Size‐Mediated Recurring Spinel Sub‐nanodomains in Li‐ and Mn‐Rich Layered Cathode Materials

Li‐ and Mn‐rich layered oxides are among the most promising cathode materials for Li‐ion batteries with high theoretical energy density. Its practical application is, however, hampered by the capacity and voltage fade after long cycling. Herein, a finite difference method for near‐edge structure (FDMNES) code was combined with in situ X‐ray absorption spectroscopy (XAS) and transmission electron microscopy/electron energy loss spectroscopy (TEM/EELS) to investigate the evolution of transition metals (TMs) in fresh and heavily cycled electrodes. Theoretical modeling reveals a recurring partially reversible LiMn₂O₄‐like sub‐nanodomain formation/dissolution process during each charge/discharge, which accumulates gradually and accounts for the Mn phase transition. From the modeling of spectra and maps of the valence state over large regions of the cathodes, it was found that the phase change is size‐dependent. After prolonged cycling, the TMs displayed different levels of inactivity.     

High‐Tc Enantiomeric Ferroelectrics Based on Homochiral Dabco‐derivatives (Dabco=1,4‐Diazabicyclo[2.2.2]octane)

1,4‐Diazabicyclo[2.2.2]octane (dabco) and its derivatives have been extensively utilized as building units of excellent molecular ferroelectrics for decades. However, the homochiral dabco‐based ferroelectric remains a blank. Herein, by adding a methyl (Me) group accompanied by the introduction of homochirality to the [H₂dabco]²⁺ in the non‐ferroelectric [H₂dabco][TFSA]₂ (TFSA=bis(trifluoromethylsulfonyl)ammonium), we successfully designed enantiomeric ferroelectrics [R and S‐2‐Me‐H₂dabco][TFSA]₂. The two enantiomers show two sequential phase transitions with transition temperature (T_c) as high as 405.8 K and 415.8 K, which is outstanding in both dabco‐based ferroelectrics and homochiral ferroelectrics. To our knowledge, [R and S‐2‐Me‐H₂dabco][TFSA]₂ are the first examples of dabco‐based homochiral ferroelectrics. This finding opens an avenue to construct dabco‐based homochiral ferroelectrics and will inspire the exploration of more eminent enantiomeric molecular ferroelectrics.     

Applications holomorphes propres d'un domaine quasi-disqué sur un domaine disqué

A result of F. Berteloot and G. Patrizio [F. Berteloot, G. Patrizio, A cartan theorem for proper holomorphic mappings of complete circular domains, Adv. Math. 153 (2000) 342-352] states that if f is a proper holomorphic map between two bounded complete circular domains Ω₁ and Ω₂ in Cn+1 (n?1), such that f−1{0}={0} and such that the principal part fp of the Taylor expansions of f at the origine is nondegenerated i.e. fp−1{0}={0}, then f=fp.Here, we give a partial extension of this result to the case where f is a nondegenerated proper holomorphic map between a quasi-circular domain Ω₁ and a complete circular domain Ω₂, which are pseudo-convex but not necessarily bounded.We show that if f and its principal part fp are nondegenerated at the origine, then fp−1(Ω₂)=Ω₁.     

Bergman polynomials on an archipelago: Estimates, zeros and shape reconstruction

Growth estimates of complex orthogonal polynomials with respect to the area measure supported by a disjoint union of planar Jordan domains (called, in short, an archipelago) are obtained by a combination of methods of potential theory and rational approximation theory. The study of the asymptotic behavior of the roots of these polynomials reveals a surprisingly rich geometry, which reflects three characteristics: the relative position of an island in the archipelago, the analytic continuation picture of the Schwarz function of every individual boundary and the singular points of the exterior Green function. By way of explicit example, fine asymptotics are obtained for the lemniscate archipelago |z^m−1|<r^m, 0<r<1, which consists of m islands. The asymptotic analysis of the Christoffel functions associated to the same orthogonal polynomials leads to a very accurate reconstruction algorithm of the shape of the archipelago, knowing only finitely many of its power moments. This work naturally complements a 1969 study by H. Widom of Szegő orthogonal polynomials on an archipelago and the more recent asymptotic analysis of Bergman orthogonal polynomials unveiled by the last two authors and their collaborators.     

On k-uniformly close-to-convex functions of complex order

In this paper, we define and study some subclasses of analytic functions by using fractional derivative operator. Some interesting properties, coefficients problems and inclusion results of these classes are investigated. It is also shown that these classes are closed under convolution with convex functions and some applications are given.     

Reachability sets of hybrid systems in the presence of successive switchings

The concept of reachability domains of hybrid systems is described together with the use of ellipsoidal methods for calculation of such domains in the case when there are successive switchings on several given hyperplanes or bands. An algorithm for calculation of the reachability sets for a hybrid system that uses ellipsoidal approximations is given for the cases in which the switching sets are planes or bands. The parametrization of nonconvex reachability domains is obtained as a union of intersections of the corresponding ellipsoidal estimates.     

Robust stability analysis of static neural network with S-type distributed delays

In this paper, we investigate local robust stability of static neural network (SNN) with S-type distributed delays. We derive some new sufficient conditions for local robust stability of equilibrium points and estimate attracting domains of equilibrium points except isolated equilibrium points. Our results not only show local robust stability of equilibrium points but also allow much broader application for static neural network with or without delays. It is shown that our results are new and improve corresponding results existing in the previous literature.     

An L p -theory of Stochastic PDEs of Divergence Form on Lipschitz Domains

Stochastic partial differential equations of divergence form are considered on Lipschitz domains. Existence and uniqueness results are given in weighted Sobolev spaces. It is allowed that the coefficients of the equations substantially oscillate or blow up near the boundary.      

Analytic combinatorics of connected graphs

We enumerate the connected graphs that contain a number of edges growing linearly with respect to the number of vertices. So far, only the first term of the asymptotics and a bound on the error were known. Using analytic combinatorics, that is, generating function manipulations, we derive a formula for the coefficients of the complete asymptotic expansion. The same result is derived for connected multigraphs.     

含有大的悬挂树图的Ramseygoodness结论(英文)

设H是阶为n的连通图.在H的某一个顶点上悬挂一棵阶为j的树,得到图H_j,用H_j表示这样的图形族.本文证明:当j充分大时,有r(G,H_j)=(x(G)-1)(n+j-1)+s(G),其中x(G),s(G)分别表示图G的色数和色数剩余.