Search results for "calculus"

Calculus of Contextual Rough Sets in Contextual Spaces

1998

ABSTRACT The palier explains the methods of approximation of set which were earlier put forth by the authors (1995a, 1995b) and by W. Marek and H. Rasiowa (1986). An essential part of this paper is devoted to the presentation of a certain calculus of rough sets and contextual rough sets in contextual spaces.

Comparison of theory and experiment

1991

In this section we are finally going to confront experimental data on total cross section, angular distributions and polarization observables with theoretical results in order to establish the present status of our knowledge of this important process. We hope this will enable us to set directions and guidelines for future experimental and theoretical studies, which kind of experiments are needed and what accuracy should be aimed for, where theoretical studies should be extended, on what they should focus and whether some basic assumptions need to be modified. For the comparison we shall use mostly the data of experiments selected in sections 6.3 and 6.4, the relative quantities and the best…

Setpoints compensation in industrial processes via multirate output feedback control

2013

This paper investigates the setpoints compensation for a class of complex industrial processes. Plants at the device layer are controlled by the local regulation controllers, and a multirate output feedback control approach for setpoint compensation is proposed such that the subsystems can reach the dynamically changed setpoints and the given economic objective can also be tracked via certain economic performance index (EPI). First, a sampled-data multivariable direct output feedback proportional integral (PI) controller is designed to regulate the performance of the subsystems. Second, the outputs and control inputs of the plants at the device layer are sampled at operation layer sampling …

Vibrations of elastic structures with external nonlinear visco-elastic damping devices

2011

A technique for the dynamic identification of civil systems

2012

A statistical moments based approach for the dynamic identification of civil structures

2012

In recent years, interest in developing identification techniques that are valid in the case of unmeasured input has increased. In this field some interesting parametric approaches have been proposed. Nevertheless, the improvement of the available techniques or the formulation of new techniques is desirable. In this paper a time domain dynamic identification approach based on the statistical moments of the response of civil structures under base random excitations is discussed. Two types of models are used: the classically damped models characterized by mass proportional damping and the so-called “potential models” which are non linear in damping and stiffness. By applying the Itô different…

Fractional calculus application to visco-elastic solid

2009

It is widely known that fractional derivative is the best mathematical tool to describe visco-elastic constitutive law. In this paper it is shown that as soon as we assume the creep compliance function as power law type, as in the linearized version of the Nutting equation, then the fractional constitutive law appears in a natural way. Moreover, using Nutting equation for the creep function, the relaxation modulus is also of power law type whose coefficients (intensity and exponent) are strictly related to those of the creep compliance. It follows that by a simple creep test (or relaxation test) by means of a best fitting procedure we may easily evaluate the parameters of Nutting equation a…

Prestress and experimental tests on fractional viscoelastic materials

2013

Creep and/or Relaxation tests on viscoelastic materials show a power-law trend. Based upon Boltzmann superposition principle the constitutive law with a power-law kernel is ruled by the Caputo’s fractional derivative. Fractional constitutive law posses a long memory and then the parameters obtained by best fitting procedures on experimental data are strongly influenced by the prestress on the specimen. As in fact during the relaxation test the imposed history of deformation is not instantaneously applied, since a unit step function may not be realized by the test machine. Aim of this paper, it is shown that, the experimental procedure, and in particular the initial ramp to reach the constan…

Nonlinear fuzzy control of a fed-batch reactor for penicillin production

2012

Abstract The process of penicillin production is characterized by nonlinearities and parameter uncertainties that make it difficult to control. In the paper the development and testing of a multivariable fuzzy control system that makes use of type-2 fuzzy sets for the control of pH and temperature are described. The performance of the type-2 fuzzy logic control system (T2FLCS) is compared by simulation with that of a type-1 fuzzy logic control system (T1FLCS) and that of a control system with traditional proportional-integral-derivative (PID) controllers proposed in the literature. The fuzzy controllers are optimized using an ANFIS algorithm. The best results are obtained with the T2FLCS pa…

Parametric Natura Morta

2018

Parametric equations can also be used to draw fruits, shells, and a cornucopia of a mathematical still life. Simple mathematics allows the creation of a variety of shapes and visual artworks, and it can also constitute a pedagogical tool for students.