Variational Inequality Formulation of a Class of Multi-Leader-Follower Games

The multi-leader-follower game can be looked on as a generalization of the Nash equilibrium problem and the Stackelberg game, which contains several leaders and a number of followers. Recently, the multi-leader-follower game has been drawing more and more attention, for example, in electricity power markets. However, when we formulate a general multi-leader-follower game as a single-level game, it will give rise to a lot of problems, such as the lack of convexity and the failure of constraint qualifications. In this paper, to get rid of these difficulties, we focus on a class of multi-leader-follower games that satisfy some particular, but still reasonable assumptions, and show that these games can be formulated as ordinary Nash equilibrium problems, and then as variational inequalities. We establish some results on the existence and uniqueness of a leader-follower Nash equilibrium. We also present illustrative numerical examples from an electricity power market model.     

Heterogeneous critical nucleation on a completely wettable substrate

Heterogeneous nucleation of a new bulk phase on a flat substrate can be associated with the surface phase transition called wetting transition. When this bulk heterogeneous nucleation occurs on a completely wettable flat substrate with a zero contact angle, the classical nucleation theory predicts that the free-energy barrier of nucleation vanishes. In fact, there always exists a critical nucleus and a free-energy barrier as the first-order prewetting transition will occur even when the contact angle is zero. Furthermore, the critical nucleus changes its character from the critical nucleus of surface phase transition below bulk coexistence (undersaturation) to the critical nucleus of bulk heterogeneous nucleation above the coexistence (oversaturation) when it crosses the coexistence. Recently, Sear [J. Chem. Phys. 129, 164510 (2008)] has shown, by a direct numerical calculation of nucleation rate, that the nucleus does not notice this change when it crosses the coexistence. In our work, the morphology and the work of formation of critical nucleus on a completely wettable substrate are re-examined across the coexistence using the interface-displacement model. Indeed, the morphology and the work of formation changes continuously at the coexistence. Our results support the prediction of Sear and will rekindle the interest on heterogeneous nucleation on a completely wettable substrate.     

Mirror Map as Generating Function of Intersection Numbers: Toric Manifolds with Two Kähler Forms

In this paper, we extend our geometrical derivation of the expansion coefficients of mirror maps by localization computation to the case of toric manifolds with two Kähler forms. In particular, we consider Hirzebruch surfaces F ₀, F ₃ and Calabi-Yau hypersurface in weighted projective space P(1, 1, 2, 2, 2) as examples. We expect that our results can be easily generalized to arbitrary toric manifolds.     

Structures and fluorescence of secondary products produced from the cope-knoevenagel reaction of 2-phenylpropionaldehyde with methyl cyanoacetate

The Cope-Knoevenagel reaction of 2-phenylpropionaldehyde ( 7 ) with methyl cyanoacetate ( 8 ) produced methyl (E)-2-cyano-4-phenylpent-2-enoate ( 9 ) and the two highly fluorescent secondary products, 2-amino-3-carbomethoxy-6-phenyl-4-(1-phenylethyl)pyridine ( 10 ) and 3-cyano-6-phenyl-4-(1-phenylethyl)-2-pyridone ( 11 ). The structure of 10 was determined by X-ray crystallography while the structure of 11 was confirmed by the conversion of 9 into 11 . The mechanism of their formation is discussed. Fluorescence of 10 and 11 and the related compounds are also described.     

Direct mono-phosphorylation of 1,3-diols. A synthesis of FTY720-phosphate

A novel method for selective and direct phosphorylation of various 1,3-diols using silver(I) oxide, tetrabenzyl pyrophosphate (TBPP), and tetrahexylammonium iodide affording mono-phosphates was developed. We applied the present method to the synthesis of FTY720-phosphate.     

Evaluation of firm’s loss due to incomplete information in real investment decision

We investigate the effect of incomplete information in a model where a start-up with a unique idea and technology pioneers a new market but will eventually be expelled from the market by a large firm’s subsequent entry. We evaluate the start-up’s loss due to incomplete information about the large firm’s behavior. We clarify conditions under which the start-up needs more information about the large firm. The proposed method of evaluating the loss due to incomplete information could also be applied to other real options models involving incomplete information.     

Study of boron nitride by electron energy-loss spectroscopy

An interband π plasmon and π* edge have been observed in the spectrum of hexagonal boron nitride (h-BN). This result is in good agreement with that