42,252 research outputs found
A -congruence for a truncated series
No full textsummary:Let denote the th cyclotomic polynomial in . Recently, Guo, Schlosser and Zudilin proved that for any integer with , where . In this note, we give a generalization of the above -congruence to the modulus case. Meanwhile, we give a corresponding -congruence modulo for . Our proof is based on the `creative microscoping' method, recently developed by Guo and Zudilin, and a summation formula
q-Differential equations for q-classical polynomials and q-Jacobi-Stirling numbers
Get PDFWe 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
Ordering trees with n vertices and matching number q by their largest Laplacian eigenvalues
No full textAbstractDenote by Tn,q the set of trees with n vertices and matching number q. Guo [On the Laplacian spectral radius of a tree, Linear Algebra Appl. 368 (2003) 379–385] gave the tree in Tn,q with the greatest value of the largest Laplacian eigenvalue. In this paper, we give another proof of this result. Using our method, we can go further beyond Guo by giving the tree in Tn,q with the second largest value of the largest Laplacian eigenvalue
Tuber mongolicum T. Bau & F. Guo 2023, sp.nov.
No full textTuber mongolicum T. Bau & F. Guo sp.nov. (Figure 2–5) MycoBank number:—846829 Diagnosis:— Tuber mongolicum differs from related species by its pseudoparenchymatous peridum, ellipsoid ascospores and 1–5 spored asci. Etymology:—‘mongolicum’ refers to its occurrence in Inner Mongolia Autonomous Region, China. Types:— CHINA, Inner Mongolia Autonomous Region, Tongliao Daqinggou National Nature Reserve, in soil under Populus sp., 42°47′N, 122°10′E, 214 m, 23 Aug. 2022, Fang Guo, Tolgor Bau, HMJAU65125 (holotypus!). Same location; Fang Guo, Tolgor Bau HMJAU65126 (paratypus!). Description:—Ascomata are spherical to irregular spherical, 0.8–1.5 cm in diameter, with depressions. The surface is yellowish-green (30B7), olive-brown (4D7) to yellowish brown (5D8) when fresh, with small protrusions at the concave part of the fruiting body. Gleba is yellow-brown with white veins that have a sparse radial distribution from the base, and starch-like aroma (Figs 2–3). Peridum is 349–506 µm, thick, with two layers: the outer layer is yellow-brown, and 71–174 μm thick, the inner layer is a clear shade, 205–418 μm thick, and composed of sub-globose pseudoparenchymatous cells of 15–33 × 9–20 µm wide (Figs 4a, 5c). Asci are usually 1–4-spored, but occasionally 5-spored. Asci are sub-globose to ellipsoid, thin-walled, and short or nearly sessile, measuring 56–91 × 46–68 µm (Figs. 4 b-c. 5b). Ascospores are oblong-ellipsoid, ellipsoid to broadly ellipsoid, yellow-brown at maturity, and reticulate. In 1-spored asci 38–50 × 30–40 µm, Q=1.1–1.28, in 2- spored asci 33–44 × 25–37 µm, Q=1.1–1.4, in 3-spored asci 28–40 × 22–28 µm, Q=1.15–1.43, in 4-spored asci 25–35 × 20–29 µm, Q=1.15–1.37, in 5-spored asci 26–31 × 22–25 µm, Q=1.1–1.24, spike ornamentation 2.92–5.06 µm length, and mostly 3–6 meshes across the spore width (Figs 4 b-c, 5b). Habitat: Hypogeous, in soil under Populus sp.; ascoma occurring in autumn. Distribution: Only within Inner Mongolia Autonomous Region, Northern China.Published as part of Guo, Fang & Bau, Tolgor, 2023, A new species of Tuber (Tuberaceae, Pezizales) from Inner Mongolia, China, pp. 39-48 in Phytotaxa 592 (1) on pages 43-45, DOI: 10.11646/phytotaxa.592.1.3, http://zenodo.org/record/783562
Combinatorial Interpretations of the q-Faulhaber and q-Salie Coefficients
No full text15 pages, see also http://math.univ-lyon1.fr/~guoRecently, Guo and Zeng discovered two families of polynomials featuring in a q-analogue of Faulhaber's formula for the sums of powers and a q-analogue of Gessel-Viennot's formula involving Salie's coefficients for the alternating sums of powers. In this paper, we show that these are polynomials with symmetric, nonnegative integral coefficients by refining Gessel-Viennot's combinatorial interpretations
EMBEDDED LEARNING ROBOT WITH FUZZY Q-LEARNING FOR OBSTACLE AVOIDANCE BEHAVIOR
No full textFuzzy Q-learning is extending of Q-learning algorithm that uses fuzzy inference system to enable Q-learning holding continuous action and state. This learning has been implemented in various robot learning application like obstacle avoidance and target searching. However, most of them have not been realized in embedded robot. This paper presents implementation of fuzzy Q-learning for obstacle avoidance navigation in embedded mobile robot. The experimental result demonstrates that fuzzy Q-learning enables robot to be able to learn the right policy i.e. to avoid obstacle
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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
Get PDFRecent 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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