On the cost of fast controls for some families of dispersive or parabolic equations in one space dimension

In this paper, we consider the cost of null controllability for a large class of linear equations of parabolic or dispersive type in one space dimension in small time. By extending the work of Tenenbaum and Tucsnak in "New blow-up rates for fast controls of Schr\"odinger and heat equations`", we are able to give precise upper bounds on the time-dependance of the cost of fast controls when the time of control T tends to 0. We also give a lower bound of the cost of fast controls for the same class of equations, which proves the optimality of the power of T involved in the cost of the control. These general results are then applied to treat notably the case of linear KdV equations and fractional heat or Schr\"odinger equations

The Econometric Specification of Input Demand Systems Implied by Cost Function Representations

In the case of input demand systems based on specification of technology by a Translog cost function, it is common to estimate either a system of share equations alone, or to supplement them by the cost function. By adding up, one of the share equations is excluded. In this paper it is argued that a system of n-1 share equations is essentially incomplete, whereas if the n-1 share equations are supplemented by the cost function the implied error structure is inadmissible. Similarly, if the technology is specified by a normalized quadratic cost function, it is common to estimate either a system of n-1 demand equations alone, or to supplement them by the cost function. In both cases, the implied error structure is again inadmissible.Cost Function; Input demands; Share equations; Translog; Normalized Quadratic; Error specification.

Development of weight and cost estimates for lifting surfaces with active controls

Equations and methodology were developed for estimating the weight and cost incrementals due to active controls added to the wing and horizontal tail of a subsonic transport airplane. The methods are sufficiently generalized to be suitable for preliminary design. Supporting methodology and input specifications for the weight and cost equations are provided. The weight and cost equations are structured to be flexible in terms of the active control technology (ACT) flight control system specification. In order to present a self-contained package, methodology is also presented for generating ACT flight control system characteristics for the weight and cost equations. Use of the methodology is illustrated

EXPLORING ALTERNATIVES FOR ESTIMATING SYSTEMS OF EQUATIONS WITH MULTIPLE CENSORED VARIABLES: FARM OUTPUT SUPPLY AND INPUT DEMAND

This paper explores two alternatives for estimating systems of equations with multiple censored variables: Maximum Simulated Likelihood and a two-step technique that seems to be well suited for large samples. The empirical part of the paper estimates a system of cost, cost shares and revenue shares equations of Italian farms using both approaches.Research Methods/ Statistical Methods,

COPTRAN - A method of optimum communication systems design

Single set of mathematical expressions describes system cost and probability of error of data transmission in terms of four basic parameters in the link equation. A Lagrange multiplier sets up equations whose solutions yield the optimum values for system design considerations and weight and cost values

IMPOSING REGULARITY CONDITIONS ON A SYSTEM OF COST AND FACTOR SHARE EQUATIONS

Systems of equations comprising cost functions and first-order derivative equations are often used to estimate characteristics of production technologies. Unfortunately, many estimated systems violate the regularity conditions implied by economic theory. Sampling theory methods can be used to impose these conditions globally, but these methods destroy the flexibility properties of most functional forms. We demonstrate how Bayesian methods can be used to maintain flexibility by imposing regularity conditions locally. The Bayesian approach is used to estimate a system of cost and share equations for the merino-woolgrowing sector. The effect of local imposition of monotonicity and concavity on the signs and magnitudes of elasticities is examined.Cost functions, Markov Chain Monte Carlo, inequality constraints, Demand and Price Analysis,