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## Editorial Addresses

### Journal of Optimization Theory and Applications (1997-10-01) 95: 239-242 , October 01, 1997

## Preliminaries

### Haar Series and Linear Operators (1997-01-01) 367: 1-13 , January 01, 1997

Let (*S, F, μ)* be a measure space. Here S is a set, F is a *σ*-algebra, *µ* is a *σ*-finite measure on F. If *F*_{0} is a *σ*-subalgebra of F, *x**∈**L*_{1} (*(S*, *F*, *μ*), then denote by *E*_{Fo} the unique, up to equivalence, *F*_{0}-measurable function satisfying
for each *A ∈ F*_{0}. By the Radon — Nikodym theorem, such function exists. The function *E*_{Fo}*x =**E*_{Fo,μ}*x* is called the conditional expectation with respect to *F*_{0}.

## Batch Process Scheduling Using Simulated Annealing

### Bayesian Heuristic Approach to Discrete and Global Optimization (1997-01-01) 17: 245-259 , January 01, 1997

The problem is formulated in the Mixed Integer Bilinear Program (MIBLP) form (see Chapter 13) as in the previous chapter. A difference is that here we optimize the randomization procedure of Simulated Annealing type using the MIBLP penalty function as a part of heuristics. Another difference is that we describe the complete batch scheduling problem, not just illustrative example as in Section 14.3 of the last chapter.

## An Infeasible Point Method for Minimizing the Lennard-Jones Potential

### Computational Optimization and Applications (1997-11-01) 8: 273-286 , November 01, 1997

Minimizing the Lennard-Jones potential, the most-studied modelproblem for molecular conformation, is an unconstrained globaloptimization problem with a large number of local minima. In thispaper, the problem is reformulated as an equality constrainednonlinear programming problem with only linear constraints. Thisformulation allows the solution to approached through infeasibleconfigurations, increasing the basin of attraction of the globalsolution. In this way the likelihood of finding a global minimizeris increased. An algorithm for solving this nonlinear program isdiscussed, and results of numerical tests are presented.

## Conditional Expectations and Projection Maps of von Neumann Algebras

### Operator Algebras and Applications (1997-01-01) 495: 449-461 , January 01, 1997

Conditional expectations have been around in operator algebras for more than 40 years. They seem to be first studied by Umegaki [26] in 1954 and have been of increasing importance since then, especially after subfactor theory became a major topic in von Neumann algebras. There is no systematic treatment of the theory in the literature; the results are scattered appearing often as lemmas needed for other theorems. The present note will partly compensate for this in that its first part will be a rudimentary survey of the theory with the aim of classifying or rather relating conditional expectations to well-known special cases. In the second part we shall study the more general class of projection maps, i.e. idempotent, unital positive linear maps of von Neumann algebras into themselves. Such maps are conditional expectations if and only if they are completely positive, and their images are Jordan algebras instead of von Neumann algebras. We shall see that their theory is intimately related to conditional expectations onto the von Neumann algebra generated by the image.

## Properties of the emden-fowler equation under stochastic disturbances that depend on parameters

### Journal of Mathematical Sciences (1997-02-01) 83: 477-484 , February 01, 1997

## Security Against Eavesdropping in Quantum Cryptography

### Quantum Communication, Computing, and Measurement (1997-01-01): 89-98 , January 01, 1997

Quantum cryptography is a method for providing two parties who want to communicate securely with a secret key to be used in established protocols of classical cryptography. For more reviews of this topic see [1–3]. Bennett and Brassard showed that it is possible, at least ideally, to create a secret key, shared by sender and receiver, without both parties sharing any secret beforehand. We refer to this protocol as the *BB84* protocol [4]. To achieve this goal, sender and receiver are linked by two channels. The first channel is a public channel. The information distributed on it is available to both parties *and* to a potential eavesdropper. To demonstrate the principle of quantum cryptography we assume that the signals on this channel can not be changed by third parties. The second channel is a channel with strong quantum features. An eavesdropper can interact with the signal in an effort to extract information about the signals. The signal states are chosen in such a way that there is always, on average, a back reaction onto the signal states. We assume the quantum channel to be noiseless and perfect so that the back reaction of the eavesdropper’s activity manifests itself as an induced error rate in the signal transmission.

## Martingale Methods in Financial Modelling

### Martingale Methods in Financial Modelling (1997-01-01): 36 , January 01, 1997

## Front Matter - Nonpositive Curvature: Geometric and Analytic Aspects

### Nonpositive Curvature: Geometric and Analytic Aspects (1997-01-01) , January 01, 1997

## The diffusion model for migration and selection in a plant population

### Journal of Mathematical Biology (1997-03-01) 35: 409-431 , March 01, 1997

### Abstract.

The diffusion approximation is derived for migration and selection at a multiallelic locus in a partially selfing plant population subdivided into a lattice of colonies. Generations are discrete and nonoverlapping; both pollen and seeds disperse. In the diffusion limit, the genotypic frequencies at each point are those determined at equilibrium by the local rate of selfing and allelic frequencies. If the drift and diffusion coefficients are taken as the appropriate linear combination of the corresponding coefficients for pollen and seeds, then the migration terms in the partial differential equation for the allelic frequencies have the standard form for a monoecious animal population. The selection term describes selection on the local genotypic frequencies. The boundary conditions and the unidimensional transition conditions for a geographical barrier and for coincident discontinuities in the carrying capacity and migration rate have the standard form. In the diallelic case, reparametrization renders the entire theory of clines and of the wave of advance of favorable alleles directly applicable to plant populations.