World-Class high quality mathematics education for all K-12 American Students

In September 1989, the United States’ Governors Conference in Charlottesville, Virginia set an ambitious goal by declaring that “By the year 2000, United States students will be first in the world in mathematics and science achievements”. However, recent results of the ‘Programme for International Student Achievement’ and ‘Trends in International Mathematics and Science Study’ indicate that the United States students’ achievements in mathematics are far below world class standards. This paper seeks to discuss issues in an international context related to the goal of creating world-class high quality mathematics education for all K-12 American students. In particular, the author also shares his reflections and depicts lessons from Singapore’s success story in mathematics education

Studies of the acoustic transmission characteristics of coaxial nozzles with inverted velocity profiles, volume 1

The efficiency of internal noise radiation through coannular exhaust nozzle with an inverted velocity profile was studied. A preliminary investigation was first undertaken to: (1) define the test parameters which influence the internal noise radiation; (2) develop a test methodology which could realistically be used to examine the effects of the test parameters; (3) and to validate this methodology. The result was the choice of an acoustic impulse as the internal noise source in the in the jet nozzles. Noise transmission characteristics of a nozzle system were then investigated. In particular, the effects of fan nozzle convergence angle, core extention length to annulus height ratio, and flow Mach number and temperatures were studied. The results are presented as normalized directivity plots

The Fekete–Szegö problem for a class of analytic functions defined by Carlson–Shaffer operator

In the present investigation we solve Fekete-Szegö problem for the generalized linear differential operator. In particular, our theorems contain corresponding results for various subclasses of strongly starlike and strongly convex functions. In the present investigation we solve Fekete-Szegö problem for the generalized linear differential operator. In particular, our theorems contain corresponding results for various subclasses of strongly starlike and strongly convex functions

On Approximating Restricted Cycle Covers

A cycle cover of a graph is a set of cycles such that every vertex is part of exactly one cycle. An L-cycle cover is a cycle cover in which the length of every cycle is in the set L. The weight of a cycle cover of an edge-weighted graph is the sum of the weights of its edges. We come close to settling the complexity and approximability of computing L-cycle covers. On the one hand, we show that for almost all L, computing L-cycle covers of maximum weight in directed and undirected graphs is APX-hard and NP-hard. Most of our hardness results hold even if the edge weights are restricted to zero and one. On the other hand, we show that the problem of computing L-cycle covers of maximum weight can be approximated within a factor of 2 for undirected graphs and within a factor of 8/3 in the case of directed graphs. This holds for arbitrary sets L.Comment: To appear in SIAM Journal on Computing. Minor change

The Impact of Link Suggestions on User Navigation and User Perception

The study reported in this paper explores the effects of providing web users with link suggestions that are relevant to their tasks. Results indicate that link suggestions were positively received. Furthermore, users perceived sites with link suggestions as more usable and themselves as less disoriented. The average task execution time was significantly lower than in the control condition and users appeared to navigate in a more structured manner. Unexpectedly, men took more advantage from link suggestions than women

Acoustically excited heated jets. 1: Internal excitation

The effects of relatively strong upstream acoustic excitation on the mixing of heated jets with the surrounding air are investigated. To determine the extent of the available information on experiments and theories dealing with acoustically excited heated jets, an extensive literature survey was carried out. The experimental program consisted of flow visualization and flowfield velocity and temperature measurements for a broad range of jet operating and flow excitation conditions. A 50.8-mm-diam nozzle was used for this purpose. Parallel to the experimental study, an existing theoretical model of excited jets was refined to include the region downstream of the jet potential core. Excellent agreement was found between theory and experiment in moderately heated jets. However, the theory has not yet been confirmed for highly heated jets. It was found that the sensitivity of heated jets to upstream acoustic excitation varies strongly with the jet operating conditions and that the threshold excitation level increases with increasing jet temperature. Furthermore, the preferential Strouhal number is found not to change significantly with a change of the jet operating conditions. Finally, the effects of the nozzle exit boundary layer thickness appear to be similar for both heated and unheated jets at low Mach numbers

Acoustically excited heated jets. 3: Mean flow data

This is Part 3 of a report on the excitability of heated jets under the influence of acoustic excitation. The effects of upstream internal acoustic excitation on jet mixing were described in Part 1. Part 2 described the effects of external excitation on flow mixing. Part 3 contains quantitative results from the measurements of mean Mach number and temperature and consists of radial profiles and centerline distributions measured at selected jet operating conditions for internally excited and unexcited jets. The mean flow data are presented in both graphical and tabulated forms. For the sake of completeness, this part contains temperature probe calibration curves also