The key feature of instability of small non-IPR closed-shell fullerenes: three isomers of C40

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Component-Mode Synthesis Method Variants in the Dynamics of Coupled Structures

The component-mode synthesis method is usually adopted in order to reduce the number of degrees-of-freedom of structures composed of two or more substructures without loosing the main physical characteristics of the whole structure. Many approaches of this method have been proposed in the literature. These approaches differ from each other for the boundary conditions which are imposed at the interface of the two substructures. In this paper four variants of interface boundary conditions are examined. For each set of conditions a suitable coordinate transformation, compatible with the conditions at the boundary degrees-of-freedom between the two substructures, is presented. Moreover, in the numerical applications a comparison between the four component-mode synthesis variants here proposed with respect to the same variants proposed in the literature is presented. The better accuracy of the proposed approach is shown.     

Pure patterns of order 2

We provide mutual elementary recursive order isomorphisms between classical ordinal notations, based on Skolem hulling, and notations from pure elementary patterns of resemblance of order 2, showing that the latter characterize the proof-theoretic ordinal $1^{\infty }$ of the fragment ${\mathrm{\Pi }}_1^1$–${\mathrm{CA}}_0$ of second order number theory, or equivalently the set theory $\mathrm{KP}{?}_0$. As a corollary, we prove that Carlson's result on the well-quasi orderedness of respecting forests of order 2 implies transfinite induction up to the ordinal $1^{\infty }$. We expect that our approach will facilitate analysis of more powerful systems of patterns.     

Perspective of Galactic dark matter subhalo detection on Fermi from the EGRET observation

The perspective of the detectability of Galactic dark matter subhaioes on the Fermi satellite is investigated in this work.Under the assumptions that dark matter annihilation accounts for the "GeV excess" of the Galactic diffuse γ-rays discovered by EGRET and the γ-ray flux is dominated by the contribution from subhaloes of dark matter, we calculate the expected number of dark matter subhaloes that Fermi may detect.We show that Fermi may detect a few tens to several hundred subhaloes in a 1-year all-sky survey.Since EGRET observation is taken as a normalization, this prediction is independent of the particle physics property of dark matter.The uncertainties of the prediction are discussed in detail.We find that the major uncertainty comes from the mass function of subhaloes, i.e., whether the subhaloes are "point like" (high-mass rich) or "diffuse like" (low-mass rich).Other uncertainties like the background estimation and the observational errors will contribute a factor of 2-3.     

Perspective of Galactic dark matter subhalo detection on Fermi from the EGRET observation

The perspective of the detectability of Galactic dark matter subhaloes on the Fermi satellite is investigated in this work. Under the assumptions that dark matter annihilation accounts for the ``GeV excess' of the Galactic diffuse $\upgamma$-rays discovered by EGRET and the $\upgamma$-ray flux is dominated by the contribution from subhaloes of dark matter, we calculate the expected number of dark matter subhaloes that Fermi may detect. We show that Fermi may detect a few tens to several hundred subhaloes in a 1-year all-sky survey. Since EGRET observation is taken as a normalization, this prediction is independent of the particle physics property of dark matter. The uncertainties of the prediction are discussed in detail. We find that the major uncertainty comes from the mass function of subhaloes, i.e., whether the subhaloes are ``point like' (high-mass rich) or ``diffuse like' (low-mass rich). Other uncertainties like the background estimation and the observational errors will contribute a factor of 2—3.     

细长结构几何非线性分析的子结构方法

将细长结构沿长度方向划分为多个子结构,并在每个子结构上建立一个随结构一起运动的连体基,则结构内任意点的位移可分解为连体基的转动和相对于连体基的小位移。利用细长结构这样的变形特征,本文详细讨论了连体基的转动,给出了与连体基选择方式相协调的节点位移及其虚变分表达式,并将子结构内部位移凝聚到了边界节点上。在此基础上,提出了一种细长结构几何非线性分析的子结构方法,可在不损失计算精度的前提下大幅度降低求解规模,从而提高了计算效率。数值算例验证了所提方法的有效性。     

Change of dislocation substructures upon high-cycle fatigue of stainless steel

Methods of transmission electron microscopy of thin foils are used to study the evolution of dislocation substructures in Fe–0.1C–1.7Mn–0.92Ti–18.2Cr–10.4Ni–0.71Si corrosion-proof austenitic steel subject to high-cycle fatigue loading to destruction. Quantitative dependences of the dislocation substructure parameters on the number of loading cycles and distances to the sample surface are established. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 42–45, March, 2009.     

Design,synthesis and crystallographic study of novel indole‐based cyano derivatives as key building blocks for heteropolycyclic compounds of major complexity

A four‐stage reaction sequence has been designed and developed for the synthesis of highly functionalized enolate esters as key building blocks for the synthesis of novel heteropolycyclic compounds of potential pharmaceutical value. The sequence starts with simple commercially available indoles and proceeds via 3‐(indol‐3‐yl)‐3‐oxopropanenitriles, which react with 2‐bromobenzaldehyde to form the corresponding chalcones; these are readily reduced to dihydrochalcones, which are in turn acylated to form the enolate esters. The compounds in this sequence have been characterized by IR and ¹H and ¹³C NMR spectroscopy, by mass spectrometry and by elemental analysis. The molecular and supramolecular structures are reported for representative examples, namely (E )‐3‐(2‐bromophenyl)‐2‐(1‐methyl‐1H‐indole‐3‐carbonyl)acrylonitrile, C₁₉H₁₃BrN₂O, (Ib ), (2RS )‐2‐(2‐bromobenzyl)‐3‐(1‐methyl‐1H‐indol‐3‐yl)‐3‐oxopropanenitrile, C₁₉H₁₅BrN₂O, (IIb ), and (2RS )‐3‐(1‐benzyl‐1H‐indol‐3‐yl)‐2‐(2‐bromobenzyl)‐3‐oxopropanenitrile, C₂₅H₁₉BrN₂O, (IIc ), the latter two of which crystallize with Z ′ = 2, and (E )‐1‐(1‐acetyl‐1H‐indol‐3‐yl)‐3‐(2‐bromophenyl)‐2‐cyanoprop‐1‐en‐1‐yl acetate, C₂₂H₁₇BrN₂O, (III), and (E )‐1‐(1‐benzyl‐1H‐indol‐3‐yl)‐3‐(2‐bromophenyl)‐2‐cyanoprop‐1‐en‐1‐yl benzoate, C₃₂H₂₃BrN₂O, (IV). The structure of the related chalcone (E )‐2‐benzoyl‐3‐(2‐bromophenyl)prop‐2‐enenitrile, (V), has been redetermined at 100 K, where it is monoclinic, as opposed to the triclinic form reported at ambient temperature.     

The moduli of substructures of a compact complex space

We construct a space of fine moduli for the substructures of an arbitrary compact complex space . A substructure of is given by a subalgebra of the structure sheaf with the additional feature that is also a complex space; and are called equivalent if and only if and are isomorphic as subalgebras of .

Since substructures are quotients, it is only natural to start with the fine moduli space of all complex-analytic quotients of . In order to obtain a representable moduli functor of substructures, we are forced to concentrate on families of quotients which satisfy some flatness condition for relative differential modules of higher order. Considering the corresponding flatification of , we realize that its open subset consisting of all substructures turns out to be a complex space which has the required universal property.