36,100 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
Remarks on Some Compact Symplectic Solvmanifolds
No full textWe study the hard Lefschetz property on compact symplectic solvmanifolds, i.e., compact quotients M = ΓG of a simply-connected solvable Lie group G by a lattice Γ, admitting a symplectic structure
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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
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.
Graphene q-switched Yb: phosphate glass channel waveguide laser
No full textQ-switched lasers can generate high-energy pulses that can have applications in medicine, material processing and defence. Waveguide lasers have several attractive features such as a low laser threshold and a high slope efficiency, provided that the propagation losses are kept low, compactness and mass-producibility. Ion-exchange is a simple and cheap technique to fabricate loss-loss waveguides in glass, with mode-locked operation being demonstrated in ion-exchanged Yb:phosphate glass lasers using a semiconductor saturable absorber mirror (SESAM). Using graphene as a saturable absorber has several key advantages over SESAMs such as a broad wavelength operating range, cost-effectiveness and ease of fabrication. Graphene has previously been used as a saturable absorber to demonstrate Q-switched mode-locking in a femtosecond-written glass waveguide laser and Q-switched operation in a carbon-irradiated Nd:YAG ceramic channel waveguide laser. In this paper we present an ion-exchanged Yb:phosphate glass waveguide laser, Q-switched using a graphene saturable absorber
Automorphism Group of q-Quantum Torus Lie Algebra with q a Root of Unity
No full textNational Science Foundation of China [10671160]Let Derskew(q) be the skew derivation algebra of the quantum torus [image omitted] with q1 a pth primitive root of unity. In this article, we investigate the automorphism group of the derived Lie subalgebra of the infinite dimensional Lie algebra [image omitted]. The result of the article generalizes those obtained in Xue et al. (2006) and Zheng and Tan (2007) with q=1 or q being generic
Optimal solution of the nearest correlation matrix problem by minimization of the maximum norm
No full textThe nearest correlation matrix problem is to find a valid (positive semidefinite) correlation matrix, R(m,m), that is nearest to a given invalid (negative semidefinite) or pseudo-correlation matrix, Q(m,m); m larger than 2. In the literature on this problem, 'nearest' is invariably defined in the sense of the least Frobenius norm. Research works of Rebonato and Jaeckel (1999), Higham (2002), Anjos et al. (2003), Grubisic and Pietersz (2004), Pietersz, and Groenen (2004), etc. use Frobenius norm explicitly or implicitly. However, it is not necessary to define 'nearest' in this conventional sense. The thrust of this paper is to define 'nearest' in the sense of the least maximum norm (LMN) of the deviation matrix (R-Q), and to obtain R nearest to Q. The LMN provides the overall minimum range of deviation of the elements of R from those of Q. We also append a computer program (source codes in FORTRAN) to find the LMN R from a given Q. Presently we use the random walk search method for optimization. However, we suggest that more efficient methods based on the Genetic algorithms may replace the random walk algorithm of optimization.Nearest correlation matrix problem; Frobenius norm; maximum norm; LMN correlation matrix; positive semidefinite; negative semidefinite; positive definite; random walk algorithm; Genetic algorithm; computer program; source codes; FORTRAN; simulation
A Q-learning based multi-strategy integrated artificial bee colony algorithm with application in unmanned vehicle path planning
No full textArtificial bee colony (ABC) is a prominent algorithm that offers great exploration capabilities among various meta-heuristic algorithms. However, its monotonous and one-dimensional search strategy limits its searching performance in the solving process. Thus, to address this issue, a Q-learning based multi-strategy integrated ABC algorithm (QMABC) is proposed. In the QMABC, multiple search strategies are proposed to utilize different individual experiences and search approaches for solution updates. Then, Q-learning is employed for strategy selection. In comparison to previous studies, this paper introduces more effective state and action configurations within the framework of Q-learning. To evaluate the performance of the QMABC, CEC 2017 benchmark functions are adopted to compare it to different meta-heuristic algorithms including ABC based and non-ABC based algorithms. Moreover, applications in path planning are implemented to further verify the effectiveness of the QMABC. Overall, it should be highlighted that the proposed QMABC demonstrates superiority in both numerical and practical experiments.Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.Discrete Mathematics and Optimizatio
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