The role of multiple solution tasks in developing knowledge and creativity in geometry

This paper describes changes in students’ geometrical knowledge and their creativity associated with implementation of Multiple Solution Tasks (MSTs) in school geometry courses. Three hundred and three students from 14 geometry classes participated in the study, of whom 229 students from 11 classes learned in an experimental environment that employed MSTs while the rest learned without any special intervention in the course of one school year. This longitudinal study compares the development of knowledge and creativity between the experimental and control groups as reflected in students’ written tests. Geometry knowledge was measured by the correctness and connectedness of the solutions presented. The criteria for creativity were: fluency, flexibility, and originality. The findings show that students’ connectedness as well as their fluency and flexibility benefited from implementation of MSTs. The study supports the idea that originality is a more internal characteristic than fluency and flexibility, and therefore more related with creativity and less dynamic. Nevertheless, the MSTs approach provides greater opportunity for potentially creative students to present their creative products than conventional learning environment. Cluster analysis of the experimental group identified three clusters that correspond to three levels of student performance, according to the five measured criteria in pre- and post-tests, and showed that, with the exception of originality, performance in all three clusters generally improved on the various criteria.     

Chaos in social learning with multiple true states

Most existing social learning models assume that there is only one underlying true state. In this work, we consider a social learning model with multiple true states, in which agents in different groups receive different signal sequences generated by their corresponding underlying true states. Each agent updates his belief by combining his rational self-adjustment based on the external signals he received and the influence of his neighbors according to their communication. We observe chaotic oscillation in the belief evolution, which implies that neither true state could be learnt correctly by calculating the largest Lyapunov exponents and Hurst exponents.     

Reliability matrix solution to multiple mechanism prediction

We present a method for predicting the failure rate and thus the reliability of an electronic system by summing the failure rate of each known failure mechanism. We use a competing acceleration factor methodology by combining the physics of failure for each mechanism with its own effect as observed by High/Low temperature and High/Low voltage stresses. Our Multiple High Temperature Overstress Life-test (M-HTOL) method assumes that the lifetime of each failure mechanism follows constant rate distribution whereby each mechanism is independently accelerated by its own stress factors. Stresses include temperature, frequency, current, and other factors that can be entered into a reliability model. The overall failure rate thus, also follows an exponential distribution and is described as the standard FIT (Failure unIT or Failure in Time). This method combines mathematical models for known failure mechanism and solves them simultaneously for a multiplicity of accelerated life test results to find a consistent set of weighting factors for each mechanism. The result of solving the system of equations is a more accurate and a unique combination for each system model by proportional summation of each of the contributing failure mechanisms.     

A numerical algorithm for pricing electricity derivatives for jump-diffusion processes based on continuous time lattices

We present a numerical algorithm for pricing derivatives on electricity prices. The algorithm is based on approximating the generator of the underlying price process on a lattice of prices, resulting in an approximation of the stochastic process by a continuous time Markov chain. We numerically study the rate of convergence of the algorithm for the case of the Merton jump-diffusion model and apply the algorithm to calculate prices and sensitivities of both European and Bermudan electricity derivatives when the underlying price follows a stochastic process which exhibits both fast mean-reversion and jumps of large magnitude.     

Arbitration procedures with multiple arbitrators

We consider two final-offer arbitration procedures in the case where there is more than one arbitrator. Two players, labeled 1 and 2 and interpreted here as Labor and Management, respectively, are in dispute about an increase in the wage rate. They submit final offers to a Referee. There are N arbitrators. Each of the arbitrators has her own assessment and selects the offer which is closest to her assessment. After that each arbitrator informs the Referee about her decision. The Referee counts the votes and declares the player obtaining the most votes to be the winner. Under the second arbitration scheme, the Referee takes into account only the assessments which lie between the players’ offers. The game is modeled as a zero-sum game. The Nash equilibrium in this arbitration game is derived.     

Fractional Bilinear Stochastic Equations with the Drift in the First Fractional Chaos

Abstract

In the paper we compute the explicit form of the fractional chaos decomposition of the solution of a fractional stochastic bilinear equation with the drift in the fractional chaos of order one and initial condition in a finite fractional chaos. The large deviations principle is also obtained for the one-dimensional distributions of the solution of the equation perturbed by a small noise.     

Indirect test of M-S circuits using multiple specification band guarding

Testing analog and mixed-signal circuits is a costly task due to the required test time targets and high end technical resources. Indirect testing methods partially address these issues providing an efficient solution using easy to measure CUT information that correlates with circuit performances. In this work, a multiple specification band guarding technique is proposed as a method to achieve a test target of misclassified circuits. The acceptance/rejection test regions are encoded using octrees in the measurement space, where the band guarding factors precisely tune the test decision boundary according to the required test yield targets. The generated octree data structure serves to cluster the forthcoming circuits in the production testing phase by solely relying on indirect measurements. The combined use of octree based encoding and multiple specification band guarding makes the testing procedure fast, efficient and highly tunable. The proposed band guarding methodology has been applied to test a band-pass Butterworth filter under parametric variations. Promising simulation results are reported showing remarkable improvements when the multiple specification band guarding criterion is used.     

The Determination Of Sub Part-Per-Billion Levels Of Volatile Organic Compounds In Air By Pre-Concentration From Small Sample Volumes

Abstract

Trace level Volatile Organic Compounds (VOCs) in ambient air are normally determined according to EPA Method TO-14. This method describes the analysis in ambient air of 41 VOCs, ranging in boiling point from -29 to 215°C. It covers a concentration range from 0.2 to 20 parts per billion, volume/volume (ppb), and specifies sample enrichment of a 400 mL air sample on glass beads at -160°C. While this sample volume provides sub-ppb levels of VOC detection for target analytes when using a quadrupole mass spectrometer detector in SIM mode or when using GC detectors, the identification of non-target analytes may only be done in full scan mode for higher concentrations. Also with this sample volume a Nafion dryer is needed for water removal thereby lowering the recovery of polar VOCs.

Because of the very high sensitivity of the ion trap MS, relatively small air volumes (60 mL) are adequate to obtain the required or lower detection levels. An integrated air analysis system based on a GC-ion-trap MS has been investigated and is described. This system has a built-in cryogenic trap and necessary valving, internal standard gas sampling loop, and is controlled from the GC-MS workstation. The linearity, precision, and method detection levels obtainable with this system when using small volumes are reported. In addition, examples of the quantitative and qualitative analysis of ambient air samples are shown.     

Multiple Statistical models for simulation and prediction of nonlinear processes

The paper describes a parameterisation procedure for multiple nonlinear equations with intercepts. These equations may consist of numerous members with few practical limitations on their structure. Examples are given on the application of the procedure to simulation in the areas of chemical technology and hydrology. Advantages of the proposed method are simplicity of the fitting procedure, high accuracy of simulations and more reliable simulations beyond the calibration range