Electronic structure of IPR and non-IPR endohedral metallofullerenes: Connecting orbital and topological rules

The electronic structure of endohedral metallofullerenes is rationalized by connecting the apparently independent orbital and topological rules that explain the stability of this family of fullerenes. The separation of the 12 pentagons of the fullerene, which is maximized in order to minimize the Coulomb repulsion, is found to be correlated with the orbital energies of the cage that accepts the electron transfer from the internal cluster. An explanation for the absence of non-IPR cages in large-size EMFs is also provided.     

相干振动动力学和高分辨非线性光谱学：空气/二甲亚砜液体界面的比较

研究了空气/二甲亚砜界面C?H伸缩振动的自由诱导衰减的相干振动动力学和亚波数高分辨宽带和频振动光谱．对于特定分子体系,频率域光谱测量和时间域动力学测量原则上应获得相同的信息．但对具有耦合或者重叠在一起的若干振动模式的分子体系,通过时域或者频域测量以获取光谱和动力学信息细节均非易事．对于振动光谱并非过于复杂的空气/二甲亚砜界面,基于亚波数高分辨宽带和频振动光谱的频域测量较超快时域测量更有益于获取界面结构和相干动力学定量信     

Abelian varieties with finite abelian group action

An automorphism of an abelian variety induces a decomposition of the variety up to isogeny. There are two such results, namely the isotypical decomposition and Roan’s decomposition theorem. We show that they are essentially the same. Moreover, we generalize in a sense this result to abelian varieties with action of an arbitrary finite abelian group. An early version of this article was inadvertently published before all the revisions had been completed and then retracted [https://doi.org/10.1007/s00013-018-1244-3]. This article is the final peer reviewed version.

     

The maximum number of columns in supersaturated designs with

Cheng and Tang [Biometrika, 88 (2001), pp. 1169–1174] derived an upper bound on the maximum number of columns that can be accommodated in a two‐symbol supersaturated design (SSD) for a given number of rows () and a maximum in absolute value correlation between any two columns (). In particular, they proved that for (mod ) and . However, the only known SSD satisfying this upper bound is when . By utilizing a computer search, we prove that for , and . These results are obtained by proving the nonexistence of certain resolvable incomplete blocks designs. The combinatorial properties of the RIBDs are used to reduce the search space. Our results improve the lower bound for SSDs with rows and columns, for , and . Finally, we show that a skew‐type Hadamard matrix of order can be used to construct an SSD with rows and columns that proves . Hence, we establish for and for all (mod ) such that . Our result also implies that when is a prime power and (mod ). We conjecture that for all and (mod ), where is the maximum number of equiangular lines in with pairwise angle .     

Isomorphisms of spaces with large distortion

Let K and S be locally compact Hausdorff spaces and let X be a strictly convex Banach space of finite dimension at least 2. In this paper, we prove that if there exists an isomorphism T from onto satisfying then K and S are homeomorphic. Here denotes the Schäffer constant of X. Even for the classical cases , and , this result is the X‐valued Banach–Stone theorem via isomorphism with the largest distortion that is known so far, namely . On the other hand, it is well known that this result is not true for , even though K and S are compact Hausdorff spaces.     

On Landis’ Conjecture in the Plane

In this paper we prove a quantitative form of Landis’ conjecture in the plane. Precisely, let W(z) be a measurable real vector-valued function and V(z) ≥0 be a real measurable scalar function, satisfying ‖W‖ _{L ^∞(R ²)} ≤ 1 and ‖V‖ _{L ^∞(R ²)} ≤ 1. Let u be a real solution of Δu ? ?(Wu) ? Vu = 0 in R ². Assume that u(0) = 1 and |u(z)| ≤exp (C ₀|z|). Then u satisfies inf _{|z 0| =R}  sup _{|z?z 0| <1}|u(z)| ≥exp (?CRlog R), where C depends on C ₀. In addition to the case of the whole plane, we also establish a quantitative form of Landis’ conjecture defined in an exterior domain.     

Synthesis of Some C‐3,4,5‐Substituted 2,6‐Dimethyl‐1,4‐dihydropyridines (4‐DHPs)

A series of C‐3,4,5‐substituted 2,6‐dimethyl‐1,4‐dihydropyridines (1,4‐DHPs) with pharmacological properties were prepared by a variation from the classical Hantzsch synthesis. The procedure involves treatment of the respective aldehyde with either ethyl‐3‐aminocrotonate or 3‐aminocrotonitrile in anhydrous acetic acid at temperatures not exceeding 60°C, thus minimizing by‐product formation. The structures of title compounds were elucidated by ¹H NMR, ¹³C NMR, FTIR, and elemental analysis.     

Effect of Concentration on the Photophysics of Dyes in Light‐Scattering Materials.

Photoactive materials based on dye molecules incorporated into thin films or bulk solids are useful for applications as photosensitization, photocatalysis, solar cell sensitization and fluorescent labeling, among others. In most cases, high concentrations of dyes are desirable to maximize light absorption. Under these circumstances, the proximity of dye molecules leads to the formation of aggregates and statistical traps, which dissipate the excitation energy and lower the population of excited states. The search for enhancement of light collection, avoiding energy wasting requires accounting the photophysical parameters quantitatively, including the determination of quantum yields, complicated by the presence of light scattering when particulate materials are considered. In this work we summarize recent advances on the photophysics of dyes in light‐scattering materials, with particular focus on the effect of dye concentration. We show how experimental reflectance, fluorescence and laser‐induced optoacoustic spectroscopy data can be used together with theoretical models for the quantitative evaluation of inner filter effects, fluorescence and triplet formation quantum yields and energy transfer efficiencies.     

Achiral diacrylate with an anticlinic smectic phase

We present an achiral diacrylate that shows a phase transition from the synclinic smectic C phase (SmC) to the anticlinic smectic C (SmCalt). This last phase has been previously reported only for swallow-tailed or dimeric compounds. Our studies using differential scanning calorimetry, X-ray diffraction, polarizing optical microscopy and broad band dielectric spectroscopy suggest the existence of this mesophase in this bifunctional smectogen.     

An evaluation of antifouling booster biocides in Gran Canaria coastal waters using SPE-LC MS/MS

A solid phase extraction (SPE) technique for seawater samples coupled to quantification using liquid chromatography tandem-mass spectrometry (LC-MS/MS) is described to quantify relevant antifouling booster biocides of ecotoxicological concern (Diuron, TCMTB, Irgarol 1051 and Dichlofluanid). The optimised methodology provides a sensitive, easy to use and efficient analytical procedure with detection limits in the range of between 0.1 and 0.2?ng?L^?1 and appropriate reproducibility (with analytical standard deviations of less than 10%). Spiked recoveries for all compounds exceeded 72%. The method was tested through a thorough monitoring regime of commercial port and marinas on the island of Gran Canaria (off the north-west coast of Africa) over a period of several months in 2008. Results provide the first data for antifouling booster biocides in the Canary Islands. Concentrations of Diuron and Irgarol 1051 in samples ranged between 2 and 195?ng?L^?1 and 2 and 146?ng?L^?1, respectively. TCMTB and Dichlofluanid were not detected.