A Laplace transform certified reduced basis method; application to the heat equation and wave equation

We present a certified reduced basis (RB) method for the heat equation and wave equation. The critical ingredients are certified RB approximation of the Laplace transform; the inverse Laplace transform to develop the time-domain RB output approximation and rigorous error bound; a (Butterworth) filter in time to effect the necessary “modal” truncation; RB eigenfunction decomposition and contour integration for Offline–Online decomposition. We present numerical results to demonstrate the accuracy and efficiency of the approach.     

Production of XynX, a Large Multimodular Protein of Clostridium thermocellum, by Protease-Deficient Bacillus subtilis Strains

XynX of Clostridium thermocellum is a large, multimodular xylanase of 116?kDa. An Escherichia coli transformant carrying the entire xynX produced three active truncated xylanase species of 105, 85, and 64?kDa intracellularly. The Bacillus subtilis WB700 transformant with the xynX, a strain deficient in seven proteases including Vpr, secreted two active truncated xylanase species of 65 and 44?kDa. The B. subtilis WB800 transformant with xynX, a strain deficient in eight proteases including Vpr and WprA, secreted more active enzymes, 8.46?U?ml^?1, mostly in the form of 105 and 85?kDa, than the WB700 transformant, 6.93?U?ml^?1. This indicates that the additional deletion of wprA enabled the WB800 to secrete XynX in its intact form. B. subtilis WB800 produced more total enzyme activity than E. coli (1,692?±?274 U vs. 141.9?±?27.1 U), and, more importantly, secreted almost all the enzyme activity. The results suggest the potential use of B. subtilis WB800 as a host system for the production of large multimodular proteins.     

Existence and exponential decay for a nonlinear wave equation with nonlocal boundary conditions of 2N‐point type

This paper is devoted to the study of a nonlinear wave equation with initial conditions and nonlocal boundary conditions of 2N‐point type, which connect the values of an unknown function u(x,t) at x = 1, x = 0, x = η_i(t) , and x = θ_i(t), where $0<{\eta }_1(t)<{\eta }_2(t)<\dots <{\eta }_{{}_{N?1}}(t)<1,$ $0<{\theta }_1(t)<{\theta }_2(t)<\dots <{\theta }_{{}_{N?1}}(t)<1,$ for all t ≥ 0. First, we prove local existence of a unique weak solution by using density arguments and applying the Banach's contraction principle. Next, under the suitable conditions, we show that the problem considered has a unique global solution u(t) with energy decaying exponentially as t → +∞ . Finally, we present numerical results.     

Geometrical nonlinear analysis of thin-walled composite beams using finite element method based on first order shear deformation theory

Based on a seven-degree-of-freedom shear deformable beam model, a geometrical nonlinear analysis of thin-walled composite beams with arbitrary lay-ups under various types of loads is presented. This model accounts for all the structural coupling coming from both material anisotropy and geometric nonlinearity. The general nonlinear governing equations are derived and solved by means of an incremental Newton–Raphson method. A displacement-based one-dimensional finite element model that accounts for the geometric nonlinearity in the von Kármán sense is developed to solve the problem. Numerical results are obtained for thin-walled composite beam under vertical load to investigate the effects of fiber orientation, geometric nonlinearity, and shear deformation on the axial–flexural–torsional response.     

Finite-sum smooth optimization with SARAH

Computational Optimization and Applications - We introduce NC-SARAH for non-convex optimization as a practical modified version of the original SARAH algorithm that was developed for convex...     

Two New Glycosides from the Water Extract of Lepisanthes rubiginosa Collected in Vietnam

Chemistry of Natural Compounds - In this attempt to seek promising compounds from Lepisanthes rubiginosa, a widely used folk medicine in the middle of Vietnam, we isolated four compounds from the...     

Direct oxidative C(sp3)─H/C(sp2)─H coupling reaction using recyclable Sr-doped LaCoO3 perovskite catalyst

A strontium-doped lanthanum cobaltite perovskite, La_0.6Sr_0.4CoO₃, was prepared and utilized as a recyclable heterogeneous catalyst for the direct oxidative C(sp³)─H/C(sp²)─H coupling reaction between cyclic ethers and alkenes or coumarins to achieve corresponding α-functionalized ethers. The α-functionalization of cyclic thioethers or amides with alkenes or coumarins was also achieved via this protocol. The La_0.6Sr_0.4CoO₃ catalyst exhibited better performance than a variety of homogeneous and heterogeneous catalysts. Utilizing a recyclable catalyst would offer a greener option for the direct oxidative C(sp³)─H/C(sp²)─H coupling reaction. To our best knowledge, the C(sp³)─H/C(sp²)─H coupling between olefins and ethers to generate α-functionalized ethers using a heterogeneous catalyst has not been previously reported, and the α-functionalization of cyclic thioethers or amides with alkenes or coumarins is new.     

Two new prenylated isoflavones from Maclura cochinchinensis collected in Hoa Binh province Vietnam

Two new prenylisoflavones, 3′,4′,5-trihydroxy-8-prenyl-dihydrofuran[2″,3″:7,6]isoflavone (1) and 4′,5-dihydroxy-8-prenyl-dihydrofuran[2″,3″:7,6]isoflavone (2), along with five known prenylisoflavones (3–7), benzylalcohol-4-O-β-d-glucoside (8) and two cinnamic acid esters (9, 10) were isolated from the leaves of Maclura cochinchinensis (Cudrania cochinchinensis). Their structures were elucidated by analysis of NMR (¹H-, ¹³C-NMR, HSQC, HMBC), MS spectra and comparison with the published data. Compounds 4–10 were the first time isolated from this species. Prenylisoflavones 1–4 and 6–7 were evaluated for their in vitro cytotoxic activity on KB and HepG2 cancer cell lines. Compound 4 showed cytotoxic activity against both cancer cell lines with IC₅₀ values of 26.99 and 19.95 μM, respectively. The other compounds were considered as inactive.