A temporal database forecasting algebra

Though forecasting methods are used in numerous fields, we have seen no work on providing a general theoretical framework to build forecast operators into temporal databases, producing an algebra that extends the relational algebra. In this paper, we first develop a formal definition of a forecast operator as a function that satisfies a suite of forecast axioms. Based on this definition, we propose three families of forecast operators called deterministic, probabilistic, and possible worlds forecast operators. Additional properties of coherence, orthogonality, monotonicity, and fact preservation are identified that these operators may satisfy (but are not required to). We show how deterministic forecast operators can always be encoded as probabilistic forecast operators, and how both deterministic and probabilistic forecast operators can be expressed as possible worlds forecast operators. Issues related to the complexity of these operators are studied, showing the relative computational tradeoffs of these types of forecast operators. We explore the integration of different forecast operators with standard relational operators in temporal databases—including extensions of the relational algebra for the probabilistic and possible worlds cases—and propose several policies for answering forecast queries. Instances where these different forecast policies are equivalent have been identified, and can form the basis of query optimization in forecasting. These policies are evaluated empirically using a prototype implementation of a forecast query answering system and several forecast operators.     

Some Problems Concerning the Mechanism of the Isotactic Polymerization of Methyl Methacrylate Initiated by Organomagnesium Compounds in Toluene Solution—Application of Modified Dilatometer and NMR Methods

A dilatometer capable of being rapidly filled with monomer and initiator solutions mixed under carefully controlled conditions and a modification of an NMR T₁ program, adapted to store and display on recall the results of frequent sweeps at 30-s intervals of relevant proton resonances of a polymerizing mixture, are reported. These techniques have been applied to the identification of the optimum conditions for efficient, initiation of isotactic polymerization and investigation of the mechanism of propagation. It is shown that heat treatment does not remove the coordinated THF (1 molecule per RMg group) when toluene-soluble “tBuMgBr” or “PhMgBr” initiators are prepared and that the optimum THF concentration is slightly in excess of this. The nature of the solute in the toluene-soluble initiator solutions is discussed. The kinetics of the polymerization change from internal zero order to internal order of one with respect to monomer as the temperature increases from 225–275 K. This is consistent with a previously proposed mechanism in which propagation proceeds through a complex between monomer and the active center.     

Hidden lessons: How a focus on slope-like properties of quadratic functions encouraged unexpected generalizations

This article presents secondary students’ generalizations about the connections between algebraic and graphical representations of quadratic functions, focusing specifically on the roles of the parameters a, b, and c in the general form of a quadratic function, y = ax² + bx + c. Students’ generalizations about these connections led to a surprising finding: two-thirds of the students interviewed identified the parameter a as the “slope” of the parabola. Analysis of qualitative data from interviews and classroom observations led to the development of three focusing phenomena in the classroom environment that inadvertently supported a focus on slope-like properties of quadratic functions: (a) the use of linear analogies, (b) the rise over run method, and (c) viewing a as dynamic rather than static.     

MM3 parameterization for the B?N dative bond

A number of compounds that contain the B? N dative bond have been found to exhibit intriguing physiological activities. Although there is no proven mechanism for this activity, one hypothesis is that some form of borane transfer reaction occurs. In this scenario, the B? N dative bond within the small molecule, putative pharmacore breaks, and the borane forms a new dative bond with a Lewis base site on some critical protein. For this hypothesis to be investigated further from a computational perspective, an improved MM3 parameter set for tetravalent B? tetravalent N bonds has been developed and is reported here. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 913–922, 2001