29,129 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
Thalictrum bouffordii Y. P. Zeng, Q. Yuan & Q. E. Yang 2021, sp. nov.
No full textThalictrum bouffordii Y. P. Zeng, Q. Yuan & Q. E. Yang, sp. nov. (Figs. 1‒4). Type:— CHINA. Sichuan: Tianquan county, Xingou town, along G318 highway, near Chizhuping, 29°53′16.75″N, 102°21′21.77″E, on moist cliffs in ravine, 1690 m, 6 July 2020, Y. P. Zeng & Q. L. Huang 352 (holotype IBSC, barcode unavailable; isotypes CDBI, IBSC, PE, barcodes unavailable). Description:—Perennial herbs. Roots fibrous. Stem to 100 cm tall, striate, distally branched. Leaves 2‒4-ternate; blade triangular, 10‒25 cm long and broad; leaflets ovate, broadly ovate or rhombic, 1‒3 cm long, 0.8‒2.5 cm broad, papery, both sides glabrous, green on adaxial side, pale green on abaxial side, base rounded or subcordate, apex obtuse or acute, 3-lobate; lobes entire or 2‒3-lobate, apex obtuse or acute; veins flat adaxially, slightly raised abaxially; petiole slender, 1.5‒10 cm long; stipule membranous, margin torn. Inflorescence a many-flowered corymbiform compound monochasium, dichotomous; rachis glabrous or sparsely pubescent. Pedicels 0.8‒1.5 cm long, glabrous or sparsely pubescent. Flowers bisexual, erect. Sepals 4‒5, caducous, cymbiform-elliptic, ca. 4 mm long, ca. 2 mm broad, whitish tinged with purplish to distinctly purple, abaxially pubescent. Stamens ca. 60, 6‒ 7 mm long; filaments clavate, ca. 5.5 mm long, purplish; anthers oblong, ca. 1.5 mm long, apex obtuse, white. Carpels 6‒10, sessile, ca. 2 mm long; ovary lunate-fusiform, shallowly ribbed, ca. 1 mm long, glabrous or sparsely pubescent; style ca. 1 mm long, recurved at apex; stigma conspicuous, linear, ca. 0.5 mm long. Immature achenes sessile, ca. 3 mm long; body fusiform, profoundly ribbed, pubescent; style persistent, recurved at apex. Distribution and habitat:— Thalictrum bouffordii is currently known from Luding, Shimian and Tianquan counties in the Qionglai mountains region in western Sichuan, China (Fig. 5). It grows along forest margins or on moist cliffs in ravines at altitudes of 1360‒3200 m above sea level. Phenology:—Flowering from June to October; fruiting from July to November. Etymology:—It is a great privilege to name our new species in honor of Dr. David E. Boufford with Harvard University Herbaria, one of the greatest hunters of Chinese plants. His specimens of Chinese plants are among the finest ever made, a real joy to study. As a member of the editorial board of the Flora of China completed in 2011, Dr. Boufford is also a very active researcher of Chinese plants and a most helpful friend of many Chinese plant taxonomists, including the third author of this paper. Additional specimens examined:— CHINA. Sichuan: Luding, K.Y. Lang, L.Q. Li & Y. Fei 1351 (KUN0689899, PE01108835, PE01108836), G.H. Xu 26353 (CDBI0026148, CDBI0026149); Shimian, C.C. Hsieh 41833 (IBSC0090544, PE00471029, PE00471091, SZ00092282, SZ00092301, WUK, barcode unavailable), Shimian Exped. 78-1050 (SM704604597, SM704604743); Tianquan, D.F. Chamberlain & F.T. Pu 148 (CDBI0026494), X.J. He & Q.S. Zhao 171869 (SZ00571393, SZ00571413, SZ00571414, SZ00571415), X.J. He & Q.S. Zhao 190519 (SZ00578647, SZ00578648), X.J. He & Q.S. Zhao 192292 (SZ00571336, SZ00571337, SZ00571338), K.C. Kuan & W.T. Wang 3247 (K, barcode unavailable, PE00471028, PE00471030), N. Liu ELS008 (BNU0020049), C. Pei 8268 (NAS00187295, NAS00187297, SZ00092590), D.Y. Peng 46583 (CDBI0026159, IBSC0090429), Sichuan Econ. Plant Exped. 540 (PE00471031, PE00471033), P.C. Tai & C.M. Teng 4378 (SZ00092589), H.L. Tsiang 34799 (IBK00012648, IBSC0090351, PE00471035, SZ00092274), H.L. Tsiang 35238 (NAS00187277, PE00470992, SZ00092272), Y.P. Zeng & Q.L. Huang 355 (IBSC, barcode unavailable). Conservation status:— Thalictrum bouffordii is currently known from Luding, Shimian, and Tianquan counties in the Qionglai mountains region in western Sichuan, China. The two populations in Luding and Tianquan, which we visited in 2020, consist of at least 100 individuals each. However, the size of the population in Shimian remains unknown. The conservation status of T. bouffordii should be considered as “Data Deficient (DD)” before adequate information of this species is acquired (IUCN Standards and Petitions Committee 2019). Notes:— Thalictrum bouffordii is most closely similar to T. xinningense Wang (2017: 408) (Figs. 6‒8) in habit and having clavate filaments, apically recurved styles, and sessile, profoundly ribbed and pubescent achenes, but differs by having proximally glabrous (vs. densely pubescent) stem (Figs. 3D, 7D), inflorescence a many-flowered corymbiform compound monochasium (vs. a thyrse) (Figs. 1, 2, 3B, 4B, 6, 7B, 8), abaxially pubescent (vs. glabrous) sepals (Figs. 3I, 4G, 7I), and purplish (vs. white) filaments (Figs. 3J, 4H, 7J) (also see Wang 2017, 2018a). Geographically T. bouffordii occurs in western Sichuan, whereas T. xinningense is widely distributed in southern Chongqing, northern Fujian, northern Guangdong, northern Guangxi, eastern Guizhou, southwestern Hubei, Hunan, northern Jiangxi, and southern Zhejiang (Zeng et al. 2020a); both species are thus geographically isolated from each other (Fig. 5). As mentioned above, specimens of Thalictrum bouffordii had all been previously misidentified as T. javanicum. Indeed, T. bouffordii is somewhat similar to T. javanicum in habit, but differs by having abaxially pubescent (vs. glabrous) sepals, purplish (vs. white) filaments, and pubescent (vs. glabrous) achenes (also see Backer & Bakhuizen van den Brink 1963). Moreover, as noted by Zeng et al. (2020b), previous records of the occurrence of T. javanicum in China might be a mistake caused by the misapplication of this name to the relevant Chinese populations. The descriptions of T. javanicum in the Chinese floristic works by various authors, including Anonymous (1972, 1976, 2014), Wang & Wang (1979), Wang (1985, 1991, 1993, 2000, 2003, 2004, 2018a), Lin & Zhao (1985), Li (1986), Lin (1992), Liu (2000), Fu & Zhu (2001), Luo & Luo (2008), Wang & Liu (2016), and Xie et al. (2016), have been made mainly based on Chinese specimens, not on material from the type locality, i.e. Java in Indonesia. These Chinese specimens actually belong to T. nepalense Wang (2018b: 641), T. xinningense, and our new species as well, respectively. An identification key to T. bouffordii and its closely similar species including T. javanicum, T. nepalense and T. xinningense is given below.Published as part of Zeng, You-Pai, Yuan, Qiong & Yang, Qin-Er, 2021, Thalictrum bouffordii (Ranunculaceae), a new species from the Qionglai mountains region in western Sichuan, China, pp. 18-28 in Phytotaxa 510 (1) on pages 18-26, DOI: 10.11646/phytotaxa.510.1.2, http://zenodo.org/record/542624
Thalictrum minshanicum Y. P. Zeng, Q. Yuan & Q. E. Yang 2021, sp. nov.
No full text1. Thalictrum minshanicum Y. P. Zeng, Q. Yuan & Q. E. Yang, sp. nov. Figs. 1, 3, 4. Type:— CHINA. Sichuan: Pingwu county, along Road S205, near Baima town, 32°44′59.83″N, 104°18′44.47″E, in forests, alt. 2090 m, 28 June 2020, Y. P. Zeng & Q. L. Huang 337 (holotype IBSC, barcode unavailable; isotypes CDBI, IBSC, PE, barcodes unavailable). Description:—Perennial herbs. Roots fibrous, distally tuberose. Stem to 150 cm tall, striate, puberulent, distally branched. Leaves 2‒4-ternate; blade triangular, 10‒18 cm long, 10‒18 cm broad; leaflets obovate, orbicular or broadly ovate, 1‒3 cm long, 1‒3 cm broad, herbaceous, both sides puberulent, green on adaxial side, pale green on abaxial side, base rounded or subcordate, apex obtuse or acute, 3-lobate; lobes entire or 2‒3-lobate, apex obtuse or acute; veins flat adaxially, slightly prominent abaxially; petiole slender, 3‒10 cm long; stipule membranous, margin torn. Inflorescence compound monochasia, corymbiform; rachis sparsely puberulent. Pedicels 1‒1.5 cm long, sparsely puberulent. Flowers bisexual, erect. Sepals 4‒5, caducous, elliptic, ca. 5 mm long, ca. 2.5 mm broad, white or purplish, glabrous. Stamens 45‒60, ca. 7 mm long; filament clavate, ca. 5.5 mm long, purplish; anther oblong, ca. 1.5 mm long, apex obtuse, white. Carpels 6‒10, sessile, ca. 2 mm long; ovary lunate-fusiform, shallowly ribbed, ca. 1 mm long; style slightly recurved, ca. 1 mm long; stigma conspicuous, linear, ca. 0.6 mm long. Achenes sessile, ca. 4 mm long, glabrous; body fusiform, profoundly ribbed; style persistent, slightly recurved at apex. Distribution and habitat:— Thalictrum minshanicum is currently known from southern Gansu (Wudu, Zhugqu) and northwestern Sichuan (Beichuan, Pingwu) (Fig. 5) in the Min Shan region of China. It grows in thickets or forests on slopes at altitudes of 1400‒2090 m above sea level. Phenology:—Flowering from June to August; fruiting from August to September. Etymology:—The specific epithet is derived from the Min Shan region, where the new species occurs. Additional specimens examined:— CHINA. Gansu: Wudu, P.C. Kuo 5090 (WUK, barcode unavailable); Zhugqu, P.C. Kuo 5390 (WUK, barcode unavailable). Sichuan: Beichuan, C.L. Tang et al. 269 (CDBI0026275, CDBI0026276); Pingwu, Anonymous 121 (CDBI0026442, CDBI0026443), Y.P. Zeng & Q.L. Huang 330 (IBSC, barcode unavailable), Y.P. Zeng & Q.L. Huang 448 (IBSC, barcode unavailable). Conservation status:— Thalictrum minshanicum is currently known from four populations in southern Gansu and northwestern Sichuan, China. The population in Pingwu, northwestern Sichuan, which we rediscovered recently, consists of no more than 100 individuals. The size of the other three populations remains unknown. The conservation status of T. minshanicum should therefore be considered as “Data Deficient (DD)” before adequate information of this species is acquired (IUCN Standards and Petitions Committee 2019). Notes:— Thalictrum minshanicum is most closely similar to T. brevisericeum Wang & Wang (1974: 603) (Figs. 6, 7) in habit and in having puberulent stem and leaves, but differs by having conspicuously 3-lobate (vs. slightly 3-lobate) leaflets, glabrous (vs. abaxially puberulent) sepals, longer (ca. 7 mm vs. ca. 4 mm) and clavate (vs. oblanceolate-linear) filaments, conspicuous (vs. inconspicuous) stigmas, and persistent styles slightly recurved (vs. circinate) at apex (Figs. 3, 4). Thalictrum brevisericeum is widely distributed in China’s eastern and southern Gansu, western Henan, central and western Shaanxi, southwestern Shanxi, northwestern Sichuan, and northwestern Yunnan (Wang & Wang 1979, Fu & Zhu 2001, Wang 2018a; Fig. 5). Populations of northwestern Yunnan have been treated as a variety, i.e. var. angustiantherum Wang (2018a: 88). Another variety from Heishui in northwestern Sichuan, var. pentagynum Wang (2018a: 88), actually should belong to T. uncinulatum Franchet ex Lecoyer (1885: 169), a species distributed in Chongqing, Gansu, Guizhou, Hubei, Hunan, Shaanxi, Sichuan, and Yunnan, China (Zeng et al. 2021a). As mentioned before, specimens of Thalictrum minshanicum have been previously misidentified as T. javanicum or T. ramosum. Thalictrum minshanicum differs from T. javanicum (Fig. 8) by having puberulent stem and leaves and apically slightly recurved (vs. circinate) styles. From T. ramosum (Figs. 9, 10) it differs by having puberulent (vs. glabrous) leaves, longer stamens (ca. 7 mm vs. ca. 3 mm), and elliptic-fusiform (vs. lanceolate) achenes. It is to be noted that the true Thalictrum javanicum probably does not occur in China. The Chinese specimens previously identified as T. javanicum should belong to two recently described species. Those with a corymbiform inflorescence and widely distributed in China’s southern Chongqing, northern Guangdong, northern Guangxi, eastern Guizhou, southwestern Hubei, Hunan, Jiangxi and southern Zhejiang belong to T. xinningense Wang (2017: 408) (Wang 2018a, Zeng et al. 2021b), and those with a paniculiform inflorescence and widely distributed in China’s northeastern Chongqing, western Guizhou, northwestern Hubei, southern Shaanxi, Sichuan, Xizang, and Yunnan, and in Nepal, belong to T. nepalense Wang (2018b: 641). The independent specific status of T. sessile Hayata (1913: 6) from China’s Taiwan, a species previously treated as a synonym of T. javanicum (Wang & Wang 1979, Li 1986, Liu 2000, Fu & Zhu 2001), has been reinstated by Wang (2018a). In fact, Liu & Hsieh (1976) and Yang & Huang (1989, 1996, 2008) recognized T. sessile as an independent species. Indeed, further studies are needed to clarify the delimitation and geographical distribution of T. javanicum.Published as part of Zeng, You-Pai, Yuan, Qiong & Yang, Qin-Er, 2021, Thalictrum minshanicum and T. pseudoramosum (Ranunculaceae), two new species from China, pp. 133-148 in Phytotaxa 502 (2) on pages 133-134, DOI: 10.11646/phytotaxa.502.2.2, http://zenodo.org/record/542498
Thalictrum longistipitatum Y. P. Zeng, Q. Yuan & Q. E. Yang 2022, sp. nov.
No full textThalictrum longistipitatum Y. P. Zeng, Q. Yuan & Q. E. Yang, sp. nov. (Figs. 2, 9‒11). Type:— CHINA. Yunnan: Dêqên, Yunling town, on the way from Xidang spring to Yubeng village, in forests on mountain slopes, alt. 3450 m, 11 July 2021, Y.P. Zeng & Y.F. Luo 528 (holotype IBSC, barcode unavailable; isotypes KUN, PE, barcodes unavailable). Fig. 11. Diagnosis:— Thalictrum longistipitatum is closely related to T. hengduanshanense, but differs by having apically abruptly recurved (vs. straight) pedicels and shorter styles (ca. 1 mm vs. ca. 2 mm long). Description:—Perennial herbs. Roots fibrous. Stem 35‒60 cm tall, distally branched, glandular-pubescent. Leaves 2‒3-ternate; blade triangular, 5‒10 cm long, 4‒10 cm broad; leaflets broadly obovate, obliquely broadly obovate, suborbicular or broadly ovate, 0.5‒2 cm long, 0.5‒2 cm broad, herbaceous, both sides densely glandularpubescent, adaxially green and abaxially pale green, base rounded or subcordate, apex obtuse or acute, 3-lobate; lobes entire or 1‒2-crenate, apex obtuse or acute; veins submerged adaxially, raised abaxially; petioles glandular-pubescent, 0.5‒4 cm long; stipules sheath-like or free, obliquely ovate, membranous, margin entire. Inflorescence a panicle, many-branched, sub-corymbiform, glandular-pubescent. Pedicels 2‒4 cm long, apically abruptly recurved, glandularpubescent. Flowers bisexual, drooping. Sepals 4‒5, broadly elliptic, ovate or broadly ovate, 2‒3 mm long, 1.5‒2 mm broad, abaxially glandular-pubescent, whitish or tinged with pinkish; basal nerves 3‒5, simple or branched. Stamens 9‒12, 2‒3 mm long; filaments narrowly oblanceolate-linear, 1.4‒2.0 mm long, white; anthers oblong, 0.6‒0.9 mm long, ca. 0.5 mm broad, apex obtuse, white. Carpels 3‒6, ca. 2.5 mm long, glandular-pubescent, subsessile; ovary obliquely narrowly obovate, ca. 1 mm long; style ca. 1.2 mm long, apically slightly recurved; stigma lanceolate. Achenes 7‒9 mm long, densely glandular-pubescent, long stipitate; stipe 3‒6 mm long; body narrowly lunate-fusiform, shallowly ribbed, compressed; style persistent, apically recurved, ca. 0.6 mm long. Chromosome number unknown. Phenology:—Flowering from June to August; fruiting from July to September. Distribution and habitat:— Thalictrum longistipitatum is currently known only from northwestern Yunnan (Dêqên) and southeastern Xizang (Bomi, Zayu), China (Fig. 13). It grows in conifer-broadleaved forests on mountain slopes at elevations of 3100‒3450 m above sea level. Etymology:—The specific epithet of the new species, “ longistipitatum ”, refers to its impressively long stipes of achenes. Additional specimens examined (paratypes):— CHINA. Xizang: Bomi, W.Q. Fei 58 (IBSC, barcode unavailable), L. Wang, X.Q. Guo & Y.P. Zeng 3350 (IBSC, barcode unavailable); Zayu, B.S. Li, S.Z. Cheng & Z.C. Ni 7224 (PE00767246), Qinghai-Xizang Exped. 73-230 (KUN0690505, KUN0690506, PE00450030, PE00450031). Yunnan: Dêqên, Qinghai-Xizang Exped. 130 (HITBC, herb. no. 074526), L. Xie & J.F. Mao 136 (PE01569411), L. Xie & J.F. Mao 137 (PE01569412), L. Xie & J.F. Mao 138 (PE01569413). Conservation status:— Thalictrum longistipitatum is currently known only from four populations in northwestern Yunnan (Dêqên) and southeastern Xizang (Bomi, Zayu), China. Both Bomi and Dêqên populations consist of more than 100 individuals. The size of the Zayu population remains unknown. The conservation status of T. longistipitatum should therefore be considered as “Data Deficient (DD)” before adequate information of this species is acquired (IUCN Standards and Petitions Committee 2019).Published as part of Zeng, You-Pai, Yuan, Qiong & Yang, Qin-Er, 2022, Thalictrum hengduanshanense and T. longistipitatum (Ranunculaceae), two new species from southeastern Xizang and northwestern Yunnan, China, pp. 1-20 in Phytotaxa 571 (1) on pages 6-16, DOI: 10.11646/phytotaxa.571.1.1, http://zenodo.org/record/727042
Thalictrum nanhuaense Y. P. Zeng, Q. Yuan & Q. E. Yang 2021, sp. nov.
No full textThalictrum nanhuaense Y.P. Zeng, Q. Yuan & Q.E. Yang, sp. nov. , Figs. 1, 2. Type:— CHINA. Yunnan province: Nanhua county, Majie town, Zhongcun village, 24°54′23.77″N, 100°52′12.01″E, in thickets on slopes, 1600 m, 6 August 2020, Y. P . Zeng & Q. L. Huang 460 (holotype IBSC; isotypes IBSC, KUN, PE). Description:—Perennial herbs. Roots succulent, tuberose. Stem to 20 cm tall, branched, proximally sparsely pubescent, distally glabrous. Leaves 2‒3-ternate; blade triangular, 3‒8 cm long and broad; leaflets orbicular or broadly ovate, 1‒2 cm long and broad, herbaceous, glabrous on both surfaces, green on adaxial surface, pale green on abaxial surface, base rounded or subcordate, apex obtuse, 3-lobate; lobes entire or inconspicuously 1‒3-crenate; veins flat adaxially, raised abaxially; petiole slender, 3‒7 cm long; stipule membranous, inconspicuous. Inflorescence compound monochasia, corymbiform. Pedicel slender, 1‒2 cm long. Flowers bisexual, erect. Sepals 4‒6, elliptic, ca. 4 mm long, ca. 3 mm broad, white. Stamens 11‒15, ca. 3 mm long; filaments filiform, ca. 2 mm long, white; anthers narrowly oblong, ca. 1 mm long, apex obtuse, pale yellow. Carpels 11‒18, sessile, ca. 2 mm long, glabrous; ovary narrowly fusiform, nearly smooth, ca. 1.5 mm long; style straight, ca. 0.6 mm long; stigma inconspicuous, point-like. Achenes sessile, ca. 3 mm long, glabrous; body subulate-terete, inconspicuously ribbed; style persistent. Distribution and habitat: Thalictrum nanhuaense is currently known only from its type locality, i.e. Nanhua county in central Yunnan province, China (Fig. 3). It grows in northern subtropical thickets dominated by Dalbergia yunnanensis Franchet (1890: 187) on slopes at an altitude of 1600 m above sea level. Phenology:—Flowering from July to August; fruiting from August to September. Etymology:—The specific epithet refers to the type locality of the new species, i.e. Nanhua county in central Yunnan province, China. Additional specimen examined:— CHINA. Yunnan: Nanhua county, Majie town, Zhongcun village, 24°54′23.77″N, 100°52′12.01″E, X. Gong et al. KIBGX001 B08 (IBSC). Conservation status:— Thalictrum nanhuaense is currently known only from its type locality in Nanhua county in central Yunnan province, China. There are no more than 200 individuals in this population which is situated very closely to farmlands (less than 200 m) and disturbed heavily by grazing and roadbuilding activities. This population is located in the northernmost region of the Ailao Shan, an area not yet well botanized, and we do not know if more populations of this new species can be discovered in the future. The distribution and other information of this species are far from adequate to make a precise and accurate assessment of its risk of threat and endangerment. The conservation status of this species, therefore, should be considered as “Data Deficient (DD)” and a further investigation on this species is required (IUCN Standards and Petitions Committee 2019). Notes:—From a morphological perspective, Thalictrum nanhuaense is similar to T. fargesii (Figs. 4, 5) in habit and having larger sepals up to 4 mm long and persistent at anthesis and straight styles, but differs by its succulent and tuberose (vs. fibrous and slender) roots, filiform (vs. clavate) filaments, point-like (vs. oblong and narrowly winged) stigmas, and subulate-terete (vs. lunate-fusiform) achenes. Geographically, T. fargesii is widely distributed in Anhui, Chongqing, Fujian, Gansu, Guizhou, Henan, Hubei, Hunan, Jiangxi, Shaanxi, Sichuan, and Zhejiang provinces, China (Wang & Wang 1979, Fu & Zhu 2001, Li et al. 2016, Wang 2018a). Our new species is currently known only from its type locality, i.e. Nanhua county in central Yunnan province, China (Fig. 3). A detailed comparison between the two species is given in Table 1.Published as part of Zeng, You-Pai, Yuan, Qiong & Yang, Qin-Er, 2021, Thalictrum nanhuaense (Ranunculaceae), a new species from central Yunnan, China, pp. 121-128 in Phytotaxa 479 (1) on pages 121-127, DOI: 10.11646/phytotaxa.479.1.10, http://zenodo.org/record/541329
On the isomorphism class of q-Gaussian C*-algebras for infinite variables
No full textFor a real Hilbert space HR and −1 < q < 1 Bozejko and Speicher introduced the C∗-algebra Aq(HR) and von Neumann algebra Mq(HR) of qGaussian variables. We prove that if dim(HR) = ∞ and −1 < q < 1, q ∕= 0 then Mq(HR) does not have the Akemann-Ostrand property with respect to Aq(HR). It follows that Aq(HR) is not isomorphic to A0(HR). This gives an answer to the C∗-algebraic part of Question 1.1 and Question 1.2 in raised by Nelson and Zeng [Int. Math. Res. Not. IMRN 17 (2018), pp. 5486–5535].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.Analysi
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
Thalictrum bouffordii Y. P. Zeng, Q. Yuan & Q. E. Yang 2021
No full textKey to Thalictrum bouffordii and its closely similar species 1a. Stamens 6‒7 mm long; achenes pubescent........................................................................................................................................2 1b. Stamens 3‒5 mm long; achenes glabrous...........................................................................................................................................3 2a. Sepals pubescent abaxially; filaments purplish................................................................................................................ T. bouffordii 2b. Sepals glabrous; filaments white................................................................................................................................... T. xinningense 3a. Inflorescence a thyrse; stamens 14‒20............................................................................................................................. T. nepalense 3b. Inflorescence dichotomous and corymbiform; stamens 40‒60....................................................................................... T. javanicumPublished as part of Zeng, You-Pai, Yuan, Qiong & Yang, Qin-Er, 2021, Thalictrum bouffordii (Ranunculaceae), a new species from the Qionglai mountains region in western Sichuan, China, pp. 18-28 in Phytotaxa 510 (1) on page 27, DOI: 10.11646/phytotaxa.510.1.2, http://zenodo.org/record/542624
Progressive Transmission of High-Dimensional Data Features for Inference at the Network Edge
No full textUploading high-dimensional features from edge devices to an edge server over wireless channels creates a communication bottleneck for edge inference. To tackle the challenge, we propose the progressive feature transmission (ProgressFTX) protocol, which minimizes the overhead by progressively transmitting features until a target confidence level is reached. The control of the protocol to accelerate inference is designed with two key operations. The first, importance-aware feature selection, guides the server to select the most discriminative feature dimensions. The second is transmission-termination control such that the feature transmission is stopped when the incremental uncertainty reduction by further transmission is outweighed by its communication cost. The indices of the selected features and transmission decision are fed back to the device in each slot. The sub-optimal policy is obtained for classification using a convolutional neural network. Experimental results on a real-world dataset shows that ProgressFTX can substantially reduce the communication latency compared to conventional feature pruning and random feature transmission
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