A geometric method in nonlinear programming

A differential geometric approach to the constrained function maximization problem is presented. The continuous analogue of the Newton-Raphson method due to Branin for solving a system of nonlinear equations is extended to the case where the system is under-determined. The method is combined with the continuous analogue of the gradient-projection method to obtain a constrained maximization method with enforced constraint restoration. Detailed analysis of the global behavior of both methods is provided. It is shown that the conjugate-gradient algorithm can take advantage of the sparse structure of the problem in the computation of a vector field, which constitutes the main computational task in the methods.This is part of a paper issued as Stanford University, Computer Science Department Report No. STAN-CS-77-643 (Ref. 45), which was presented at the Gatlinburg VII Conference, Asilomar, California, 1977. This work was supported in part by NSF Grant No. NAT BUR OF ECON RES/PO No. 4369 and by Department of Energy Contract No. EY-76-C-02-0016.The main part of this work was presented at the Japan-France Seminar on Functional Analysis and Numerical Analysis, Tokyo, Japan, 1976. The paper was prepared in part while the author was a visitor at the Department of Mathematics, North Carolina State University, Raleigh, North Carolina, 1976–77, and was completed while he was a visitor at the Computer Science Department, Stanford University, Stanford, California, 1977. He acknowledges the hospitality and stimulating environment provided by Professor G. H. Golub, Stanford University, and Professors N. J. Rose and C. D. Meyer, North Carolina State University.     

Colloid chemical studies of polystyrene latices polymerized without any surface-active agents

Summary The influence of secondary minimum for the stability of spherical colloid has been studied using a series of soap-free polystyrene latices from 350 m to 1400 m in diameter.The critical flocculation concentration (c. f. c.) and the zeta-potential at the c. f. c. for each latex were determined with several salts of different ionic valencies. The values of c. f. c. varied with the particle size, reaching a maximum value at 750 m and then decreasing gradually with the diameter.Another phenomenon detected in the experiment was the complete reversibility of coagulation which was observed only in the cases of large size latices, i. e., the coagulates of large size particles were fully redispersed in the solution by stirring. The time-dependence of their sedimentation curves was reproducible.These experimental results could not be explained by the simple theoretical consideration for stability of suspension. The satisfactory explanation is given only using the term of secondary minimum of interaction potential, i. e., the origin of coagulation was shifted from the ordinary primary minimum to the shallow secondary minimum at about 750 m of the particle diameter.

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Zusammenfassung Der Einfluß des Sekundär-Minimum auf die Stabilität von Kolloiden wurde an seifenfreien Polystyrol-Latex-Suspensionen mit einem Durchmesser von 350 m bis 1400 m untersucht. Die kritische Flockungskonzentration (c. f. c.) und das Zeta-Potential bei c. f. c. wurde mit verschiedenen Salzen bestimmt.Der Wert von c. f. c. ändert sich mit der Teilchengröße.Ein weiterer wichtiger experimenteller Befund ist die vollständige Reversibilität der Flockung bei größeren Latices.Derartige Versuchsergebnisse können durch das Sekundär-Minimum befriedigend erklärt werden.

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With 7 figures in 10 details and 2 tables     

Near-infrared emissions with widely different widths in two kinds of Er-doped oxide glasses with high refractive indices and low phonon energies

Er³⁺-doped alkali-barium-bismuth-tellurite (LKBBT) and alkali-barium-bismuth-gallate (LKBBG) glasses with high refractive indices and low phonon energies have been designed, fabricated, characterized and compared. Intense 1.53 μm emissions with widely different widths in the two kinds of glasses were observed and recorded under 980 nm diode laser excitation. The full-widths at half-maximum of the 1.53 μm emission bands in LKBBT and LKBBG glasses are 58 and 40 nm, and the lifetimes of them were measured to be 3.21 and 3.97 ms, respectively. The quantum efficiencies for the ⁴I_13/2 level in both glasses are almost 100%. The 1.53 μm broad and narrow emissions with high spontaneous emission probabilities and large emission cross-sections indicate that Er³⁺-doped LKBBT and LKBBG glasses are suitable materials in developing broadband optical amplifier and infrared laser, respectively.     

3-H-YDROXYRETINAL AS A CHROMOPHORE OF Drosophila melanogaster VISUAL PIGMENT ANALYZED BY HIGH-PRESSURE LIQUID CHROMATOGRAPHY

Abstract— The chromophore of the visual pigment of the fruit fly Drosophila melanogaster was studied by high-pressure liquid chromatography (HPLC). Oxime derivatives of the chromophore were successfully analyzed with a more polar solvent than has been used for retinaloximes. A preceding monochromatic irradiation resulted in reversible interchanges in the amount among geometric isomers of the oximes that reflected the photointerconversion of rhodopsin and metarhodopsin of the peripheral photoreceptors (Rl-R6). Authentic all- trans -3-h-ydroxyretinal was used to identify the chromophore from metarhodopsin. Results demonstrated that the chromophore of the visual pigment in Drosophila is 3-h-ydroxyretinal as was proposed in larger flies.     

Thermal rearrangements of allyl 2,2-dichlorovinyl and 1,2,2-trichlorovinyl sulfides

Unique rearrangements of allyl 2,2-dichlorovinyl and 1,2,2-trichlorovinyl sulfides have been found. On heating the former gave 1,2-dichloro-l,4-pentadienes and the latter 2,3-dichloro-5-chloromethyl-4,5-dihydrothiophenes and 3,5,6-trichloro-3,4-dihydro-2H-thiopyranes .     

Observation of B Meson decays to b1pi and b1K

We present the results of searches for decays of B mesons to final states with a b1 meson and a charged pion or kaon. The data, collected with the BABAR detector at the Stanford Linear Accelerator Center, represent 382x10(6) BB[over ] pairs produced in e+e- annihilation. The results for the branching fractions are, in units of 10(-6), B(B+-->b1(0)pi+)=6.7+/-1.7+/-1.0, B(B+-->b1(0)K+)=9.1+/-1.7+/-1.0, B(B0-->b1(-/+)pi(+/-))=10.9+/-1.2+/-0.9, and B(B0-->b1(-)K+)=7.4+/-1.0+/-1.0, with the assumption that B(b1-->omega pi)=1. We also measure charge and flavor asymmetries A(ch)(B+-->b1(0)pi+)=0.05+/-0.16+/-0.02, Ach(B+-->b1(0)K+)=-0.46+/-0.20+/-0.02, A(ch)(B0-->b1(-/+)pi(+/-))=-0.05+/-0.10+/-0.02, C(B0-->b1(-/+)pi(+/-))=-0.22+/-0.23+/-0.05, DeltaC(B0-->b1(-/+)pi(+/-))=-1.04+/-0.23+/-0.08, and A(ch)(B0-->b1(-)K+)=-0.07+/-0.12+/-0.02. The first error quoted is statistical, and the second systematic.     

Nonlinear conduction in two-dimensional CDW system: 1T-TaS2

Non-linear electrical conductivity is observed in 1T-TaS₂ in the lowest-temperature phase (the commensurate charge density wave state). The collective excitations are suggested to contribute to the electronic conduction as in the case of the linear chain metals TTF-TCNQ and NbSe₃.     

Accurate and rapid estimation on spectral interferences in routine analysis by ICP-AES: use of mutual interference coefficients

A practical method to estimate spectral interferences and to select optimum analytical lines in ICP-AES is suggested. Depending on the matrix composition and the amounts of the analyte, the analytical lines suffering from little interferences and the limit of determination can be determined from calculation using spectral interference coefficients. For this calculation, the spectral interference coefficients, which are defined as apparent mass of the analyte equivalent to the spectral interference from unit mass of the interferent, are obtained experimentally for 639 emission lines of 68 elements. There is a good correlation between the coefficients obtained on two spectrometers having different resolutions.