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 ...

Batch and continuous systems are of multivariable in nature. A multivariable system is one in which one input not only affects its own outputs but also one or more other outputs in the plant. Multivariable processes are difficult to control due to the presence of the interactions. Increase in complexity and interactions between inputs and outputs yield degraded process behavior. Such processes ...

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...

This paper reports a comprehensive survey of well drilling time and cost. The models include both specific correlations on various types generalised for rough estimation. are derived from robust multivariable regression to minimise the residuals. Africa has highest construction cost component in United States lowest. Data regions compared with European World average data. Drilling Italy is simi...

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...