Another universality property for crumpled cubes

Let C denote a crumpled n-cube in the n-sphere Sⁿ such that every Cantor set in its boundary is tamely embedded in Sⁿ. The main theorem shows C to be universal in the sense that however it is sewn to a crumpled n-cube D of type 2A, a large class containing most of the explicitly described examples, the resultant space is homeomorphic to Sⁿ.     

连续SiC(Al)纤维的耐超高温性能及其机理

以有机金属聚合物聚铝碳硅烷为原料, 利用先驱体转化法制备出连续SiC(Al)纤维. 采用一系列分析测试对纤维的组成、结构以及耐超高温性能进行了表征, 通过与Nicalon纤维的比较, 对连续SiC(Al)纤维的耐超高温机理进行了研究. 结果表明, 连续SiC(Al)纤维具有优异的耐超高温性能,在1800 ℃氩气中处理1 h后, 纤维的强度保留率为80%左右; 元素分析和27Al MAS核磁共振等分析表明, 连续SiC(Al)纤维为近化学计量比的SiC纤维, 纤维中微量的铝元素以Al—O和Al—C键两种形式存在; 在超高温条件下, 两种不同存在形式的铝均能够抑制纤维中晶粒的长大. 纤维具有近化学计量比的组成和铝元素在高温条件下对于晶粒长大的抑制, 是连续SiC(Al)纤维具有优异耐超高温性能的原因.     

Stochastic Integration of Operator-Valued Functions with Respect to Banach Space-Valued Brownian Motion

Let E be a real Banach space with property (α) and let W _Γ be an E-valued Brownian motion with distribution Γ. We show that a function is stochastically integrable with respect to W _Γ if and only if Γ-almost all orbits Ψx are stochastically integrable with respect to a real Brownian motion. This result is derived from an abstract result on existence of Γ-measurable linear extensions of γ-radonifying operators with values in spaces of γ-radonifying operators. As an application we obtain a necessary and sufficient condition for solvability of stochastic evolution equations driven by an E-valued Brownian motion. The first named author gratefully acknowledges the support by a ‘VIDI subsidie’ in the ‘Vernieuwingsimpuls’ programme of The Netherlands Organization for Scientific Research (NWO) and the Research Training Network HPRN-CT-2002–00281. The second named author was supported by grants from the Volkswagenstiftung (I/78593) and the Deutsche Forschungsgemeinschaft (We 2847/1–1).     

Synthesis of a π-Extended Double [9]Helicene

Double helicenes are appealing chiral frameworks. Their π-extension is desirable to achieve (chir)optical response in the visible and near-infrared (NIR) region, but access to higher double [n]helicenes (n≥8) has remained challenging. Herein, we report an unprecedented π-extended double [9]helicene ( D9H ), unambiguously revealing its structure by single-crystal X-ray diffraction. D9H shows remarkable NIR emission from 750 to 1100 nm with a high photoluminescence quantum yield of 18 %. In addition, optically pure D9H exhibits panchromatic circular dichroism with a notable dissymmetry factor (g_CD) of 0.019 at 590 nm, which is among the highest in the visible region for reported helicenes.     

Manipulating Electron-Transfer Events in [Fe4Co4] Cubes via a Mixed-Ligand Approach: The Impact of Elastic Frustration

The engineering of intermolecular interaction is challenging but critical for magnetically switchable molecules. Here, we prepared two cyanide-bridged [Fe₄Co₄] cube complexes via the alkynyl- and alcohol-functionalized trispyrazoyl capping ligands. The alkynyl-functionalized complex 1 exhibited a thermally-induced incomplete metal-to-metal electron transfer (MMET) behaviour at around 220 K, while the mixed alkynyl/alcohol-functionalized cube of 2 showed a complete and abrupt MMET behaviour at 232 K. Remarkably, both compounds showed a long-lived photo-induced metastable state up to 200 K. The crystallographic study demonstrated that the incomplete transition of 1 was likely due to the possible elastic frustration originating from the competition between the anion-propagated elastic interactions and inter-cluster alkynyl-alkynyl & CH-alkynyl interactions, whereas the latter are eliminated in 2 as a result of the partial substitution by the alcohol-functionalized ligand. Additionally, the introduction of chemically distinguishable cobalt centers within the cube unit of 2 did not lead to a two-step but a one-step transition, possibly because of the strong ferroelastic intramolecular interaction through the cyanide bridges.     

Achieving Near-unity Photoluminescence Quantum Yields in Organic-Inorganic Hybrid Antimony (III) Chlorides with the [SbCl5] Geometry

Hybrid organic–inorganic antimony halides have attracted increasing attention due to the non-toxicity, stability, and high photoluminescence quantum yield (PLQY). To shed light on the structural factors that contribute to the high PLQY, five pairs of antimony halides with general formula A₂SbCl₅ and A₂Sb₂Cl₈ are synthesized via two distinct methods and characterized. The A₂SbCl₅ type adopts square pyramidal [SbCl₅] geometry with near-unity PLQY, while the A₂Sb₂Cl₈ adopts seesaw dimmer [Sb₂Cl₈] geometry with PLQY≈0 %. Through combined data analysis with the literature, we have found that A₂SbCl₅ series with square pyramidal geometry generally has much longer Sb⋅⋅⋅Sb distances, leading to more expressed lone pairs of Sb^III. Additional factors including Sb−Cl distance and stability of antimony chlorides may also affect PLQY. Our targeted synthesis and correlated insights provide efficient tools to precisely form highly emissive materials for optoelectronic applications.     

Synthesis and Chiroptical Properties of Binaphthyl-Hinged [5]Helicenes

The synthesis, structure, and circularly polarized luminescence (CPL) of two types of shape-persistent [5]helicenes, hinged by a tethered (−OCH₂CH₂O−) or untethered (−OCH₃) binaphthyl, are reported. The binaphthyl tethering system facilitated an effective Wittig ring-closure reaction in the synthesis of a macrocyclic precursor, which could be easily converted to the title compound via successive photocyclization. The tethered groups were replaced with untethered −OCH₃ groups by treatment with BBr₃ followed by methylation. Both compounds exhibited similar spectra, and their longest wavelength absorption band with a low intensity was attributed to the transition from HOMO to LUMO+1. These compounds exhibited CPL with higher dissymmetry factors g_lum values than unlocked helicenes.     

反对角算子矩阵及其平方的(ω)性质的摄动

设H为复的无限维可分的Hilbert空间,B(H)为H上的有界线性算子的全体.若σ_a(T)\σ_(ea)(T)=π_(00)(T),则称T∈B(H)满足(ω)性质,其中σ_a(T)和σ_(ea)(T)分别表示算子T的逼近点谱和本质逼近点谱,π_(00)(T)={λ∈isoσ(T):0dimN(T-λI)∞}.T∈B(H)称为满足(ω)性质的摄动,若对任意的紧算子K,T+K满足(ω)性质.本文证明了反对角算子矩阵及其平方具有(ω)性质的摄动的等价性.     

Effect of ultrasound assisted konjac glucomannan treatment on properties of chicken plasma protein gelation

The effect of ultrasound assisted konjac glucomannan treatment on the properties of chicken plasma protein gelation was investigated in this study. There were four gelation groups as follows: untreated plasma protein gelation (Control), gelation added konjac glucomannan (KGG), gelation by ultrasound treatment alone (UG) and gelation added konjac glucomannan combined with ultrasound treatment (KGUG). The data showed that the gelation strength and water-holding capacity of the treated groups were significantly increased compared with those of Control. The strongest bonding water was present in KGUG, followed by KGG and UG in low-field nuclear magnetic resonance. The storage energy (G′) and loss energy modulus (G″) of KGUG showed the largest rheological properties, and the G′ value was higher than that of G″. Furthermore, the elastic and gelatinous properties of UG, KGG and KGUG played a dominant role in viscoelasticity. After konjac glucomannan addition, the particle size of KGG increased significantly. Compared with that of the Control and KGG, the average particle size of UG and KGUG decreased significantly after ultrasound treatment. The hydrophobicity and disulfide bonds mainly affected the formation of heat-induced gelation in these four groups. Furthermore, KGUG with the highest hydrophobicity and disulfide bonds revealed the best stability. Therefore, the gelation of chicken plasma protein by ultrasound assisted konjac glucomannan treatment had excellent gelling properties.     

Property ∏σ and tensor products of operator algebras

In this paper, we introduce Property ∏σ of operator algebras and prove that nest subalgebras and the finite-width CSL subalgebras of arbitrary von Neumann algebras have Property ∏σ.Finally, we show that the tensor product formula alg ML1-(×)algNL2 = algM-(×)N(L1 (×) L2) holds for any two finite-width CSLs L1 and L2 in arbitrary von Neumann algebras M and N, respectively.