This paper is concerned with linear uniformly elliptic and par abolic partial di erential equations in divergence form It is assumed that the coe cients of the equations are random variables constant in time The Green s functions for the equations are then random variables Regularity properties for expectation values of Green s functions are obtained In par ticular it is shown that the expectat...

The present paper gives a new view point for the di erential operators with respect to the coordinates of the quantum matrix space. A special emphasis is put on an inductive construction of these di erential operators from the q-di erence operators de ned on each columns (resp. rows). This idea for understanding our operators provides us with two important applications: (1) a construction of th...

The methods of temporal di erences (Samuel, 1959; Sutton 1984, 1988) allow agents to learn accurate predictions about stationary stochastic future outcomes. The learning is e ectively stochastic approximation based on samples extracted from the process generating the agent's future. Sutton (1988) proved that for a special case of temporal di erences, the expected values of the predictions conve...

The northern latitudes have warmed by about 0.8 C since the early 1970s, but not all areas have warmed equally. Eurasia shows an overall warming trend, while North America exhibits warming at a lower rate and even a slight cooling trend during the last 50 years in the Eastern USA. We analyzed a recently developed satellite normalized di erence vegetation index (NDVI) data set (July 1981 to Dece...

The most commonly used space in architectural education is the studio, which functions both as a learning centre and as a complex social organization. The behavioural elements in the design studio are analysed with respect to the social processes of environmental psychology; namely privacy, personal space, territoriality and crowding. A case study was conducted to evaluate the di¡erences betwee...

Programmers frequently have to retrieve and link information from various software documents to accomplish a maintenance task. Ciao is a graph-based navigator that helps programmers query and browse structural connections embedded in di erent software and document repositories. A repository consists of a collection of source documents with an associated database that describes their structure. ...

A two dimensional nite di erence model for elastic waves in the ground has been developed The model uses the equation of motion and the stress strain relation from which a rst order stress velocity formulation is obtained The resulting system of equations is discretized using centered nite di erences A perfectly matched layer surrounds the discretized solution space and absorbs the outward trav...

Two hundred seventy-seven position angle and separation measures of 154 double stars are presented. Three of the systems were previously unknown to be double, and 16 other systems were discovered earlier this decade by the Hipparcos satellite. Measures are derived from speckle observations taken with the Wisconsin-Indiana-Yale-NOAO (WIYN) 3.5 m telescope located at Kitt Peak, Arizona. Speckle i...

In raw data in the UK, the income loss on separation for women who were cohabiting is less than the loss for those who were married. Cohabitees lose less even after matching on observable characteristics including age and children. This di¤erence is not explained by di¤erences in access to bene…ts or labour supply responses after separation. We show that the di¤erence arises because of di¤erenc...

The transformation which assigns to a linear operator L the recurrence satis ed by coe cient se quences of the polynomial series in its kernel is shown to be an isomorphism of the corresponding operator algebras We use this fact to help factoring q di erence and recurrence operators and to nd nice power series solutions of linear di erential equations In particular we characterize generalized h...