Pre-service elementary teachers’ strategies for tiling and relating area units

It has been established that preservice elementary school teachers (PSTs) often employ procedural methods when solving measurement problems without conceptual understanding or flexibility, but a significant gap exists in the literature identifying why. Through the lens of discrete and continuous interpretations of area, this study extends the research base by describing strategies PSTs use to tile a two-dimensional space with varying size tiles and what these strategies imply about PSTs’ conceptions of area measurement. These strategies and implied conceptions enable further discussion on the multiple purposes of the area model as an illustrative measure for mathematics throughout the elementary school curriculum.     

Asymptotic behavior of continuous stochastic games

Summary The aim of this paper is to analyze the asymptotic behavior of the value functions of a continuous stochastic game as the number of stages grows to infinity or the discount factor approaches 1. After the setup of the problem we prove that, in both cases, the extrema of the value functions converge to the same limits. The convergence of the value functions is then obtained from the unicity of the solution of a functional problem and it is thus possible to design hypotheses that assure the convergence to a constant. This allows to assign a value to an undiscounted infinite-stage stochastic game in several senses and to show that optimal strategies are available for both players. Furthermore the boundedness of the remainders of the value function after removing the principal terms is analyzed, with appropriate hypotheses, and related to the existence of solutions of a Howard's type functional equation. This allows to show that for an infinite-stage undiscounted stochastic game optimal stationary strategies exist at least if this functional equation has some solution.     

On hedging in finite security markets

A market is considered where trading can take place only at discrete time points, the trading frequency cannot grow without bound, and the number of states of nature is finite. The main objectives of the paper are to show that the market can be completed also with highly correlated risky assets, and to describe an efficient algorithm to compute a self-financing hedging strategy. The algorithm consists off-line of a backwards recursion and on-line of the solution, in each period, of a system of linear equations; it is a consequence of a proof where, using a well-known mathematical property, it is shown that uniqueness of the martingale measure implies completeness also in our setting. The significance of ‘multistate’ models versus the familiar binomial model is discussed and it is shown how the evolution of prices of the (correlated) risky assets can be chosen so that a given probability measure is already the unique equivalent martingale measure.     

Prognostic of glial tumours: Presentation of the problem with solution

A study of glial tumours involving 192 cases is presented. Different issues are addressed: (i) the interrelationships between the histological variables, (ii) the problem of the prediction of the survival time, (iii) the causal role of the variables in the progress of the disease. We propose a three-level grade which can be defined alternatively with perivascular lymphocites or with the signs necrosis and neovascularization. We constructed a predictive model based on the Cox model in which the variables were chosen according to Akaike's criterion. In the explanatory analysis we dropped the variables which could be considered as consequences rather than causes of the disease and we first tested groups of variables (factors): we found that age, the topology and the histology of the tumour were explanatory.     

Strategies and simulations in a semantic framework

By means of several examples of structural operational semantics for a variety of languages, we justify the importance and interest of using the notions of strategies and simulations in the semantic framework provided by rewriting logic and implemented in the Maude metalanguage. On the one hand, we describe a basic strategy language for Maude and show its application to CCS, the ambient calculus, and the parallel functional language Eden. On the other hand, we show how the concept of stuttering simulation can be used inside Maude to show that a stack machine correctly implements the operational semantics of a simple functional language.     

On stationary equilibria of a single-controller stochastic game

We consider a two-person, general-sum, rational-data, undiscounted stochastic game in which one player (player II) controls the transition probabilities. We show that the set of stationary equilibrium points is the union of a finite number of sets such that, every element of each of these sets can be constructed from a finite number of extreme equilibrium strategies for player I and from a finite number of pseudo-extreme equilibrium strategies for player II. These extreme and pseudo-extreme strategies can themselves be constructed by finite (but inefficient) algorithms. Analogous results can also be established in the more straightforward case of discounted single-controller games.     

Nonlinear programming and stationary strategies in stochastic games

We show that an undiscounted stochastic game possesses optimal stationary strategies if and only if a global minimum with objective value zero can be found to an appropriate nonlinear program with linear constraints. This nonlinear program arises as a method for solving a certain bilinear system, satisfaction of which is also equivalent to finding a stationary optimal solution for the game. The objective function of the program is a nonnegatively valued quadric polynomial.This research was supported in part by the National Science Foundation under the grant #ECS-8503440. We wish to thank the referee for many helpful comments and in streamlining the presentation.     

Distinct Selectivity Control in Solar-Driven Bio-Based α-Hydroxyl Acid Conversion: A Comparison of Pt Nanoparticles and Atomically Dispersed Pt on CdS

Solar-driven photocatalytic lignocellulose conversion is a promising strategy for the sustainable production of high-value chemicals, but selectivity control remains a challenging goal in this field. Here, we report efficient and selective conversion of lignocellulose-derived α-hydroxyl acids to tartaric acid derivatives, α-keto acids, and H₂ using Pt-modified CdS catalysts. Pt nanoparticles on CdS selectively produce tartaric acid derivatives via C−C coupling, while atomically dispersed Pt on CdS switches product selectivity to the oxidation reaction to produce α-keto acids. The atomically dispersed Pt species stabilized by Pt−S bonds promote the activation of the hydroxyl group and thus switch product selectivity from tartaric acid derivatives to α-keto acids. A broad range of lignocellulose-derived α-hydroxyl acids was applied for preparing the corresponding tartaric acid derivatives and α-keto acids over the two Pt-modified CdS catalysts. This work highlights the unique performance of metal sulfides in coupling reactions and demonstrates a strategy for rationally tuning product selectivity by engineering the interaction between metal sulfide and cocatalyst.     

以竞赛为抓手,提高化学师范生综合素质

To improve normal university students' comprehensive quality has become a tendency in current innovation of teacher education. Combining with the teaching practice and obtained achievements of students studying in College of Chemistry and Pharmaceutical Science of Guangxi Normal University, this paper discusses the functions of chemistry competitions in cultivating excellent quality, knowledges and skills of normal students, and emphatically introduces principles and implementation strategies.     

Games with Unknown Past

We define a new type of two player game occurring on a tree. The tree may have no root and may have arbitrary degrees of nodes. These games extend the class of games considered by Gurevich-Harrington in [5]. We prove that in the game one of the players has a winning strategy which depends on finite bounded information about the past part of a play and on future of each play that is isomorphism types of tree nodes. This result extends further the Gurevich-Harrington determinacy theorem from [5].