For multiple model adaptive control systems, “multi-controller” architecture can be efficiently implemented (multirealised) by means of a “state-shared” parameterdependent feedback system. Necessary and sufficient conditions for the multirealisation of a family of linear multivariable systems based on matrix fractional descriptions are presented. The problem of the minimal generic multirealisat...

The purpose of this study is to develop a new approach in modeling and simulation of a reverse osmosis desalination system by using fractional differential equations. Using the Legendre wavelet method combined with the decoupling and quasi-linearization technique, we demonstrate the validity and applicability of our model. Examples are developed to illustrate the fractional differential techniq...

This paper deals with a ratio-dependent functional response predator-prey model with a fractional order derivative. The ratio-dependent models are very interesting, since they expose neither the paradox of enrichment nor the biological control paradox. We study the local stability of equilibria of the original system and its discretized counterpart. We show that the discretized system, which is...

In the present paper, we use analytical techniques to solve fractional nonlinear differential equations systems that arise in Bergman’s minimal model, used to describe blood glucose and insulin metabolism, after intravenous tolerance testing. We also discuss the stability and uniqueness of the solution.

Address reprint requests to Dr. Richard N. Bergman, Department of Physiology and Biophysics, University of Southern California School of Medicine, Los Angeles, Calif. 90033. Received for publication 28 November 1980 and in revised form 17 August 1981. 1456 product ofsecond-phase ,-cell responsivity and insulin sensitivity (b2-SI). Thus, these two factors were primarily responsible for overall d...

Comparison results of the nonlinear scalar Riemann-Liouville fractional differential equation of order q, 0 < q ≤ 1, are presented without requiring Hölder continuity assumption. Monotone method is developed for finite systems of fractional differential equations of order q, using coupled upper and lower solutions. Existence of minimal and maximal solutions of the nonlinear fractional different...

We present an embedding of the three-dimensional relativistic Landau-Ginzburg model for condensed matter systems in an N = 6, U(N) × U(N) Chern-Simons-matter theory [the Aharony-Bergman-Jafferis-Maldacena model] by consistently truncating the latter to an Abelian effective field theory encoding the collective dynamics of O(N) of the O(N(2)) modes. In fact, depending on the vacuum expectation va...

The tropical variety defined by linear equations with constant coefficients is the Bergman fan of the corresponding matroid. Building on a self-contained introduction to matroid polytopes, we present a geometric construction of the Bergman fan, and we discuss its relationship with the simplicial complex of nested sets in the lattice of flats. The Bergman complex is triangulated by the nested se...

The Umehara algebra is studied with motivation on the problem of non-existence common complex submanifolds. In this paper, we prove some new results in and obtain applications. particular, if a manifolds admits holomorphic polynomial isometric immersion to one indefinite space form, then it cannot another form different type. Other consequences include submanifolds for projective or hyperbolic ...