Knowledge based proximal support vector machines

We propose a proximal version of the knowledge based support vector machine formulation, termed as knowledge based proximal support vector machines (KBPSVMs) in the sequel, for binary data classification. The KBPSVM classifier incorporates prior knowledge in the form of multiple polyhedral sets, and determines two parallel planes that are kept as distant from each other as possible. The proposed algorithm is simple and fast as no quadratic programming solver needs to be employed. Effectively, only the solution of a structured system of linear equations is needed.     

Examining the design features of a communication-rich,problem-centred mathematics professional development

While there is considerable scholarship describing principles for effective professional development, there have been few attempts to examine these principles in practice. In this paper, we identify and examine the particular design features of a mathematics professional development experience provided for middle grades teachers over 14 weeks. The professional development was grounded in a set of mathematical tasks that each had one right answer, but multiple solution paths. The facilitator engaged participants in problem solving and encouraged participants to work collaboratively to explore different solution paths. Through analysis of this collaborative learning environment, we identified five design features for supporting teacher learning of important mathematics and pedagogy in a problem-solving setting. We discuss these design features in depth and illustrate them by presenting an elaborated example from the professional development. This study extends the existing guidance for the design of professional development by examining and operationalizing the relationships among research-based features of effective professional development and the enacted features of a particular design.     

Optimal execution with weighted impact functions: a quadratic programming approach

In this paper, we develop optimal trading strategies for a risk averse investor by minimizing the expected cost and the risk of execution. Here we consider a law of motion for price which uses a convex combination of temporary and permanent market impact. In the special case of unconstrained problem for a risk neutral investor, we obtain a closed form solution for optimal trading strategies by using dynamic programming. For a general problem, we use a quadratic programming approach to get approximate dynamic optimal trading strategies. Further, numerical examples of optimal execution strategies are provided for illustration purposes.     

Understanding a Teacher's Reflections: A Case Study of a Middle School Mathematics Teacher

The purpose of this research was to understand how one teacher reflected on different classroom situations and to understand whether the teacher's approach to these reflections changed over time. For the purposes of this study, we considered reflection as the teacher's act of interpreting her own practices and students' thinking to make sense of student understanding and how teaching might relate to that understanding. We investigated a middle school mathematics teacher's reflection on her students while watching videotapes of her classroom and categorized the reflection as Assess, Interpret, Describe, Justify, and Extend. The results show a higher percentage of Extend instances in later interviews than in earlier ones indicating the teacher's increasing attention to her own teaching in how her students developed their understanding. In addition, her reflection became clearer and better integrated as defined by the Cohen and Ball's triangle of interactions.     

A note on mixed summation-integral-type operators

Very recently Deo, in the paper “Simultaneous approximation by Lupas operators with weighted function of Szasz operators” [J. Inequal. Pure Appl. Math., 5, No. 4 (2004)] claimed to introduce the integral modifications of Lupas operators. These operators were first introduced in 1993 by Gupta and Srivastava. They estimated the simultaneous approximation for these operators and called them Baskakov-Szasz operators. There are several misprints in the paper by Deo. This motivated us to perform subsequent investigations in this direction. We extend the study and estimate a saturation result in simultaneous approximation for the linear combinations of these summation-integral-type operators. Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 8, pp. 1135–1139, August, 2007.     

Modeling of thermal effects in antivascular ultrasound therapy

Antivascular ultrasound consisting of low-intensity sonication in the presence of circulating microbubbles of an ultrasound contrast agent has been demonstrated to disrupt blood flow in solid cancers. In this study a mathematical framework is described for the microbubble-induced heating that occurs during antivascular ultrasound. Biological tissues are modeled as a continuum of microbubble-filled vasculature, cells, and interstitial fluids with compressibility equal to the sum of the compressibility of each component. The mathematical simulations show that the absorption of ultrasound waves by viscous damping of the microbubble oscillations induced significant local heating of the tissue vasculature. The extent and the rate of temperature increase not only depends on the properties of the microbubbles and the sonication parameters but is also influenced markedly by the blood flow. Slow flow conditions lead to higher tissue temperatures due to a stronger interaction between microbubbles and ultrasound and reduced heat dissipation. Because tumors have slower blood flow than healthy tissue, the microbubble-induced ultrasound antivascular therapy is likely to affect cancerous tissue more extensively than healthy tissue, providing a way to selectively target the vasculature of cancers.     

A facile strategy for the fabrication of uniform CdS nanowires with high yield and its controlled morphological growth with the assistance of PEG in hydrothermal route

A series of novel wurtzite cadmium sulphide (CdS) nanowires with uniform diameter were synthesized by using a rapid and simple solvothermal route. CdS nano structures with certain morphology could be selectively produced by only varying the concentration of poly ethylene glycol (PEG) as a surfactant in the reaction system with cadmium acetate, sulphur powder and ethelynediamine (EDA). We extensively studied UV-vis absorption spectra, photoluminescence spectra after confirming CdS nanowires with diameter 24-25 nm and length ranging up to several nano meters by field emission scanning electron microscopy (FE-SEM). Therefore we may definitely propose a new formation mechanism of CdS nanowires assisted by PEG with its illustrating optical properties.