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.     

q-Analogues of two “divergent” Ramanujan-type supercongruences

The Ramanujan Journal - Guillera and Zudilin proved three “divergent” Ramanujan-type supercongruences by means of the Wilf–Zeilberger algorithmic technique. In this paper we prove...     

Second moment of error term of mean value for binary Egyptian fractions

We study the mean square of the error term of the mean value for binary Egyptian fractions.We get an asymptotic formula under the Riemann Hypothesis.     

Pairwise distance-based heteroscedasticity test for regressions

Science China Mathematics - In this study, we propose nonparametric testing for heteroscedasticity in nonlinear regression models based on pairwise distances between points in a sample. The test...     

Single-level reformulations of a specific non-smooth bilevel programming problem and their applications

Optimization Letters - We study a bilevel programming problem (BLPP) with a maximin lower level problem which is non-smooth and sometimes even non-convex. We reformulate such a non-smooth BLPP as a...     

Solution-Based,Anion-Doping of Li4Ti5O12 Nanoflowers for Lithium-Ion Battery Applications

Solution-based, anionic doping represents a convenient strategy with which to improve upon the conductivity of candidate anode materials such as Li₄Ti₅O₁₂ (LTO). As such, novel synthetic hydrothermally-inspired protocols have primarily been devised herein, aimed at the large-scale production of unique halogen-doped, micron-scale, three-dimensional, hierarchical LTO flower-like motifs. Although fluorine (F) doping has been explored, the use of chlorine (Cl) dopants is the primary focus here. Several experimental variables, such as dopant amount, lithium hydroxide concentration, and titanium butoxide purity, were probed and perfected. Furthermore, the Cl doping process did not damage the intrinsic LTO morphology. The analysis, based on interpreting a compilation of SEM, XRD, XPS, and TEM-EDS results, was used to determine an optimized dopant concentration of Cl. Electrochemical tests demonstrated an increased capacity via cycling of 12 % for a Cl-doped sample as compared with pristine LTO. Moreover, the Cl-doped LTO sample described in this study exhibited the highest discharge capacity yet reported at an observed rate of 2C for this material at 143mAh g⁻¹. Overall, these data suggest that the Cl dopant likely enhances not only the ion transport capabilities, but also the overall electrical conductivity of our as-prepared structures. To help explain these favorable findings, theoretical DFT calculations were used to postulate that the electronic conductivity and Li diffusion were likely improved by the presence of increased Ti³⁺ ion concentration coupled with widening of the Li migration channel.     

Bioinspired Healable Mechanochromic Function from Fluorescent Polyurethane Composite Film

Camouflage and wound healing are two vital functions for cephalopods to survive from dangerous ocean risks. Inspired by these dual functions, herein, we report a new type of healable mechanochromic (HMC) material. The bifunctional HMC material consists of two tightly bonded layers. One layer is composed of polyvinyl alcohol (PVA) and titanium dioxide (TiO₂) for shielding. Another layer contains supramolecular hydrogen bonding polymers and fluorochromes for healing. The as-synthesized HMC material exhibits a tunable and reversible mechanochromic function due to the strain-induced surface structure of composite film. The mechanochromic function can be further restored after damage because of the incorporated healable polyurethane. The healing efficiency of the damaged HMC materials can even reach 98 % at 60 °C for 6 h. The bioinspired HMC material is expected to have potential applications in the information encryption and flexible displays.     

Li[LiCs2Cl][Ga3S6]: A Nanoporous Framework of GaS4 Tetrahedra with Excellent Nonlinear Optical Performance

A large nonlinear optical (NLO) coefficient and a wide band gap are two crucial but contradictory parameters that are difficult to achieve simultaneously in a single infrared (IR) NLO compound. A salt‐inclusion chalcogenide (SIC), Li[LiCs₂Cl][Ga₃S₆] ( 1 ), was prepared that presents a nanosized tunnel framework constructed from monotype chalcogenide tetrahedra. Highly oriented covalent GaS₄ tetrahedra in the host lead to a moderate second harmonic generation response (0.7 AgGaS₂), and ionic guests effectively broaden the band gap to the widest value (4.18 eV) among all IR NLO chalcogenides, thereby achieving a remarkable balance between NLO efficiency and band gap.     

Gravitational wave imprint of new symmetry breaking

It is believed that there are more fundamental gauge symmetries beyond those described by the Standard Model of particle physics. The scales of these new gauge symmetries are usually too high to be reachable by particle colliders. Considering that the phase transition (PT) relating to the spontaneous breaking of new gauge symmetries to the electroweak symmetry might be strongly first order, we propose considering the stochastic gravitational waves (GW) arising from this phase transition as an indirect way of detecting these new fundamental gauge symmetries. As an illustration, we explore the possibility of detecting the stochastic GW generated from the PT of begin{document}$ {bf{B}}-{bf{L}}$end{document} in the space-based interferometer detectors. Our study demonstrates that the GW energy spectrum is reachable by the LISA, Tianqin, Taiji, BBO, and DECIGO experiments only for the case where the spontaneous breaking of begin{document}$ {bf{B}}-{bf{L}}$end{document} is triggered by at least two electroweak singlet scalars.