Tenth Peregrine breather solution to the NLS equation

In this paper we construct a particularly important solution to the focusing NLS equation, namely a Peregrine breather of the rank 10 which we call, P₁₀$P_{10}$ breather. The related explicit formula is given by the ratio of two polynomials of degree 110 with integer coefficients times trivial exponential factor. This formula drastically simplifies for the “initial values” namely for t=0$t=0$ or x=0$x=0$. This formula confirms a general conjecture saying that between all quasi-rational solutions of the rank N$N$ fixed by the condition that its absolute value tends to 1 at infinity and its highest maximum is located at the point (x=0,t=0)$(x=0,t=0)$, the P_N$P_N$ breather is distinguished by the fact that P_N(0,0)=2N+1$P_N(0,0)=2N+1$ and, in the aforementioned class of quasi-rational solutions, it is an absolute maximum. At the end we also make a few remarks concerning the rational deformations of P₁₀$P_{10}$ breather involving 2N−2$2N-2$ free real parameters chosen in a way that P_N$P_N$ breather itself corresponds to the zero values of these parameters although we have no intention to discuss the properties of these deformations here.     

A New Chemical Method to Desulfenylate Indol-3-yl Sulfides

Abstract

Desulfenylation of indol-3-yl sulfides liberates the most reactive position of the ring for further transformations. The usual procedure, utilizing Raney Nickel (P. G. Gassman, et. al., J. Am. Chem. SOC. 1974,96, 5495) offers a limited scope due to incompatibility of a number of functional groups towards the reducing agent. Based on our recent mechanistic studies of the acid-catalysed rearrangement of indol-3-yl sulfides to indol-2-yl sulfides (P. Hamel, et. al., Chem. Commun. 1989, 63; J. Org. Chem. 1992, 57, 2694), we have developed a novel, non-reductive desulfenylation method which permits easy access to 3-unsubstituted indoles bearing a wide array of substituents. Thus, 3-indolyl sulfides, readily obtained from appropriate phenylhydrazines (via Fischer indolization) or anilines (Gassman method, vide infra) are smoothly desulfenylated in good yields in trifluoroacetic acid in the presence of an appropriate nucleophilic trapping agent. Thiols proved to be very effective trapping agents and thiosalicylic acid (TSA) is a thiol of choice, being non-volatile and easily separable from reaction products.     

Synthesis and Antimicrobial Activities of Some 1-[(N,N-Disubstitutedthiocarbamoylthio)acetyl]-3,5-diaryl-2-pyrazolines

The increasing clinical importance of drug-resistant fungal and bacterial pathogens has lent additional urgency to microbiological research and new antimicrobial compound development. For this purpose, new pyrazoline derivatives were synthesized and evaluated for antimicrobial activity.

Some 1-[(N, N-disubstitutedthiocarbamoylthio)acetyl]-3,5-diaryl-2-pyrazolines derivatives were synthesized by reacting 1-(chloroacetyl)-3,5-diaryl-2-pyrazolines with appropriate potassium salts of secondary amine dithiocarbamic acids. The chemical structures of the compounds were elucidated by IR, ¹ H-NMR, and FAB⁺-MS spectral data. Their antimicrobial activities against Staphylococcus aureus (B-767), Escherichia coli (B-3704), Pseudomonas aeruginosa (ATCC 27853), Proteus vulgaris (NRLL B-123), and Candida albicans (NRRL-27077) were investigated. The results showed that some of the compounds have notable activity against S. aureus and C. albicans.     

Transfer and Termination Reactions in “Living” Carbocationic Polymerizations

Abstract

The available data concerning the polymerization of three classes of monomers deemed to yield living polymers, vinyl ethers, styrenic monomers and isobutylene, are discussed from the point of view of transfer and termination reaction. In the case of vinylethers, linearity of [Mbar]_n with a yield up to 30,000 has been obtained, but when higher [Mbar]_n are planned, there is evidence for the occurrence of transfer reactions. In the case of isobutylene, indene, and p-Me-styrene, the linearity (up to [Mbar]_n ～ 10⁵) of [Mbar]_n with the amount of monomer polymerized which has been observed (but only at low temperature) is compatible with values of transfer constants to monomer measured in “conventional” systems. In these living systems, irreversible terminations are often not very important but may become significant toward the end of monomer consumption. The main termination process is reversible termination which may lead to narrow molecular weight distributions. The linearity of [Mbar]_n with yield is not conclusive evidence for the absence of transfer and termination and for the presence of particular active centers. The control of the polymerizations achieved up to now can be accounted for by the mechanisms of conventional cationic polymerizations, transfer reactions included.     

A Complex between C-Methylcalix[4]resorcinarene and Triethylammonium Nitrate

Abstract

The synthesis and crystal structure of the complex formed by the all-cis epimer of C-methylcalix[4]resorcinarene (1) and triethylammonium nitrate are reported. “1.(HNEt⁺ ₃)₄. (NO^? ₃)₄(2)”, crystallizes in the monoclinic space group P2₁/n, a=25.796(2), b=16.6048(11), c=29.5659(10) Å, β=94.636(4)°, V=12623(2) ų, Z=8. Refinement led to a final conventional R₁ value of 0.128 for 12428 reflections and 1473 parameters. The resorcinarene displays the usual bowl-type shape, with four hydroxyl protons involved in intramolecular hydrogen bonds, whereas the remaining four make hydrogen bonds with four bridging nitrate ions, which results in the formation of infinite chains. Those chains are arranged so as to form layers, between which the triethylammonium ions and the remaining nitrate ions are hydrogen-bonded one to another.     

Calixarenes as Polyhapto-aromatic Ligands: Alkali Metal Ions and Sulfonated Calixarenes

Crystal structure determinations for the hexarubidium and octacesium derivatives of calix[6]arene hexasulfonic acid, as well as of a new solvate of the pentasodium derivative of calix[4]arene tetrasulfonic acid, and comparison with structural data from the literature for alkali metal complexes of sulfonated calixarenes, have provided further evidence for the importance of interactions with aromatic ~ -electrons for the heavier alkali metal cations. There is evidence as well that this interaction can be enhanced by extended ionization of the sulfonated calixarene.     

A Bis(p-tert-butyloctahomotetraoxacalix[8]arene) Capsule with [(UO2)2(OH)2] Links and a Disordered [Rb4(H2O)4] Inner Core

p-tert-Butyloctahomotetraoxacalix[8]arene (LH⁸) reacts with uranyl nitrate hexahydrate in the presence of rubidium hydroxide to give a mixed complex that can be viewed as a tetrauranate dimer [(UO²)⁴(LH⁴)²(OH)⁴] containing four disordered rubidium ions and water molecules. Two uranyl ions are complexed in an “external” fashion by each macrocycle, each of them bound to two phenoxide groups and one ether group, as well as to two bridging hydroxide ions. The latter ensure the formation of a dimeric capsule that contains the disordered set of alkali metal ions. Apart from water molecules, the Rb⁺ ions are bound to the uranyl oxo groups directed towards the inner cavity, and to phenol and ether oxygen atoms from the macrocycle. The resulting octanuclear complex presents an unprecedented geometry evidencing the assembling potential of uranyl ions.

p-tert-Butyloctahomotetraoxacalix[8]arene (LH₈) reacts with uranyl nitrate hexahydrate in the presence of rubidium hydroxide to give a mixed complex that can be viewed as a tetrauranate dimer [(UO₂)₄(LH₄)₂(OH)₄] containing four disordered rubidium ions and water molecules. Two uranyl ions are complexed in an “external” fashion by each macrocycle, each of them bound to two phenoxide groups and one ether group, as well as to two bridging hydroxide ions. The latter ensure the formation of a dimeric capsule that contains the disordered set of alkali metal ions. Apart from water molecules, the Rb^+| ions are bound to the uranyl oxo groups directed towards the inner cavity, and to phenol and ether oxygen atoms from the macrocycle. The resulting octanuclear complex presents an unprecedented geometry evidencing the assembling potential of uranyl ions.     

Orthogonal organic and aqueous‐based washes of tissue sections to enhance protein sensitivity by MALDI imaging mass spectrometry

Imaging mass spectrometry (IMS) is an emergent and innovative approach for measuring the composition, abundance and regioselectivity of molecules within an investigated area of fixed dimension. Although providing unprecedented molecular information compared with conventional MS techniques, enhancement of protein signature by IMS is still necessary and challenging. This paper demonstrates the combination of conventional organic washes with an optimized aqueous‐based buffer for tissue section preparation before matrix‐assisted laser desorption/ionization (MALDI) IMS of proteins. Based on a 500 mM ammonium formate in water–acetonitrile (9:1; v/v, 0.1% trifluororacetic acid, 0.1% Triton) solution, this buffer wash has shown to significantly enhance protein signature by profiling and IMS (~fourfold) when used after organic washes (70% EtOH followed by 90% EtOH), improving the quality and number of ion images obtained from mouse kidney and a 14‐day mouse fetus whole‐body tissue sections, while maintaining a similar reproducibility with conventional tissue rinsing. Even if some protein losses were observed, the data mining has demonstrated that it was primarily low abundant signals and that the number of new peaks found is greater with the described procedure. The proposed buffer has thus demonstrated to be of high efficiency for tissue section preparation providing novel and complementary information for direct on‐tissue MALDI analysis compared with solely conventional organic rinsing. Copyright © 2013 John Wiley & Sons, Ltd.     

How Strain Affects the Reactivity of Surface Metal Oxide Catalysts

Highly dispersed molybdenum oxide supported on mesoporous silica SBA‐15 has been prepared by anion exchange resulting in a series of catalysts with changing Mo densities (0.2–2.5 Mo atoms nm^?2). X‐ray absorption, UV/Vis, Raman, and IR spectroscopy indicate that doubly anchored tetrahedral dioxo MoO₄ units are the major surface species at all loadings. Higher reducibility at loadings close to the monolayer measured by temperature‐programmed reduction and a steep increase in the catalytic activity observed in metathesis of propene and oxidative dehydrogenation of propane at 8 % of Mo loading are attributed to frustration of Mo oxide surface species and lateral interactions. Based on DFT calculations, NEXAFS spectra at the O‐K‐edge at high Mo loadings are explained by distorted MoO₄ complexes. Limited availability of anchor silanol groups at high loadings forces the MoO₄ groups to form more strained configurations. The occurrence of strain is linked to the increase in reactivity.