Dynamic covalent approach to [2]- and [3]roxtanes by utilizing a reversible thiol-disulfide interchange reaction

A dynamic covalent approach to disulfide-containing [2]- and [3]rotaxanes is described. Symmetrical dumbbell-shaped compounds with two secondary ammonium centers and a central located disulfide bond were synthesized as components of rotaxanes. The rotaxanes were synthesized from the dumbbell-shaped compounds and dibenzo-[24]crown-8 (DB24C8) with catalysis by benzenethiol. The yields of isolated rotaxanes reached about 90 % under optimized conditions. A kinetic study on the reaction forming [2]rotaxane 2 a and [3]rotaxane 3 a suggested a plausible reaction mechanism comprising several steps, including 1) initiation, 2) [2]rotaxane formation, and 3) [3]rotaxane formation. The whole reaction was found to be reversible in the presence of thiols, and thermodynamic control over product distribution was thus possible by varying the temperature, solvent, initial ratio of substrates, and concentration. The steric bulk of the end-capping groups had almost no influence on rotaxane yields, but the structure of the thiol was crucial for reaction rates. Amines and phosphines were also effective as catalysts. The structural characterization of the rotaxanes included an X-ray crystallographic study on [3]rotaxane 3 a.     

W(CO)5(L)-catalyzed endo-selective cyclization of allenyl silyl enol ethers: an efficient method for the cyclopentene annulation onto alpha,beta-unsaturated ketones

[reaction: see text] Indium-mediated allenylation of alpha,beta-unsaturated ketones in the presence of tert-butyldimethylsilyl triflate and dimethyl sulfide gives 6-siloxy-1,2,5-trienes, which undergo W(CO)(5)(L)-catalyzed 5-endo cyclization to give the corresponding cyclopentene derivatives in good yield. Furthermore, this novel W(CO)(5)(L)-catalyzed cyclization of allenyl silyl enol ethers proceeds in a 6-endo manner when 5-siloxy-1,2,5-trienes are employed as a substrate. In these reactions, effective electrophilic activation of allenyl compounds for attack by silyl enol ethers is achieved using a catalytic amount of W(CO)(6).     

Cross-axis synchronous flow-through coil planet centrifuge (type XLL). I. Design of the apparatus and studies on retention of stationary phase

The fourth prototype holds a pair of column holders in the lateral position at 15 cm from the center of the rotary shaft horizontally mounted on the rotary frame at 7.6 cm from the central axis of the apparatus. Using short coils of 2.6 mm I.D. PTFE (polytetrafluoroethylene) tubing with 7.6 cm and 24 cm helical diameters, retention of the stationary phase was measured in ten pairs of two-phase solvent systems under various experimental conditions. Satisfactory retention was obtained by choosing proper combinations of three factors, i.e., the direction of planetary motion, head-tail elution mode, and inward-outward elution mode. The polar butanol solvent systems showed excellent retention from 65 to 80% in the 7.6 cm helical diameter left-handed coil.     

Furan ring oxidation strategy for the synthesis of macrosphelides A and B

By using the convenient protocol for conversion of 2-substituted furans into 4-oxo-2-alkenoic acids ((i) NBS, (ii) NaClO(2)), macrosphelide B (2) was synthesized from furyl alcohol 5 (>98% ee) and acid 6 (99% ee). The protocol was first applied to the PMB ether of 5 to afford acid 13b. On the other hand, DCC condensation of acid 6 with 5 gave 16 after deprotection of the TBS group. Condensation was again carried out between 13b and 16 to furnish the key ketone 17, which upon reduction with Zn(BH(4))(2) afforded anti alcohol 18 stereoselectively (15:1). After protection/deprotection steps, the furan 18 was converted to seco acid 3 by using the furan oxidation protocol mentioned above, and lactonization of 3 with Cl(3)C(6)H(2)COCl, Et(3)N, and DMAP afforded 22 (MOM ether of 2), which upon deprotection with TFA produced 2. Transformation of 22 to macrosphelide A (1) was then investigated. Although the chelation-controlled reduction of 22 should afford the desired anti alcohol 24, Zn(BH(4))(2) at <-90 degrees C gave a 2 approximately 1:1 mixture of anti/syn alcohols. On the contrary, reduction with NaBH(4) in MeOH at -15 degrees C produced the syn isomer 23 with >10:1 diastereoselectivity. Mitsunobu inversion of the resulting C(14)-hydroxyl group and deprotection of the MOM group with TFA afforded 1. Similarly, reduction of 2 with NaBH(4) afforded the C(14)-epimer of 1 stereoselectively. The observed stereoselectivity in the reductions of 22 and 2 could be explained on the basis of computer-assisted calculation, which showed presence of the low-energy conformers responsible for the stereoselective reduction. In addition, conversion of 2 to 1 was established, for the first time.     

CesA protein is included in the terminal complex of <Emphasis Type="Italic">Acetobacter</Emphasis>

Cellulose is a major biopolymer on the earth that is produced by cellulose synthase in the cell membrane of living organisms. Cellulose synthase is a hetero-subunit complex composed of several different protein subunits, and is visualized as a supermolecular complex called a “terminal complex” by electron microscopy. Such supermolecular organization of an enzyme complex is believed to be important for the fiber formation or crystallization of cellulose microfibrils in cellulose biosynthesis. In the case of the cellulose-producing bacterium Acetobacter, it is hypothesized that the enzyme complex includes at least six subunits given its genetic constitution. However, to date, only three of these molecules have been experimentally confirmed as the subunits included in the terminal complex: CesB, CesD, and ccp2. In this study, we used fluorescence immuno-microscopy to show that CesA protein, the catalytic subunit, is included in the terminal complex of Acetobacter. Furthermore we discuss the obtained microscopic data for improving our understanding of the molecular organization of the bacterial cellulose synthase complex.     

The Stein phenomenon for monotone incomplete multivariate normal data

We establish the Stein phenomenon in the context of two-step, monotone incomplete data drawn from , a (p+q)-dimensional multivariate normal population with mean and covariance matrix . On the basis of data consisting of n observations on all p+q characteristics and an additional N−n observations on the last q characteristics, where all observations are mutually independent, denote by the maximum likelihood estimator of . We establish criteria which imply that shrinkage estimators of James-Stein type have lower risk than under Euclidean quadratic loss. Further, we show that the corresponding positive-part estimators have lower risk than their unrestricted counterparts, thereby rendering the latter estimators inadmissible. We derive results for the case in which is block-diagonal, the loss function is quadratic and non-spherical, and the shrinkage estimator is constructed by means of a nondecreasing, differentiable function of a quadratic form in . For the problem of shrinking to a vector whose components have a common value constructed from the data, we derive improved shrinkage estimators and again determine conditions under which the positive-part analogs have lower risk than their unrestricted counterparts.     

Numerical Analysis of the Allen-Cahn Equation with Coarse Meshes

In this paper, we consider the finite difference semi-discretization of the Allen-Cahn equation with the diffuse interface parameter $\varepsilon$. While it is natural to make the mesh size parameter $h$ smaller than $\varepsilon$, it is desirable that $h$ is as big as possible in view of computational costs. In fact, when $h$ is bigger than $\varepsilon$ (i.e., the mesh is relatively coarse), it is observed that the numerical solution does not move at all. The purpose of this paper is to clarify the mechanism of this phenomenon. We will prove that the numerical solution converges to that of the ordinary equation without the diffusion term if $h$ is bigger than $\varepsilon$. Numerical examples are presented to support the result.     

Discretized Tikhonov regularization by reproducing kernel Hilbert space for backward heat conduction problem

In this paper we propose a numerical reconstruction method for solving a backward heat conduction problem. Based on the idea of reproducing kernel approximation, we reconstruct the unknown initial heat distribution from a finite set of scattered measurement of transient temperature at a fixed final time. Standard Tikhonov regularization technique using the norm of reproducing kernel is adopt to provide a stable solution when the measurement data contain noises. Numerical results indicate that the proposed method is stable, efficient, and accurate.     

Scalar auxiliary variable approach for conservative/dissipative partial differential equations with unbounded energy functionals

BIT Numerical Mathematics - In this paper, we present a novel investigation of the so-called SAV approach, which is a framework to construct linearly implicit geometric numerical integrators for...