Uncertainty,belief, and probability1

We introduce a new probabilistic approach to dealing with uncertainty, based on the observation that probability theory does not require that every event be assigned a probability. For a nonmeasurable event (one to which we do not assign a probability), we can talk about only the inner measure and outer measure of the event. In addition to removing the requirement that every event be assigned a probability, our approach circumvents other criticisms of probability-based approaches to uncertainty. For example, the measure of belief in an event turns out to be represented by an interval (defined by the inner and outer measures), rather than by a single number. Further, this approach allows us to assign a belief (inner measure) to an event E without committing to a belief about its negation -E (since the inner measure of an event plus the inner measure of its negation is not necessarily one). Interestingly enough, inner measures induced by probability measures turn out to correspond in a precise sense to Dempster-Shafer belief functions. Hence, in addition to providing promising new conceptual tools for dealing with uncertainty, our approach shows that a key part of the important Dempster-Shafer theory of evidence is firmly rooted in classical probability theory. Cet article présente une nouvelle approche probabiliste en ce qui concerne le traitement de l'incertitude; celle-ci est basée sur l'observation que la théorie des probabilityés n'exige pas qu'une probabilityé soit assignée à chaque événement. Dans le cas d'un événement non mesurable (un événement pour lequel on n'assigne aucune probabilityé), nous ne pouvons discuter que de la mesure intérieure et de la mesure extérieure de l'évenément. En plus d'éliminer la nécessité d'assigner une probabilityéà l'événement, cette nouvelle approche apporte une réponse aux autres critiques des approches à l'incertitude basées sur des probabilityés. Par exemple, la mesure de croyance dans un événement est représentée par un intervalle (défini par la mesure intérieure et extérieure) plutǒt que par un nombre unique. De plus, cette approche nous permet d'assigner une croyance (mesure intérieure) à un événement E sans se compromettre vers une croyance à propos de sa négation -E (puisque la mesure intérieure d'un événement et la mesure intérieure de sa négation ne sont pas nécessairement une seule et unique mesure). II est intéressant de noter que les mesures intérieures qui résultent des mesures de probabilityé correspondent d'une manière précise aux fonctions de croyance de Dempster-Shafer. En plus de constituer un nouvel outil conceptuel prometteur dans le traitement de l'incertitude, cette approche démontre qu'une partie importante de la théorie de l'évidence de Dempster-Shafer est fermement ancrée dans la theorie classique des probabilityés.     

High-Temperature Stress-Strain Behavior of MgO in Compression

Compressive stress-strain curves for several types of polycrystalline MgO specimens were correlated with those for single crystals and analyzed as a function of grain size and grain-boundary character at 1200° and 1400°C for several strain rates. The results for fully dense specimens were explained in terms of grain-boundary sliding and intergranular separation in addition to slip. The modification of grain-boundary nature concurrent with heat treatment for grain growth, caused by residual LUF, was associated with enhanced grain-boundary sliding and intergranular separation. For grain sizes <30 μm, it was concluded that the von Miss criteria for ductility could be relaxed by the Occurrence of dislocation climb and, to a limited extent, by intergranular separation. Yield drop corresponding to dislocation multiplication occurred when grain-boundary sliding was initially promoted. Specimens with a liquid phase of adequate viscosity also indicated plasticity accompanied by high strength. Specimens with clean grain boundaries exhibited ductility and normal strain hardening with no intergranular separation.     

Stability of Aqueous α-Al2O3 Suspensions with Poly(methacrylic acid) Polyelectrolyte

Stability of aqueous α-Al₂O₃ suspensions with Na⁺ salt of poly(methacrylic acid) (PMAA-Na) polyelectrolyte was studied as a function of pH. At a given pH, the transition from the flocculated to the dispersed state corresponded to the adsorption saturation limit of the powders by the PMAA. As the pH was decreased, the adsorption saturation limit increased until insolubility and charge neutralization of the PMAA was approached. The critical amount of PMAA required to achieve stability is outlined in a stability map.     

SIMULATION OF FILLING AND EMPTYING IN A HEXAGONAL-SHAPE SOLAR GRAIN SILO

ABSTRACT

A new silo design for grain-storage is examined using a numerical procedure to model its 3D granular flows during the filling and emptying processes. The authors in Hemández-Cordero, et al. Korea-Australia Rheol. J. 12(1)269-281(2000)] have previously presented the design of the new silo and its observed flow behavior. Its main characteristic is the almost complete elimination of excessive dynamics stresses. Since the required computational resources to model the transient phenomena in these experiments are enormous, here, we present basic numerical results related to packing and dynamics of grains considering this complex design. Especial emphasis is given to simulate in great detail collisions of spherical grains with the walls, between themselves, as well as the complex geometry of the new silo, such as filling and unloading openings, inclined walls, etc. The interactions include compressive normal forces between grains as well as tangential forces involved in sliding and rolling between two kernels. Virtual contact mechanics valid in the vicinity of the symmetry plane of the silo are also prescribed, permitting predictions closer to experimentally observed behavior. In spite of the complexity of interactions, steady flow patterns results obtained with reasonable computational times are presented.     

A Review of: “ADVANCES IN MATHEMATICAL SYSTEMS THEORY” Edited by Preston C. Hammer. The Pennsylvania State University Press,University Park,Penn., 1969, 174 pp

It is proposed that Nature's most fundamental design involves a global hierarchy with discrete, self-similar systems populating each level. Evidence supporting this cosmological paradigm is cited and several predictions are made.     

URBAN BUILT ENVIRONMENTS,ACCESSIBILITY, AND TRAVEL BEHAVIOR IN A DECLINING URBAN CORE: THE EXTREME CONDITIONS OF DISINVESTMENT AND SUBURBANIZATION IN THE DETROIT REGION

The research explores the impact of socioeconomic and racial variables on accessibility to urban amenities and travel in compact urban built environments that have traditionally been viewed as improving access to daily destinations and promoting nonmotorized travel: urban environments characterized by high densities, mixed land uses, and high connectivity. The study focuses on six neighborhoods in the Detroit region. Two neighborhoods are within the city itself, and predominantly poor and Black, and four of the neighborhoods are in the region surrounding the city, and they are predominantly wealthy and White. This study at the neighborhood scale enables an analysis into how class and race affect accessibility and travel in neighborhoods experiencing urban disinvestment and decline. The research shows that the traditional relationship between high densities, mixed land uses, high connectivity, greater accessibility, and pedestrian activity is significantly weaker in declining inner cities.     

PRICE ADJUSTING SAMPLING PLANS

A novel idea for the development of statistical sampling plans is presented. The salient feature of this inspection plan is that rejection of lots cannot take place, yet the consumer is indifferent to lot quality. Simple examples are discussed. Advantages and disadvantages of this type plan are suggested.