In the present paper we define the notion of fuzzy inner productand study the properties of the corresponding fuzzy norm. In particular, it isshown that the Cauchy-Schwarz inequality holds. Moreover, it is proved thatevery such fuzzy inner product space can be imbedded in a complete one andthat every subspace of a fuzzy Hilbert space has a complementary subspace.Finally, the notions of fuzzy bo...

Brian Tung Leonard Kleinrock Computer Science Department Computer Science Deparment University of California, Los Angeles University of California, Los Angeles Los Angeles, CA 90024 Los Angeles, CA 90024 Abstract The distributed system is becoming increasingly popular, and this produces the need for more sophisticated distributed control techniques. In this paper, we present a method for distri...

A description of the number N(K) of eigenvalues less than K for a pseudo-differential operator with positive symbol is given in terms of the number of unit cubes canonically imbedded in the subset of phase space where the symbol is less than CK. This gives back in particular the order of magnitude of N(K) for elliptic symbols.

We show that the group of piecewise-linear homeomorphisms of R having bounded slopes surjects onto the group QI(R) of all quasi-isometries of R. We prove that the following groups can be imbedded in QI(R): the group of compactly supported piecewise-linear homeomorphisms of R, the Richard Thompson group F , and the free group of continuous rank.

It is shown that the space of all vector elds with divergence and curl in L q ((), q 2 such that the normal-component vanishes one part of @ and the tangential-component vanishes on the other, is compactly imbedded in L 2 (().

• " … make a computer so imbedded, so fitting, so natural, that we use it without even thinking about it. " • " Ubiquitous (pervasive) computing is roughly the opposite of virtual reality. Where virtual reality puts people inside a computer-generated world, ubiquitous computing forces the computer to live out here in the world with people. " – Mark Weiser, Xerox PARC