Wiener method

The solution was first obtained independently by Wertheim [32] and Thiele [33] using Laplace transfonns. Subsequently, Baxter [34] obtained the same solutions by a Wiener-Hopf factorization teclmique. This method has been generalized to charged hard spheres. 

Figure C3.5.6 compares the result of this ansatz to the numerical result from the Wiener-Kliintchine theorem. They agree well and the ansatz exliibits the expected exponential energy-gap law (VER rate decreases exponentially with Q). The ansatz was used to detennine the VER rate with no quantum correction Q= 1), with the Bader-Beme hannonic correction [61] and with a correction based [83, M] on Egelstaff s method [62]. The Egelstaff corrected results were within a factor of five of experiment, whereas other corrections were off by orders of magnitude. This calculation represents the present state of the art in computing VER rates in such difficult systems, inasmuch as the authors used only a model potential and no adjustable parameters. However the ansatz procedure is clearly not extendible to polyatomic molecules or to diatomic molecules in polyatomic solvents.

Duduchava R., Wendland W. (1995) The Wiener-Hopf method for system of pseudodifferential equations with applications to crack problems. Integr. Eqs. and Oper. Theory 23, 294-335. 

The Wiener filter therefore avoids noise amplification and provides the best solution according to some quality criterion. We will see that these features are common to all other methods which correctly solve the deconvolution inverse problem. The result of applying Wiener inverse-filter to the simulated image is shown in Fig. 3b. 

Among many theoretical approaches, the quantitative structure-property/ activity relationships (QSPR/QSAR) methods in conjunction with experimental data pave the way to characterization of properties of new compounds. Properly calibrated such methods provide tools for the prediction of physicochemical parameters (QSPR) and/or biological activity (QS AR) for substances, which have not been yet examined in experiments (Wiener, 1947a, b, 1948a, b Randic and Basak, 1999, 2001 Randic and Pompe, 2001a, b Basak et al., 2001). 

Wiener MC. 2004. A pedestrian guide to membrane protein crystallization. Methods 34 364-372. 

The proposed technique is based on an extension to time-varying systems of Wiener s optimal filtering method (l-3). The estimation of the corrected chromato gram is optimal in the sense of minimizing the estimation error variance. A test for verifying the results is proposed, which is based on a comparison between the "innovations" sequence and its corresponding expected standard deviation. The technique is tested on both synthetic and experimental examples, and compared with an available recursive algorithm based on the Kalman filter ( ). 

We now give a brief description of a new expansion which is more accurate for Z(p). It is based on a suggestion of Feynman and Hibbs4 who calculated the Wiener integral corresponding to the first term in this expansion. Our method of calculation uses probability techniques and treats both the Wiener and Uhlenbeck-Ornstein processes. In the latter case we first rewrite Eq. (20) in the form... 

Certainly the most popular methods for noise reduction in audio signals to date are based upon short-time Fourier processing. These methods, which can be derived from non-stationary adaptations to the frequency-domain Wiener filter, are discussed fully in section 4.5.1. 

Bmckel J, Kerner W, Zier H, Steinbach G, Pfeiffer EF. In vivo measurement of subcutaneous glucose concentrations with an enzymatic glucose sensor and a wick method. Wiener Klinische Wochenschrift 1989, 67, 491 495. 

The wave lengths of electrons are so short that it is not possible to perform experiments like Young s or Wiener s experiments with them. The method by which Davisson established the wave aspect of electrons was similar to that used... 

Wiener, M. C. and White, S. H. (1991b). Fluid bilayer stmcture determination by the combined use of x-ray and neutron diffraction II. Composition space refinement method. Biophys. J. 59 174. 

This is the approximation of a Wiener variable, which renders the system (4.3) a coupled Langevin system. The correlation function for F is therefore of the character of a diffusion coefficient, and the system can be solved by standard Lagrangian methods. 

Savage DF, Anderson CL, Robles-Cohnenares Y, Newby ZE, Stroud RM. Cell-free complements in vivo expression of the E. coli membrane proteome. Protein Sci. 2007 16 966-976. Wiener MC. A pedestrian guide to membrane protein crystallization. Methods 2004 34 364-372. 

The same method based on the bond contribution w for the Wiener index calculation was proposed by Pisanski-Zerovnik [Pisanski and Zerovnik, 1994] together with a more general edge weight iv based on paths, defined as ... 

Gutman, I. (1993a). A New Method for the Calculation of the Wiener Number of Acyclic Molecules. J.Mol.Struct.(Theochem), 285,137-142. 

Gutman, I. (1993b). Calculating the Wiener Number The Doyle-Graver Method. J.Serb.Chem. Soc., 58, 745-750. 

Wiener, M. C. 2004. A pedestrian guide to membrane protein crystallization. Methods A Companion to Methods in Enzymology, Macromolecular Crystallization (ed. A. McPherson) 34(3), 364—372. 

Wiener K. A review of methods for plasma paracetamol estimation. Ann CBn Biochem 1978 15 187-96. 

M Verhaegen and D Westwick. Identifying MIMO Wiener systems using subspace model identification methods. In Proc. of Sfth Conf. on Decision and Control, number FP14, 1995. 

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