Many years ago, one of us was reading through L. J. Mordell’s “Diophantine Equations” and was struck by a curious statement—namely, that the curve C : y2 = x3 + 17 contains exactly sixteen points (x, y) with x and y integers (see [6, p. 250]). A list of the points followed. Many questions immediately came to mind. How did they find these points, called integer points? How did they prove that th...

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Such a space is unique up to isometry. We shall investigate group LIP(U) of bilipschitz homeomorphisms of U and some related groups. Indeed, the group H(U) of all homeomorphisms of U comes to mind first. However, by V. Uspenskiy [Us], U is homeomorphic to l2. So H(U) is in fact the group of homeomomorphisms of a Banach space, and can be better understood as such. For LIP(U) and for other groups...

The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this document are to be interpreted as described in RFC 2119 [6]. Although RFC 2119 was written with protocols in mind, the key words are used in this document for similar reasons. They are used to ensure the results of measurements from two different implementatio...

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Communication among nuclear family is a complex but immediate problem due to the small number of family members and the diverse daily schedule of modern society. Because family members have to live together every day, so they must consider and coordinate mutually in communication to avoid estranging by over indifference. With the ambient environment and sensible space technology mentioned above...

Consumer theory is concerned with how a rational consumer would make consumption decisions. What makes this problem worthy of separate study, apart from the general problem of choice theory, is its particular structure that allows us to derive economically meaningful results. The structure arises because the consumer’s choice sets sets are assumed to be defined by certain prices and the consume...

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Applications of Bayesian inference to human decisionmaking have met with mixed success, but new theoretical developments and experimental paradigms are helping to form a clearer picture of the role that inference plays in human cognition. We combine the latest ideas to provide evidence that at a computational level, the mind’s ability to make predictions may be grounded in Bayesian theory. Our ...

popular and promising members, has cut short a career of great industry and usefulness in administration and science, and deprived a large circle ot friends of a staunch and greatly respected and cherished acquaintance. Dr. Barclay had just completed 39 years of age, and on the 30th of September next would have completed 17 years' service. He was therefore entering that period of life and servi...