The decision data of human judgments with preferences are often vague in many real life cases. Human judgments with preferences are often unclear and hard to estimate by exact numerical values. So that the traditional ways of using crisp values are inadequate. The relationship among criteria and choosing and rating alternatives based on criterion are often expressed in terms of linguistic terms...

Heat transfer in the thermal entrance region of trapezoidal microchannels is investigated for hydrodynamically fully developed, single-phase, laminar flow with no-slip conditions. Three-dimensional numerical simulations were performed using a finite-volume approach for trapezoidal channels with a wide range of aspect ratios. The sidewall angles of 54.7 and 45 are chosen to correspond to etch-re...

Last Time: We discussed quadrature rules, which are means of estimating integrals of functions using a weighted sum of function values. Among these, one of the simplest is the trapezoidal rule, which derives its name from the fact that it attempts to approximate the area under the curve using a trapezoid. Although it can be proved the accuracy of this rule increases quadratically with the numbe...

Bovine brain tubulin, purified by phosphocellulose chromatography (PC), was assembled in the presence of 10% dimethyl sulfoxide (DMSO), and the reaction was monitored turbidimetrically. Samples were fixed in glutaraldehyde-tannic acid after completion of polymerization, as indicated by no further change in absorbance, and then sectioned and studied electron microscopy, with special attention be...

We study the behavior of rules for the adjudication of conflicting claims when there are a large number of claimants with small claims. We model such situations by replicating some basic problem. We show that under replication, the random arrival rule (O’Neill, 1982) behaves like the proportional rule, the rule that is the most often recommended in this context. Also, under replication, the min...

A “scoring rule” is an assignment of a value to every tuple (of varying sizes). This paper is concerned with the issue of how to modify a scoring rule to apply to the case where weights are assigned to the importance of each argument. We give an explicit formula for incorporating weights that can be applied no matter what the underlying scoring rule is. The formula is surprisingly simple, in th...

The effects of cutting edge shapes on the phenomena of rubbing and ploughing in nano-abrasive machining were investigated. The shapes under investigation include flat, spherical and trapezoidal shapes. The tool with the flat end geometry shows a fast initiation of ploughing, because it has the largest surface area to engage more atoms. It doesn’t show rubbing phenomenon at the (initial) depth o...

The main aim of this paper is to give an axiomatic characterization of the interval Baker-Thompson rule.