High pressure organic chemistry; XV. Non-catalyzed cleavage reaction of ethers with acyl halides

Abstract

A variety of cyclic and acyclic ethers are efficiently reacted with acyl chlorides or acyl bromides to afford the ether-cleaved compounds of ω-chloro-or ω-bromoesters under high pressure conditions. The reactivity of ethers is found to be roughly depend on the basicity of the ether oxygen atom.     

Existence of global decaying solutions to the exterior problem for the Klein–Gordon equation with a nonlinear localized dissipation and a derivative nonlinearity

We prove the existence of global decaying solutions to the exterior problem for the Klein–Gordon equation with a nonlinear localized dissipation and a derivative nonlinearity. To derive the required estimates of solutions we employ a ‘loan’ method.     

Numerical Verification Methods for Solutions of the Free Boundary Problem

We propose two methods to enclose the solution of an ordinary free boundary problem. The problem is reformulated as a nonlinear boundary value problem on a fixed interval including an unknown parameter. By appropriately setting a functional space that depends on the finite element approximation, the solution is represented as a fixed point of a compact map. Then, by using the finite element projection with constructive error estimates, a Newton-type verification procedure is derived. In addition, numerical examples confirming the effectiveness of current methods are given.     

A Theorem for Numerical Verification on Local Uniqueness of Solutions to Fixed-Point Equations

We give a theoretical result with respect to numerical verification of existence and local uniqueness of solutions to fixed-point equations which are supposed to have Fréchet differentiable operators. The theorem is based on Banach's fixed-point theorem and gives sufficient conditions in order that a given set of functions includes a unique solution to the fixed-point equation. The conditions are formulated to apply readily to numerical verification methods.

We already derived such a theorem in [11 N. Yamamoto ( 1998 ). A numerical verification method for solutions of boundary value problems with local uniqueness by Banach's fixed-point theorem . SIAM J. Numer. Anal. 35 : 2004 – 2013 .[Crossref] , [Google Scholar]], which is suitable to Nakao's methods on numerical verification for PDEs. The present theorem has a more general form and one may apply it to many kinds of differential equations and integral equations which can be transformed into fixed-point equations.     

Hodge algebra structures on certain rings of invariants and applications

Let B be a commutative ring with identity, m, n, and r be positive integers such that r ≤ min{m, n}, a ₁, …, a _r (resp. b ₁, … b _r ) be integers such that 1 ≤ a ₁< … < a _r ≤ m (resp. 1 ≤ b ₁ < … < b _r < n) and U (resp. V) be the most general m × r (resp. r × n) matrix such that s-minors of first a _s ? 1 rows (resp. b _s ? 1 columns) of U (resp. V) are all zero for s = 1, …, r. We investigate the B-algebra C generated by all the entries of UV and all the r-minors of U and V. We introduce a Hodge algebra structure, to which the discrete Hodge algebra associate is Cohen Macaulay, on C and prove that C is Cohen-Macaulay if so is B. Using this Hodge algebra structure, we show that C is the ring of absolute invariants of a certain group action, compute the divisor class group and the canonical class of C, and give a criterion of Gorenstein property of C in terms of a ₁ ,…, a _r and b ₁…, b _r .     

Unusual Attractive Au–π Interactions in Small Diacetylene‐Modified Gold Clusters

It is well known that alkynes act as π‐acids in the formation of complexes with metals. We found unprecedented attractive Au–π interactions in diacetylene‐modified [core+exo]‐type [Au₈]⁴⁺ clusters. The 4‐phenyl‐1,3‐butadiynyl‐modified cluster has unusually short Au–C_α distances in the crystal structure, revealing the presence of attractive interactions between the coordinating C≡C moieties and the neighboring bitetrahedral Au₆ core, which is further supported by IR and NMR spectra. Such weak interactions are not found in mono‐acetylene‐modified clusters, which indicates that they are specific for diacetylenic ligands. The attractive Au–π interactions are likely associated with the low energy of the π* orbital in the diacetylenic moieties, into which the valence electrons of the gold core may be back donated. The [Au₈]⁴⁺ clusters show clear red‐shifts of >10 nm with respect to the corresponding mono‐acetylenic clusters in UV/Vis absorption bands, which indicates substantial electronic perturbation effects of the Au–π interactions.     

Non‐Thermoresponsive Decanano‐sized Domains in Thermoresponsive Hydrogel Microspheres Revealed by Temperature‐Controlled High‐Speed Atomic Force Microscopy

Despite the tremendous efforts devoted to the structural analysis of hydrogel microspheres (microgels), many details of their structures remain unclear. Reported in this study is that thermoresponsive poly(N‐isopropyl acrylamide) (pNIPAm)‐based microgels exhibit not only the widely accepted core–shell structures, but also inhomogeneous decanano‐sized non‐thermoresponsive spherical domains within their dense cores, which was revealed by temperature‐controlled high‐speed atomic force microscopy (TC‐HS‐AFM). Based on a series of experiments, it is concluded that the non‐thermoresponsive domains are characteristic for pNIPAm microgels synthesized by precipitation polymerization, and plausible structures for microgels prepared by other polymerization techniques are proposed.     

Search for doubly charged Higgs bosons with lepton-flavor-violating decays involving tau leptons

We search for pair production of doubly charged Higgs particles (H+/- +/-) followed by decays into electron-tau (etau) and muon-tau (mutau) pairs using data (350 pb(-1) collected from [over]pp collisions at sqrt[s]=1.96 TeV by the CDF II experiment. We search separately for cases where three or four final-state leptons are detected, and combine results for exclusive decays to left-handed etau (mutau) pairs. We set an H+/- +/- lower mass limit of 114(112) GeV/c(2) at the 95% confidence level.     

Search for Bs0 --> micro+ micro- and B0 --> micro+ micro- decays with 2 fb-1 of pp collisions

We have performed a search for B(s)(0) --> micro(+) micro(-) and B(0) --> micro(+) micro(-) decays in pp collisions at square root s = 1.96 TeV using 2 fb(-1) of integrated luminosity collected by the CDF II detector at the Fermilab Tevatron Collider. The observed number of B(s)(0) and B0 candidates is consistent with background expectations. The resulting upper limits on the branching fractions are B(B(s)0) --> micro(+) micro(-)) <5.8 x 10(-8) and B(B(0) --> micro(+) micro(-))<1.8 x 10(-8) at 95% C.L.