Synthesis and characterization of four metal-organophosphonates with one-, two-, and three-dimensional structures

A series of metal-organic hybrid compounds were synthesized using two new phosphonic acids, pyridyl-4-phosphonic acid and p-xylylenediphosphonic acid (H(2)O(3)PCH(2)C(6)H(4)CH(2)PO(3)H(2)). The phosphonic acid ligands have been synthesized from their corresponding bromides following two different types of reactions. The reaction of pyridyl-4-phosphonic acid with three different divalent metal salts results in the formation of molecular structures of different dimensionality. The reaction of Cu(II) with the phosphonic acid under hydrothermal conditions yields a three-dimensional (3D) open framework structure having the molecular formula [Cu(4)(NC(5)H(4)-PO(3))(4)(H(2)O)(10)] (1). The reactions with Mn(II) and Zn(II) salts with the same phosphonic acid resulted in a two-dimensional layered and a dinuclear compound with molecular formulas [Mn(3)(NC(5)H(4)-PO(3))(4)(H(2)O)(6)(ClO(4))(2)] (2) and [Zn(2)(NHC(5)H(4)-PO(3)H)(2)Cl(4)] (3), respectively. Compound 1 crystallizes in the triclinic crystal system having space group P with structural parameters a = 7.4564(15) Angstrom, b = 9.1845(19) Angstrom, c = 11.582(2) Angstrom, alpha = 100.842(3) degrees, beta = 104.303(3) degrees, gamma = 94.774(3) degrees, and Z = 1. Compound 2 crystallizes in the triclinic crystal system, space group P, with structural parameters a = 7.6871(14) Angstrom, b = 10.576(2) Angstrom, c = 14.470(3)Angstrom, alpha = 81.340(3) degrees, beta = 81.561(3) degrees, gamma = 68.757(3) degrees, and Z = 2, whereas compound 3 crystallizes in a monoclinic crystal system with space group P2(1)/n. The structural parameters are as follows: a = 8.4969 (5) Angstrom, b = 9.3911 (5) Angstrom, c = 12.3779 (6) Angstrom, beta = 90.860(17) degrees, and Z = 4. The pyridylphosphonate ligand shows different ligation behavior toward the three divalent metal ions. On the other hand, p-xylylenediphosphonic acid on reaction with Co(II) formed a 3D compound [Co(2)(O(3)PCH(2)C(6)H(4)CH(2)PO(3))(2)(H(2)O)(2)] (4) with a layered and pillared structure. Compound 4 crystallizes in an orthorhombic crystal system with space group Pnma. The structural parameters are a = 21.744(4) Angstrom, b = 5.6744(10) Angstrom, c = 4.7927(9) Angstrom, and Z = 4.     

The investigation of water diffusion into teflon copolymer revealed by fiber-optic evanescent wave spectroscopy

Fiber-optic evanescent wave infrared spectroscopy was used for the study of water diffusion in Teflon and has provided valuable information about the structure of water in amorphous hydrophobic polymers. Time-dependent absorption measurements were carried out in two spectral ranges: 3000-3800 cm(-1), associated with the O-H stretching mode, and 1620-1670 cm(-1), associated with the H-O-H bending mode of water. The results indicate that the IR spectra could be expressed as a superposition of spectra due to two species of water molecules: strongly and weakly hydrogen-bonded. We suggest that water molecules form clusters with strongly hydrogen-bonded molecules at the cores and with weakly hydrogen-bonded molecules at the external parts of the clusters. A mathematical model, based on a linear diffusion equation with a moving boundary, gave a ratio of 3.5 between the total number of molecules in a cluster and the number of water molecules at the core of the cluster.     

Encapsulation and diffraction-pattern-correction methods to reduce the effect of damage in x-ray diffraction imaging of single biological molecules

Short and intense x-ray pulses may be used for atomic-resolution diffraction imaging of single biological molecules. Radiation damage and a low signal-to-noise ratio impose stringent pulse requirements. In this Letter, we describe methods for decreasing the damage and improving the signal by encapsulating the molecule in a sacrificial layer (tamper) that reduces atomic motion and by postprocessing the pulse-averaged diffraction pattern to correct for ionization damage. Simulations show that these methods greatly improve the image quality.     

Studies toward the total synthesis of sorangiolides and their analogues. A convergent stereoselective synthesis of the macrocyclic lactone precursors

Stereoselective synthesis of the fully protected 18-membered macrocyclic lactones as the immediate precursors of the natural products, sorangiolides A and B, is described. The key steps used in the synthesis include the sp3-hybridized carbon-carbon Fu cross coupling, the stereoselective Evans' aldol reaction with 1,5-anti induction, the 1,3-diastereoselective syn reduction of a beta-hydroxyketone intermediate, and Mukaiyama macrolactonization reactions.     

Observable signatures of a black hole ejected by gravitational-radiation recoil in a galaxy merger

According to recent simulations, the coalescence of two spinning black holes (BHs) could lead to a BH remnant with recoil speeds of up to thousands of km s(-1). Here we examine the circumstances resulting from a gas-rich galaxy merger under which the ejected BH would carry an accretion disk and be observable. As the initial BH binary emits gravitational radiation and its orbit tightens, a hole is opened in the disk which delays the consumption of gas prior to the eventual BH ejection. The punctured disk remains bound to the ejected BH within the region where the gas orbital velocity is larger than the ejection speed. For a approximately 10(7) M[middle dot in circle] BH the ejected disk has a characteristic size of tens of thousands of Schwarzschild radii and an accretion lifetime of approximately 10(7) yr. During that time, the ejected BH could traverse a considerable distance and appear as an off-center quasar with a feedback trail along the path it left behind.     

Bipartite density of cubic graphs

We first obtain the exact value for bipartite density of a cubic line graph on n vertices. Then we give an upper bound for the bipartite density of cubic graphs in terms of the smallest eigenvalue of the adjacency matrix. In addition, we characterize, except in the case n=20, those graphs for which the upper bound is obtained.     

Advances in metric embedding theory

Metric Embedding plays an important role in a vast range of application areas such as computer vision, computational biology, machine learning, networking, statistics, and mathematical psychology, to name a few. The mathematical theory of metric embedding is well studied in both pure and applied analysis and has more recently been a source of interest for computer scientists as well. Most of this work is focused on the development of bi-Lipschitz mappings between metric spaces. In this paper we present new concepts in metric embeddings as well as new embedding methods for metric spaces. We focus on finite metric spaces, however some of the concepts and methods are applicable in other settings as well.One of the main cornerstones in finite metric embedding theory is a celebrated theorem of Bourgain which states that every finite metric space on n points embeds in Euclidean space with distortion. Bourgain?s result is best possible when considering the worst case distortion over all pairs of points in the metric space. Yet, it is natural to ask: can an embedding do much better in terms of the average distortion? Indeed, in most practical applications of metric embedding the main criteria for the quality of an embedding is its average distortion over all pairs.In this paper we provide an embedding with constant average distortion for arbitrary metric spaces, while maintaining the same worst case bound provided by Bourgain?s theorem. In fact, our embedding possesses a much stronger property. We define the ?q-distortion of a uniformly distributed pair of points. Our embedding achieves the best possible ?q-distortion for all 1?q?∞simultaneously.The results are based on novel embedding methods which improve on previous methods in another important aspect: the dimension of the host space. The dimension of an embedding is of very high importance in particular in applications and much effort has been invested in analyzing it. However, no previous result improved the bound on the dimension which can be derived from Bourgain?s embedding. Our embedding methods achieve better dimension, and in fact, shed new light on another fundamental question in metric embedding, which is: whether the embedding dimension of a metric space is related to its intrinsic dimension? I.e., whether the dimension in which it can be embedded in some real normed space is related to the intrinsic dimension which is reflected by the inherent geometry of the space, measured by the space?s doubling dimension. The existence of such an embedding was conjectured by Assouad,⁴and was later posed as an open problem in several papers. Our embeddings give the first positive result of this type showing any finite metric space obtains a low distortion (and constant average distortion) embedding in Euclidean space in dimension proportional to its doubling dimension.Underlying our results is a novel embedding method. Probabilistic metric decomposition techniques have played a central role in the field of finite metric embedding in recent years. Here we introduce a novel notion of probabilistic metric decompositions which comes particularly natural in the context of embedding. Our new methodology provides a unified approach to all known results on embedding of arbitrary finite metric spaces. Moreover, as described above, with some additional ideas they allow to get far stronger results.The results presented in this paper⁵have been the basis for further developments both within the field of metric embedding and in other areas such as graph theory, distributed computing and algorithms. We present a comprehensive study of the notions and concepts introduced here and provide additional extensions, related results and some examples of algorithmic applications.     

Linear alkyl diamine-uranium-phosphate systems: U(VI) to U(IV) reduction with ethylenediamine

Mild-hydrothermal reactions in acidic medium using 1,3-diaminopropane, 1,4-diaminobutane, and 1,5-diaminopentane as structure directing agents led to three-dimensional (3D) uranyl phosphates (CH?)?(NH?)?{[(UO?)(H?O)][(UO?)(PO?)]?} (C3U5P4), (CH?)?(NH?)?{[(UO?)(H?O)][(UO?)(PO?)]?} (C4U5P4) and (CH?)5(NH?)?{[(UO?)(H?O)][(UO?)(PO?)]?} (C5U5P4). The structures of (C4U5P4) and (C5U5P4) were solved in the space group Cmc2? using single-crystal X-ray diffraction data. The compounds are isostructural to the corresponding uranyl vanadates and contain the same 3D inorganic framework built from uranyl-phosphate layers of uranophane-type anion topology pillared by [UO?(H?O)] pentagonal bipyramids. In neutral or basic medium the alkyl diamines decompose to give ammonium uranyl phosphate trihydrate. In the same conditions by using ethylenediamine, unexpected reduction of uranium(VI) to uranium(IV) occurs leading to the formation of (CH?)?(NH?)?[U(PO?)?] (C2UP2) single crystals. C2UP2 undergoes a reversible phase transition from triclinic to monoclinic symmetry at about 230 °C. The structure of the two forms results from the stacking of inorganic layers (∞)1[U(PO?)?]2?, and organic layers containing ethylene diammonium ions, the two layers being linked by hydrogen bonds. Single crystals of (CH?)?(NH?)?[PO?OH] (C2HP) are formed by evaporation of the solution after filtering of C2UP2 single crystals. The structure of C2HP contains infinite (∞)1[PO?OH]2? chains connected by (CH?)?(NH?)?2? ions through hydrogen bonds.     

Selective surface and near-surface modification of a noncatenated, catalytically active metal-organic framework material based on Mn(salen) struts

From a combination of chiral Mn(salen) struts and the tetratopic ligand tetrakis(4-carboxyphenyl)benzene, a large-pore, noncatenated metal-organic framework (MOF) material, MnSO-MOF, has been synthesized. Following solvent exchange with hydrophobic CHCl(3), treatment of MnSO-MOF with aqueous H(2)O(2) allowed for the selective demetalation of Mn(salen) struts at and near the surface of the crystals. The resulting crystals displayed greatly enhanced size-selective catalysis compared to the as-synthesized material. Handling of the mechanically fragile MnSO-MOF crystals was greatly facilitated by activation with supercritical CO(2).