188 research outputs found
Online Catalogs and User Education
Stephen F. Austin State University library designs a user education program in conjunction with the academic assistance services
Online Catalogs and User Education
Online catalogs affect library instruction in a positive way. Comparison of features in each online catalog supplied by the current vendors is discussed
On -gaps between zeros of the Riemann zeta-function
Under the Riemann Hypothesis, we prove for any natural number there exist
infinitely many large natural numbers such that
and
for
explicit absolute positive constants and , where
denotes an ordinate of a zero of the Riemann zeta-function on the critical
line. Selberg published announcements of this result several times but did not
include a proof. We also suggest a general framework which might lead to
stronger statements concerning the vertical distribution of nontrivial zeros of
the Riemann zeta-function.Comment: to appear in the Bulletin of the London Mathematical Societ
Online Catalogs and User Education
Online catalogs affect library instruction in a positive way. Comparison of features in each online catalog supplied by the current vendors is discussed
Flame detector operable in presence of proton radiation
A detector of ultraviolet radiation for operation in a space vehicle which orbits through high intensity radiation areas is described. Two identical ultraviolet sensor tubes are mounted within a shield which limits to acceptable levels the amount of proton radiation reaching the sensor tubes. The shield has an opening which permits ultraviolet radiation to reach one of the sensing tubes. The shield keeps ultraviolet radiation from reaching the other sensor tube, designated the reference tube. The circuitry of the detector subtracts the output of the reference tube from the output of the sensing tube, and any portion of the output of the sensing tube which is due to proton radiation is offset by the output of the reference tube. A delay circuit in the detector prevents false alarms by keeping statistical variations in the proton radiation sensed by the two sensor tubes from developing an output signal
Access to Federal Documents: An Information Age Approach.
Government documents are often underutilized primary source of information. However, with the widespread availability of computers in libraries and the virtual explosion of electronic products and information, there are now other choices to access government documents in libraries
Making the Connection: Library Services for Distance Education and Off-campus Students.
Librarians have long recognized that the needs of distance and off-campus students differ from those of traditional, on-campus students. In the last decade, librarians have adapted to the challenges posed by an increasingly physically isolated yet electronically linked community of education stakeholders
Gaussian Behavior of the Number of Summands in Zeckendorf Decompositions in Small Intervals
Zeckendorf's theorem states that every positive integer can be written
uniquely as a sum of non-consecutive Fibonacci numbers , with initial
terms . We consider the distribution of the number of
summands involved in such decompositions. Previous work proved that as the distribution of the number of summands in the Zeckendorf
decompositions of , appropriately normalized, converges
to the standard normal. The proofs crucially used the fact that all integers in
share the same potential summands.
We generalize these results to subintervals of as ; the analysis is significantly more involved here as different integers
have different sets of potential summands. Explicitly, fix an integer sequence
. As , for almost all the distribution of the number of summands in the Zeckendorf
decompositions of integers in the subintervals ,
appropriately normalized, converges to the standard normal. The proof follows
by showing that, with probability tending to , has at least one
appropriately located large gap between indices in its decomposition. We then
use a correspondence between this interval and to obtain
the result, since the summands are known to have Gaussian behavior in the
latter interval. % We also prove the same result for more general linear
recurrences.Comment: Version 1.0, 8 page
Benford Behavior of Zeckendorf Decompositions
A beautiful theorem of Zeckendorf states that every integer can be written
uniquely as the sum of non-consecutive Fibonacci numbers . A set is said to satisfy Benford's law if
the density of the elements in with leading digit is
; in other words, smaller leading digits are more
likely to occur. We prove that, as , for a randomly selected
integer in the distribution of the leading digits of the
Fibonacci summands in its Zeckendorf decomposition converge to Benford's law
almost surely. Our results hold more generally, and instead of looking at the
distribution of leading digits one obtains similar theorems concerning how
often values in sets with density are attained.Comment: Version 1.0, 12 pages, 1 figur
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