Some results on zero-sum games with incomplete information: The dependent case

In games with incomplete information, the players' states of information may be determined either through independent chance moves or through a unique one. Generally, a unique chance move generates some dependance in the players' state of information thus giving rise to significant complications in the analysis. However, it turns out that many results obtained in the simpler independent case have their counterpart in the dependent one. This is proved in this paper for several previous results of the authors.     

The axiom of spheres in quaternionic geometry

Summary We show that a quaternion manifold satisfying the axiom of quaternionic spheres is a quaternion space-form.

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Riassunto Si mostra che una varietà quaternionica che verifica l'assioma delle sfere quaternioniche è una forma spaziale quaternionica.

     

On Transversally Holomorphic Maps of Kählerian Foliations

Any transversally holomorphic foliated map of Kählerianfoliations with harmonic, is shown to be a transversallyharmonic map and an absolute minimum of the energy functional inits foliated homotopy class.     

Compactifications of Homeomorphism Groups of Linearly Ordered Compacta

Mathematical Notes - Topological groups of transformations are studied (their structure and equivariant compactifications) on which the pointwise convergence topology is an admissible group...     

Asymptotic properties in dynamic programming

In the framework of dynamic programming we provide two results:

The topological structure of the unitary and automorphism groups of a factor

It is proved that a large class ofII ₁ factors have unitary group which is contractible in the strong operator topology, but whose fundamental group in the norm topology is isomorphic to the additive real numbers as proven by Araki-Smith-Smith [1]. The class includes the approximately finite dimensional factor of typeII ₁ and the group factor associated with the free group on infinitely many generators. This contractibility is used to prove the contractibility of the automorphism group of the approximately finite dimensional factor of typeII ₁ and typeII . It is further shown that the fundamental group of the automorphism group of the approximately finite dimensional factor of typeIII , 0<<1, is isomorphic to the integer group .Dedicated to Huzihiro ArakiThis research is supported in part by NSF Grant DMS-9206984     

The ‘Miracle’ of Applicability? The Curious Case of the Simple Harmonic Oscillator

The paper discusses to what extent the conceptual issues involved in solving the simple harmonic oscillator model fit Wigner’s famous point that the applicability of mathematics borders on the miraculous. We argue that although there is ultimately nothing mysterious here, as is to be expected, a careful demonstration that this is so involves unexpected difficulties. Consequently, through the lens of this simple case we derive some insight into what is responsible for the appearance of mystery in more sophisticated examples of the Wigner problem.     

Cyclodextrin inclusion of four phenylurea herbicides: determination of complex stoichiometries and stability constants using solution 1H NMR spectroscopy

An inclusion complex formation between α- and β-cyclodextrin and four phenylurea analogues, namely metobromuron, monolinuron, monuron and fenuron, is reported. Complex formation was established using solution ¹H NMR spectroscopy. Complex stoichiometries were determined by the method of continuous variation using the chemically induced shifts of both the host and guest protons. An analysis of the spectroscopic data revealed the stoichiometry as 1:1 in all cases while a further analysis of the same data yielded values for the association constant K ranging from 208 to 2749 M^? 1. From the observed chemical shifts it was deduced that in all cases, only the guest aromatic ring enters the host cavities, the substituted urea moiety protruding from the secondary rim in the case of α-cyclodextrin, but from the primary rim in the case of β-cyclodextrin.