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The criteria for uniform monotonicity, locally uniformly monotonicity and monotonicity of of Oríicz spaces with Luxexnburg and Orlicz norms are given. The monotone coefficients of a point and of the spaces are computed.The monotonicity and the uniform monotonicity are important properties of Banach lattices. lii 1985, Akcoglu and Sucheston [1) showed how these properties are related to ergodic theory. Moreover, in 1992 Kurc [8] discovered that the role of monotonicity properties lii Banach lattices is similar to the role of rotundity properties in Banach spaces. For example, he proved that for any Banach laltice X Ihe following statements are equivalent: (1) X is monotone; (2) for every z E X and every order interval [y,z] in X satisfying z~ [y, z], Card (~h¡,~(al) =1, where PK(X) = {y E K

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Background Borrelia miyamotoi is a newly described relapsing fever spirochete transmitted by ixodid tick species. Little is known about the prevalence of B. miyamotoi infections in humans and ticks in Inner Mongolia, China. Therefore, we investigated the prevalence of B. miyamotoi in Ixodes persulcatus ticks, and we aimed to isolateB. miyamotoi from I. persulcatus from four regions of Greater Khingan, Inner Mongolia, China. Methods From May to June each year during the period 2016–2019, host-seeking adult I. persulcatus ticks were collected from vegetation. Genomic DNA was prepared from half of each tick body for PCR template, and the remaining half was used to cultivate B. miyamotoi in BSK-M medium. We employed quantitative real-time PCR (qPCR) to detect Borrelia DNA in the ticks and to calculate the prevalence of B. miyamotoi and infections with other borreliae. For characterization of the isolated B. miyamotoi, we performed draft genome sequencing and multilocus sequencing analysis (MLSA). Results A total of 2656 adult I. persulcatus ticks were collected. The overall prevalence of relapsing fever (RF) borreliae in ticks was 5.0% (134/2656) and that of Lyme disease (LD) borreliae was 43.8% (1164/2656). Co-infection with RF and LD borreliae was observed in 63 ticks (2.4%). Ticks that were positive for RF borreliae by qPCR were subjected to glycerophosphodiester diester phosphodiesterase gene (glpQ) PCR amplification and sequencing, through which we identified the RF borrelia specimens as B. miyamotoi. Furthermore, the B. miyamotoi strain Hetao-1 was isolated from I. persulcatus, and a draft genome sequence was obtained from the isolate. Sequencing determined the strain Hetao-1 genome to be approximately 906.1 kbp in length (28.9% average GC content), and MLSA identified the strain as ST633, which has previously been reported in Japan and Mongolia. Conclusion We detected B. miyamotoi from I. persulcatus ticks collected in Inner Mongolia, and successfully isolated a B. miyamotoi strain. To our knowledge, this is the first study to culture a B. miyamotoi isolate from China. The data on the prevalence of B. miyamotoi and other borreliae in I. persulcatus ticks will be fundamental for future epidemiological studies of B. miyamotoi disease in Inner Mongolia.