On solving sparse band systems with three algorithms of the ABS family

In this paper, we examine three algorithms in the ABS family and consider their storage requirements on sparse band systems. It is shown that, when using the implicit Cholesky algorithm on a band matrix with band width 2q+1, onlyq additional vectors are required. Indeed, for any matrix with upper band widthq, onlyq additional vectors are needed. More generally, ifa _kj 0,j>k, then thejth row ofH _i is effectively nonzero ifj>i>k. The arithmetic operations involved in solving a band matrix by this method are dominated by (1/2)n ² q. Special results are obtained forq-band tridiagonal matrices and cyclic band matrices.The implicit Cholesky algorithm may require pivoting if the matrixA does not possess positive-definite principal minors, so two further algorithms were considered that do not require this property. When using the implicit QR algorithm, a matrix with band widthq needs at most 2q additional vectors. Similar results forq-band tridiagonal matrices and cyclic band matrices are obtained.For the symmetric Huang algorithm, a matrix with band widthq requiresq–1 additional vectors. The storage required forq-band tridiagonal matrices and cyclic band matrices are again analyzed.This work was undertaken during the visit of Dr. J. Abaffy to Hatfield Polytechnic, sponsored by SERC Grant No. GR/E-07760.     

Improving the rate of convergence of interior point methods for linear programming

This paper proposes a procedure for improving the rate of convergence of interior point methods for linear programming. If (x ^k ) is the sequence generated by an interior point method, the procedure derives an auxiliary sequence ( ). Under the suitable assumptions it is shown that the sequence ( ) converges superlinearly faster to the solution than (x ^k ). Application of the procedure to the projective and afflne scaling algorithms is discussed and some computational illustration is provided.     

Partially and totally asynchronous algorithms for linear complementarity problems

A unified treatment is given for partially and totally asynchronous parallel successive overrelaxation (SOR) algorithms for the linear complementarity problem. Convergence conditions are established and compared to previous results. Convergence of the partially asynchronous method for the symmetric linear complementarity problem can be guaranteed if the relaxation factor is sufficiently small. Unlike previous results, this relaxation factor interval does not depend explicitly on problem size.This material is based on research supported by the Air Force Office of Scientific Research Grant No. AFOSR-89-0410.The author wishes to thank the referee for pointing out how to improve the bound (12). The same technique can be used to reduce the factorn in Ref. 5, p. 553, to .     

Numerical solution of minimax problems of optimal control,part 1

This paper contains general transformation techniques useful to convert minimax problems of optimal control into the Mayer-Bolza problem of the calculus of variations [Problem (P)]. We consider two types of minimax problems: minimax problems of Type (Q), in which the minimax function depends on the state and does not depend on the control; and minimax problems of Type (R), in which the minimax function depends on both the state and the control. Both Problem (Q) and Problem (R) can be reduced to Problem (P).For Problem (Q), we exploit the analogy with a bounded-state problem in combination with a transformation of the Jacobson type. This requires the proper augmentation of the state vectorx(t), the control vectoru(t), and the parameter vector , as well as the proper augmentation of the constraining relations. As a result of the transformation, the unknown minimax value of the performance index becomes a component of the parameter vector being optimized.For Problem (R), we exploit the analogy with a bounded-control problem in combination with a transformation of the Valentine type. This requires the proper augmentation of the control vectoru(t) and the parameter vector , as well as the proper augmentation of the constraining relations. As a result of the transformation, the unknown minimax value of the performance index becomes a component of the parameter vector being optimized.In a subsequent paper (Part 2), the transformation techniques presented here are employed in conjunction with the sequential gradient-restoration algorithm for solving optimal control problems on a digital computer; both the single-subarc approach and the multiple-subarc approach are discussed.This research was supported by the National Science Foundation, Grant No. ENG-79-18667, and by Wright-Patterson Air Force Base, Contract No. F33615-80-C3000. This paper is a condensation of the investigations reported in Refs. 1–7. The authors are indebted to E. M. Coker and E. M. Sims for analytical and computational assistance.     

New Methods for the Synthesis of Glycosides and Oligosaccharides—Are There Alternatives to the Koenigs-Knorr Method? [New Synthetic Methods (56)]

Glycoproteins, glycolipids, and glycophospholipids (glycoconjugates) are components of membranes. The oligosaccharide residue is responsible for intercellular recognition and interaction; it acts as a receptor for proteins, hormones, and viruses and governs immune reactions. These significant activities have stimulated interest in oligosaccharides and glycoconjugates. With their help it should be possible to clarify the molecular basis of these phenomena and to derive new principles of physiological activity. Major advances in the synthesis of oligosaccharides have been made by the use of the Koenigs-Knorr method, in which glycosyl halides in the presence of heavy-metal salts are employed to transfer the glycosyl group to nucleophiles. The disadvantages of this procedure have led to an intensive search for new methods. Such methods will be discussed in this article. Emphasis is placed on glycoside and saccharide formation by 1-O-alkylation, on the trichloroacetimidate method, and on activation through the formation of glycosylsulfonium salts and glycosyl fluorides.     

A dual-electrode approach for highly selective detection of glucose based on diffusion layer theory: experiments and simulation

A dual-electrode configuration for the highly selective detection of glucose in the diffusion layer of the substrate electrode is presented. In this approach, a glassy carbon electrode (GCE, substrate) modified with a conductive layer of glucose oxidase/Nafion/graphite (GNG) was used to create an interference-free region in its diffusion layer by electrochemical depletion of interfering electroactive species. A Pt microelectrode (tip, 5 microm in radius) was located in the diffusion layer of the GNG-modified GCE (GNG-G) with the help of scanning electrochemical microscopy. Consequently, the tip of the electrode could sense glucose selectively by detecting the amount of hydrogen peroxide (H2O2) formed from the oxidization of glucose on the glucose oxidase layer. The influences of parameters, including tip-substrate distance, substrate potential, and electrolyzing time, on the interference-removing efficiency of this dual-electrode approach have been investigated systematically. When the electrolyzing time was 30 s, the tip-substrate distance was 1.8 a (9.0 microm) (where a is the radius of the tip electrode), the potentials of the tip and substrate electrodes were 0.7 V and 0.4 V, respectively, and a mixture of ascorbic acid (0.3 mM), uric acid (0.3 mM), and 4-acetaminophen (0.3 mM) had no influence on the glucose detection. In addition, the current-time responses of the tip electrode at different tip-substrate distances in a solution containing interfering species were numerically simulated. The results from the simulation are in good agreement with the experimental data. This research provides a concept of detection in the diffusion layer of a substrate electrode, as an interference-free region, for developing novel microelectrochemical devices.     

Theoretical Study of Rotational Isomerism in Ethyl Pseudohalides

The structure and conformational stability of ethyl pseudohalides CH₃CH₂ — XCN (X = O, S, Se) were investigated using ab initiocalculations at the MP2 level of theory with a triple- basis set augmented with polarization and diffusion functions. Full optimization was performed on the minimum energy structures as well as on the transition state forms. The relative stabilities of rotational conformers were calculated at the MP4 level using MP2 optimized reference geometries. The nature of all considered stationary points was verified by calculation of the harmonic vibrational frequencies. The calculated bond lengths, bond angles, dipole moments, and rotational constants of optimized global minima structures agree very well with the corresponding experimental data obtained from microwave spectroscopic studies. Also, available experimental frequencies are in good accord with the theoretical values. For ethyl cyanate CH₃CH₂ — OCN, the antiperiplanar (trans) form is predicted to be more stable than the synclinal (gauche) form, and the synperiplanar (cis) form corresponds to the transition state. For both ethyl thiocyanate CH₃CH₂ — SCN and ethyl selenocyanate CH₃CH₂ — SeCN, the gaucheform is the global minimum while the trans-conformer is a local minimum and the cis-form is a transition state.     

The Studies of the Heterogeneous Properties of Solid Surfaces by Means of the Derivatograph Q-1500 D

A simple method has been adopted to obtain an important information on the heterogeneous properties of materials studied, adsorbed liquid films and liquid-solid interactions. The method utilizes Q-TG mass loss and the first derivative Q-DTG mass loss curves with respect to temperature and time obtained during programmed liquid thermodesorption in quasi-isothermal conditions. The values of the adsorption capacity, total porosity of material, the value of active centers, desorption energy distribution and mesopore-size distribution functions obtained by this method are in good agreement with those estimated on the basis of independent methods. The theoretical and experimental results provided novel and unique data on the heterogeneity of solid surfaces, properties of liquid adsorbed films and thermal stability of the liquid/solid interfaces. This paper presents the more important results obtained so far in the studies the liquid/solid systems by means of the Paulik's classical and quasi-isothermal techniques. This revised version was published online in July 2006 with corrections to the Cover Date.     

线性代数是蓝色的——大学非数学专业《线性代数》的课程设计

线性代数不仅是处理多元问题的有力工具,而且具有强烈的思辨性.大学本科教育应该是"泛专业的高等素质教育",作为公共基础课之一的《线性代数》,也应着眼于学生综合科学素质的培养,注意对学生进行思维训练.本文提出线性代数的教学理念:"提出处理多元问题的新要求,沿着多元整合的集成化思路推进,逐步把学生引上线性变换和线性空间的思维平台."为此,本文进行了"五模块、两阶段、三层次"的课程设计,希望对讲授该课程的教师有所裨益.     

Which Extraction Solvents and Methods Are More Effective in Terms of Chemical Composition and Biological Activity of Alcea fasciculiflora from Turkey?

The bioactive content, antioxidant properties, and enzyme inhibition properties of extracts of Alcea fasciculiflora from Turkey prepared with different solvents (water, methanol, ethyl acetate) and extraction methods (maceration, soxhlet, homogenizer assisted extraction, and ultrasound assisted extraction) were examined in this study. UHPLC-HRMS analysis detected or annotated a total of 50 compounds in A. fasciculiflora extracts, including 18 hydroxybenzoic and hydroxycinnamic acids, 7 Hexaric acids, 7 Coumarins, 15 Flavonoids, and 3 hydroxycinnamic acid amides. The extracts had phenolic and flavonoid levels ranging from 14.25 to 24.87 mg GAE/g and 1.68 to 25.26 mg RE/g, respectively, in the analysis. Both DPPH and ABTS tests revealed radical scavenging capabilities (between 2.63 and 35.33 mg TE/g and between 13.46 and 76.27 mg TE/g, respectively). The extracts had reducing properties (CUPRAC: 40.38–78 TE/g and FRAP: 17.51–42.58 TE/g). The extracts showed metal chelating activity (18.28–46.71 mg EDTAE/g) as well as total antioxidant capacity (phosphomolybdenum test) (0.90–2.12 mmol TE/g). DPPH, ABTS, FRAP, and metal chelating tests indicated the water extracts to be the best antioxidants, while the ethyl acetate extracts had the highest overall antioxidant capacity regardless of the extraction technique. Furthermore, anti-acetylcholinesterase activity was identified in all extracts (0.17–2.80 mg GALAE/g). The water extracts and the ultrasound-assisted ethyl acetate extract were inert against butyrylcholinesterase, but the other extracts showed anti-butyrylcholinesterase activity (1.17–5.80 mg GALAE/g). Tyrosine inhibitory action was identified in all extracts (1.79–58.93 mg KAE/g), with the most effective methanolic extracts. Only the ethyl acetate and methanolic extracts produced by maceration and homogenizer aided extraction showed glucosidase inhibition (0.11–1.11 mmol ACAE/g). These findings showed the overall bioactivity of the different extracts of A. fasciculiflora and provided an overview of the combination of solvent type and extraction method that could yield bioactive profile and pharmacological properties of interest and hence, could be a useful reference for future studies on this species.