Regiocontrolled intramolecular cyclizations of carboxylic acids to carbon-carbon triple bonds promoted by acid or base catalyst

We systematically investigated, for the first time, the relationship between regioselectivity and acid/base effects in the cyclization reactions between carboxylic acids and carbon-carbon triple bonds. We found novel acid- and base-promoted cyclizations to selectively give isocoumarin or pyran-2(2H)-one and phthalide or furan-2(5H)-one skeletons, respectively, and established a catalytic version of regioselective heterocyclic ring synthesis. Density functional theory calculations and application to a short route to thunberginol A were also described. [reaction: see text].     

Extended string field theory for massless higher-spin fields

We propose a new gauge field theory which is an extension of ordinary string field theory by assembling multiple state spaces of the bosonic string. The theory includes higher-spin fields in its massless spectrum together with the infinite tower of massive fields. From the theory, we can easily extract the minimal gauge-invariant quadratic action for tensor fields with any symmetry. As examples, we explicitly derive the gauge-invariant actions for some simple mixed symmetric tensor fields. We also construct covariantly gauge-fixed action by extending the method developed for string field theory.     

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.