Operator-valued multivariable Bohr type inequalities are obtained for: (i) a class of noncommutative holomorphic functions on the open unit ball of B(H)n, generalizing the analytic functions on the open unit disc; (ii) the noncommutative disc algebra An and the noncommutative analytic Toeplitz algebra F∞ n ; (iii) a class of noncommutative selfadjoint harmonic functions on the open unit ball of...

Abstract. By multidimensional matrix inversion, combined with an Ar extension of Jackson’s 8φ7 summation formula by Milne, a new multivariable 8φ7 summation is derived. By a polynomial argument this 8φ7 summation is transformed to another multivariable 8φ7 summation which, by taking a suitable limit, is reduced to a new multivariable extension of the nonterminating 6φ5 summation. The latter is ...

an attempt has been made in this paper to investigate the effect of particle size distribution on coal flotation kinetics. the effect of particle size (ps) on kinetics constant (k) and maximum theoretical flotation recovery (ri) was investigated while other operational parameters were kept constant. the relationship between flotation kinetics constant and theoretical flotation recovery with par...

The problem of tracking a reference vector variable from a given class is considered for discrete-time linear multi-input-output plants. The plant and the reference are both described by an input/output relation and the objective is to track exactly in a minimum number of steps. The optimal control law is shown to contain both feedback and feedforward terms and it is obtained by solving only th...

Multivariable Appell functions show up in the work of Kac and Wakimoto in the computation of character formulas for certain s`(m, 1)∧ modules. Recently Bringmann and Ono showed that the character formulas for the s`(m, 1)∧ modules L(Λ(s)), where L(Λ(s)) is the irreducible s`(m, 1) ∧ module with highest weight Λ(s), can be seen as the “holomorphic parts” of certain nonholomorphic modular functio...

[ I j M. Athans and P. Falb. Optimal Corzrrol. New York: McGrawHill, 1966. [2j D. L. Kleinman and M. Athans. "The design of suboptimal linear time-varying systems." I E E E Trans. Automatic Corm.. vol. AC-13, pp. 150-158. April 1968. [3j T. Chen, "Sensitivity analysis and optimum design of multivariable regulators with application to VTOL aircraft stabilization," Ph.D. dissertation, Universit...

The multivariable feedback system tracking error is related to the sensitivity matrix S = [I + L]–1and to the uncertainty of plant and instrumentation. The ‘popular' highly interacting 2×2 distillation column problem is solved in a novel manner.

Utility functions of several variables are ubiquitous in economics. Their maximization requires inversion of the gradient map. Using convex analysis tools, we provide a representation of an extension of this inverse that accounts for possible constraints. To solve economic equilibrium problems, the utility functions of the agents are frequently aggregated into a representative (agent’s) utility...

In this paper we give a critical overview of recent development in MIMO control performance monitoring. We discuss a number of MIMO control benchmarks including minimum variance, LQG, and user selected benchmarks. Performance measures are extended from variance based measures in SISO control to covariance based measures in MIMO control. Pros and cons of various benchmarks are discussed. The dia...