The Newton modified barrier method for QP problems

The Modified Barrier Functions (MBF) have elements of both Classical Lagrangians (CL) and Classical Barrier Functions (CBF). The MBF methods find an unconstrained minimizer of some smooth barrier function in primal space and then update the Lagrange multipliers, while the barrier parameter either remains fixed or can be updated at each step. The numerical realization of the MBF method leads to the Newton MBF method, where the primal minimizer is found by using Newton's method. This minimizer is then used to update the Lagrange multipliers. In this paper, we examine the Newton MBF method for the Quadratic Programming (QP) problem. It will be shown that under standard second-order optimality conditions, there is a ball around the primal solution and a cut cone in the dual space such that for a set of Lagrange multipliers in this cut cone, the method converges quadratically to the primal minimizer from any point in the aforementioned ball, and continues, to do so after each Lagrange multiplier update. The Lagrange multipliers remain within the cut cone and converge linearly to their optimal values. Any point in this ball will be called a hot start. Starting at such a hot start, at mostO(In In ^-1) Newton steps are sufficient to perform the primal minimization which is necessary for the Lagrange multiplier update. Here, >0 is the desired accuracy. Because of the linear convergence of the Lagrange multipliers, this means that onlyO(In ^-1)O(In In ^-1) Newton steps are required to reach an -approximation to the solution from any hot start. In order to reach the hot start, one has to perform Newton steps, wherem characterizes the size of the problem andC>0 is the condition number of the QP problem. This condition number will be characterized explicitly in terms of key parameters of the QP problem, which in turn depend on the input data and the size of the problem.Partially supported by NASA Grant NAG3-1397 and National Science Foundation Grant DMS-9403218.     

A five-channel grating spectrometer for millimeter-waves

A five-channel grating spectrometer for use in millimeter wave band (25100GHz) is described with its design theory of optical path, and measured results of insertion loss and resolving power.     

Enantiomerentrennung und chiroptische Eigenschaften eines 2,3-Dihydrobilatriens-abc

The enantiomers of the 2,3-dihydrobilatriene-abc1 have been separated by recycling chromatography on triacetylcellulose. Comparison of their chiroptical properties with those of amino acid substituted analogues, like3, reveals the chirality of center 3 to be of minor influence on the values. Stabilization of a definite helical conformation of these pigments seems to depend on this influence together with an appropriate dipole-dipole interaction.

     

The determination of starting conditions for modifier optimization in reversed-phase HPLC

Summary After a brief introduction of the subject, the paper focusses on the first step in any optimization procedure: the delineation of the parameter space, wherein the global optimum is to be found. For organic modifier optimization in reversed-phase liquid chromatography it is shown that the necessary information can be derived from a single water-methanol gradient. It first yields an estimate of the total number of solutes in the sample, which is vital to define the peak capacity needed to achieve separation at a certain confidence level. Next, the gradient allows the prediction of suitable isocratic methanol binary solvents, and transfer rules formulate the iso-eluotropic composition of the common binary solvents (tetrahydrofuran and acetonitrile). Because all predictions are based on a statistical analysis of a limited data base, attention is given to the practical situation where an actual sample deviates from the average solute behaviour. Such deviations are revealed in the first isocratic run and can be used to arrive at a better estimate of solute retention.     

Polymeric pH indicators immobilized PVA membranes for optical sensors of high basicity based on a kinetic process

Two kinds of polymeric pH indicators PPF (phenolphthalein-formaldehyde product) and CPF (o-cresolphthalein-formaldehyde product) immobilized cross-linked poly(vinyl alcohol) membranes (PPF-PVA and CPF-PVA) for optical intermittent determination of high basicity ([OH⁻] = 1-8 M) based on a kinetic process were developed. In our previous work, we had demonstrated that PPF-PVA and CPF-PVA could perform the determination of high pH values from pH 10.0 to 14.0. Here the discoloring kinetic behaviors of PPF-PVA and CPF-PVA were compared with those of free phenolphthalein, o-cresolphthalein and thymolphthalein. Experimental results and theoretical analysis indicated that the response behaviors of the optodes’ membranes in concentrated NaOH solutions were diffusion-independent and still complied with the pseudo-first-order kinetics. In addition, two data analysis methods for determination were presented. One was directly based on the reduced absorbance; the other was based on the discoloring kinetic constant. It was found that the latter could perform a rapid (60 s) and reliable (relative standard deviation: 2.6%) determination for high basicity. These kinds of optodes can be used repeatedly when they are immersed in low-pH solutions to regain the protonated form after each determination.     

Optical spectra of Yb and Yb–Nd interaction in Cs2NaNd0,4Yb0,6Cl6

Interaction between octahedrally coordinated Nd³⁺ and Yd³⁺ in Cs₂NaNd_0,4Yb_0,6Cl₆ reduces the Nd³⁺ luminescence lifetime by roughly two orders of magnitude with respect to that found in Cs₂NaNdCl_{6– · –} Analysis of low temperature absorption and emission spectra reveals that the nonradiative Nd³⁺–Yb³⁺ energy transfer has to be assisted by lattice phonon emission, nevertheless the rate of the transfer is high in the 4–300 K temperature region and attains 5.8×10⁵s^-1 at room temperature. A phase transition of Cs₂NaNd_0,4Yb_0,6Cl₆ between 12 and 13 K is evidenced by abrupt change of both the spectra and lifetimes of Yb³⁺. Reduction of Yb³⁺ lifetime from 5.3 ms to 150 μs is at the transition from low symmetry phase to high symmetry phase is supposed to be associated with a three ion interaction which occurs in ordered lattice and disappears in low temperature disordered structure.     

Hapten immobilization for antibody sensing using a dynamic modification protocol

Optical fiber (OF) sensors are often limited by the immobilization technique used to associate a specific sensing ligand with the OF surface. This is particularly true when the ligand is biologically active as, for example, in the case of immobilized haptens or antibodies. The dynamic modification protocol is a regenerable and experimentally simple way to immobilize a variety of sensing molecules on an OF surface. Furthermore, the protocol is immune to hydrolysis and not limited by diffusion through a membrane or sol–gel. In this publication the approach is extended by immobilizing the hydrophobic hapten (octadecyl 6-(2,4 dinitrophenyl)aminohexanoic acid) as a means to prepare an OF sensor for antibodies specific for 2,4 dinitrophenyl (DNP). The LOD for anti-DNP is 0.5 nanomolar and the K_apparent is 1.0±0.2×10⁶. Nonspecific antibody adsorption is problematic in this sensing approach and was found to limit the quantitative capabilities of the sensor. However, time discrimination can be used to allow the nonspecific antibody to desorb prior to measurement thus minimizing the influence of nonspecific binding on sensor performance.     

光纤松耦合型传感器特性研究

本文介绍一种实用的光纤传感器,它由二根光纤或多根光纤紧靠一起,并在同一位置除去局部包层,成为松耦合状态,在这种状态下,研究了它的特性和应用。 当耦合间隙中充满某种液体介质时,耦合效率明显增大,因此可以方便地判别该介质是否存在。并且实验证明了一种光纤只能有一种相近于光纤芯子折射率的介质具有最大的灵敏度。当间隙内的介质不变时,耦合功率的大小决定于耦合距离d和耦合长度l,l一旦决定以后,d的调节精度为0.1mm量级,易于在机械结构上实现线性检测。     

The MPE/UCB far-infrared imaging Fabry-Perot interferometer (FIFI)

FIFI is an imaging spectrometer with two or three Fabry-Perot interferometers (FPI) in series for airborne astronomical observations in the far-infrared range (=40...200m). It employs 5×5 arrays of photoconducting detectors and offers spectral resolutions as small as 2km/s. Resolution and bandwidth can be set over a wide range to match a variety of astronomical sources. Cryogenic optics minimizes thermal background radiation and provides for in-flight step tunable spatial resolution. At 158 m wavelength the background-limited NEP is 3 × 10^-15W/Hz at 40 km/s resolution and with two FPI's; with three FPI's the expected NEP is 10^-15WHz at 5 km/s resolution.The frequency-chopping mode of the high-resolution Fabry-Perot allows for line detection in extended objects. Absolute internal flux calibration ensures adequate flat fielding of the array elements.     

能动抛光磨盘的变形实验研究

 能动抛光磨盘实时产生不同的表面变形，在对大口径非球面光学元件进行精磨和抛光时实现与工件表面良好的大尺寸吻合，可以消除传统光学加工采用小尺寸磨头时带来的高频残余误差并提高加工效率。以加工直径1.3m左右，F/2的抛物面光学元件为例，对能动磨盘在不同离轴度时能够产生的变形进行了计算和实验。结果表明，能动磨盘能够以较高精度产生旋转对称或非对称的抛物面形状。对能动磨盘产生变形后的残余误差进行了分析。