A compact minimal Lagrangian submanifold immersed in a Kähler manifold is called Hamiltonian stable if the second variation of its volume is nonnegative under all Hamiltonian deformations. We study compact Hamiltonian stable minimal Lagrangian submanifolds with parallel second fundamental form embedded in complex projective spaces. Moreover, we completely determine Hamiltonian stability of all real forms in compact irreducible Hermitian symmetric spaces, which were classified previously by M. Takeuchi.

We present a method for computing the 3-point genus zero Gromov-Witten invariants of the complex flag manifold G/B from the relations of the small quantum cohomology algebra QH * G/B (G is a complex semisimple Lie group and B is a Borel subgroup). In [Fo-Ge-Po] and [Ki-Ma], at least in the case G = GL n C, two algebraic/combinatoric methods have been proposed, based on suitably designed axioms. Our method is quite different, being differential geometric in nature; it is based on the approach to quantum cohomology described in [Gu], which is in turn based on the integrable systems point of view of Dubrovin and Givental.In §1 we shall review briefly the method of [Gu]. In §2 we discuss the special properties of G/B which lead to a computational algorithm. In fact the same method works for any Fano manifold whose cohomology is generated by two-dimensional classes, so our approach is more general than those of [Fo-Ge-Po] and [Ki-Ma]. In §3 we present explicit results for the case G = GL n C, n = 2, 3, 4. In §4, we show how to produce "quantum Schubert polynomials" for G/B, by which we mean specific polynomial representatives of quantum Schubert classes.The second author thanks Josef Dorfmeister for essential suggestions concerning the proof of Proposition 2.2. We are very grateful to the referee for pointing out several inaccuracies in an earlier version of this paper. §1 Quantum cohomology via D-modulesWe list some well known properties of the cohomology and quantum cohomology algebras of G/B (see [Ci], [Gi-Ki], [Ki]). The cohomology algebra of G/B (with complex coefficients) has the form

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This paper proposes an effective and robust hand tracking and fingertip detection method and applies it to a novel vision based human computer interaction system: Visual Keyboard System For Smart TV (VKS). The both hands tracking and fingertip recognition approach consists of three stages. First, based on the CAMSHIFT, Motion Template and Shape Template Matching, the both hands were tracked by Multi Object Tracking CAMSHIFT. Then, the location of fingertip was localized precisely based on Motion Template. After those process, we have the Robust Shape Template Matching to recognize a fingertip. Experiments suggest that the proposed our method is capable of detecting fingertip recognition in a reliable manner even in a complex background under different light conditions without any markers. The Fingertip Recognition Visual Keyboard System in this paper is particularly advantageous for Human-computer Interaction (HCI) in that users can communicate with SMART TV by their favorite mean: fingertip gesturing. At the same time, they can perform typing with only their fingertip directly.

The purpose of this study is to assess object and schema conceptions of transformations of functions for undergraduate level students of Mongolian National University. The research participants were 37 undergraduate students who attended the Calculus course of the third author. To achieve our purpose two of the authors analyzed students’ project work independently based on the pre-developed rubrics and further analyses were made. Students’ project work included recognition of simple and complicated transformation of functions visually, expressing algebraic forms of such transformations and drawing a doll using transformations of a half circle of radius one. The research results show that students’ object and schema conception of transformations of functions were poor. Finding the reason for these poor results is a subject for future research. Moreover, students who were able to recognize more complicated transformations visually could draw a doll using the half circle while the ones who could express transformations of both simple and complicated transformations in algebraic form were able to construct a doll using transformations of the half circle.