Allocating electricity transmission costs through tracing: a game-theoretic rationale

Tracing is a method of assigning flows in an electricity network to particular generators and loads, assuming perfect mixing at each node. It can be used to assign costs to transmission users. We show that the resulting allocation is equal to the Shapley value of an equivalent co-operative game.     

A branch and bound algorithm for the robust shortest path problem with interval data

Many real problems can be modelled as robust shortest path problems on interval digraphs, where intervals represent uncertainty about real costs and a robust path is not too far from the shortest path for each possible configuration of the arc costs.A branch and bound algorithm for this problem is presented.     

On the Essential Self-Adjointness of Wick Powers of Relativistic Fields and of Fields Unitary Equivalent to Random Fields

The essential self-adjointness on a natural domain of the sharp-time Wick powers of the relativistic free field in two space-time dimension is proven. Other results on Wick powers are reviewed and discussed.     

Polynomial Quantization on Rank One Para-Hermitian Symmetric Spaces

We construct the polynomial quantization on the space G/H where G=SL(n,R),H=GL(n–1,R). It is a variant of quantization in the spirit of Berezin. In our case covariant and contravariant symbols are polynomials on G/H. We introduce a multiplication of covariant symbols, establish the correspondence principle, study transformations of symbols (the Berezin transform) and of operators. We write a full asymptotic decomposition of the Berezin transform.     

An approach to deciding the observational equivalence of Algol-like languages

We prove that the observational equivalence of third-order finitary (i.e. recursion-free) Idealized Algol (IA) is decidable using Game Semantics. By modelling the state explicitly in our games, we show that the denotation of a term M of this fragment of IA is a compactly innocent strategy-with-state, i.e. the strategy is generated by a finite view function f_M. Given any such f_M, we construct a real-time deterministic pushdown automaton (DPDA) that recognizes the complete plays of the knowing-strategy denotation of M. Since such plays characterize observational equivalence, and there is an algorithm for deciding whether any two DPDAs recognize the same language, we obtain a procedure for deciding the observational equivalence of third-order finitary IA. Restricted to second-order terms, the DPDA representation cuts down to a deterministic finite automaton; thus our approach gives a new proof of Ghica and McCusker’s regular-expression characterization for this fragment. Our algorithmic representation of program meanings, which is compositional, provides a foundation for model-checking a wide range of behavioural properties of IA and other cognate programming languages. Another result concerns second-order IA with full recursion: we show that observational equivalence for this fragment is undecidable.     

Analysis of end point vibrations of a two-link manipulator by integrated CAD/CAE procedures

In this work, the effect of flexibility on the trajectory of a planar two-link manipulator is studied using integrated computer-aided design/analysis (CAD/CAE) procedures. The solid models and finite element models of the parts of the manipulator are created by using the CAD/CAE software I-DEAS. The assembly is defined, and knowing the payload and the end point trajectory, the velocities and accelerations of the parts, joint forces and driving torques are calculated using the rigid body dynamics. All the time dependent nodal forces acting on the parts including distributed gravity and inertia forces are created in files with the I-DEAS program file format. The finite element vibration analysis of the parts is performed by I-DEAS. The end point vibrations and the deviations from the rigid-body trajectory are analyzed for different types of end point acceleration curves. A circular trajectory is considered as an example. It is observed that the precision of the manipulator can be increased by testing different end point acceleration curves without changing the trajectory and the duration of the end point work. The procedure explained in this work can be used for this purpose successfully.     

Some non‐standard problems in viscous flow

Energy bounds are derived for Dirichlet type boundary value problems for the Navier–Stokes and Stokes equations when a combination of the solution values initially and at a later time is prescribed. The bounds are obtained by means of a differential inequality and imply uniqueness and continuous data dependence of the solutions for a range of values of the parameter in the non‐standard auxiliary condition. Copyright © 2004 John Wiley & Sons, Ltd.     

Diffusion in poro‐plastic media

A model is developed for the flow of a slightly compressible fluid through a saturated inelastic porous medium. The initial‐boundary‐value problem is a system that consists of the diffusion equation for the fluid coupled to the momentum equation for the porous solid together with a constitutive law which includes a possibly hysteretic relation of elasto‐visco‐plastic type. The variational form of this problem in Hilbert space is a non‐linear evolution equation for which the existence and uniqueness of a global strong solution is proved by means of monotonicity methods. Various degenerate situations are permitted, such as incompressible fluid, negligible porosity, or a quasi‐static momentum equation. The essential sufficient conditions for the well‐posedness of the system consist of an ellipticity condition on the term for diffusion of fluid and either a viscous or a hardening assumption in the constitutive relation for the porous solid. Copyright © 2004 John Wiley & Sons, Ltd.     

Microwave-accelerated conjugate addition of aldehydes to α,β-unsaturated ketones

Aldehydes undergo smooth conjugate addition to α,β-unsaturated ketones in the presence of 5-(2-hydroxyethyl)-1,3-thiazolium halides and DBU adsorbed onto the surface of basic alumina under microwave irradiation and solvent-free conditions to afford 1,4-diketones in enhanced yields and reduced reaction times compared to conventional methods.     

Uniformity in Computable Structure Theory

We investigate the effects of adding uniformity requirements to concepts in computable structure theory such as computable categoricity (of a structure) and intrinsic computability (of a relation on a computable structure). We consider and compare two different notions of uniformity, previously studied by Kudinov and by Ventsov. We discuss some of their results and establish new ones, while also exploring the connections with the relative computable structure theory of Ash, Knight, Manasse, and Slaman and Chisholm and with previous work of Ash, Knight, and Slaman on uniformity in a general computable structure-theoretical setting.