A central idea of minimal model theory as formulated by Mori is to study algebraic varieties using convex geometry. The cone of curves of a projective variety is defined as the convex cone spanned by the numerical equivalence classes of algebraic curves; the dual cone is the cone of nef line bundles. For Fano varieties (varieties with ample anticanonical bundle), these cones are rational polyhe...

The recent result of Strominger, Yau and Zaslow relating mirror symmetry to the quantum field theory notion of T-duality is reinterpreted as providing a way of geometrically characterizing which Calabi–Yau manifolds have mirror partners. The geometric description—that one Calabi–Yau manifold should serve as a compactified, complexified moduli space for special Lagrangian tori on the other Calab...

In this paper we study 15 complete intersection K3-fibered Calabi–Yau variety types in biprojective space P1 × P These are all the CICY-types that are K3 fibered by the projection on the second factor. We prove existence of isolated rational curves of bidegree (d, 0) for every positive integer d on a general Calabi– Yau variety of these types. The proof depends heavily on existence theorems for...

In the papers [FS1], [FS2] we described some Siegel modular threefolds which admit a weak Calabi–Yau model.*) Not all of them admit a projective model. In fact, Bert van Geemen, in a private communication, pointed out a significative example which cannot admit a projective model. His comment was a starting motivation for this paper. We mention that a weak Calabi–Yau threefold is projective if, ...

Let Σ be a smooth projective complex curve and g a simple Lie algebra of type ADE with associated adjoint group G. For a fixed pair (Σ, g), we construct a family of quasiprojective Calabi-Yau threefolds parameterized by the base of the Hitchin integrable system associated to (Σ, g). Our main result establishes an isomorphism between the Calabi-Yau integrable system, whose fibers are the interme...

Simple mean field methods can be used to describe transitions between different space-time models in string theory. These include transitions between different Calabi-Yau manifolds, and more exotic things such as the Calabi-Yau/Landau-Ginzberg correspondence.

321 6. Cheng TO. Ventricular function curves. Am Heart J 1975; 89: 406. 7. Cheng TO. Diastolic heart failure among Chinese patients. Am J Cardiol 1999; 84: 1280. 8. Zhang ZB, Cheng TO, Zhang YC. Textbook of Congestive Heart Failure. Beijing, China: Science & Technology Publishers, 2003, pp. 15–19; 662–682. 9. Cheng TO. Therapeutic implications of diastolic dysfunction in heart failure. Postgrad...

This paper investigates the global chaos synchronization of identical Lü-Chen-Cheng four-scroll chaotic systems (Lü, Chen and Cheng, 2004) by sliding mode control. The stability results derived in this paper for the complete synchronization of identical Lü-Chen-Cheng four-scroll chaotic systems are established using Lyapunov stability theory. Since the Lyapunov exponents are not required for th...

We study the existence of special Lagrangian submanifolds log Calabi–Yau manifolds equipped with complete Ricci-flat Kähler metric constructed by Tian and Yau. prove that if X is a Tian–Yau manifold compact at infinity admits single Lagrangian, then infinitely many disjoint Lagrangians. In complex dimension 2, we Y del Pezzo surface or rational elliptic D∈|−KY| smooth divisor D2=d, X=Y∖D torus ...

It has been claimed that the power PC theory reconciles regularity and power theories of causal judgment by showing how contingency information is used for inferences about unobservable causal powers. Under the causal powers theory causal relations are understood as generative relations in which a causal power of one thing acts on a liability of another thing under some releasing condition. The...