The flip side of buckling

Buckling of slender structures under compressive loading is a failure of infinitesimal stability due to a confluence of two factors: the energy density non-convexity and the smallness of Korn’s constant. The problem has been well understood only for bodies with simple geometries when the slenderness parameter is well defined. In this paper, we present the first rigorous analysis of buckling for bodies with complex geometry. By limiting our analysis to the “near-flip” instability, we address the universal features of the buckling phenomenon that depend on neither the shape of the domain nor the degree of constitutive nonlinearity of the elastic material.      

Facile Synthesis and Properties of 2‐λ5‐Phosphaquinolines and 2‐λ5‐Phosphaquinolin‐2‐ones

Treatment of 2‐ethynylanilines with P(OPh)₃ gives either 2,2‐diphenoxy‐2‐λ⁵‐phosphaquinolines or 2‐phenoxy‐2‐λ⁵‐phosphaquinolin‐2‐ones under transition‐metal‐free conditions. This reaction offers access to an underexplored heterocycle, which opens up the study of the fundamental nature of the N?P^V double bond and its potential for delocalization within a cyclic π‐electron system. This heterocycle can serve as a carbostyril mimic, with application as a bioisostere for pharmaceuticals based on the 2‐quinolinone scaffold. It also holds promise as a new fluorophore, since initial screening reveals quantum yields upwards of 40 %, Stokes shifts of 50–150 nm, and emission wavelengths of 380–540 nm. The phosphaquinolin‐2‐ones possess one of the strongest solution‐state dimerization constants for a D–A system (130 M ^?1) owing to the close proximity of a strong acceptor (P?O) and a strong donor (phosphonamidate N? H), which suggests that they might hold promise as new hydrogen‐bonding hosts for optoelectronic sensing.     

Biodistribution and toxicity of engineered gold nanoparticles: a review of in vitro and in vivo studies

Recent advances in wet chemical synthesis and biomolecular functionalization of gold nanoparticles have led to a dramatic expansion of their potential biomedical applications, including biosensorics, bioimaging, photothermal therapy, and targeted drug delivery. As the range of gold nanoparticle types and their applications continues to increase, human safety concerns are gaining attention, which makes it necessary to better understand the potential toxicity hazards of these novel materials. Whereas about 80 reports on the in vivo biodistribution and in vitro cell toxicity of gold nanoparticles are available in the literature, there is lack of correlation between both fields and there is no clear understanding of intrinsic nanoparticle effects. At present, the major obstacle is the significant discrepancy in experimental conditions under which biodistribution and toxicity effects have been evaluated. This critical review presents a detailed analysis of data on the in vitro and in vivo biodistribution and toxicity of most popular gold nanoparticles, including atomic clusters and colloidal particles of diameters from 1 to 200 nm, gold nanoshells, nanorods, and nanowires. Emphasis is placed on the systematization of data over particle types and parameters, particle surface functionalization, animal and cell models, organs examined, doses applied, the type of particle administration and the time of examination, assays for evaluating gold particle toxicity, and methods for determining the gold concentration in organs and distribution of particles over cells. On the basis of a critical analysis of data, we arrive at some general conclusions on key nanoparticle parameters, methods of particle surface modification, and doses administered that determine the type and kinetics of biodistribution and toxicity at cellular and organismal levels (197 references).     

Reactions of coordinated hydroxymethylphosphines with NH-functional amines: the phosphorus lone pair is crucial for the phosphorus Mannich reaction

Non-coordinated hydroxymethylphosphines react readily with primary and secondary amines by the phosphorus Mannich reaction. To determine if this reactivity can be used to synthesize phosphine macrocycles, trans-Fe(DHMPE)(2)Cl(2) (DHMPE = 1,2-bis(dihydroxymethylphosphino)ethane) was prepared and reacted with various amines. However, no phosphorus Mannich reactivity was observed. In order to understand why no reactions occurred, the Mannich reactivity of the borane-coordinated hydroxymethylphosphines DHMPE·2BH(3) and Ph(2)PCH(2)OH·BH(3) was investigated. These borane-coordinated phosphines also did not undergo the phosphorus Mannich reaction. These results suggest that the lone pair of electrons on the phosphorus atom is essential for the phosphorus Mannich reaction to occur, and therefore it is not possible to use this reaction in a templated synthesis of phosphine macrocycles. It is speculated that the mechanism of the phosphorus Mannich reaction may involve a methylenephosphonium intermediate, analogous to an iminium in the standard Mannich reaction. X-ray crystal structures of trans-Fe(DHMPE)(2)Cl(2) and DHMPE·2BH(3) are also presented. Both crystal structures display an extended hydrogen-bonding network in the solid state.     

Iterative stereospecific reagent-controlled homologation using a functionalized α-chloroalkyllithium: synthesis of cyclic targets related to epibatidine

Enantioenriched 1-chloro-2-(1,3-dioxolan-2-yl)ethyllithium was generated by PhLi initiated sulfoxide-ligand exchange and deployed in situ for sequential double stereospecific reagent-controlled homologation (StReCH) of B-(2-chloro-pyrid-5-yl) pinacol boronate. This process afforded highly functionalized contiguous stereodiad motifs (typically, % ee ≥ 98%, dr ≥ 85:15) amenable to subsequent annulative transformations as demonstrated by the concise synthesis (5-7 steps) of cyclic adducts related to the analgesic alkaloid epibatidine.     

Translation invariance in groups of prime order

We prove that there is an absolute constant c>0 with the following property: if Z/pZ denotes the group of prime order p, and a subset A⊂Z/pZ satisfies 1<|A|<p/2, then for any positive integer there are at most 2m non-zero elements b∈Z/pZ with |(A+b)?A|?m. This (partially) extends onto prime-order groups the result, established earlier by S. Konyagin and the present author for the group of integers. We notice that if A⊂Z/pZ is an arithmetic progression and m<|A|<p/2, then there are exactly 2m non-zero elements b∈Z/pZ with |(A+b)?A|?m. Furthermore, the bound c|A|/ln|A| is best possible up to the value of the constant c. On the other hand, it is likely that the assumption can be dropped or substantially relaxed.     

Equilibrium acidities of superacids

In this paper, we report the most comprehensive equilibrium superacidity scale that is available to date. Contrary to most of the past works, this scale is set up in a medium of constant composition and the obtained acidity values characterize the acidities of molecules rather than acidities of media. The current scale is thus complementary to the well-known H(0) scale in the information that it provides. The solvent used is 1,2-dichloroethane (DCE). DCE has very weak basic properties (but sufficiently high polarity) and is an appropriate solvent for measuring acidities of very strong acids of diverse chemical nature. DCE acidities of well-known superacids (CF(3)SO(2)OH, (CF(3)SO(2))(2)NH, cyanocarbon acids, etc.) as well as common mineral acids (H(2)SO(4), HI, HBr, etc.) are reported. Acidities of altogether 62 acids have been determined from 176 interlinked relative acidity measurements. The scale spans 15 orders of magnitude (from picric acid to 1,1,2,3,3-pentacyanopropene) and is expected to be a useful tool in design, use, and further acidity measurements of superacidic molecules.     

Anomeric effect in N-azidomethylpyrrolidine: gas-phase electron diffraction and theoretical study

Gas-phase electron-diffraction data and high-level quantum chemical calculations have been used to study the conformational behaviour of N-azidomethylpyrrolidine. The two most stable conformers with a relative abundance of about 80% at 298 K possess gauche orientation of the azidomethyl group around the C-N(pyr) bond (C-N(azido)gauche with respect to the endocyclic N(pyr)-C bond). This orientation is a strong manifestation of an anomeric effect. The influence of the anomeric effect is also reflected in shortening of the C-N(pyr) bond and lengthening of the C-N(azido) bond as compared to such bonds in other compounds.     

A multipole superconducting wiggler for Canadian light source

A contract for multipole superconducting wiggler design and fabrication between The University of Saskatchewan and Budker Institute of Nuclear Physics was signed in October 2003. A wiggler with the photons energy range 4 to 40 keV, the maximum field 1.9 T, and the period length as small as possible was required for the micro-XAFS beamline. In 2004 the 2 T 63-pole superconducting wiggler with the average period length 34 mm was fabricated in BINP. To eliminate the undulator-type spectrum, the periodicity of the wiggler was broken. A new approach to the cryostat design enabled long-time (up to 6 months) machine operation without liquid helium refilling (LHe consumption <0.03 l/h). After successful tests the wiggler was installed on the Canadian Light Source (CLS) storage ring with the energy 2.9 GeV in January 2005. The main parameters of the magnet and the cryogenic systems, as well as magnet measurements data, cryogenic system test data, and experimental results during machine operation on the CLS storage ring are presented.     

Problems with Initial- and Final-State Interactions in Deep-Inelastic Scattering

Although there exists a vast literature devoted to the theory of deep-inelastic scattering, the restrictions imposed on the (electromagnetic or weak) current operator by its commutation relations with the representation operators of the Poincaré group and locality have not been considered. We argue that there is a problem with the current operator, leading to the standard parton-model results, satisfying these restrictions. At the same time, there exist models where the correct commutation relations and locality are satisfied but the initial- and final-state interactions of the struck quark with the remnants of the target cannot be neglected even in the Bjorken limit. Received June 13, 1997; revised January 19, 1998; accepted for publication January 27, 1998