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The problem of multi-objective H2/H-infinity optimal controller design is reviewed. There is as yet no exact solution to this problem. We present a method based on that proposed by Scherer. The proble...
Review of Mathematical Control Theory: Deterministic Finite-Dimensional Systems, by E. Sontag. Published by Springer, New York, 1990, as number 6 of series Textbooks in Applied Mathematics.
The problem of multi-objective H2/H-infinity optimal controller design is reviewed. There is as yet no exact solution to this problem. We present a method based on that proposed by Scherer. The proble...
The goal of this paper is to derive a formula for the finite dimensional joint characteristic function (the Fourier transform of the finite dimensional distribution) of the coupled process ${(W_{t},L_...
We present a finite-dimensional version of the quantum model for the stock market proposed in [C. Zhang and L. Huang, A quantum model for the stock market, Physica A 389(2010) 5769]. Our approach is a...
Finite W-algebras are certain associative algebras arising in Lie theory. Each W-algebra is constructed from a pair of a semisimple Lie algebra g (our base field is algebraically closed and of charact...
Abstract: We prove the Lefschetz property for a certain class of finite-dimensional Gorenstein algebras associated to matroids. Our result implies the Sperner property of the vector space lattice. We ...
Abstract: In this paper we present Affine.m - program for computations in representation theory of finite-dimensional and affine Lie algebras and describe implemented algorithms. Algorithms are based ...
Abstract: Generalized uncertainty principle and breakdown of the spacetime continuum certainly represent two important results derived of various approaches related to quantum gravity and black hole p...
In recent studies, properties of the set of affine maps between two convex sets have been investigated with intensive motivation from quantum physics, but in those preceding works the underlying con...
Let A be a connected commutative C-algebra with derivation D,G a finite linear automorphism group of A which preserves D, and R = AG the fixed point subalgebra of A under the action of G. We show that...
Consider an automorphism group of a finite-dimensional algebra. S. Halperin conjectured that the unity component of this group is solvable if the algebra is a complete intersection.
We introduce and study families of finite-dimensional Hopf algebras with the Chevalley property arising as twistings of quantum linear spaces. These Hopf algebras generalize the examples introduced in...
We consider a hydrodynamic system that models the Smectic-A liquid crystal flow. The model consists of the Navier-Stokes equation for the fluid velocity coupled with a fourth-order equation for the la...
We construct finite-dimensional approximations of solution spaces of divergence form operators with $L^\infty$-coefficients. Our method does not rely on concepts of ergodicity or scale-separation, but...

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