue samples in the pg-range, using a GC/MF instrument LKB-2091 provided with a multiple ion detection (MID) system and capillary columns. The simultaneous detection of “fingerprints” with fourteen and more compounds during one single GC run was achieved after the intoduction of “time gates” for the detection of the different characteristic masses. Several modifications to the LKB equipment permitted exact reproducibility of retention times, which is essential for the use of “time gates”. The detection of “fingerprints” with these acidic, basic and alcoholic substances was achieved by the extraction of the dried biological samples with silylating agents.     

An RQP algorithm using a differentiable exact penalty function for inequality constrained problems

In this paper we propose a recursive quadratic programming algorithm for nonlinear programming problems with inequality constraints that uses as merit function a differentiable exact penalty function. The algorithm incorporates an automatic adjustment rule for the selection of the penalty parameter and makes use of an Armijo-type line search procedure that avoids the need to evaluate second order derivatives of the problem functions. We prove that the algorithm possesses global and superlinear convergence properties. Numerical results are reported.     

ε-optimality criteria for convex programming problems via exact penalty functions

In this paper, we present-optimality criteria for convex programming problems associated with exact penalty functions. Several authors have given various criteria under the assumption that such convex problems and the associated dual problems can be solved. We assume the solvability of neither the convex problem nor the dual problem. To derive our criteria, we estimate the size of the penalty parameter in terms of an-solution for the dual problem.     

半定矩阵秩极小的非凸精确松弛

本文主要研究半定矩阵秩极小问题(P)的非凸精确松弛及其性质.首先,为求解问题(P),我们引入其Schatten p-范数(0＜p＜1)松弛,记为(Sp).其次,通过定义半定限制等距常数和半定限制正交常数,我们给出了问题(P)有唯—解的充分条件.最后,利用半定限制等距性质,我们给出了问题(P)和(Sp)有相同唯一解的充分条件.特别地,对任意0＜p＜1,我们还得到—个一致的精确恢复条件.     

Approximation by complex szász-durrmeyer operators in compact disks

In the present paper, we deal with the complex Szász-Durrmeyer operators and study Voronovskaja type results with quantitative estimates for these operators attached to analytic functions of exponential growth on compact disks. Also, the exact order of approximation is found.     

Simple Equations Method (SEsM): Algorithm,Connection with Hirota Method,Inverse Scattering Transform Method,and Several Other Methods

The goal of this article is to discuss the Simple Equations Method (SEsM) for obtaining exact solutions of nonlinear partial differential equations and to show that several well-known methods for obtaining exact solutions of such equations are connected to SEsM. In more detail, we show that the Hirota method is connected to a particular case of SEsM for a specific form of the function from Step 2 of SEsM and for simple equations of the kinds of differential equations for exponential functions. We illustrate this particular case of SEsM by obtaining the three- soliton solution of the Korteweg-de Vries equation, two-soliton solution of the nonlinear Schrödinger equation, and the soliton solution of the Ishimori equation for the spin dynamics of ferromagnetic materials. Then we show that a particular case of SEsM can be used in order to reproduce the methodology of the inverse scattering transform method for the case of the Burgers equation and Korteweg-de Vries equation. This particular case is connected to use of a specific case of Step 2 of SEsM. This step is connected to: (i) representation of the solution of the solved nonlinear partial differential equation as expansion as power series containing powers of a “small” parameter ϵ; (ii) solving the differential equations arising from this representation by means of Fourier series, and (iii) transition from the obtained solution for small values of ϵ to solution for arbitrary finite values of ϵ. Finally, we show that the much-used homogeneous balance method, extended homogeneous balance method, auxiliary equation method, Jacobi elliptic function expansion method, F-expansion method, modified simple equation method, trial function method and first integral method are connected to particular cases of SEsM.     

Half Exact Functors Associated with Cotorsion Pairs on Exact Categories

In the previous article “Hearts of twin cotorsion pairs on exact categories. J. Algebra, 394, 245–284 (2013)”, we introduced the notion o     

Exact solution of the two-mode quantum Rabi model

An analytical method is developed to study the two-mode quantum Rabi model. For certain specific parameter conditions, especially for the resonant conditions, we obtain an infinite number of the exact solutions of the eigenfunctions and associated energies. It is shown that there exist new types of the exact energies which do not correspond to the level-crossings. Our analytical method may find applications in some related models.     

Exact Eigenfunctions of N-body System with Quadratic Pair Potential

We obtain the energy spectrum and all the corresponding eigenfunctions of N-body Bose and Fermi systems with Quadratic Pair Potentials in one dimension. The original first excited state or energy level is disappeared in one dimension, which results from the operation of symmetry or antisymmetry of identical particles. In two and higher dimensions, we give the energy spectrum and the analytical ground state wave functions and the degree of degeneracy. By comparison, we refine Avinash Khare's results by making some items in his article precisely.     

New simple exact penalty function for constrained minimization

By adding one variable to the equality-or inequality-constrained minimization problems, a new simple penalty function is proposed. It is proved to be exact in the sense that under mild assumptions, the local minimizers of this penalty function are precisely the local minimizers of the original problem, when the penalty parameter is sufficiently large.