The use of a visual representation in learning about proportional relations studied, examining students' understandings of the invariance of a multiplicative relation on both sides of a proportion equation and the invariance of the structural relations that exist in different semantic types of proportion problems. Subjects were 49 high-ability sixth-grade mathematics students using the Jasper A...

We consider elections where the voters come one at a time, in a streaming fashion, and devise space-efficient algorithms which identify an approximate winning committee with respect to common multiwinner proportional representation voting rules; specifically, we consider the Approval-based and the Borda-based variants of both the Chamberlin– Courant rule and the Monroe rule. We complement our a...

A nonuniform multi-Gabor expansion (MGE) scheme is studied under proportional time and fi'equency (TF) shifts among different window indices m. In particular, TF parameters for each m are different, but proportional and relevant to windows' TF patterns. The generation of synthesis waveforms for nonuniform MGE is generally difficult. 'Ne show constructively that there is a set of basic synthesis...

In this paper, we focus on efficiently achieving Proportional Delay Differentiation (PDD), an instance of the Proportional Differentiation Model first proposed under the DiffServ framework [IEEE Network (1999)]. PDD can be achieved using a few algorithms, one of the most well-known being Waiting Time Priority(WTP). Using WTP [Proc. ACM SIGCOMM (1999)] as a reference, we show that our proposed S...

The goal of this paper is to examine the incentives to vote insincerely, other than those induced by rounding, faced by voters under proportional representation. We investigate two models of voters. We show that ‘seat maximisers can have an incentive to manipulate only if a threshold is present. We show that ‘power maximisers can have an incentive to manipulate both in the presence and in the a...

 Appreciate the history of proportional control valves.  Explain the operation of proportional solenoids.  Describe various design considerations for proportional control valves.  Describe various proportional direction and proportional pressure control valves.  Explain the working of two-stage proportional valves.  Compare a proportional valve and a servo valve.  Describe the various ap...

The purpose of this project is to show observations taken from the Iterative Proportional Scaling algorithm when used with data taken from Hierarchical LogLinear Models. We show with empirical proof that the difference between decomposable and non-decomposable graph models used is not exceedingly different. For the purpose of this project we looked at the properties of the two, three, and four ...

Most studies of the so-called Proportion Problem seek to understand how lexical and structural properties of sentences containing adverbial quanti ers give rise to various proportional readings. This paper explores a related but distinct problem: given a use of a particular sentence in context, why do only some of the expected proportional readings seem to be available? That is, why do some sen...