Kripke submodels and universal sentences

We define two notions for intuitionistic predicate logic: that of a submodel of a Kripke model, and that of a universal sentence. We then prove a corresponding preservation theorem. If a Kripke model is viewed as a functor from a small category to the category of all classical models with (homo)morphisms between them, then we define a submodel of a Kripke model to be a restriction of the original Kripke model to a subcategory of its domain, where every node in the subcategory is mapped to a classical submodel of the corresponding classical model in the range of the original Kripke model. We call a sentence universal if it is built inductively from atoms (including ? and ⊥) using ∧, ∨, ?, and →, with the restriction that antecedents of → must be atomic. We prove that an intuitionistic theory is axiomatized by universal sentences if and only if it is preserved under Kripke submodels. We also prove the following analogue of a classical model‐consistency theorem: The universal fragment of a theory Γ is contained in the universal fragment of a theory Δ if and only if every rooted Kripke model of Δ is strongly equivalent to a submodel of a rooted Kripke model of Γ. Our notions of Kripke submodel and universal sentence are natural in the sense that in the presence of the rule of excluded middle, they collapse to the classical notions of submodel and universal sentence. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A practical general approximation criterion for methods of multipliers based on Bregman distances

 This paper demonstrates that for generalized methods of multipliers for convex programming based on Bregman distance kernels – including the classical quadratic method of multipliers – the minimization of the augmented Lagrangian can be truncated using a simple, generally implementable stopping criterion based only on the norms of the primal iterate and the gradient (or a subgradient) of the augmented Lagrangian at that iterate. Previous results in this and related areas have required conditions that are much harder to verify, such as ε-optimality with respect to the augmented Lagrangian, or strong conditions on the convex program to be solved. Here, only existence of a KKT pair is required, and the convergence properties of the exact form of the method are preserved. The key new element in the analysis is the use of a full conjugate duality framework, as opposed to mainly examining the action of the method on the standard dual function of the convex program. An existence result for the iterates, stronger than those possible for the exact form of the algorithm, is also included. Received: February 6, 2001 / Accepted: January 25, 2003 Published online: March 21, 2003 Mathematics Subject Classification (1991): 90C25, 90C46, 47H05     

New Families of Semi-Regular Relative Difference Sets

We give two constructions for semi-regular relative difference sets (RDSs) in groups whose order is not a prime power, where the order u of the forbidden subgroup is greater than 2. No such RDSs were previously known. We use examples from the first construction to produce semi-regular RDSs in groups whose order can contain more than two distinct prime factors. For u greater than 2 these are the first such RDSs, and for u=2 we obtain new examples.     

The Algebraic K-Theory of Operator Algebras

We the study the algebraic K-theory of C *-algebras, forgetting the topology. The main results include a proof that commutative C*-algebras are K-regular in all degrees (that is, all theirN ^T K _iand extensions of the Fischer-Prasolov Theorem comparing algebraic and topological K-theory with finite coefficients.     

Synthesis and Structure of a Macrocyclic Europium Complex and its possible role as a catalyst for phosphodiester transesterification

The synthesis and X-ray crystal structure of a europium macrocyctic complex 1 , an important catalyst used for the sequence-specific cleavage of RNA, is reported. The role of this metal complex in facilitating phosphate transesterification is discussed.     

Robustness in Practice—The Regional Planning of Health Services

Earlier work has criticized the dominant tendencies in operational research contributions to health services planning as characterized by optimization, implausible demands for data, depoliticization, hierarchy and inflexibility. This paper describes an effort which avoids at least some of these pitfalls. The project was to construct a planning system for a regional health council in Ontario, Canada, which would take account of the possible alternative future states of the health-care system's environment and would aim to keep options for future development open. The planning system devised is described in the paper. It is based on robustness analysis, which evaluates alternative initial action sets in terms of the useful flexibility they preserve. Other features include the explicit incorporation of pressures for change generated outside the health-care system, and a satisficing approach to the identification of both initial action sets and alternative future configurations of the health-care system. It was found possible to borrow and radically 're-use' techniques or formulations from the mainstream of O.R. contributions. Thus the 'reference projection' method was used to identify inadequacies in performance which future health-care system configurations must repair. And Delphi analysis, normally a method for generating consensus, was used in conjunction with cluster analysis of responses to generate meaningfully different alternative futures.     

Accurate vocal compensation for sound intensity loss with increasing distance in natural environments

Human abilities to adjust vocal output to compensate for intensity losses due to sound propagation over distance were investigated. Ten normally hearing adult participants were able to compensate for propagation losses ranging from -1.8 to -6.4 dBdoubling source distance over a range of distances from 1 to 8 m. The compensation was performed to within 1.2 dB of accuracy on average across all participants, distances, and propagation loss conditions with no practice or explicit training. These results suggest that natural vocal communication processes of humans may incorporate tacit knowledge of physical sound propagation properties more sophisticated than previously supposed.     

E-FiRST: Electric field responsive shear thickening fluids

A novel electrorheological (ER) effect is presented where the application of an electric field, orthogonal to the vorticity-flow plane, increases the critical hydrodynamic stress required to shear thicken concentrated, colloidal dispersions (the E-FiRST effect). The shear thickening behavior of a Brownian charge stabilized dispersion (226 nm silica in 4-methylcyclohexanol at 53, 50. and 41 vol.%) is studied in the presence of an electric field as a function of the field strength and coupling parameter ( ß) where the latter is a function of a.c. field frequency due to diffusion limitations on the polarization of the particles' double layer. A mechanism is proposed whereby the applied electric field suppresses the formation of the self-organized hydrocluster microstructure responsible for shear thickening, thus delaying the onset of shear thickening to higher applied shear stresses. A Mason-number type scaling law is found to scale the effect, which supports the proposed mechanism.