17,386 research outputs found
Unexpected local extrema for the Sendov conjecture
Let S(n) be the set of all polynomials of degree n with all roots in the unit
disk, and define d(P) to be the maximum of the distances from each of the roots
of a polynomial P to that root's nearest critical point. In this notation,
Sendov's conjecture asserts that d(P)<=1 for every P in S(n).
Define P in S(n) to be locally extremal if d(P)>=d(Q) for all nearby Q in
S(n), and note that maximizing d(P) over all locally extremal polynomials P
would settle the Sendov conjecture.
Prior to now, the only polynomials known to be locally extremal were of the
form P(z)=c(z^n+a) with |a|=1. In this paper, we determine sufficient
conditions for real polynomials of a different form to be locally extremal, and
we use these conditions to find locally extremal polynomials of this form of
degrees 8, 9, 12, 13, 14, 15, 19, 20, and 26.Comment: 10 pages, AMS-LaTeX, no figures. The Maple code and results used in
this paper are included in the source files. We constructed an unexpected
locally extremal polynomial of degree 8 in version 1, then added degrees 12,
14, 20 and 26 in version 2, and degrees 9, 13, 15 and 19 in version
Nearctic \u3ci\u3eAcleris\u3c/i\u3e: Resurrection of \u3ci\u3eA. Stadiana\u3c/i\u3e and a Revised Identity for \u3ci\u3eA. Semiannula\u3c/i\u3e (Lepidoptera: Tortricidae)
Type study showed that Acleris stadiana (Barnes & Busck), currently considered a junior synonym of A. semiannula (Robinson), is in fact a distinct taxon. Although superficially similar, these taxa differ markedly in genital structure. In males of A. semiannula, the aedeagus is short, broad, and virtually straight, whereas in those of A. stadiana, it is long, thin, and sharply bent. What was known in literature as A. semiannula proved to be A. stadiana. We redefine both A. semiannula and the resurrected A. stadiana
Design of a Recreational Fishing Survey and Mark-Recapture Study for the Blue Crab, Callinectes sapidus, in Chesapeake Bay
The development of bay wide estimates of recreational harvest has been identified as a high priority by the Chesapeake Bay Scientific Advisory Committee (CBSAC) and by the Chesapeake Bay Program as reflected in the Chesapeake Bay Blue Crab Fishery Management Plan (Chesapeake Bay Program 1996). In addition, the BiState Blue Crab Commission (BBCAC), formed in 1996 by mandate from the legislatures of Maryland and Virginia to advise on crab
management, has also recognized the importance of estimating the levels and trends in catches in the recreational fishery. Recently, the BBCAC has adopted limit and target biological reference points. These analyses have been predicated on assumptions regarding the relative magnitude of the recreational and commercial catch. The reference points depend on determination of the total
number of crabs removed from the population. In essence, the number removed by the various fishery sectors, represents a minimum estimate of the population size. If a major fishery sector is not represented, the total population will be accordingly underestimated. If the relative contribution of the unrepresented sector is constant over time and harvests the same components of
the population as the other sectors, it may be argued that the population estimate derived from the other sectors is biased but still adequately represents trends in population size over time. If either of the two constraints mentioned above is not met, the validity of relative trends over time is suspect. With the recent increases in the human population in the Chesapeake Bay watershed, there is reason to be concerned that the recreational catch may not have been a constant proportion of the total harvest over time. It is important to assess the catch characteristics and the magnitude of the recreational fishery to evaluate this potential bias. (PDF contains 70 pages
Does electronic coherence enhance anticorrelated pigment vibrations under realistic conditions?
The light-harvesting efficiency of a photoactive molecular complex is largely
determined by the properties of its electronic quantum states. Those, in turn,
are influenced by molecular vibrational states of the nuclear degrees of
freedom. Here, we reexamine two recently formulated concepts that a coherent
vibronic coupling between molecular states would either extend the electronic
coherence lifetime or enhance the amplitude of the anticorrelated vibrational
mode at longer times. For this, we study a vibronically coupled dimer and
calculate the nonlinear two-dimensional (2D) electronic spectra which directly
reveal electronic coherence. The timescale of electronic coherence is initially
extracted by measuring the anti-diagonal bandwidth of the central peak in the
2D spectrum at zero waiting time. Based on the residual analysis, we identify
small-amplitude long-lived oscillations in the cross-peaks, which, however, are
solely due to groundstate vibrational coherence, regardless of having resonant
or off-resonant conditions. Our studies neither show an enhancement of the
electronic quantum coherence nor an enhancement of the anticorrelated
vibrational mode by the vibronic coupling under ambient conditions
Cross-Disciplinary Prospecting: Educational Technology Offers Up Gold for Library and Information Science Curricula
This article provides an overview of the current trends in information and communication technology affecting library services and recommends how, because of these trends, library and information science (LIS) curricula should turn an inquisitive, interdisciplinary eye toward the field of educational technology. Gaps in current LIS professional training and practice are cited, curriculum standards in LIS and educational technology programs are described and compared, and examples are presented to demonstrate how educational technology pedagogy and practice help to successfully augment library skills, service, and practice
Vocal learning promotes patterned inhibitory connectivity.
Skill learning is instantiated by changes to functional connectivity within premotor circuits, but whether the specificity of learning depends on structured changes to inhibitory circuitry remains unclear. We used slice electrophysiology to measure connectivity changes associated with song learning in the avian analog of primary motor cortex (robust nucleus of the arcopallium, RA) in Bengalese Finches. Before song learning, fast-spiking interneurons (FSIs) densely innervated glutamatergic projection neurons (PNs) with apparently random connectivity. After learning, there was a profound reduction in the overall strength and number of inhibitory connections, but this was accompanied by a more than two-fold enrichment in reciprocal FSI-PN connections. Moreover, in singing birds, we found that pharmacological manipulations of RA's inhibitory circuitry drove large shifts in learned vocal features, such as pitch and amplitude, without grossly disrupting the song. Our results indicate that skill learning establishes nonrandom inhibitory connectivity, and implicates this patterning in encoding specific features of learned movements
Librarians Building Digital Learning Objects Supporting Cultural Understanding: Fulbright-Hays Seminar Abroad in Morocco and Tunisia
Chapter explores a 2011 Fulbright- Hays Seminar experience in Morocco/Tunisia related to comparative religion. The grant process is explained, Seminar is detailed, and the curriculum project is detailed
- …