On Ito-Kurzweil-Henstock Integral and Integration-by-Part Formula

In this paper we derive the Integration-by-Parts Formula using the generalized Riemann approach to stochastic integrals, which is called the Ito-Kurzweil-Henstock integral.     

A≈110质量区奇A核形状演化研究

应用E-GOS（E-Gamma Over Spin）曲线方法研究了A≈110质量区奇A核结构随角动量增加的演化, 发现随着角动量的增加原子核的激发特性从振动逐渐演化为转动。 The E-GOS（E-Gamma Over Spin）curves were used to investigate the structure evolution in the odd A nuclei around A≈110 as a function of spin. The result shows that there is a clear transition from vibration to rotation while increasing spin.     

Teacher preparation for a problem-solving curriculum in Singapore

Problem solving is at the heart of the Singapore Mathematics curriculum. However, it remains a challenge for teachers to realise this curricular goal in practice. Here, we review the efforts of Singapore mathematics teacher educators in incorporating problem-solving (teaching) competency in teacher education and PD programmes. We discuss conceptual and practical issues, actions taken and changes made in building teachers?? capacity to enact a problem-solving curriculum in a school-based design experiment project. In the project, teachers learnt problem solving, observed and then carried out lessons, using the ??Mathematics Practical????akin to the science practical??as key to instruction and assessment.     

Properties of the πh 9/2 ⊗ νi 13/2 band in odd-odd 188Au

A new rotational band has been identified and assigned to ¹⁸⁸Au for the first time using the ¹⁷³Yb(¹⁹F,4nγ) reaction at the beam energies of 86 and 90 MeV. This band is proposed to be built on the πh _9/2 ⊗ νi _13/2 configuration by comparing the band properties with known bands in neighboring nuclei. The prolate-to-oblate shape transition through triaxial shape has been proposed to occur around ¹⁸⁸Au for the ηh _9/2 ⊗ νi _13/2 bands in odd-odd Au isotopes on the basis of total Routhian surface (TRS) calculations.

     

High-j proton alignments in 101Pd

High-spin states in ¹⁰¹Pd have been investigated by means of in-beam γ-ray spectroscopic techniques via the ⁷⁶Ge(²⁸Si, 3n) reaction at beam energies of 85 and 95 MeV. The previously known d _5/2 and 1/2^?[550] bands were extended to higher spins, and the unfavored signature branch of the 1/2^?[550] band was built. The band crossings observed experimentally are explained by the alignment of g _9/2 protons. The band properties in ¹⁰¹Pd are compared with those in the neighboring nuclei and are discussed within the framework of the cranked shell model (CSM).     

Modular Decomposition of the Orlik-Terao Algebra

Let ${\mathcal{A}}$ be a collection of n linear hyperplanes in ${\mathbb{k}^\ell}$ , where ${\mathbb{k}}$ is an algebraically closed field. The Orlik-Terao algebra of ${\mathcal{A}}$ is the subalgebra ${{\rm R}(\mathcal{A})}$ of the rational functions generated by reciprocals of linear forms vanishing on hyperplanes of ${\mathcal{A}}$ . It determines an irreducible subvariety ${Y (\mathcal{A})}$ of ${\mathbb{P}^{n-1}}$ . We show that a flat X of ${\mathcal{A}}$ is modular if and only if ${{\rm R}(\mathcal{A})}$ is a split extension of the Orlik-Terao algebra of the subarrangement ${\mathcal{A}_X}$ . This provides another refinement of Stanley’s modular factorization theorem [34] and a new characterization of modularity, similar in spirit to the fibration theorem of [27]. We deduce that if ${\mathcal{A}}$ is supersolvable, then its Orlik-Terao algebra is Koszul. In certain cases, the algebra is also a complete intersection, and we characterize when this happens.     

Polynomiality of an inexact infeasible interior point algorithm for semidefinite programming

In this paper we present a primal-dual inexact infeasible interior-point algorithm for semidefinite programming problems (SDP). This algorithm allows the use of search directions that are calculated from the defining linear system with only moderate accuracy, and does not require feasibility to be maintained even if the initial iterate happened to be a feasible solution of the problem. Under a mild assumption on the inexactness, we show that the algorithm can find an -approximate solution of an SDP in O(n²ln(1/)) iterations. This bound of our algorithm is the same as that of the exact infeasible interior point algorithms proposed by Y. Zhang.Research supported in part by the Singapore-MIT alliance, and NUS Academic Research Grant R-146-000-032-112.Mathematics Subject Classification (1991): 90C05, 90C30, 65K05     

Reviving Pólya's “Look Back” in a Singapore school

This study is based on the stance that Pólya's “Look Back,” though understudied, remains relevant to Mathematics curricula that place emphasis on problem solving. Although the Singapore Mathematics curriculum adopts the goal of teaching Look Back, research about how it is carried out in actual classroom practice is rare. In our project, we focus on a redesign of a teacher development programme that is targeted to help teachers realize Pólya's original vision of Look Back in the classroom. We report the cases of two teachers who have participated in the teacher development programme: their thinking about Look Back (through interview records) and their interpretation of Look Back in their classroom practice (through video records). By bringing these two spheres of data together, we discuss their degree of ‘buy-in’ to Look Back in the overall problem solving enterprise.