Discrete-Time Constrained Average Stochastic Games with Independent State Processes

In this paper, we consider the discrete-time constrained average stochastic games with independent state processes. The state space of each player is denumerable and one-stage cost functions can be unbounded. In these game models, each player chooses an action each time which influences the transition probability of a Markov chain controlled only by this player. Moreover, each player needs to pay some costs which depend on the actions of all the players. First, we give an existence condition of stationary constrained Nash equilibria based on the technique of average occupation measures and the best response linear program. Then, combining the best response linear program and duality program, we present a non-convex mathematic program and prove that each stationary Nash equilibrium is a global minimizer of this mathematic program. Finally, a controlled wireless network is presented to illustrate our main results.

An Artificial Neural Networks Model for Compressive Strength of Self-Compacting Concrete

An experimental program was undertaken to evaluate the compressive strength of self-compacting concrete using commercial mathematic program. Sample variation was monitored using an experimental cylinder of concrete measuring 150 mm in diameter and 300 mm in height. This research examined various mixture designs in the laboratory tests with the goal of creating mixtures with desirable flow specification that did not require additional vibration yet provided adequate compressive strength. After 28 days, compressive strength of cylinder concrete determination, a model of Artificial Neural Networks (ANNs) was designed for this research and the results were obtained in this model of ANN. Both experimental tests and mix design program data was analyzed with statistical packet software. The result of statistical analysis has been done in 98.54 percent of confidence interval. It has been seen that the ANN can be used as reliable modelling method for similar experiment.

Teacher To Teacher: Take-Home Kits

Our half-day kindergarten did not permit us to extend and enrich our mathematic program the way we wanted to pre ent it. Therefore, we decided to develop take-home kits. They were intended to be of high interest, fun, and yet simple enough that a student could do the activities alone. For a student fortunate enough to have help, extended activities were included. Each kit contained a pictorial evalumion sheet that could be completed by the tudent. The evaluation were intended to keep us infanned about the appeal of the activity and the abilities of the students. The evaluation sheets were filed and made into a book for each student to take home at the end of the year.

By Way of Introduction

The decription of the goal of elementary chool mathematics is often made using a two-dimensional model. One dimension include the content objectives, the other, the process objectives. Content objectives include the topics in mathematics that are studied. whereas proce objectives are the behaviors, the procees that student hould develop and use as the content objectives are studied and mastered. One such model used in the 1981–82 National Assessment of Educational Progress (NAEP 1981) is shown in figure 1. As an alternative to thi framework. some groups have identified a set of basic-skill area to be studied in elementary school mathematics. The ten areas listed by the National Council of Supervisors of Mathematic (1977) arc as follow: (1) problem solving: (2) applying mathematics to everyday situations: (3) alertness to the reasonableness of result; (4) estimation and approximation; (5) appropriate computational skills; (6) geometry: (7) measurement: (8) reading, interpreting. and contructing tables; (9) using mathematics to predict; and (10) computer literacy. One important goal not specifically mentioned in either of these two cheme is that of mathematical thinking. yet the development of mathematical thinking in students should be a central goal of any mathematic program.