Exceptional Cycles in the Bounded Derived Categories of Quivers

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.     

Certain fractional calculus and integral transform results of incomplete ℵ-functions with applications

In this paper, we study certain interesting and useful properties of incomplete $\aleph$-functions. The incomplete $\aleph$-function is an extension of the $\aleph$-function. We find several useful classical integral transforms of these functions. Further, we examine the fractional calculus with the incomplete $\aleph$-functions and point out several special cases. Finally, we give the applications of incomplete $\aleph$-functions in detecting glucose supply in human blood.     

New findings for two new type sine hyperbolic potentials

We propose two new type sine hyperbolic potentials $V(x)=a^2{\sinh }^2?(x)?k{\tanh }^2?(x)$ and $V(x)=c^2{\sinh }^4?(x)?k{\tanh }^2?(x)$. They may become single- or double-well potentials depending on the potential parameters $a,c$ and k. We find that its exact solutions can be written as the confluent Heun functions $H_c(\alpha ,\beta ,\gamma ,\delta ,\eta ;z)$, 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 $a,c$ and k, are illustrated.     

A novel UPLC–MS/MS method for simultaneous quantification of trigonelline, 4-hydroxyisoleucine,and diosgenin from Trigonella foenum-graecum extract: Application to pharmacokinetic study in healthy and type 2 diabetic rats

Trigonelline (TR), 4-hydroxyisoleucine (4-HI), and diosgenin (DG) are the main bioactives of the purified standardized extract of the popular plant Trigonella foenum-graecum L. (TFG), and it has been proven effective for the treatment of various diseases. However, to the best of our knowledge, no study has investigated the pharmacokinetic parameters of purified standardized T. foenum-graecum extract in normal and diabetic Wistar rats. The present study has developed and validated a rapid, reliable, and sensitive simultaneous ultra-performance liquid chromatography MS method to estimate these bioactives. The chromatographic separation was achieved using methanol, acetonitrile, and 0.1% formic acid with the ideal gradient flow system on a BEH Shield RP 18 column. A positive electrospray ionization mode was selected to estimate m/z values of TR (138.14 > 94.63), 4-HI (148.19 > 74.08), and DG (415.54 > 271.33). The method was robust and reproducible over the linearity range of 60–5000, 6–5000, and 15–5000 ng/mL for TR, 4-HI, and DG, respectively. Using this novel validated method, we investigated the pharmacokinetic parameters of bioactives using Phoenix WinNonlin version 8.0 (Certera) in normal and diabetic rats. The assay was successfully applied for the estimation of pharmacokinetic parameters using noncompartmental analysis. This investigation shows that the absorption rate increased, whereas distribution and elimination processes slowed down in diabetic rats compared with normal rats.     

Information percolation and cutoff for the random‐cluster model

We consider the random‐cluster model (RCM) on with parameters p∈(0,1) and q ≥ 1. This is a generalization of the standard bond percolation (with edges open independently with probability p) which is biased by a factor q raised to the number of connected components. We study the well‐known Fortuin‐Kasteleyn (FK)‐dynamics on this model where the update at an edge depends on the global geometry of the system unlike the Glauber heat‐bath dynamics for spin systems, and prove that for all small enough p (depending on the dimension) and any q>1, the FK‐dynamics exhibits the cutoff phenomenon at with a window size , where λ_∞ is the large n limit of the spectral gap of the process. Our proof extends the information percolation framework of Lubetzky and Sly to the RCM and also relies on the arguments of Blanca and Sinclair who proved a sharp mixing time bound for the planar version. A key aspect of our proof is the analysis of the effect of a sequence of dependent (across time) Bernoulli percolations extracted from the graphical construction of the dynamics, on how information propagates.     

Synthesis of Moracin C and Its Derivatives with a 2-arylbenzofuran Motif and Evaluation of Their PCSK9 Inhibitory Effects in HepG2 Cells

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.