A note on trivial nonmultidimensional superstable theories

Research supported by the NSERC of Canada     

A note on countable models of 1-based theories

 We prove that the existence of a nonisolated type having a finite domain and which is orthogonal to ?in a 1-based theory implies that it has a continuum nonisomorphic countable models. Received: 6 March 2000 Published online: 12 July 2002     

A note on generating generalized two-dimensional plate and shell theories

Summary Ordinary two dimensional linear shell theory may be formulated by using six differential equations for stress resultants and couples and for middle surface force and moment load intensities, in conjunction with the principle of virtual work, for the derivation of strain displacement relations. The present paper deals with a more general formulation, involving additional two-dimensional equilibrium equations, as a consequence of three-dimensional equations for force and moment stresses, in conjunction with a stipulation of surface force and moment load intensities for two face surfaces in place of the one middle surface. The main intent of the analysis is an illumination of the concept of a mechanical Cosserat-surface theory, in comparison with ordinary two-dimensional shell theory.

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Zusammenfassung Die übliche zweidimensionale Schalentheorie kann formuliert werden, indem man sechs Differentialgleichungen für Spannungsresultierende, Momente, Mittel flächenkraft und Momentlastintensität zusammen mit dem Prinzip der virtuellen Verschiebungen dazu benutzt, um ein System von Dehnungs-Verschiebungsgleichungen abzuleiten. Die vorliegende Arbeit beschäftigt sich mit einer verallgemeinerten Formulierung, mit zusätzlichen zweidimensionalen Gleichgewichtsbedingungen, die von einer dreidimensionalen Theorie für Kraft- und Momentenspannungen abgeleitet werden, zusammen mit einer Vorschrift über zwei Systeme von Ober flächenkräften und Momentlastintensitäten anstelle des einen Mittelfllächenlastsystems. Der Hauptzweck der Analyse ist die Beleuchtung des Begriffs der mechanischen Cosserat-Flächentheorie im Vergleich zur üblichen zweidimensionalen linearen Schalentheorie.

     

A note on integration of the Navier–Stokes equations

In this study the 2D Navier–Stokes equations are used to obtain a new self-similar equation. The latter equation, subject to appropriate boundary conditions and volume discharge, describes the pressure distribution and velocity field of a plane free jet.     

A note on stationarity of types over models in simple theories

We investigate stationarity of types over models in simple theories. In particular, we show that in simple theories with finite SU‐rank, any complete type over a model having Cantor‐Bendixson rank is stationary. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A note on the error growth in the numerical integration of periodic orbits

The aim of this note is to extend the analysis of B. Cano and J. M. Sanz-Serna [2] on the global error behaviour of general one step methods in the numerical integration of a periodic orbit to the case that such a periodic orbit can be embedded into a family of periodic orbits. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A note on stable sets,groups, and theories with NIP

Let M be an arbitrary structure. Then we say that an M ‐formula φ (x) defines a stable set in M if every formula φ (x) ∧ α (x, y) is stable. We prove: If G is an M ‐definable group and every definable stable subset of G has U ‐rank at most n (the same n for all sets), then G has a maximal connected stable normal subgroup H such that G /H is purely unstable. The assumptions hold for example if M is interpretable in an o‐minimal structure. More generally, an M ‐definable set X is weakly stable if the M ‐induced structure on X is stable. We observe that, by results of Shelah, every weakly stable set in theories with NIP is stable. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A note on the convergence of product integration and Galerkin method for weakly singular integral equations

We consider weakly singular integral equations of Fredholm-type whose kernels satisfy certain algebraic estimates with their derivatives. In particular, we establish optimal convergence order estimates for product integration and Galerkin method applied on suitable grading mesh for the solution of such equations. Some superconvergence results are also derived.     

A note on the nucleolus

It was shown byKohlberg [1972] that the nucleolus can be obtained by solving a linear program of extremely large size (2 ⁿ ! constraints). We show here how this program can be reduced to a more tractable size (4 ⁿ constraints).     

A note on the core

This note studies an exchange economy in which there are n traders and n “kinds” of commodities. Each trader has n utility functions corresponding to n “kinds” of commodities, respectively. Thus, a multiple non-transferable utility game can be derived from this exchange economy. It is shown that a sufficient condition for non-emptiness of the core of a multiple non-transferable utility game. The result is an extension of Scarf-Billera theorem.     

A note on the hypercube model

We consider a variation of the hypercube model in which there are N distinguishable servers and R types of customers. Customers that find all servers busy (blocked customers) are lost. When service times are exponentially distributed and customers arrive according to independent Poisson streams, we show that the policy which always assigns customers to the fastest available server minimizes the long-run average number of lost customers. Furthermore, we derive an upper bound for the blocking probability and the long-run average number of customers lost.     

A note on the finesse point

Introduced by Saari and Asay (2010), the “finesse point” extends the notion of core. Its definition is similar to the finagle point. Unlike the finagle point, there is a relatively simple geometrical construction of finesse point. In this note, we show that the aforementioned points do not agree. This questions the original definition of finesse point.     

A note on the splitting principle

We offer a new perspective on the splitting principle. We give an easy proof that applies to all classical types of vector bundles and in fact to G-bundles for any compact connected Lie group G. The perspective gives precise calculational information and directly ties the splitting principle to the specification of characteristic classes in terms of classifying spaces.     

A note on the syzygy problem

In the theorem of Evans and Griffith on the syzygy problem. The restriction on the ring being Cohen Macaulay domain is completely eliminated.     

A note on the p-local rank

In this paper, we give an inductive definition of p-local rank of a p-block in a finite group G with p||G| and show a necessary and sufficient condition for a p-block B such that plr(B) = 2.Received: 10 March 2004     

A note on the exact games

The Shapley value need not be in the core of an exact game.