Smoothing positive currents and the existence of K?hler-Einstein metrics

In this paper,we prove a general existence theorem of Khler-Einstein metrics on complete Khler manifolds.We use the heat equation method smoothing certain positive (1,1) current in the canonical class.     

By How Much Can Residual Minimization Accelerate the Convergence of Orthogonal Residual Methods?

We capitalize upon the known relationship between pairs of orthogonal and minimal residual methods (or, biorthogonal and quasi-minimal residual methods) in order to estimate how much smaller the residuals or quasi-residuals of the minimizing methods can be compared to those of the corresponding Galerkin or Petrov–Galerkin method. Examples of such pairs are the conjugate gradient (CG) and the conjugate residual (CR) methods, the full orthogonalization method (FOM) and the generalized minimal residual (GMRES) method, the CGNE and BiCG versions of applying CG to the normal equations, as well as the biconjugate gradient (BiCG) and the quasi-minimal residual (QMR) methods. Also the pairs consisting of the (bi)conjugate gradient squared (CGS) and the transpose-free QMR (TFQMR) methods can be added to this list if the residuals at half-steps are included, and further examples can be created easily.The analysis is more generally applicable to the minimal residual (MR) and quasi-minimal residual (QMR) smoothing processes, which are known to provide the transition from the results of the first method of such a pair to those of the second one. By an interpretation of these smoothing processes in coordinate space we deepen the understanding of some of the underlying relationships and introduce a unifying framework for minimal residual and quasi-minimal residual smoothing. This framework includes the general notion of QMR-type methods.     

Do mergers enhance the performance of hospital efficiency?

Due to the wave of mergers that have taken place in the USA, the early 1990s could be labelled as a restructuring era for health care systems. The question of whether mergers have an impact on organizational performance is still an area of interest for health services researchers. In this study, we examined the impacts of horizontal mergers of US hospital's technical efficiency before and after merger using longitudinal Data Envelopment Analysis (DEA). The findings of our study illustrate that mergers do increase a hospital's level of efficiency. Constant returns-to-scale model indicated an overall reduction in input utilisation after merger, compared to variable returns-to-scale model. This indicates the role of scale efficiency as a dominant source of improvement in inefficiency of hospitals involved in horizontal mergers, but not for technical efficiency. Suggestions for future study are provided.     

The Measurement of Volume: Why Do Young Children Measure Inaccurately?

A total of 257 children in grades 2–5 were individually interviewed to find the grade level at which they demonstrated transitive reasoning and unit iteration in the measurement of volume. In the transitivity task, the children were asked if a larger, empty container could be used to compare the quantity of popcorn kernels (about 350 cc) in two containers that looked very different. The unit‐iteration task was similar except that children were asked if a small cup could be used to compare similar quantities of rice in two containers. It was found that a majority of children (51%) demonstrated transitive reasoning by third grade and that a majority (56%) demonstrated unit iteration by fourth grade. A conclusion reached is that the standard of the National Council of Teachers of Mathematics (2000) expecting children to understand units of measurement by grade 2 is unrealistic. Better principles of teaching are also suggested to encourage children to think logically.     

Comparative studies of mathematics teaching: does the means of analysis determine the outcome?

This paper addresses four questions concerning the influence of culture on mathematics teachers’ professional practice. Firstly, drawing on categorical data yielded by the application of low inference coding schedule to video recordings of sequences of lessons taught by case study teachers on four common topics in England, Flanders, Hungary and Spain, we undertook an exploratory factor analysis to examine the ways in which such coded variables interact. This process yielded five factors, each of which was interpretable against the literature and highlighted the extent to which dichotomisations of mathematics teaching as reform or traditional are not necessarily helpful, not least because all project teachers exhibited characteristics of both. Secondly, factors scores were analysed by nationality to reveal culturally located practices resonant with the available literature. Thirdly, cluster analyses yielded four well-defined cross-cultural clusters of episodes, each indicative of particular didactical perspectives that appeared to challenge the exclusivity of these culturally located practices. Finally, the key methodological finding was that the manner in which data are analysed influences greatly the outcomes of comparative mathematics research.     

The Prevalence and Disadvantage of Min-Counting in Seventh Grade: Problems with Confidence As Well As Accuracy?

In this research, we examined how 200 students in seventh grade (around 12 years old) solved simple addition problems. A cluster approach revealed that less than half of the cohort displayed proficiency with simple addition: 35% predominantly used min-counting and were accurate, and 16% frequently made min-counting errors. Students who frequently used min-counting for simple addition, regardless of accuracy, showed lower achievement in mathematics compared to students who relied on accurate retrieval-based strategies. The findings indicate that for many students at this stage of schooling, performance is characterized by accurate min-counting, which is suggestive of a lack of confidence with retrieval. Further, this pattern of performance appears to be more prominent among girls. Confidence with retrieval may be impeding strategy development and hindering learning. The role of confidence in retrieval development needs to be better understood and possibilities for further research are discussed.     

An inventory model: What is the influence of the shape of the lead time demand distribution?

In this paper the influence of the shape of the lead time demand distribution is studied for a specific inventory model which is described in a preceding paper by Heuts and van Lieshout [4]. This continuous review inventory model uses as lead time demand distribution a Schmeiser-Deutsch distribution (S-D distribution) [9]. In a previous paper [4] an algorithm was given to solve the decision problem.In the literature attention is given to the following problem: what information on the demand during the lead time is necessary and sufficient to obtain good decisions. Using a (s, S) policy; Naddor [8] concluded that thespecific form of the lead time demand distribution is negligible, and that only its first two moments are essential. For a simple (s, q) control system Fortuin [3] comes to the same conclusion. Both authors analysed the case with known lead times and with given demand distributions from the class of two parameter distributions. So in fact their results are obvious, as the lead time demand distributions resulting from their suppositions are all nearly symmetric. We shall demonstrate that the skewness of the lead time demand distribution in our inventory model is also an important measure, which should be taken into account, as the cost differences with regard to the case where this skewness measure is not used, can be considerable.     

Do Log Factors Matter? On Optimal Wavelet Approximation and the Foundations of Compressed Sensing

Foundations of Computational Mathematics - A signature result in compressed sensing is that Gaussian random sampling achieves stable and robust recovery of sparse vectors under optimal conditions...     

Two Orbits: When is one in the closure of the other?

Let G be a connected linear algebraic group, let V be a finite dimensional algebraic G-module, and let and be two G-orbits in V. We describe a constructive way to find out whether or not lies in the closure of . Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2009, Vol. 264, pp. 152–164. In memory of V.A. Iskovskikh     

Do the generalized polynomial chaos and Fröbenius methods retain the statistical moments of random differential equations?

The aim of this paper is to explore whether the generalized polynomial chaos (gPC) and random Fröbenius methods preserve the first three statistical moments of random differential equations. There exist exact solutions only for a few cases, so there is a need to use other techniques for validating the aforementioned methods in regards to their accuracy and convergence. Here we present a technique for indirectly study both methods. In order to highlight similarities and possible differences between both approaches, the study is performed by means of a simple but still illustrative test-example involving a random differential equation whose solution is highly oscillatory. This comparative study shows that the solutions of both methods agree very well when the gPC method is developed in terms of the optimal orthogonal polynomial basis selected according to the statistical distribution of the random input. Otherwise, we show that results provided by the gPC method deteriorate severely. A study of the convergence rates of both methods is also included.     

Evolving to the edge of chaos: Chance or necessity?

We show that ecological systems evolve to edges of chaos (EOC). This has been demonstrated by analyzing three diverse model ecosystems using numerical simulations in combination with analytical procedures. It has been found that all these systems reside on EOC and display short-term recurrent chaos (strc). The first two are non-linear food chains and the third one is a linear food chain. The dynamics of first two is dictated by deterministic changes in system parameters. In contrast to this, dynamics of the third model system (the linear food chain) is governed by both deterministic changes in system parameters as well as exogenous stochastic perturbations (unforeseen changes in initial conditions) of these dynamical systems.     

What part of the concept of acceleration is difficult to understand: the mathematics, the physics, or both?

In this paper, details of student difficulties in understanding the concept of acceleration and the mathematical and physical/intuitive sources of these are delineated by utilizing the teaching experiment methodology. As a result of the study, two anchoring analogies are proposed that can be used as a diagnostic tool for students’ alternative conceptions. These can be used in teaching to highlight the peculiarity of acceleration concept. This study portrays how seeing acceleration as ‘rate of change’ of a quantity (velocity) and recognizing the consequences of such a definition are hindered in certain ways which in turn negatively affect learning the concept of force. This is also an example that illustrates that a rather “simple” mathematical concept (i.e., rate of change) for the expert can become a complex phenomenon when embedded in a physical concept (i.e., acceleration) which is consistently found to be as a misconception among learners at various levels that is widely occurring and very resistant to change.     

How Do Cultural Classes Emerge from Assimilation and Distinction? An Extension of the Cucker-Smale Flocking Model

When cultural tastes are not neutral but hierarchically matched to social status, people assimilate themselves to higher status by consuming cultural goods while distinguishing themselves from lower status by developing new tastes. Extending the Cucker-Smale model for mutual influence among agents, we examine when and how many cultural classes emerge from continuous distributions of tastes and what conditions those classes satisfy, through the assimilation-distinction mechanism. We simulate the models with different initial distributions of tastes (uniform, normal, and chi-square), given various ranges of 2 parameters: (a) the strength and (b) the range of distinction relative to assimilation. Tastes are flocking and cultural classes emerge when the range of assimilation is much larger than that of distinction. The number of classes increases with the strength of distinction, whereas the distance between classes equals the range of distinction. Some properties of emergent classes are mathematically proved. First, in a two-class system, the stronger distinction, the larger the upper class. Second, in a three-class system, the middle class is necessarily larger than the lower class and likely larger than the upper class. Third, a 3-class system cannot emerge if distinction is weaker than assimilation. These properties are universal and do not depend on the initial distribution of cultural tastes. This independence predicts homogeneous cultural classes emerging across different social conditions. Also, the cultural middle class as the largest group may explain why subjective class consciousness is often higher than objective position. Unless assimilating efforts can reach an infinite range, there emerges a cultural outcast at the lowest end of the cultural hierarchy.     

Playing with Representations: How Do Kids Make Use of Quantitative Representations in Video Games?

This paper describes the use of quantities in video games by young people as part of a broader effort to understand thinking and learning across naturally occurring contexts of activity. Our approach to investigating the use of quantities in game play is ethnographic; we have followed eight children over a six-month period as they play their own games at home. The data set is composed of video recordings and artifact-based interviews. The concept of disciplined perception is used to understand how quantities are coordinated during game play. The current study shows young people using quantities in games to make predictions and organize their actions based on those predictions. Some ideas based on the study’s findings for using video games in school are discussed.