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An exceptional n-cycle in a Hom-finite triangulated category with Serre functor has been recently introduced by Broomhead,Pauksztello and Ploog.When n=1,it is a spherical object.We explicitly determine all the exceptional cycles in the bounded derived category D^b(kQ)of a finite quiver Q without oriented cycles.In particular,if Q is an Euclidean quiver,then the length type of exceptional cycles in D^b(kQ)is exactly the tubular type of Q;if Q is a Dynkin quiver of type E_m(m=6,7,8),or Q is a wild quiver,then there are no exceptional cycles in D^b(kQ);and if Q is a Dynkin quiver of type An or D_n,then the length of an exceptional cycle in D^b(kQ)is either h or h/2,where h is the Coxeter number of Q. 相似文献
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Manish Kumar Bansal Devendra Kumar K. S. Nisar Jagdev Singh 《Mathematical Methods in the Applied Sciences》2020,43(8):5602-5614
In this paper, we study certain interesting and useful properties of incomplete -functions. The incomplete -function is an extension of the -function. We find several useful classical integral transforms of these functions. Further, we examine the fractional calculus with the incomplete -functions and point out several special cases. Finally, we give the applications of incomplete -functions in detecting glucose supply in human blood. 相似文献
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We propose two new type sine hyperbolic potentials and . They may become single- or double-well potentials depending on the potential parameters and k. We find that its exact solutions can be written as the confluent Heun functions , in which the energy level E is involved inside the parameter η. The properties of the wave functions, which is strongly relevant for the potential parameters and k, are illustrated. 相似文献
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Jagadeesh Nagarajappa Masagalli Melanayakanakatte Kuberappa BasavanaGowda Hee-Sung Chae Won Jun Choi 《Molecules (Basel, Switzerland)》2021,26(5)
Proprotein convertase subtilisin/kexin type 9 (PCSK9) is a key factor in several cardiovascular diseases, as it is responsible for the elevation of circulating low-density lipoprotein cholesterol (LDL-C) levels in blood plasma by direct interaction with the LDL receptor. The development of orally available drugs to inhibit this PCSK9-LDLR interaction is a highly desirable objective. Here, we report the synthesis of naturally occurring moracin compounds and their derivatives with a 2-arylbenzofuran motif to inhibit PCSK9 expression. In addition, we discuss a short approach involving the three-step synthesis of moracin C and a divergent method to obtain various analogs from one starting material. Among the tested derivatives, compound 7 (97.1%) was identified as a more potent inhibitor of PCSK9 expression in HepG2 cells than berberine (60.9%). These results provide a better understanding of the structure–activity relationships of moracin derivatives for the inhibition of PCSK9 expression in human hepatocytes. 相似文献
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Dahui Luo JinRong Wang Dong Shen 《Mathematical Methods in the Applied Sciences》2019,42(13):4543-4553
This paper considers the consensus tacking problem for nonlinear fractional‐order multiagent systems by presenting a PDα‐type iterative learning control update law with initial learning mechanisms. The asymptotical convergence of the proposed distributed learning algorithm is strictly proved by using the properties of fractional calculus. A sufficient condition is derived to guarantee the whole multiagent system achieving an asymptotic output consensus. An illustrative example is given to verify the theoretical results. 相似文献
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Cheng and Tang [Biometrika, 88 (2001), pp. 1169–1174] derived an upper bound on the maximum number of columns that can be accommodated in a two‐symbol supersaturated design (SSD) for a given number of rows () and a maximum in absolute value correlation between any two columns (). In particular, they proved that for (mod ) and . However, the only known SSD satisfying this upper bound is when . By utilizing a computer search, we prove that for , and . These results are obtained by proving the nonexistence of certain resolvable incomplete blocks designs. The combinatorial properties of the RIBDs are used to reduce the search space. Our results improve the lower bound for SSDs with rows and columns, for , and . Finally, we show that a skew‐type Hadamard matrix of order can be used to construct an SSD with rows and columns that proves . Hence, we establish for and for all (mod ) such that . Our result also implies that when is a prime power and (mod ). We conjecture that for all and (mod ), where is the maximum number of equiangular lines in with pairwise angle . 相似文献