Application of Mathieu functions for the study of non-slanted reflection gratings

In this work we prensent an analysis of non-slanted reflection gratings by using exact solution of the second order differential equation derived from Maxwell equations, in terms of Mathieu functions. The results obtained by using this method will be compared to those obtained by using the well known Kogelnik's Coupled Wave Theory which predicts with great accuracy the response of the efficieny of the zero and first order for volume phase gratings, for both reflection and transmission gratings.

Mathematical programming model for heat exchanger design through optimization of partial objectives

Mathematical programming can be used for the optimal design of shell-and-tube heat exchangers (STHEs). This paper proposes a mixed integer non-linear programming (MINLP) model for the design of STHEs, following rigorously the standards of the Tubular Exchanger Manufacturers Association (TEMA). Bell–Delaware Method is used for the shell-side calculations. This approach produces a large and non-convex model that cannot be solved to global optimality with the current state of the art solvers. Notwithstanding, it is proposed to perform a sequential optimization approach of partial objective targets through the division of the problem into sets of related equations that are easier to solve. For each one of these problems a heuristic objective function is selected based on the physical behavior of the problem. The global optimal solution of the original problem cannot be ensured even in the case in which each of the sub-problems is solved to global optimality, but at least a very good solution is always guaranteed. Three cases extracted from the literature were studied. The results showed that in all cases the values obtained using the proposed MINLP model containing multiple objective functions improved the values presented in the literature.

Behaviours, Processes and Probabilistic Environmental Functions in H-Open Systems

The Patten’s Theory of the Environment, supposes an impotent contribution to the Theoretical Ecology. The hypothesis of the duality of environments, the creaon and genon functions and the three developed propositions are so much of great importance in the field of the Applied Mathematical as Ecology. The authors have undertaken an amplification and revision of this theory, developing the following steps: 1) A theory of processes. 2) A definition of structural and behavioural functions. 3) A probabilistic definition of the environmental functions. In this paper the authors develop the theory of behavioural functions, begin the theory of environmental functions and give a complementary focus to the theory of processes that has been developed in precedent papers.

Theory of functions of a real variable.

Mode of access: Internet.

Statistical decision functions.

Mode of access: Internet.

Minimization of switching networks using negative functions

Bibliography: p. 46.

The Princeton colloquium; lectures on mathematics, delivered September 15 to 17, 1909, before members of the American Mathematical Society in connection with the summer meeting held at Princeton University, Princeton, N. J

Mode of access: Internet.

Cohomology operations and obstructions to extending continuous functions /

"Work supported in part by U.S. Air Force Contract AF 18 (600)-1494."

A course in mathematical analysis.

An unabridged and unaltered republication of the Hedrick-Dunkel translation (v. 1-2); v. 3. newly translated by Howard G. Bergmann.

On the automorphic functions of the group (0, 3; £, £, £) ...

"Reprinted from the Transactions of the American Mathematical Society, vol. 7, no. 3 ... July, 1906."

A course in mathematical analysis,

Vol. II translated by Earle Raymond Hedrick and Otto Dunkel, published in 2 parts.

The Princeton Colloquium; lectures on mathematics, delivered September 15 to 17, 1909, before members of the American Mathematical Society in connection with the summer meeting held at Princeton University, Princeton, N.J.

Fundamental existence theorems, by G. A. Bliss.--Differential-geometric aspects of dynamics, by E. Kasner.

Utility functions on locally connected spaces

We investigate the role of local connectedness in utility theory and prove that any continuous total preorder on a locally connected separable space is continuously representable. This is a new simple criterion for the representability of continuous preferences, and is not a consequence of the standard theorems in utility theory that use conditions such as connectedness and separability, second countability, or path-connectedness. Finally we give applications to problems involving the existence of value functions in population ethics and to the problem of proving the existence of continuous utility functions in general equilibrium models with land as one of the commodities. (C) 2003 Elsevier B.V. All rights reserved.

Extremal circular permutations with concave functions

Let {a(1), a(2), ..., a(n)} be a set of n distinct real numbers and let alpha(1), alpha(2), ..., alpha(n) an be a permutation of the numbers. We construct the permutation to maximise L-f = Sigma(i=1)(n) f(\alpha(i+1) - alpha(i)\), for any increasing concave function f, where we denote alpha(n+1) equivalent to alpha(1). The optimal permutation depends on the particular numbers {a(1), a(2), ..., a(n)} and the function f, contrary to a postulate by Chao and Liang (European J. Combin. 13 (1992) 325). (C) 2004 Elsevier Ltd. All rights reserved.

A Bayesian approach to imposing curvature on distance functions

The estimated parameters of output distance functions frequently violate the monotonicity, quasi-convexity and convexity constraints implied by economic theory, leading to estimated elasticities and shadow prices that are incorrectly signed, and ultimately to perverse conclusions concerning the effects of input and output changes on productivity growth and relative efficiency levels. We show how a Bayesian approach can be used to impose these constraints on the parameters of a translog output distance function. Implementing the approach involves the use of a Gibbs sampler with data augmentation. A Metropolis-Hastings algorithm is also used within the Gibbs to simulate observations from truncated pdfs. Our methods are developed for the case where panel data is available and technical inefficiency effects are assumed to be time-invariant. Two models-a fixed effects model and a random effects model-are developed and applied to panel data on 17 European railways. We observe significant changes in estimated elasticities and shadow price ratios when regularity restrictions are imposed. (c) 2004 Elsevier B.V. All rights reserved.