A Three-Dimensional M3AB-Type Hybrid Organic–Inorganic Antiperovskite Ferroelectric: [C3H7FN]3[SnCl6]Cl

Since the first perovskite CaTiO₃ was discovered in 1839, the development of perovskite has a history of 180 years. The emergence of solar cells (CH₃NH₃)PbI₃ has set off the trend of hybrid organic–inorganic perovskite (HOIP) materials. Since then, various HOIPs have sprung up and been widely used in various material devices. Among them, HOIP ferroelectrics have gained widespread attention. However, antiperovskite, as a twin brother of perovskite, has been neglected although it has similar structure with perovskite. Here, we successfully found that [C₃H₇FN]₃[SnCl₆]Cl has a three-dimensional (3D) antiperovskite structure with the formula M₃AB. Importantly, the compound exhibits obvious ferroelectric properties with an Aizu notation of 622F6 at 391 K. To the best of our knowledge, this is the first 3D hybrid organic–inorganic antiperovskite ferroelectric, which will greatly promote the development of antiperovskite families with more superior physical properties.     

Density of multivariate homogeneous polynomials on star like domains

The famous Weierstrass theorem asserts that every continuous function on a compact set in ${\mathbb{R}}^d$ can be uniformly approximated by algebraic polynomials. A related interesting problem consists in studying the same question for the important subclass of homogeneous polynomials containing only monomials of the same degree. The corresponding conjecture claims that every continuous function on the boundary of convex 0-symmetric bodies can be uniformly approximated by pairs of homogeneous polynomials. The main objective of the present paper is to review the recent progress on this conjecture and provide a new unified treatment of the same problem on non convex star like domains. It will be shown that the boundary of every 0-symmetric non convex star like domain contains an exceptional zero set so that a continuous function can be uniformly approximated on the boundary of the domain by a sum of two homogeneous polynomials if and only if the function vanishes on this zero set. Thus the Weierstrass type approximation problem for homogeneous polynomials on non convex star like domains amounts to the study of these exceptional zero sets. We will also present an extension of a theorem of Varjú which describes the exceptional zero sets for intersections of star like domains. These results combined with certain transformations of the underlying region will lead to the discovery of some new classes of convex and non convex domains for which the Weierstrass type approximation result holds for homogeneous polynomials.     

亏指数为可数无穷的对称微分算子的自伴扩张

应用Ｈｉｌｂｅｒｔ空间内对称算子自伴域一种新的描述方法，得到直和空间内亏指数为可数无穷的对称微分算子自伴扩张的完全解析描述。     

Factorization theory of root closed monoids of small rank

In this note, we investigate ideal and factorization-theoretic properties of some root closed cancellative commutative monoids of rank at most two.     

MISTRAL: a transmission soft X‐ray microscopy beamline for cryo nano‐tomography of biological samples and magnetic domains imaging

The performance of MISTRAL is reported, the soft X‐ray transmission microscopy beamline at the ALBA light source (Barcelona, Spain) which is primarily dedicated to cryo soft X‐ray tomography (cryo‐SXT) for three‐dimensional visualization of whole unstained cells at spatial resolutions down to 30 nm (half pitch). Short acquisition times allowing for high‐throughput and correlative microscopy studies have promoted cryo‐SXT as an emerging cellular imaging tool for structural cell biologists bridging the gap between optical and electron microscopy. In addition, the beamline offers the possibility of imaging magnetic domains in thin magnetic films that are illustrated here with an example.     

Long-term analysis of degenerate parabolic equations in ℝ N

Longtime behavior of degenerate equations with the nonlinearity of polynomial growth of arbitrary order on the whole space R^N is considered. By using -trajectories methods, we proved that weak solutions generated by degenerate equations possess an (L_U² (R^N), L_loc² (R^N))-global attractor. Moreover, the upper bounds of the Kolmogorov ε-entropy for such global attractor are also obtained.     

Almost Integrally Closed Domains

Abstract

A domain R is called almost integrally closed if R is integrally closed in R _P for each nonzero P ∈ Spec(R). Arbitrary quasilocal domains of (Krull) dimension 1 and arbitrary integrally closed domains are examples of almost integrally closed domains. There are no other examples in the contexts of Noetherian, one-dimensional or pseudo-valuation domains, as a consequence of the fact that any almost integrally closed domain that is not integrally closed has at most one height 1 prime ideal. However, a pullback example shows that a non-integrally closed domain that is almost integrally closed need not be semiquasilocal or of dimension at most 1. By analyzing the behavior of the almost integrally closed property for CPI-extensions, we obtain a characterization of the almost integrally closed locally divided domains. Applications are given to the case of G-domains. It also follows that if a divided domain R is not a field, then R is almost integrally closed if and only if some (resp., each) nonzero P ∈ Spec(R) is such that R _P is almost integrally closed and R is integrally closed in R _P .     

Superconvergence of Solution Derivatives of the Shortley–Weller Difference Approximation to Elliptic Equations with Singularities Involving the Mixed Type of Boundary Conditions

This paper presents a superconvergence analysis for the Shortley–Weller finite difference approximation of second-order self-adjoint elliptic equations with unbounded derivatives on a polygonal domain with the mixed type of boundary conditions. In this analysis, we first formulate the method as a special finite element/volume method. We then analyze the convergence of the method in a finite element framework. An O(h ^1.5)-order superconvergence of the solution derivatives in a discrete H ¹ norm is obtained. Finally, numerical experiments are provided to support the theoretical convergence rate obtained.     

Resolvent Estimates for Boundary Value Problems on Large Intervals Via the Theory of Discrete Approximations

In many applications such as the stability analysis of traveling waves, it is important to know the spectral properties of a linear differential operator on the whole real line. We investigate the approximation of this operator and its spectrum by finite interval boundary value problems from an abstract point of view. Under suitable assumptions on the boundary operators, we prove that the approximations converge regularly (in the sense of discrete approximations) to the all line problem, which has strong implications for the behavior of resolvents and spectra. As an application, we obtain resolvent estimates for abstract coupled hyperbolic–parabolic equations. Furthermore, we show that our results apply to the FitzHugh–Nagumo system.