38,677 research outputs found
q-Differential equations for q-classical polynomials and q-Jacobi-Stirling numbers
No full textWe introduce, characterise and provide a combinatorial interpretation for the so-called q-Jacobi–Stirling numbers.
This study is motivated by their key role in the (reciprocal) expansion of any power of a second order
q-differential operator having the q-classical polynomials as eigenfunctions in terms of other even order operators,
which we explicitly construct in this work. The results here obtained can be viewed as the q-version of
those given by Everitt et al. and by the first author, whilst the combinatorics of this new set of numbers is a
q-version of the Jacobi–Stirling numbers given by Gelineau and the second author
Tobin's Q and Financial Policy
No full textRecent research in macroeconomics has emphasized the importance of linking the financial and real sectors and the need for working with optimizing models. Tobin’s Q model of investment would appear to provide a framework that can satisfy these two criteria. In contrast to the original presentation of the Q model, the formal development has not recognized that the firm actively participates in a number of financial markets; in this broader context, we show that Q is likely to be an uninformative and possibly misleading signal for investment expenditures . We then endeavor to turn this negative theoretical result to positive advantage in resolving a number of empirical problems with Q models, but the modifications dictated by the theory receive little support from the data.
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Network Q
No full textA press release from Network Q announcing that they will begin featuring Brian McNaught, a gay columnist and author, for a monthly segment
Network Q
No full textA press release from Network Q announcing that they will begin featuring Brian McNaught, a gay columnist and author, for a monthly segment
Ultrahigh–Q Microtoroid On-Chip Resonators for Low Threshold Microlasers
No full textRecently demonstrated silica toroidal microcavities, as on-chip resonant cavities, become one of the most promising laser resonators due to their exceptional ability to confine optical energy temporarily and spatially (high Q-factor and small mode volume) while being integrated on a silicon substrate.
In the first part of this thesis, semianalytic theory is presented for an in-depth understanding of the high-Q toroidal microcavity coupled to a tapered fiber waveguide. Basic properties of toroidal microcavities such as cavity mode field, resonance wavelength, cavity mode volume, radiative Q-factor, and phase-matching condition are described within the limit of an iterative perturbation expansion method. With this theoretical background, various laser systems with different gain media, utilizing the high-Q toroidal microcavity as a laser resonator, are demonstrated in the latter parts.
As a first example, II-VI semiconductor nanocrystal, CdSe/ZnS (core/shell), quantum dots are coated on the surface of ultrahigh-Q toroidal microcavities. By pulsed excitation of quantum dots on the surface, either through tapered fiber waveguides or free-space, lasing is observed at both room and liquid nitrogen temperature. Use of a tapered fiber coupling substantially lowered the threshold energy when compared to the case of free-space excitation. Further threshold reduction down to 9.9 fJ was made possible by quantum dot density control.
Lasing from an erbium-implanted high-Q silica toroidal microcavity is demonstrated and analyzed in the next chapter. A minimum threshold power as low as 4.5 uW and a maximum output lasing power as high as 39.4 uW are obtained. Control of lasing wavelength is demonstrated by changing the cavity loading. Analytic formulas predicting threshold power, differential slope efficiency are derived and their dependence on cavity loading, erbium ion concentration and Q-factor is found and compared with the experimental results.
The nonlinear oscillation in an ultrahigh-Q silica toroidal microcavity is investigated in the last chapter. A controllable and reversible transition between parametric and Raman oscillation is experimentally demonstrated and theoretically analyzed. By direct change of cavity loading and indirect adjustment of frequency detuning, parametric and/or Raman oscillation can be accessed selectively without modification of cavity geometry in a toroidal microcavity with large enough aspect ratio. Based on an effective cavity gain theory, this transition is analyzed in terms of cavity loading and frequency detuning leading to a better understanding of the combined effects of parametric and Raman processes in silica microcavities.</p
Academic Writing Q&A Series 4
No full textThe presentation describes the processes that typically follow article submission. This presentation serves as the basis for a video from the Academic Writing Q&A series that was created as a supplement to the My First Scientific Article webinar. This presentation highlights the critical issues the author needs to take into account during the writing or peer review process that are essential to publishing. The content is useful for Early Career Researchers and for everyone who is interested in scholarly communication and publishing
Inferring national trends in discourse research using Q methodology
No full textAims:
The current presentation aims to invite discussion around the possibility or impossibility of using Q methodology to infer potential national trends with regard to dominant and alternative discourses. This will be achieved by presenting cross-national Q data from a study looking at discourses of sexual relationships in Germany and England.
Method:
Q methodology was used to explore discourses drawn on by 105 young people between 16 and 19 from Germany and England when making sense of sexual relationships.
Results:
Using PCA and varimax rotation, six discourses emerged: Sex as responsible, intimate and shared experience; Sex as joint fun; Ideal vs reality; Sex has to be responsible, consensual and shared; Caring relationships offer the perfect context for fulfilling sex; and Equality between partners.
Results:
The author concluded that the data appeared to show national trends with regard to dominant and alternative discourses around sexual relationships based on the distribution of German and English participants across the 6 factors and assertions from previous research.
Conclusion:
Considering Q methodology’s qualitative nature, claims regarding national level differences of emergent discourses have to be made with caution. However, as with all qualitative methods, trends might appear in the data, which, although they cannot be seen as authoritative, can give an indication of possible national level differences. Exploring views around this with an audience that are knowledgeable of the premises and assumptions of Q methodology appears a useful activity furthering our understanding of Q methodology’s remit
The limiting case of Haglund's (q,t)-Schröder theorem and an involution formula
No full textAbstractAs a generalization of Haglund's statistic on Dyck paths [Conjectured statistics for the q,t-Catalan numbers, Adv. Math. 175 (2) (2003) 319–334; A positivity result in the theory of Macdonald polynomials, Proc. Nat. Acad. Sci. 98 (2001) 4313–4316], Egge et al. introduced the (q,t)-Schröder polynomial Sn,d(q,t), which evaluates to the Schröder number when q=t=1 [A Schröder generalization of Haglund's statistic on Catalan paths, Electron. J. Combin. 10 (2003) 21pp (Research Paper 16, electronic)]. In their paper, Sn,d(q,t) was conjectured to be equal to the coefficient of a hook shape on the Schur function expansion of the symmetric function ∇en, which Haiman [Vanishing theorems and character formulas for the Hilbert scheme of points in the plane, Invent. Math. 149 (2002) 371–407] has shown to have a representation-theoretic interpretation. This conjecture was recently proved by Haglund [A proof of the q,t-Schröder conjecture, Internat. Math. Res. Not. (11) (2004) 525–560]. However, because that proof makes heavy use of symmetric function identities and plethystic machinery, the combinatorics behind it is not understood. Therefore, it is worthwhile to study it combinatorially. This paper investigates the limiting case of the (q,t)-Schröder Theorem and obtains interesting results by looking at some special cases
Song post exposure, song features, and predation risk
No full textMale birds use song to attract mates and deter other males, but in doing so, they also attract the attention of predators and parasites. Such viability costs are inherent in reliable signals, potentially causing females to prefer mates that display from the most exposed sites. However, viability costs of sexual signals may be ameliorated by affecting the choice of microhabitat, which in turn may affect the design of song features that are most efficiently transmitted in this microhabitat. We estimated the exposure of song posts (microsites used by males when singing) used by passerine birds in relation to prey selection by the sparrowhawk Accipiter nisus, by calculating the proportion of males that sang from song posts that were at the maximum level of the vegetation, in an attempt to quantify the costs of sexual selection. We quantified prey susceptibility to predation as the difference between the log-transformed observed number of prey minus the log-transformed expected number of prey in the environment. This prey susceptibility index increased with increasing song post exposure similarly in sexually dichromatic and monochromatic species, although the prey susceptibility index was related to sexual dichromatism. Song post exposure was dependent on habitat, but comparative models controlling for the potentially confounding effects of habitat, sexual dichromatism, hole nesting, coloniality, body mass, cognitive capacities, and flying abilities indicated that the relationship between the prey susceptibility index and song post exposure is strong. Path analyses of the relationship between song post exposure, sexual dichromatism, and prey susceptibility index revealed that selection acting on sexual dichromatism and song post exposure has secondary impact on prey susceptibility index. The opposite causal mechanisms by which predation affects sexual traits are less likely. These models suggest that female preference for high song posts or dichromatic plumage increases predation risk on an evolutionary time scale. Copyright 2006.birds; costs of sexual selection; prey selection; sound transmission
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