An interior-point affine-scaling trust-region method for semismooth equations with box constraints

An algorithm for the solution of a semismooth system of equations with box constraints is described. The method is an affine-scaling trust-region method. All iterates generated by this method are strictly feasible. In this way, possible domain violations outside or on the boundary of the box are avoided. The method is shown to have strong global and local convergence properties under suitable assumptions, in particular, when the method is used with a special scaling matrix. Numerical results are presented for a number of problems arising from different areas.     

Two-Phase Image Segmentation by Nonconvex Nonsmooth Models with Convergent Alternating Minimization Algorithms

Two-phase image segmentation is a fundamental task to partition an image into foreground and background. In this paper, two types of nonconvex and nonsmooth regularization models are proposed for basic two-phase segmentation. They extend the convex regularization on the characteristic function on the image domain to the nonconvex case, which are able to better obtain piecewise constant regions with neat boundaries. By analyzing the proposed non-Lipschitz model, we combine the proximal alternating minimization framework with support shrinkage and linearization strategies to design our algorithm. This leads to two alternating strongly convex subproblems which can be easily solved. Similarly, we present an algorithm without support shrinkage operation for the nonconvex Lipschitz case. Using the Kurdyka-Łojasiewicz property of the objective function, we prove that the limit point of the generated sequence is a critical point of the original nonconvex nonsmooth problem. Numerical experiments and comparisons illustrate the effectiveness of our method in two-phase image segmentation.     

Integrated quality by design (QbD) and design of experiments (DoE) approach for UFLC determination of telaprevir in rat serum

An ultrafast liquid chromatographic bioanalytical method was developed and validated for the determination of telaprevir in Wistar albino rat serum. Principles of quality by design (QbD) were implemented for enhancing the bioanalytical liquid–liquid extraction of telaprevir from rat serum. A Box–Behnken design was utilized in the studies by selecting extraction time, centrifugation speed, and vortex time as the critical method variables for evaluating their effect on the critical analytical attribute, i.e., %recovery of telaprevir. Chromatographic separation was achieved within a run time of 10?min using a C-18 column and mobile phase comprising of methanol:borate buffer of pH 9 (90:10 v/v) flowing at 1.2?mL/min. Photodiode array detection was performed at 270?nm. Results of validation studies were satisfactory. The method was linear over a concentration of 25–10,000?ng/mL. Limit of detection for the developed method was 10?ng/mL. Further, design of experiments (DoE) used for inter-day accuracy and precision study suggested superior method reliability. This integrated QbD- and DoE-based approach ensured the development of a validated and reliable analytical method for optimum bioanalysis of telaprevir in biological matrix.     

伽罗瓦环上的一类No序列的构造

近年来,伽罗瓦环上的序列理论成为人们研究的热点问题.有限域上的No序列是一类伪随机序列,它在序列密码中占具十分重要的角色.本文利用伽罗瓦环上的置换,构造了伽罗瓦环Z_(p~e)上的一类新的No序列,并且研究了其线性复杂度.研究的结果表明此类No序列具有相当大的线性复杂度.     

Structured minimal-memory inexact quasi-Newton method and secant preconditioners for augmented Lagrangian optimization

Augmented Lagrangian methods for large-scale optimization usually require efficient algorithms for minimization with box constraints. On the other hand, active-set box-constraint methods employ unconstrained optimization algorithms for minimization inside the faces of the box. Several approaches may be employed for computing internal search directions in the large-scale case. In this paper a minimal-memory quasi-Newton approach with secant preconditioners is proposed, taking into account the structure of Augmented Lagrangians that come from the popular Powell–Hestenes–Rockafellar scheme. A combined algorithm, that uses the quasi-Newton formula or a truncated-Newton procedure, depending on the presence of active constraints in the penalty-Lagrangian function, is also suggested. Numerical experiments using the Cute collection are presented.     

A novel procedure for the aromatization of ring a in 19-nortestosterone

A convenient, 40% overall yield synthesis of 2,3,17β-triacetoxy-1,3,5(10)-estratriene is described, which involves epoxidation of 19-nortestosterone and subsequent acetylation, lead tetra-acetate acetoxylation of the so-formed 17β-acetoxy-4β,5-epoxy-5β-estran-3-one, and aromatization of ring A, by means of acidic alumina, of the resulting 2α and 2β epimers of 2,17β-diacetoxy-4β,5-epoxy-5β-estran-3-one.     

Definitive evidence that the ESR spectrum observed during photolysis of Mn2(CO)10 in THF is due to octahedral high-spin (d5) manganese(II)

The reassignment to a manganese(0) quartet state by C.L. Kwan and J.K. Kochi (J. Organometal. Chem., 101 (1975) C9) of the ESR spectrum obtained during photolysis of Mn₂(CO)₁₀ in THF is shown to be in error; computer simulation of the X-band spectrum and observation of the S-band spectrum confirm our previous assignment to sextet manganese(II) and chemical and IR evidence indicate the presence of [Mn(CO)₅]^? as a counter ion.     

A computer program system for kinetic analysis of non-isothermal thermogravimetric data: I. Data acquisition and preparation for kinetic analysis

FORTRAN software is described which enables the generation of rate of weight change data (DTG) from percentage weight change measurements (TG), obtained under non-isothermal conditions. The program also transposes this information into the dimensionless extent and rate of reaction at unit temperature intervals by means of a cubic spline interpolation. A simple search routine identifies all DTG spikes in the thermogravimetric record, and the temperature and extent of reaction at which the rate attains its maximum value. This total information serves as input data for the kinetic analysis software to be discussed in part II of this communication. An example of the application of this program to the pyrolysis of bituminous coal is presented.     

Mulliken population analysis and quantum mechanical probability

It is shown that, under certain conditions, the use of Mulliken gross atom populations for the analysis of molecular electronic wavefunctions is not without a basis in the rigorous probabilistic interpretation of quantum mechanics,     

Microcomputers and pattern recognition

Microcomputer software for chemists is becoming available at an ever increasing rate. Following Professor Forina's general pattern recognition program, published in last month's Computer Corner, we present a specific technique, the linear learning machine. This is also available in Professor Forina's PARVUS but the software presented here has additional possibilities. It is proposed by Dr D.C. Leegwater from the Central Institute of Food and Nutrition Research of the Dutch organization of Applied Scientific Research (CIVO-TNO) at Zeist and by his son, who is studying physics and mathematics at the State University of Utrecht.