By Peter Whittle
The concept that of a process as an entity in its personal correct has emerged with expanding strength long ago few a long time in, for instance, the components of electric and regulate engineering, economics, ecology, city constructions, automaton idea, operational learn and undefined. The extra convinced notion of a large-scale procedure is implicit in those functions, yet is especially glaring in fields corresponding to the examine of verbal exchange networks, laptop networks and neural networks. The Wiley-Interscience sequence in platforms and Optimization has been tested to serve the wishes of researchers in those speedily constructing fields. it really is meant for works serious about advancements in quantitative platforms thought, purposes of such conception in components of curiosity, or linked method. this can be the 1st book-length therapy of risk-sensitive regulate, with many new effects. The quadratic rate functionality of the normal LQG (linear/quadratic/Gaussian) remedy is changed through the exponential of a quadratic, giving the so-called LEQG formula making an allowance for a level of optimism or pessimism at the a part of the optimiser. the writer is the 1st to accomplish formula and facts of risk-sensitive models of the certainty-equivalence and separation rules. extra research permits one to formulate the optimization because the extremization of a direction quintessential and to signify the answer by way of canonical factorization. it truly is hence attainable to accomplish the long-sought aim of an operational stochastic greatest precept, legitimate for a higher-order version, and in reality merely glaring while the types are prolonged to the risk-sensitive classification. extra effects contain deduction of compact family members among price capabilities and canonical elements, the exploitation of the equivalence among coverage development and Newton Raphson tools and the direct relation of LEQG the way to the H??? and minimum-entropy equipment. This ebook will turn out crucial interpreting for all graduate scholars, researchers and practitioners who've an curiosity up to speed conception together with mathematicians, engineers, economists, physicists and psychologists. 1990 Stochastic Programming Peter Kall, collage of Zurich, Switzerland and Stein W. Wallace, college of Trondheim, Norway Stochastic Programming is the 1st textbook to supply an intensive and self-contained creation to the topic. rigorously written to hide all helpful history fabric from either linear and non-linear programming, in addition to likelihood concept, the publication attracts jointly the tools and methods formerly defined in disparate assets. After introducing the phrases and modelling concerns while randomness is brought in a deterministic mathematical programming version, the authors disguise determination bushes and dynamic programming, recourse difficulties, probabilistic constraints, preprocessing and community difficulties. routines are supplied on the finish of every bankruptcy. all through, the emphasis is at the acceptable use of the strategies, instead of at the underlying mathematical proofs and theories, making the e-book perfect for researchers and scholars in mathematical programming and operations study who desire to enhance their abilities in stochastic programming. 1994
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Example text
For example, the following function takes two arguments and returns their product: prod :: Integer -> Integer -> Integer prod x y = x*y A full application is an expression giving prod all of its arguments: for example, prod 4 5 ⇒ 20. However, the partial application prod 4 supplies just one argument, and the result of this is a new function that takes a number and multiplies it by 4. For example, suppose the following equations are defined in the script file: g = prod 4 p = g 6 q = twice g 3 Then p ⇒ 24, and q ⇒ 48.
The second style is becoming standard for research papers. In doing your own proofs, you may use whichever style you prefer, although it’s important to be able to read both styles. The example above is just elementary mathematics, but exactly the same technique can be used to reason about Haskell programs, because equations in Haskell are true mathematical equations—they are not assignment statements. 2 Equational Reasoning as Hand-execution An important skill for all programmers is hand execution: taking a program and its data, and working out by hand what the result should be.
Polymorphism is a very important invention because it makes it easier to reuse programs. 8 Common Functions on Lists Haskell provides a number of operations on lists. A few of the most important ones are presented in this section. We will have more to say about these functions later in the book, where we will use them in a variety of practical applications, show how they are implemented, and prove theorems stating some of their mathematical properties. ] =>