Residual Julia set for functions with the Ahlfors' Property

We consider two classes of functions studied by Epstein [A.L. Epstein, Towers of finite type complex analytic maps, Ph.D. thesis, City University of New York, 1993] and by Herring [M.E. Herring, An extension of the Julia–Fatou theory of iteration, Ph.D. thesis, Imperial College, London, 1994], which have the Ahlfors' Property. We prove under some conditions on the Fatou and Julia sets that the singleton buried components are dense in the Julia set for these classes of functions.     

The structure of irreducible matrix groups with submultiplicative spectrum

We describe the structure of irreducible matrix groups with submultiplicative spectrum. Since all such groups are nilpotent, the study is focused on p-groups. We obtain a block-monomial structure of matrices in irreducible p-groups and build polycyclic series arising from that structure. We give an upper bound to the exponent of these groups. We determine all minimal irreducible groups of p× p matrices with submultiplicative spectrum and discuss the case of p ²× p ² matrices if p is an odd prime.     

Strongly Bounded Groups and Infinite Powers of Finite Groups

We define a group as strongly bounded if every isometric action on a metric space has bounded orbits. This latter property is equivalent to the so-called uncountable strong cofinality, recently initiated by Bergman.

Our main result is that G ^I is strongly bounded when G is a finite, perfect group and I is any set. This strengthens a result of Koppelberg and Tits. We also prove that ω₁-existentially closed groups are strongly bounded.     

"地小氢"和"月小氢"

Hydrogen is the most abundant chemical element in the Universe and is tightly related to human life. This article personifies hydrogen, bringing a close interaction between the hydrogen on the moon and the hydrogen on the Earth. Through lively and interesting dialogues, the history of hydrogen discovery and the properties are introduced, and the application of hydrogen in different aspects of the future is prospected.     

A Hydrogen Bonded Supramolecular Framework Birefringent Crystal

Birefringent crystals could modulate the polarization of light and are widely used as polarizers, waveplates, optical isolators, etc. To date, commercial birefringent crystals have been exclusively limited to purely inorganic compounds such as α-BaB₂O₄ with birefringence of about 0.12. Herein, we report a new hydrogen bonded supramolecular framework, namely, Cd(H₂C₆N₇O₃)₂⋅8 H₂O, which exhibits exceptionally large birefringence up to about 0.60. To the best of our knowledge, the birefringence of Cd(H₂C₆N₇O₃)₂⋅8 H₂O is significantly larger than those of all commercial birefringent crystals and is the largest among hydrogen bonded supramolecular framework crystals. First-principles calculations and structural analyses reveal that the exceptional birefringence is mainly ascribed to strong covalent interactions within (H₂C₆N₇O₃)⁻ organic ligands and the perfect coplanarity between them. Given the rich structural diversity and tunability, hydrogen bonded supramolecular frameworks would offer unprecedented opportunities beyond the traditional purely inorganic oxides for birefringent crystals.     

Boosting Charge Transport in a 2D/3D Perovskite Heterostructure by Selecting an Ordered 2D Perovskite as the Passivator

We demonstrate that an ordered 2D perovskite can significantly boost the photoelectric performance of 2D/3D perovskite heterostructures. Using selective fluorination of phenyl-ethyl ammonium (PEA) lead iodide to passivate 3D FA_0.8Cs_0.2PbI₃, we find that the 2D/3D perovskite heterostructures passivated by a higher ordered 2D perovskite have lower Urbach energy, yielding a remarkable increase in photoluminescence (PL) intensity, PL lifetime, charge-carrier mobilities (ϕμ), and carrier diffusion length (L_D) for a certain 2D perovskite content. High performance with an ultralong PL lifetime of ≈1.3 μs, high ϕμ of ≈18.56 cm² V⁻¹ s⁻¹, and long L_D of ≈7.85 μm is achieved in the 2D/3D films when passivated by 16.67 % para-fluoro-PEA₂PbI₄. This carrier diffusion length is comparable to that of some perovskite single crystals (>5 μm). These findings provide key missing information on how the organic cations of 2D perovskites influence the performance of 2D/3D perovskite heterostructures.     

Quasi-linear functional differential equations with Property A

We study oscillatory properties of solutions of a functional differential equation of the form

(0.1)     

N指标d维广义Wiener过程的极性

本文讨论了N指标d维广义Wiener过程的极性,并得到了一个集合为极集的充分必要条件．     

On the finite dimensional unitary representations of Kazhdan groups

We use A. Weil's criterion to prove that all finite dimensional unitary representations of a discrete Kazhdan group are locally rigid. It follows that any such representation is unitarily equivalent to a unitary representation over some algebraic number field.

     

模糊关系的对偶合成及其在传递性中的应用

引入了模糊关系的一种新的合成：对偶合成。这种新的合成使我们十分容易地刻画反向传递性。利用合成和对偶合成,我们建立了传递性、反向传递性、半传递性和Ferrers性质的若干有趣的等价条件。