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Intersective polynomials and the primes
Intersective polynomials are polynomials in having roots every
modulus. For example, and are intersective
polynomials, but is not. The purpose of this note is to deduce,
using results of Green-Tao \cite{gt-chen} and Lucier \cite{lucier}, that for
any intersective polynomial , inside any subset of positive relative density
of the primes, we can find distinct primes such that
for some integer . Such a conclusion also holds in the Chen primes (where by
a Chen prime we mean a prime number such that is the product of at
most 2 primes)
The seventh visual object tracking VOT2019 challenge results
180The Visual Object Tracking challenge VOT2019 is the seventh annual tracker benchmarking activity organized by the VOT initiative. Results of 81 trackers are presented; many are state-of-the-art trackers published at major computer vision conferences or in journals in the recent years. The evaluation included the standard VOT and other popular methodologies for short-term tracking analysis as well as the standard VOT methodology for long-term tracking analysis. The VOT2019 challenge was composed of five challenges focusing on different tracking domains: (i) VOTST2019 challenge focused on short-term tracking in RGB, (ii) VOT-RT2019 challenge focused on 'real-time' shortterm tracking in RGB, (iii) VOT-LT2019 focused on longterm tracking namely coping with target disappearance and reappearance. Two new challenges have been introduced: (iv) VOT-RGBT2019 challenge focused on short-term tracking in RGB and thermal imagery and (v) VOT-RGBD2019 challenge focused on long-term tracking in RGB and depth imagery. The VOT-ST2019, VOT-RT2019 and VOT-LT2019 datasets were refreshed while new datasets were introduced for VOT-RGBT2019 and VOT-RGBD2019. The VOT toolkit has been updated to support both standard shortterm, long-term tracking and tracking with multi-channel imagery. Performance of the tested trackers typically by far exceeds standard baselines. The source code for most of the trackers is publicly available from the VOT page. The dataset, the evaluation kit and the results are publicly available at the challenge website.openopenKristan M.; Matas J.; Leonardis A.; Felsberg M.; Pflugfelder R.; Kamarainen J.-K.; Zajc L.C.; Drbohlav O.; Lukezic A.; Berg A.; Eldesokey A.; Kapyla J.; Fernandez G.; Gonzalez-Garcia A.; Memarmoghadam A.; Lu A.; He A.; Varfolomieiev A.; Chan A.; Tripathi A.S.; Smeulders A.; Pedasingu B.S.; Chen B.X.; Zhang B.; Baoyuanwu B.; Li B.; He B.; Yan B.; Bai B.; Li B.; Li B.; Kim B.H.; Ma C.; Fang C.; Qian C.; Chen C.; Li C.; Zhang C.; Tsai C.-Y.; Luo C.; Micheloni C.; Zhang C.; Tao D.; Gupta D.; Song D.; Wang D.; Gavves E.; Yi E.; Khan F.S.; Zhang F.; Wang F.; Zhao F.; De Ath G.; Bhat G.; Chen G.; Wang G.; Li G.; Cevikalp H.; Du H.; Zhao H.; Saribas H.; Jung H.M.; Bai H.; Yu H.; Peng H.; Lu H.; Li H.; Li J.; Li J.; Fu J.; Chen J.; Gao J.; Zhao J.; Tang J.; Li J.; Wu J.; Liu J.; Wang J.; Qi J.; Zhang J.; Tsotsos J.K.; Lee J.H.; Van De Weijer J.; Kittler J.; Ha Lee J.; Zhuang J.; Zhang K.; Wang K.; Dai K.; Chen L.; Liu L.; Guo L.; Zhang L.; Wang L.; Wang L.; Zhang L.; Wang L.; Zhou L.; Zheng L.; Rout L.; Van Gool L.; Bertinetto L.; Danelljan M.; Dunnhofer M.; Ni M.; Kim M.Y.; Tang M.; Yang M.-H.; Paluru N.; Martinel N.; Xu P.; Zhang P.; Zheng P.; Zhang P.; Torr P.H.S.; Wang Q.Z.Q.; Guo Q.; Timofte R.; Gorthi R.K.; Everson R.; Han R.; Zhang R.; You S.; Zhao S.-C.; Zhao S.; Li S.; Li S.; Ge S.; Bai S.; Guan S.; Xing T.; Xu T.; Yang T.; Zhang T.; Vojir T.; Feng W.; Hu W.; Wang W.; Tang W.; Zeng W.; Liu W.; Chen X.; Qiu X.; Bai X.; Wu X.-J.; Yang X.; Chen X.; Li X.; Sun X.; Chen X.; Tian X.; Tang X.; Zhu X.-F.; Huang Y.; Chen Y.; Lian Y.; Gu Y.; Liu Y.; Chen Y.; Zhang Y.; Xu Y.; Wang Y.; Li Y.; Zhou Y.; Dong Y.; Xu Y.; Zhang Y.; Li Y.; Luo Z.W.Z.; Zhang Z.; Feng Z.-H.; He Z.; Song Z.; Chen Z.; Zhang Z.; Wu Z.; Xiong Z.; Huang Z.; Teng Z.; Ni Z.Kristan, M.; Matas, J.; Leonardis, A.; Felsberg, M.; Pflugfelder, R.; Kamarainen, J. -K.; Zajc, L. C.; Drbohlav, O.; Lukezic, A.; Berg, A.; Eldesokey, A.; Kapyla, J.; Fernandez, G.; Gonzalez-Garcia, A.; Memarmoghadam, A.; Lu, A.; He, A.; Varfolomieiev, A.; Chan, A.; Tripathi, A. S.; Smeulders, A.; Pedasingu, B. S.; Chen, B. X.; Zhang, B.; Baoyuanwu, B.; Li, B.; He, B.; Yan, B.; Bai, B.; Li, B.; Li, B.; Kim, B. H.; Ma, C.; Fang, C.; Qian, C.; Chen, C.; Li, C.; Zhang, C.; Tsai, C. -Y.; Luo, C.; Micheloni, C.; Zhang, C.; Tao, D.; Gupta, D.; Song, D.; Wang, D.; Gavves, E.; Yi, E.; Khan, F. S.; Zhang, F.; Wang, F.; Zhao, F.; De Ath, G.; Bhat, G.; Chen, G.; Wang, G.; Li, G.; Cevikalp, H.; Du, H.; Zhao, H.; Saribas, H.; Jung, H. M.; Bai, H.; Yu, H.; Peng, H.; Lu, H.; Li, H.; Li, J.; Li, J.; Fu, J.; Chen, J.; Gao, J.; Zhao, J.; Tang, J.; Li, J.; Wu, J.; Liu, J.; Wang, J.; Qi, J.; Zhang, J.; Tsotsos, J. K.; Lee, J. H.; Van De Weijer, J.; Kittler, J.; Ha Lee, J.; Zhuang, J.; Zhang, K.; Wang, K.; Dai, K.; Chen, L.; Liu, L.; Guo, L.; Zhang, L.; Wang, L.; Wang, L.; Zhang, L.; Wang, L.; Zhou, L.; Zheng, L.; Rout, L.; Van Gool, L.; Bertinetto, L.; Danelljan, M.; Dunnhofer, M.; Ni, M.; Kim, M. Y.; Tang, M.; Yang, M. -H.; Paluru, N.; Martinel, N.; Xu, P.; Zhang, P.; Zheng, P.; Zhang, P.; Torr, P. H. S.; Wang, Q. Z. Q.; Guo, Q.; Timofte, R.; Gorthi, R. K.; Everson, R.; Han, R.; Zhang, R.; You, S.; Zhao, S. -C.; Zhao, S.; Li, S.; Li, S.; Ge, S.; Bai, S.; Guan, S.; Xing, T.; Xu, T.; Yang, T.; Zhang, T.; Vojir, T.; Feng, W.; Hu, W.; Wang, W.; Tang, W.; Zeng, W.; Liu, W.; Chen, X.; Qiu, X.; Bai, X.; Wu, X. -J.; Yang, X.; Chen, X.; Li, X.; Sun, X.; Chen, X.; Tian, X.; Tang, X.; Zhu, X. -F.; Huang, Y.; Chen, Y.; Lian, Y.; Gu, Y.; Liu, Y.; Chen, Y.; Zhang, Y.; Xu, Y.; Wang, Y.; Li, Y.; Zhou, Y.; Dong, Y.; Xu, Y.; Zhang, Y.; Li, Y.; Luo, Z. W. Z.; Zhang, Z.; Feng, Z. -H.; He, Z.; Song, Z.; Chen, Z.; Zhang, Z.; Wu, Z.; Xiong, Z.; Huang, Z.; Teng, Z.; Ni, Z
Positivity properties of Jacobi-Stirling numbers and generalized Ramanujan polynomials
Generalizing recent results of Egge and Mongelli, we show that each diagonal
sequence of the Jacobi-Stirling numbers \js(n,k;z) and \JS(n,k;z) is a
P\'olya frequency sequence if and only if and study the
-total positivity properties of these numbers. Moreover, the polynomial
sequences \biggl\{\sum_{k=0}^n\JS(n,k;z)y^k\biggr\}_{n\geq 0}\quad \text{and}
\quad \biggl\{\sum_{k=0}^n\js(n,k;z)y^k\biggr\}_{n\geq 0} are proved to be
strongly -log-convex. In the same vein, we extend a recent result of
Chen et al. about the Ramanujan polynomials to Chapoton's generalized Ramanujan
polynomials. Finally, bridging the Ramanujan polynomials and a sequence arising
from the Lambert function, we obtain a neat proof of the unimodality of the
latter sequence, which was proved previously by Kalugin and Jeffrey.Comment: 17 pages, 2 tables, the proof of Lemma 3.3 is corrected, final
version to appear in Advances in Applied Mathematic
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