Controllability of linear systems,differential geometry curves in grassmannians and generalized grassmannians,and riccati equations

We study the linear system =Ax+Bu from a differential geometric point of view. It is well-known that controllability of the system is related to the one-parameter family of operators e^t B. We use this to give a proof of the classical controllability conditions in terms of the differential geometry of certain curves in ⁿ. We then view (t)=Im(e^t B) as a curve in appropriate Grassmannian and see that, in local coordinates, is an integral curve of the flow induced by a matrix Riccati equation. We obtain qualitative geometric conditions on that are equivalent to the controllability of the system. To get quantitiative results, we lift to a curve l' in a splitting space, a generalized Grassmannian, which has the advantage of being a reductive homogeneous space of the general linear group, GL(ⁿ). Explicit and simple expressions concerning the geometry of are computed in terms of the Lie algebra of GL(ⁿ), and these are related to the controllability of the system.James Wolper was a visiting professor in the Department of Mathematics at Texas Tech University while much of this research was conducted. He would like to express appreciation for the hospitality he received during his visit.     

Gas chromatographic determination of estrone,estradiol and estriol in non-pregnancy plasma

Summary A gas Chromatographic method for the determination of estrone, estradiol and estriol in plasma of normal females is described. Purification is done by means of TLC of the free compounds and the acetates and quantitation is achieved by electron capture-gas chromatography of the estrogen heptafluorobutyrates. Experiments on the validation of the method are described along with some examples of its application.

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Zusammenfassung Eine gaschromatographische Methode zur Bestimmung von Östron, Östradiol und Östriol im normalen weiblichen Plasma wurde beschrieben. Die Reinigung erfolgte durch Dünnschichtchromatographie der freien Verbindungen und ihrer Acetate. Die quantitative Bestimmung wurde gaschromatographisch mit Hilfe eines Elektroneneinfangdetektors an Hand der Östrogenheptafluorobutyrate bewerkstelligt. Versuche zur Bewertung dieser Methode sowie Beispiele für ihre Anwendung wurden beschrieben.

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Supported by USPHS Grants AM 09908 and RCDA 5 K 3-AM-31, 321 (S. K.) and a grant from the Ford Foundation.     

CHEMISTRY OF SINGLET OXYGEN—XXVI. PHOTOOXYGENATION OF PHENOLSy†

Abstract— The aerobic dye-sensitized photooxygenation of monohydric phenols proceeds by way of singlet oxygen under the conditions studied. Various phenols give different proportions of reaction with and quenching of singlet oxygen. Para-substituted 2,6-di-t-butylphenols show a linear correlation between the log of the total rate of singlet oxygen removal and their halfwave oxidation potentials; the same correlation is given for certain phenol methyl ethers. A Hammett plot using s?⁺ gives ρ - 1.72 ± 0.12, consistent with development of some charge in the quenching step. Reaction of photo-chemically generated singlet oxygen with 2,4,6-triphenylphenol gives 2,4,6-triphenylphenoxy radical as an intermediate in singlet oxygen quenching, although no overall reaction occurs. Kinetic analysis indicates that the radical is derived exclusively from the interaction of 2,4,6-triphenylphenol with singlet oxygen. A charge-transfer mechanism for quenching of singlet oxygen by phenols is proposed.     

Tuning the singlet oxygen quantum yield of near-IR-absorbing porphyrazines

We report the quantum yields for singlet oxygen production by a series of porphyrazines (pz) of the form M[pz(An;B4-n)] (Scheme 1), where the peripheral substituent A is [S-R]2 with R = (CH2CH2O)3H, B is a fused alpha,alpha'-dialkoxybenzo group and M = 2H, Mg or Zn. These compounds show intense near-IR absorbance/emission (longest wavelength emission, approximately 830 nm). Their solubilities vary with R, whereas their optical properties do not. We show that singlet oxygen sensitization by these luminescent compounds can be "tuned" from essentially off to on by varying n and selection among M = 2H, Mg or Zn. The quantum yields vary ca 60-fold within the set of compounds studied, from phidelta = 0.007 for compound 3 to phidelta = approximately 0.4 for compound 11.     

CHEMISTRY OF SINGLET OXYGEN—XXV. PHOTOOXYGENATION OF METHIONINE*

Abstract— Methionine (Met) photooxidation sensitized by rose bengal has been studied as a function of pH and other variables. At pH ≤ 6, the reaction is a simple one, 2 Met + O₂→ 2 Methionine sulfoxide (MetO). At pH 6–10, another mechanism becomes important, leading to dehydromethionine; the structure of this compound was correctly assigned by Lavine (1945) as the heterocyclic N-S compound 2. One mole of H₂O₂ is also produced in this process. Dehydromethionine hydrolyzes slowly to MetO. Above pH9, a process leading directly to MetO + H₂O₂ becomes important. The stoichiometry of the latter two processes are Met + O₂+ H₂O → MetO + H₂O₂; competition among these three processes accounts for the puzzling variations in O₂ uptake. N-Formylated derivatives of methionine undergo only the first and third processes. Substantial catalytic effects of buffers complicate the picture. All the reactions appear to involve singlet oxygen, since there is the predicted effect of D₂O vs H₂O on the rate of reaction, although the situation is complicated by apparent aggregation of Met above 5 mM.     

Reaction of singlet oxygen with trans-4-propenylanisole. Formation Of

We report the effects of added acid in the reaction of singlet oxygen with trans-4-propenylanisole (1). We provide evidence that solvent acidity modifies the behavior of the transient intermediates. Relative to reactions in aprotic solvent, enhanced dioxetane concentrations are observed in MeOH and in nonprotic solvents with acid. We suggest a new mechanism that invokes a proton transfer from MeOH and benzoic acid to perepoxide (2) and zwitterion (3) intermediates.     

Stacking due to ionic transport number mismatch during sample sweeping on microchips

Sample stacking can occur in isoconductive buffer systems as a result of ion transport mismatches that cause changes in buffer conductivity during electrophoresis. Fluorescence imaging was used to examine this effect in the sweeping of hydrophobic dyes with sodium dodecyl sulfate (SDS) on microchips. Imaging revealed the occurrence of a stacking effect in a sodium borate buffer system in which the sample buffer and SDS-containing run buffer had the same initial conductivity. Injected sample plugs were first swept by SDS micelles and the swept band was then stacked at the trailing end of the sample zone. This effect is due to changes in conductivity at both the front and back interfaces of the injected sample plug and can be modeled by moving boundary equations. Maximum signal enhancements of 86-, 160- and 560-fold were obtained for Rhodamine 560, Rhodamine B and Rhodamine 6G, respectively, by the combination of sweeping and stacking within a 1 cm section of microchannel. Based on sample sweeping/stacking and manipulation of the electric field polarity, a method of trapping and concentrating analyte from multiple injections was also demonstrated.     

Lens alpha-crystallin and hypericin: a photophysical mechanism explains observed lens

Determining whether alpha-crystallin (the major lens protein) affects the photophysics of hypericin, a photosensitizing agent found in various plants, such as St. John's Wort, is important. Hypericin shows promise in cancer and human immunodeficiency virus therapy but may harm individuals taking St. John's Wort extracts (for mild to moderate depression). Hypericin causes hypericism, which is characterized by cellular damage in light-exposed areas. Ocular tissues are at risk for photosensitized damage; thus, we investigated the effects on hypericin photophysics by alpha-crystallin. We measured the transient absorption spectra and the 1270 nm luminescence of singlet (1Deltag) oxygen produced from hypericin in the presence of alpha-crystallin. alpha-Crystallin complexes hypericin, extending the lifetime of its triplet excited state; the Stern-Volmer slope is negative, but not linear, after a saturation curve. Damage to the lens protein by hypericin is known to occur via singlet oxygen, which oxidizes methionine, tryptophan and histidine residues. Binding to alpha-crystallin does not inhibit singlet oxygen formation by hypericin. alpha-Crystallin reacts with singlet oxygen with a rate constant of 1.3 x 10(8) M(-1) s(-1). Thus, we anticipate that hypericin will be an effective photosensitizer in the lens.     

OBSERVATIONS ON THE PHOTOSENSITIZED BREAKAGE OF DNA BY 2-THIOURACIL AND 334-nm ULTRAVIOLET RADIATION

Abstract— Breaks induced in purified DNA by 334-nm ultraviolet (UV) radiation are enhanced 30 times when 2-thiouracil (s²Ura) is present during aerobic irradiation. This enhancement by s²Ura is maximally effective at a concentration of about 1 m M. Anoxic irradiation reduces the s²Ura-enhanced breakage by 90%, indicating a Type II photosensitization. Benzoate, glycerol, diazabicyclo[2.2.2.]octane (DABCO) and histidine all inhibit formation of s²Ura photosensitized breaks, unlike diethylenetriaminepenta-acetic acid (DETAPAC) and catalase, which do not. The relationships between the concentration of DABCO. benzoate and histidine and their protection against induction of single strand breaks (SSBs) were similar, with little inhibition below 10 m M and maximal inhibition near 0.1 M for all compounds. Irradiation of the DNA-s²Ura mixture dissolved in D₂O instead of H₂O enhanced the rate of induction of SSBs in DNA by 334-nm light almost five times. Addition of superoxide dismutase (40, 80 and 200 μg/ml) decreased the rate of induction of breaks in DNA by 334-nm radiation plus s²Ura (in H₂O) by about 40%. Boiled superoxide dismutase had no effect.     

Novel Synthesis of Differentially Substituted 5,7-Dialkoxyquinazolin-4-ones

The preparation of 7-ethoxy-5-fluoroquinazolin-4-one, starting from 3,5-difluorophenol, is described. Further reaction with alkoxide then gives differentially substituted 5,7-dialkoxyquinazolin-4-ones.