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7 Feb 2012: Show that f (x) = 0 for allx. 8. Let f : [a, b] R be bounded. ... 13. Let f : R R be a function which has the intermediate value property: If f (a) < c < f (b),then f (x) = c for some x between a and b.

26 Nov 2012: To complete the investigation, some biological specimens are also examined with the phase plate in position, and a comparison is. ... a). (b). 1 1. FIGURE 9. Densitometer traces of some features shown in figures 8(a) and (b) illustrating improvements in

13 Sep 2012: Thenlog f = h̄y for some y. 3. Rdf(x)dx = 1. ... with fnd f for some density f. Then:. (a) f is log-concave.

29 Oct 2012: a sequence of points in [a, b] with xm x then fn(xn) f (x). ... f. Prove that there is some subinterval [a, b] of [0, 1] with a < b on which f is bounded.

15 Aug 2012: It may be possible to derive some, at least, of. Random-cluster representation of the Blume–Capel model 3. ... Graham and G. R. Grimmett. as required. We make some observations based on Theorem 3.7 and the method ofproof.

27 Jan 2012: Xn be independent Poisson random variables, with Xi having meaniθ, for some θ > 0. ... b) For some n > 2, let X1,. ,Xn be iid with Xi Exponential(θ).

6 Sep 2012: We end this section with such an example Consider the network illustrated in Figure where TCP connections send packets from node a tonode d with some connections routed via node b ... links Next suppose a short highcapacity link at which no congestion

23 Feb 2012: domain. Could there be some other Euclidean function φ making Z[3] into a Euclidean. ... Does it follows that the ring R is either a field or a polynomial ringF [X] for some field F?

8 Feb 2012: 3. An element r of a ring R is nilpotent if rn = 0 for some n. ... 6. Let A and B be elements of the power-set ring P(S), for some set S.

29 Feb 2012: α for some α.(iv) Any limit ordinal can be written in the form α. ... Given a subset b Pα withmore than one element, consider the least β belonging to some but not all members of b.].