Linear Functional Systems Research Articles

Fractal approximation of the stress-strain curve of frozen soil

A method to approach the stress-strain curve of frozen soil is presented based on the fact that the stressstrain curve of frozen soil has fractal property. First, a linear hyperbolic iterated function system (LHJB) in which the perpendicular contraction factors are regarded as parameters is established using fractal geometry theories. Secondly, a method to calculate the best point which makes the attractor of the LHIFS an optimal approximation of the stress-strain curve of frozen soil is presented. Then, a method for calculating the fractal dimension of the stress-strain curve of frozen soil is obtained. Finally, a simple example is provided. The method presented in this paper provides a new method for simulating the stress-strain curve and calculating its fractal dimension of geomaterials that have the fractal feature by using computer

EG-eliminations*

We propose an algorithm to put linear recurrent systems in a form which is convenient for using the systems to search for polynomial, power series, Laurent series, and other types of solutions of various linear functional systems (differential,difference and q-difference). Some algorithms to search for solutions of functional systems are described. None of the proposed algorithms requires preliminary uncoupling of linear systems

Sampled-analog implementation of application-specific fuzzy controllers

Sampled-analog circuit techniques are exploited in an application-specific integrated fuzzy controller design. A circuit library comprising a sample-and-hold amplifier, positive and negative ramp amplifiers, an inference cell, adder, and weighted adder amplifiers, and a divider unit was developed for this purpose. Any expert system of piecewise linear input membership functions, conjunctive rules and singleton output classes can be implemented with this library. The library was implemented in a 1.2 /spl mu/m double-metal double-poly CMOS technology. Test results indicate excellent linearity and accuracy in full 5 V rail-to-rail operation in all units. A controller of four inputs, 16 rules, and two outputs fabricated with these library units occupies 1.76 mm/sup 2/ silicon. Test results indicate full functionality. The measured speed, 85 k samples per second, is limited by the unbuffered outputs. Sampling rate can be increased by 50% in those applications where pipelining is permissible.

A third order optimum property of the ML estimator in a linear functional relationship model and simultaneous equation system in econometrics

The maximum likelihood (ML) estimator and its modification in the linear functional relationship model with incidental parameters are shown to be third-order asymptotically efficient among a class of almost median-unbiased and almost mean-unbiased estimators, respectively, in the large sample sense. This means that the limited information maximum likelihood (LIML) estimator in the simultaneous equation system is third-order asymptotically efficient when the number of excluded exogenous variables in a particular structural equation is growing along with the sample size. It implies that the LIML estimator has an optimum property when the system of structural equations is large.

Structure of the class of linear functional time systems under output feedback transformation

In this paper, we discuss from a qualitative and unified viewpoint the change of system behaviour produced by output feedback primarily to clarify mutual relationships between systems under feedback transformation. We first define the class of all linear functional time systems that are characterized by four system-theoretic properties. Next we define feedback as an operation on a class of systems and discuss the change of system behaviour produced by feedback as a system transformation either between two classes of system or within one class of system. Finally we clarify the structure of a class under feedback transformation in terms of system-theoretic concepts. We obtain three major results which provide a theoretical basis for systems science: (1) we specified the subclass of linear systems on which the feedback transformation can be well defined; (2) we characterize a relation between the system transformation under dynamic output feedback and that under static output feedback; (3) we show that the subclass consisting of all symmetric systems is closed under dynamic output feedback transformation.

Linear demand functions in theory and practice

Integrability conditions for an incomplete system of linear demand functions are considered. The parameter restrictions consistent with integrability are identified, and the structure of the conditional preference map is obtained. It is found that the conditional preferences for a set of linear demand functions are either quadratic or Leontief from a translated origin. Welfare analysis with linear demand models is also considered.

Holomorphic solutions of functional differential systems near singular points

Functional analysis techniques are used to prove a theorem, analogous to the Harris-Sibuya-Weinberg theorem for ordinary differential equations, which yields as corollaries a number of existence theorems for holomorphic solutions of linear functional differential systems of the form z D y ′ ( z ) = A ( z ) y ( z ) + B ( z ) y ( α z ) + C ( z ) y ′ ( α z ) {z^D}y’(z) = A(z)y(z) + B(z)y(\alpha z) + C(z)y’(\alpha z) in the neighborhood of the singularity at z = 0 z = 0 .