QUALITATIVE AND QUANTITATIVE ANALYSIS OF STOCHASTIC PROCESSES BASED ON MEASURED DATA, II: APPLICATIONS TO EXPERIMENTAL DATA

Analysis of stochastic processes governed by the Langevin equation is discussed. The analysis is based on a general method for non-parametric estimation of deterministic and random terms of the Langevin equation directly from given data. Separate estimation of the terms corresponds to the decomposition of process dynamics into deterministic and random components. Part I of the paper presented several possibilities for qualitative and quantitative analysis of process dynamics based on such decomposition. In Part II, some of these analysis possibilities are applied to experimental datasets from metal cutting and laser-beam welding.     

Control of a liquid–liquid heat exchanger

 The analytical solutions of equations describing the dynamics of distributed parameter systems are usually complicated in form and derivations and inconvenient to use for simulation and control system design. The liquid–liquid counter flow heat exchanger is an example of these disturbed parameter systems. An analytical solution of the dynamics of a symmetrically operated counter flow heat exchanger in the form of transfer function matrix is investigated in open-loop and close-loop conditions. The resulting non-linear model was linearized using perturbation approach. A feed-forward path controller to counteract at any disturbances in the boundary temperature and a non-interactive controller to decouple the outputs were implemented. Received on 22 February 2001 / Published online: 29 November 2001     

Zinc-Containing Polymers and Their Latexes: Structure and Properties

This work deals with the polymer latexes synthesized using zinc-containing monomers. The effect of the ligand environment of the zinc-containing monomers on the colloidal and rheological properties of the latexes, as well as on mechanical properties of their films is studied. Mixed zinc salts containing the residues of saturated and unsaturated carboxylic acids are shown to be more efficient cross-linking agents than the symmetric salts of this metal.     

Aeolian Tones of a Honeycomb Lattice Cell

Aeroacoustic resonant oscillations (aeolian tones) are studied for flow past two plates forming a cross in a square cross section channel. Possible oscillation modes are classified on the basis of admissible symmetry groups and the existence of the modes is proved. The infinite linear system of equations for these modes obtained by the sewing method was simplified and studied numerically. Curves of eigenfrequency versus plate length are constructed. The form of the eigenfunctions is studied.     

A parametric representation of linguistic hedges in Zadeh’s fuzzy logic

This paper proposes a model for the parametric representation of linguistic hedges in Zadeh’s fuzzy logic. In this model each linguistic truth-value, which is generated from a primary term of the linguistic truth variable, is identified by a real number r depending on the primary term. It is shown that the model yields a method of efficiently computing linguistic truth expressions accompanied with a rich algebraic structure of the linguistic truth domain, namely De Morgan algebra. Also, a fuzzy logic based on the parametric representation of linguistic truth-values is introduced.     

A new monitoring system of cultured myocardial cell motion: effect of pilose antler extract and cardioactive agents on spontaneous beating of myocardial cell sheets

Effects of various cardioactive agents and a water extract of the pilose antler of Cervus nippon var. mantchuricus on periodic beating of cultured myocardial cell sheets were examined by using an image analyzing system. Norepinephrine increased the beating rate and the beating amplitude, whereas digoxin and forskolin enlarged only the beating amplitude. Verapamil and propranolol decreased both the beating rate and the beating amplitude. The water extract of the pilose antler showed no remarkable effects in a standard medium (2.1 mM Ca2+). However, it significantly increased the beating amplitude when the beating was suppressed by replacement with a low calcium medium (0.5 mM Ca2+). A similar effect was found for 70% ethanol-soluble and -insoluble fractions of the extract.     

Unified approach to best unbiased estimation in control problems and linear models

An analog of a sufficient statistic is proposed in the finite-dimensional linear space of statistics. It is shown that the unbiased estimator of the linear function of a parameter closest to a given function, expressed in terms of a minimal linearly sufficient statistic, is potentially unbiased and optimal.Translated from Statisticheskie Metody Otsenivaniya i Proverki Gipotez, pp. 51–58, 1986.     

Scientific heritage of Boris Lukich Laptev (4/23/05–1/15/89)

Biographical information on the eminent Soviet geometer Boris Lukich Laptev (4/23/05–1/15-89) is given as well as a survey of his research in the areas of differential geometry and history of mathematics.Translated from Itogi Nauki i Tekhniki, Seriya Problemy Geometrii, Vol. 21, pp.27–42, 1989.