Tensor Bogolyubov representations of the renormalized square of white noise (RSWN) algebra

We introduce the quadratic analog of the tensor Bogolyubov representation of the CCR. Our main result is the determination of the structure of these maps: each of them is uniquely determined by two arbitrary complex-valued Borel functions of modulus [Formula: see text] and two maps of [Formula: see text] into itself whose inverses induce transformations that map the Lebesgue measure [Formula: see text] into measures [Formula: see text] absolutely continuous with respect to it. Furthermore, the Radon–Nikodyn derivatives [Formula: see text], of these measures with respect to [Formula: see text], must satisfy the relation [Formula: see text] for [Formula: see text]-almost every [Formula: see text]. This makes a surprising bridge with the hyperbolic sine and cosine defining the structure of usual (i.e. first-order) Bogolyubov transformations. The reason of the surprise is that the linear and quadratic commutation relations are completely different.

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On the Bogolyubov endomorphisms of the renormalized square of white noise algebra

Infinite Dimensional Analysis Quantum Probability and Related Topics ◽

10.1142/s0219025721500235 ◽

2021 ◽

Author(s):

Habib Rebei ◽

Slaheddine Wannes

Keyword(s):

White Noise ◽

Function Space ◽

The Other ◽

Linear Transformations ◽

Test Function ◽

Canonical Commutation Relations ◽

Arbitrary Complex ◽

Borel Functions ◽

Test Function Space ◽

Complex Valued

We introduce the quadratic analogue of the Bogolyubov endomorphisms of the canonical commutation relations (CCR) associated with the re-normalized square of white noise algebra (RSWN-algebra). We focus on the structure of a subclass of these endomorphisms: each of them is uniquely determined by a quadruple [Formula: see text], where [Formula: see text] are linear transformations from a test-function space [Formula: see text] into itself, while [Formula: see text] is anti-linear on [Formula: see text] and [Formula: see text] is real. Precisely, we prove that [Formula: see text] and [Formula: see text] are uniquely determined by two arbitrary complex-valued Borel functions of modulus [Formula: see text] and two maps of [Formula: see text], into itself. Under some additional analytic conditions on [Formula: see text] and [Formula: see text], we discover that we have only two equivalent classes of Bogolyubov endomorphisms, one of them corresponds to the case [Formula: see text] and the other corresponds to the case [Formula: see text]. Finally, we close the paper by building some examples in one and multi-dimensional cases.

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Distribution of iterates of first order difference equations

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972700006407 ◽

1980 ◽

Vol 22 (1) ◽

pp. 133-143 ◽

Cited By ~ 5

Author(s):

James B. McGuire ◽

Colin J. Thompson

Keyword(s):

Invariant Measure ◽

Difference Equation ◽

Lebesgue Measure ◽

Difference Equations ◽

Absolutely Continuous ◽

Order Difference ◽

First Order ◽

Order Difference Equation ◽

The Difference ◽

Biological Context

An invariant measure which is absolutely continuous with respect to Lebesgue measure is constructed for a particular first order difference equation that has an extensive biological pedigree. In a biological context this invariant measure gives the density of the population whose growth is governed by the difference equation. Further asymptotically universal results are obtained for a class of difference equations.

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Antithrombin-mediated Inhibition of Factor Vlla-Tissue Factor Complex by the Synthetic Pentasaccharide Representing the Heparin Binding Site to Antithrombin

Thrombosis and Haemostasis ◽

10.1055/s-0038-1650512 ◽

1996 ◽

Vol 76 (01) ◽

pp. 005-008 ◽

Cited By ~ 22

Author(s):

Jean Claude Lormeau ◽

Jean Pascal Herault ◽

Jean Marc Herbert

Keyword(s):

Binding Site ◽

Tissue Factor ◽

Residual Activity ◽

Coagulation Factors ◽

Heparin Binding ◽

Experimental Conditions ◽

First Order ◽

Heparin Binding Site ◽

Coagulant Activity

SummaryWe examined the effect of the synthetic pentasaccharide representing the minimal binding site of heparin to antithrombin on the antithrombin-mediated inactivation of factor Vila bound to tissue factor. This effect was compared to the effect of unfractionated heparin. Using purified recombinant human coagulation factors and either a clotting or an amidolytic assay for the determination of the residual activity of factor Vila, we showed that the pentasaccharide was an efficient antithrombin-dependent inhibitor of the coagulant activity of tissue factor-factor Vila complex. In our experimental conditions, assuming a mean MW of 14,000 for heparin, the molar pseudo-first order rate constants for ATIII-mediated FVIIa inhibition by ATIII-binding heparin and by the synthetic pentasaccharide were found to be similar with respective values of 104,000 ± 10,500 min-1 and 112,000 ± 12,000 min-1 (mean ± s.e.m., n = 3)

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Statistical method of steepest improvement of response

Industrial laboratory Diagnostics of materials ◽

10.26896/1028-6861-2018-84-11-74-87 ◽

2018 ◽

Vol 84 (11) ◽

pp. 74-87

Author(s):

V. B. Bokov

Keyword(s):

Statistical Method ◽

Linear Model ◽

Response Prediction ◽

Initial Experiment ◽

First Order ◽

Prediction Response ◽

Conditional Extremum ◽

Order Polynomial ◽

Limiting Values

A new statistical method for response steepest improvement is proposed. This method is based on an initial experiment performed on two-level factorial design and first-order statistical linear model with coded numerical factors and response variables. The factors for the runs of response steepest improvement are estimated from the data of initial experiment and determination of the conditional extremum. Confidence intervals are determined for those factors. The first-order polynomial response function fitted to the data of the initial experiment makes it possible to predict the response of the runs for response steepest improvement. The linear model of the response prediction, as well as the results of the estimation of the parameters of the linear model for the initial experiment and factors for the experiments of the steepest improvement of the response, are used when finding prediction response intervals in these experiments. Kknowledge of the prediction response intervals in the runs of steepest improvement of the response makes it possible to detect the results beyond their limits and to find the limiting values of the factors for which further runs of response steepest improvement become ineffective and a new initial experiment must be carried out.

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Development of first-order Derivative Spectrophotometry for Simultaneous Determination of Domperidone and Ilaprazole

International Journal of Pharmaceutical Research ◽

10.31838/ijpr/2020.12.01.258 ◽

2020 ◽

Vol 12 (01) ◽

Keyword(s):

Simultaneous Determination ◽

Derivative Spectrophotometry ◽

Order Derivative ◽

First Order

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Development and Validation of Derivative Spectroscopic Method for Simultaneous Estimation of Cefadroxil and Probenecid

International Journal of Pharmaceutical Sciences and Nanotechnology ◽

10.37285/ijpsn.2014.7.1.6 ◽

2014 ◽

Vol 7 (1) ◽

pp. 2350-2355

Author(s):

Pratik S Mehta ◽

Pratik R. Patel ◽

Rajesh R Parmar ◽

M M K Modasiya ◽

Dushyant A Shah

Keyword(s):

Spectroscopic Method ◽

Spectral Interference ◽

Synthetic Mixture ◽

Simultaneous Estimation ◽

Zero Crossing ◽

First Order ◽

Derivative Spectroscopy ◽

Development And Validation ◽

Crossing Point

A novel, simple, accurate, sensitive, precise and economical derivative spectroscopic method was developed and validated for the determination of cefadroxil and probenecid in synthetic mixture. First order derivative spectroscopy method was adopted to eliminate spectral interference. The method obeys Beer’s Law in concentration ranges of 4-36 μg/ml for cefadroxil and of 5-25 μg/ml of probenecid. The zero crossing point for cefadroxil and probenecid was 260 nm and 237.8 nm respectively in 0.1N HCl. The method was validated in terms of accuracy, precision, linearity, limits of detection, limits of quantitation. This method has been successively applied to synthetic mixture and no interference from the synthetic mixture’s excipients was found.

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A general treatment for the kinetics of two consecutive irreversible first-order reactions. Determination of rate constants for the tin(II)-ion catalysed esterification of alkali metal carboxybenzenesulphonates with ethylene glycol

Collection of Czechoslovak Chemical Communications ◽

10.1135/cccc19781907 ◽

1978 ◽

Vol 43 (7) ◽

pp. 1907-1916 ◽

Cited By ~ 4

Author(s):

Lubomír Nondek ◽

Jaroslav Málek

Keyword(s):

Alkali Metal ◽

Ethylene Glycol ◽

Rate Constants ◽

General Treatment ◽

First Order ◽

Kinetics Of

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DETERMINATION OF Pd(II) AND Rh(III) IN SILICATE ROCKS BY DIRECT AND FIRST-ORDER DERIVATIVE SPECTROPHOTOMETRY

Spectroscopy Letters ◽

10.1081/sl-120016283 ◽

2002 ◽

Vol 35 (6) ◽

pp. 821-834 ◽

Cited By ~ 2

Author(s):

A. Youssef El-Sayed

Keyword(s):

Derivative Spectrophotometry ◽

Order Derivative ◽

First Order ◽

Silicate Rocks

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UV Spectrophotometric Simultaneous Determination of Paracetamol and Ibuprofen in Combined Tablets by Derivative and Wavelet Transforms

The Scientific World JOURNAL ◽

10.1155/2014/313609 ◽

2014 ◽

Vol 2014 ◽

pp. 1-13 ◽

Cited By ~ 4

Author(s):

Vu Dang Hoang ◽

Dong Thi Ha Ly ◽

Nguyen Huu Tho ◽

Hue Minh Thi Nguyen

Keyword(s):

Simultaneous Determination ◽

Wavelet Transforms ◽

Hybrid Approach ◽

Uv Spectra ◽

Order Derivative ◽

First Order ◽

Spectrophotometric Methods ◽

Combined Use ◽

Linear Concentration

The application of first-order derivative and wavelet transforms to UV spectra and ratio spectra was proposed for the simultaneous determination of ibuprofen and paracetamol in their combined tablets. A new hybrid approach on the combined use of first-order derivative and wavelet transforms to spectra was also discussed. In this application, DWT (sym6 and haar), CWT (mexh), and FWT were optimized to give the highest spectral recoveries. Calibration graphs in the linear concentration ranges of ibuprofen (12–32 mg/L) and paracetamol (20–40 mg/L) were obtained by measuring the amplitudes of the transformed signals. Our proposed spectrophotometric methods were statistically compared to HPLC in terms of precision and accuracy.

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