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  • 1
    Electronic Resource
    Electronic Resource
    Synthetic and kinetic studies on tricarbonates and dicarbonates (1978)
    s.l. : American Chemical Society
    The @journal of organic chemistry 43 (1978), S. 2410-2414 
    Details
    ISSN: 1520-6904
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1021/jo00406a023
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  • 2
    Electronic Resource
    Electronic Resource
    Diffusion processes on graphs: stochastic differential equations, large deviation principle (2000)
    Springer
    Probability theory and related fields 116 (2000), S. 181-220 
    Details
    ISSN: 1432-2064
    Keywords: Mathematics Subject Classification (1991): Primary 60J60; Secondary 60H10, 60J55, 60F10 ; Key words and phrases: Diffusions on graphs – Local time – Small random perturbation – Large deviations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract. Ito's rule is established for the diffusion processes on the graphs. We also consider a family of diffusions processes with small noise on a graph. Large deviation principle is proved for these diffusion processes and their local times at the vertices.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/PL00008726
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  • 3
    Electronic Resource
    Electronic Resource
    A generalization of Chernoff inequality via stochastic analysis (1987)
    Springer
    Probability theory and related fields 75 (1987), S. 149-157 
    Details
    ISSN: 1432-2064
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Let μ be a probability measure on R dwith density c(exp(-2U(x)), where U∈C 2(Rd), $$\left| {\nabla U(x)} \right|^2 - \Delta U(x) \to \infty $$ and U(x)→∞ as |x|→∞. By using stochastic analysis and theorems in Schrödinger operators we have the following result: there exists a constant c〉0 such that (1) $$Var_\mu f\underline \leqslant c E_\mu \left| {\nabla f} \right|^2 $$ for any f∈L 1(μ) with a well-defined distributional gradient ∇f. Under our condition, the operator $$ - \frac{1}{2}\Delta + \nabla U \cdot \nabla $$ in L 2(μ) has discrete spectrum 0 = λ1 〈 λ2 = ... = λm 〈 λm + 1 ≦ ... with corresponding eigenfunctions {φ n} which form a C.O.N.S. (complete orthonormal system). If the R.H.S. of (1) is finite then equality holds iff $$f = \sum\limits_{i = 1}^m {b_i \phi _i } $$ for some b 1,...,bm∈R. Moreover, the constant c can be taken as (2λ2)−1. When U is a quadratic form, (1) is the Chernoff inequality (Chernoff 1981; Chen 1982). The approach here can be generalized to infinite dimensional Gaussian measures, or the case with μ being a probability measure in a bounded domain of R dor some discrete cases.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00320088
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  • 4
    Electronic Resource
    Electronic Resource
    Singular perturbed Markov chains and exact behaviors of simulated annealing processes (1992)
    Springer
    Journal of theoretical probability 5 (1992), S. 223-249 
    Details
    ISSN: 1572-9230
    Keywords: Simulated annealing ; singular perturbed Markov chains ; large deviation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We study asymptotic properties of discrete and continuous time generalized simulated annealing processesX(·) by considering a class of singular perturbed Markov chains which are closely related to the large deviation of perturbed diffusion processes. Convergence ofX(t) in probability to a setS 0 of desired states, e.g., the set of global minima, and in distribution to a probability concentrated onS 0 are studied. The corresponding two critical constants denoted byd and Λ withd≤Λ are given explicitly. When the cooling schedule is of the formc/logt, X(t) converges weakly forc〉0. Whether the weak limit depends onX(0) or concentrates onS 0 is determined by the relation betweenc, d, and Λ. Whenc〉Λ, the expression for the rate of convergence for each state is also derived.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01046734
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  • 5
    Electronic Resource
    Electronic Resource
    Large-time behavior of perturbed diffusion markov processes with applications to the second eigenvalue problem for fokker-planck operators and simulated annealing (1990)
    Springer
    Acta applicandae mathematicae 19 (1990), S. 253-295 
    Details
    ISSN: 1572-9036
    Keywords: Primary 60H10 ; 60J70 ; secondary 60F10 ; 35P15 ; Diffusion process ; large deviation ; large time behavior ; Fokker-Planck operator ; simulated annealing
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We study the large-time behavior and rate of convergence to the invariant measures of the processes dX ε(t)=b(X) ε(t)) dt + εσ(X ε(t)) dB(t). A crucial constant Λ appears naturally in our study. Heuristically, when the time is of the order exp(Λ − α)/ε2 , the transition density has a good lower bound and when the process has run for about exp(Λ − α)/ε2, it is very close to the invariant measure. LetL ε=(ε2/2)Λ − ∇U · ∇ be a second-order differential operator on ℝd. Under suitable conditions,L z has the discrete spectrum $$\begin{gathered} 0 = \lambda _1^\varepsilon 〉 - \lambda _2^\varepsilon ...and lim \varepsilon ^2 log \lambda _2^\varepsilon = - \Lambda \hfill \\ \varepsilon \to 0 \hfill \\ \end{gathered} $$ LetU be a function from ℝd to [0,∞) with suitable conditions. A nonhomogeneous Markov processY(·) governed by $$dY(t) = - \nabla U(Y(t))dt + \sqrt {c/log(2 + t)} dB(t)$$ withY(0)=x is used to search for a global minimum ofU. LetS={x|U(x)=min y U(y)}. There exists a critical constantd * such that forc 〉 d *,Y(t) uniformly converges toS in probability overx in a compact set. The above statement fails forc 〈d *. Forc 〉 Λ,Y(t) converges weakly to a probability measure which does not depend on the starting pointx and concentrates onS. The techniques can also be used to study discrete simulated annealing.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01321859
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  • 6
    Electronic Resource
    Electronic Resource
    Determination of Cinnamomi Constituents by High-performance Liquid Chromatography and Capillary Electrophoresis (2000)
    Weinheim : Wiley-Blackwell
    Journal of High Resolution Chromatography 23 (2000), S. 561-564 
    Details
    ISSN: 0935-6304
    Keywords: Retention factors ; Cinnamomi ramulus ; high-performance liquid chromatography ; capillary electrophoresis ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: ---No abstract
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Capillary electrophoresis determination of six bioactive constituents in San-huang-hsieh-hsin-tang (1996)
    Weinheim : Wiley-Blackwell
    Journal of High Resolution Chromatography 19 (1996), S. 409-412 
    Details
    ISSN: 0935-6304
    Keywords: Micellar electrokinetic chromatography ; Rhei Rhizoma ; Scutellariae Radix ; Coptidis Rhizoma ; Bioactive constituents determination ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A capillary electrophoretic method for simultaneous determination of six bioactive ingredients (berberine, palmatine, baicalin, sennoside B, emodin, and sennoside A) in the Chinse herbal formula San-huang-hsieh-hsin-tang was established. A carrier composed of aqueous buffer solution (50 mM sodium cholate, 15 mM sodium dihydrogen phosphate, and 4.25 mM sodium borate)-acetonitrile (3:2) was found to be the most suitable electrolyte for this separation. Contents of these constituents in a non-pretreated methanol-water extract of San-huang-hsieh-hsin-tang sample could be easily determined within 20 min. The effects of borate, cholate, and organic modifier (acetonitrile) concentration of the carrier on the migration behavior of the solutes were also studied.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jhrc.1240190709
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  • 8
    Electronic Resource
    Electronic Resource
    Liquid Chromatographic Determination of the Constituents in Shao-yao-tang and Related Chinese Herbal Preparations (1998)
    Weinheim : Wiley-Blackwell
    Journal of High Resolution Chromatography 21 (1998), S. 569-573 
    Details
    ISSN: 0935-6304
    Keywords: Chinese herbal preparation ; Shao-yao-tang ; pharmaceutical analysis ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: ---A high-performance liquid chromatographic method for the separation of twenty one constituents of Shao-yao-tang including six flavonoids, six alkaloids, three anthraquinones, three carboxylic acids, one monoterpene, one saponin, and one aldehyde was developed. Detection at 275 nm with a linear gradient elution system consisting of tetrabutylammonium bromide (TBA) and acetic acid solution was found to be suitable for determination of nineteen marker substances in an unpretreated Shao-yao-tang extract within 75 min. This method can also be used to analyze 11-14 components in a number of Chinese herbal preparations such as San-huang-hsieh-hsin-tang, Ching-chieh-lien-chiao-tang, San-tsung-kuei-chien-tang, Chai-hu-ching-kan-tang, and Ching-yin-li-ke-tang.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    Separation of Anthraquinones by Capillary Electrophoresis and High-Performance Liquid Chromatography (2000)
    Weinheim : Wiley-Blackwell
    Journal of High Resolution Chromatography 23 (2000), S. 143-148 
    Details
    ISSN: 0935-6304
    Keywords: Analysis of anthraquinones ; capillary electrophoresis ; high-performance liquid chromatography ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: ---The separation and determination of twelve anthraquinones, viz. anthraquinone 1, chrysphanol 2, aloe-emodin 3, alizarin 4, anthraquinone-2-carboxylic acid 5, purpurin 6, sennoside B 7, sennoside A 8, emodin 9, quinalizarin 10, rhein 11, and anthraflavic acid 12, were achieved by capillary electrophoresis (CE) and high-performance liquid chromatography (HPLC). Detection at 260 nm with a buffer solution containing 30 mM sodium borate (adjusted to pH = 10.56 with 0.05N NaOH) and acetonitrile (9 : 1) in CE or with a linear gradient elution containing 20 mM KH2PO4 with 0.05% phosphoric acid (pH = 2.91) and methanol in HPLC was found to be the most suitable approach for this separation. Contents of six components (2, 3, 7, 8, 9, 11) in crude Rhei Rhizoma extract could easily be determined within 39 min by CE or 63 min by HPLC. The effects of buffers on this separation and the validation of the two methods were studied.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    HPLC Separation of the Major Constituents of Gardeniae Fructus (1998)
    Weinheim : Wiley-Blackwell
    Journal of High Resolution Chromatography 21 (1998), S. 523-526 
    Details
    ISSN: 0935-6304
    Keywords: High-performance liquid chromatography ; gardenia constituent separation ; genipin gentiobioside ; geniposide ; crocin ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
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