L1-type smoothness indicators based weighted essentially nonoscillatory scheme for Hamilton-Jacobi equations

This article presents an improved fifth-order finite difference weighted essentially nonoscillatory (WENO) scheme to solve Hamilton-Jacobi equations. A new type of nonlinear weights is introduced with the construction of local smoothness indicators on each local stencil that are measured with the help of generalized undivided differences in L¹-norm. A novel global smoothness measurement is also constructed with the help of local measurements from its linear combination. Numerical experiments are conducted in one- and two-dimensions to demonstrate the performance enhancement, resolution power, numerical accuracy for the proposed scheme, and compared it with the classical WENO scheme.     

Improved third‐order weighted essentially nonoscillatory scheme

A new third‐order WENO scheme is proposed to achieve the desired order of convergence at the critical points for scalar hyperbolic equations. A new reference smoothness indicator is introduced, which satisfies the sufficient condition on the weights for the third‐order convergence. Following the truncation error analysis, we have shown that the proposed scheme achieves the desired order accurate for smooth solutions with arbitrary number of vanishing derivatives if the parameter ε satisfies certain conditions. We have made a comparative study of the proposed scheme with the existing schemes such as WENO‐JS, WENO‐Z, and WENO‐N3 through different numerical examples. The result shows that the proposed scheme (WENO‐MN3) achieves better performance than these schemes.     

Third‐order WENO scheme with a new smoothness indicator

In this article, we have devised a new reference smoothness indicator for third‐order weighted essentially non‐oscillatory (WENO) scheme to achieve desired order of convergence at critical points. In the context of the weighted essentially non‐oscillatory scheme, reference smoothness indicator is constructed in such a way that it satisfies the sufficient condition on the weights for the third‐order convergence. The goal is to construct a reference smoothness indicator such that the resulted scheme have to achieve the required order of accuracy even if the first two derivatives vanish but not the third derivative. The construction of such reference smoothness indicator is not possible through a linear combination of local smoothness indicators only. We have proposed a reference smoothness indicator to be of the fourth order of accuracy on three‐point stencil that contains the linear combination of the first derivative information of the local and global stencils. The performance enhancement of the WENO scheme through this reference smoothness indicator is verified through the standard numerical experiments. Numerical results indicate that the new scheme provides better results in comparison with the earlier third‐order WENO schemes like WENO‐JS and WENO‐Z. Copyright © 2017 John Wiley & Sons, Ltd.     

Stereoselective total synthesis of styryl-lactones: (+)-crassalactones B and C, (+)-howiionol A, (+)-tricinnamate, (+)-goniofufurone and (+)-dicinnamoyl goniofufurone

The total synthesis of (+)-crassalactone B, (+)-crassalactone C, (+)-howiionol A, (+)-tricinnamate, (+)-goniofufurone, and (+)-dicinnamoyl goniofufurone is achieved by a ‘chiron approach’ starting from diacetone d-glucose (DAG). Mitsunobu inversion, Wittig olefination and ring closing metatheses were used as key steps for (+)-howiionol A and (+)-tricinnamate. Meldrum’s acid was used for the synthesis of (+)-crassalactone C, (+)-goniofufurone, and (+)-dicinnamoyl goniofufurone. Yamaguchi esterification was used for (+)-crassalactone B, while a Grignard reaction followed by concomitant deallylation was first reported in the synthesis of (+)-dicinnamoyl goniofufurone.     

Structural and adsorption characteristics and catalytic activity of titania and titania-containing nanomaterials

Morphological, structural, adsorption, and catalytic properties of highly disperse titania prepared using sulfate and pyrogenic methods, and fumed titania-containing mixed oxides, were studied using XRD, TG/DTA, nitrogen adsorption, (1)H NMR, FTIR, microcalorimetry on immersion of oxides in water and decane, thermally stimulated depolarization current (TSDC) and catalytic photodecomposition of methylene blue (MB). Phase composition and aggregation characteristics of nanoparticles (pore size distribution) of sulfate and pyrogenically prepared titania are very different; temperature dependent structural properties are thus very different. Catalytic activity for the photodecomposition of MB is greatest (per gram of TiO(2) for the pure oxide materials) for non-treated ultrafine titania PC-500, which has the largest S(BET) value and smallest particle size of the materials studied. However, this activity calculated per m(2) is higher for PC-105, possessing a much smaller S(BET) value than PC-500. The activity per unit surface area of titania is greatest for the fumed silica-titania mixed oxide ST20. Calcination of PC-500 at 650 degrees C leads to enhancement of anatase content and catalytic activity, but heating at 800 and 900 degrees C lowers the anatase content (since rutile appears) and diminishes catalytic activity, as well as the specific surface area because of nanoparticle sintering.     

Transition-Metal Acetate-Promoted Intramolecular Nitrene Insertion to Vinylogous Carbonates for Divergent Synthesis of Azirinobenzoxazoles and Benzoxazines

Synthesis and isolation of highly unstable azirinobenzoxazole and benzoxazines in a chemodivergent fashion from aryl azido vinylogous carbonates by simple change in transition metal acetate is described. Thermal or rhodium(II) acetate-mediated decomposition of these azides gave dihydroazirino benzoxazole. Their nickel(II) acetate-promoted reaction gave 4-dihydro-2H-benzoxazines, whereas copper(II) acetate led to the corresponding oxidized imine derivatives. Benzaoxazine derivative could be kinetically resolved using a proline-catalyzed Mannich reaction. The benzoxazines were rapidly elaborated to angularly fused tetracyclic systems and coumarin-fused derivatives in a “one pot” fashion.     

Concise Total Synthesis of (−)-Erinapyrone B from D-(+)-Malic Acid

A convenient and facile enantioselective synthesis of (?)-erinapyrone B from commercially available D-(+)-malic acid has been achieved in seven steps. One of the key steps in this synthesis was the one-pot reaction of palladium(II)-mediated Wacker-type oxidative cyclization in the presence of a catalytic amount of p-toluenesulphonic acid (p-TsOH) which has been found to be effective for the preparation of enantiopure 2,3-dihydro-4H-pyran-4-one from the corresponding enantiopure β-hydroxyenone via enantio-enriched diketohydroxy intermediate.

[Supplementary materials are available for this article. Go to the publisher's online edition of Synthetic Communications® for the following free supplemental resource(s): Full experimental and spectral details.]     

Synthesis,characterization, and thermal property of phosphate-based cobalt mixture of non-calcined,calcined, and composite material

Monatshefte für Chemie - Chemical Monthly - The phosphate-containing cobalt mixtures of non-calcined, calcined, and composite materials were synthesized in atmospheric conditions and...     

Two new macrocyclic diaryl ether heptanoids from Boswellia ovalifoliolata

The stems of Boswellia ovalifoliolata BAL. & HENRY (Burseraceae) afforded two new macrocyclic diaryl ether heptanoids, ovalifoliolatin A (1) and B (2) together with three known compounds; acerogenin C (3), 3 alpha-hydroxyurs-12-ene (4), and sitost-4-en-3-one (5). The structures were established by means of spectroscopic analysis and compounds 1, 3-5 were evaluated for their antibacterial activity.     

Measurement of Strain Distributions in Mouse Femora with 3D-Digital Speckle Pattern Interferometry

Bone is a mechanosensitive tissue that adapts its mass, architecture and mechanical properties to external loading. Appropriate mechanical loads offer an effective means to stimulate bone remodeling and prevent bone loss. A role of in situ strain in bone is considered essential in enhancement of bone formation, and establishing a quantitative relationship between 3D strain distributions and a rate of local bone formation is important. Digital speckle pattern interferometry (DSPI) can achieve whole-field, non-contacting measurements of microscopic deformation for high-resolution determination of 3D strain distributions. However, the current system does not allow us to derive accurate strain distributions because of complex surface contours inherent to biological samples. Through development of a custom-made piezoelectric loading device as well as a new DSPI-based force calibration system, we built an advanced DSPI system and integrated local contour information to deformation data. Using a mouse femur in response to a knee loading modality as a model system, we determined 3D strain distributions and discussed effectiveness and limitations of the described system.