On a nonlinear heat equation with viscoelastic term associated with Robin conditions

This paper is devoted to study of a nonlinear heat equation with a viscoelastic term associated with Robin conditions. At first, by the Faedo–Galerkin and the compactness method, we prove existence, uniqueness, and regularity of a weak solution. Next, we prove that any weak solution with negative initial energy will blow up in finite time. Finally, by the construction of a suitable Lyapunov functional, we give a sufficient condition to guarantee the global existence and exponential decay of weak solutions.     

Can Tetrylone Act in a Similar Fashion to Tetrylene in Ni(CO)2 Complexes? A Theoretical Study based on a Comparison using DFT Calculations

A comparison was made to investigate the structures and bonding of nickel complex that carry tetrylone and tetrylene ligands [(CO)₂Ni‐{E(PH₃)₂}] ( Ni1E ) and [(CO)₂Ni‐{NHE_Me}] ( Ni2E ) (E = C to Pb) using quantum chemical calculations at the BP86 level with various basis sets (SVP, TZVPP, TZ2P+). The nature of the Ni–E bonds was analyzed with charge‐ and energy decomposition methods. The structures of tetrylone complexes Ni1E exhibit an interesting trend with the ligands E(PH₃)₂ are bonded in a tilted orientation relative to the fragment Ni(CO)₂. In contrast, the calculated equilibrium structures of complexes Ni2E exhibit the NHE_Me ligands (E = C to Sn) bonded in a head‐on way to the Ni(CO)₂ fragment, while the bending angle gives the strongest side‐on bonded ligand NHPb_Me when E = Pb. The interesting trend of the bond dissociation energy (BDE) is observed for the tetrylone, which has the same trend BDEs compared with tetrylene complexes. The EDA‐NOCV results indicate that the tetrylone ligands {E(PH₃)₂} in complexes are similar to the tetrylene ligands NHE_Me as strong σ‐donors and weak π‐acceptors. The BDEs calculated for the Ni–E bonds in Ni1E and Ni2E show that the effect of bulky ligands may obscure the intrinsic Ni–E bond strength. The bonding analysis shows that the tetrylone ligands in Ni1E may act in a similar fashion to the tetrylene ligands in Ni2E . All complexes Ni1E and Ni2E are suitable targets for synthesis.     

Biosynthetic production of universally <Superscript>13</Superscript>C-labelled polyunsaturated fatty acids as reference materials for natural health product research

Long-chain polyunsaturated fatty acids (LCPUFA) including eicosapentaenoic acid (EPA, 20:5n-3) and docosahexaenoic acid (DHA, 22:6n-3) have become important natural health products with numerous proven benefits related to brain function and cardiovascular health. Not only are omega-3 fatty acids available in a plethora of dietary supplements, but they are also increasingly being incorporated as triglycerides into conventional foods, including bread, milk, yoghurt and confectionaries. Recently, transgenic oil seed crops and livestock have been developed that enhance omega-3 fatty acid content. This diverse array of matrices presents a difficult analytical challenge and is compounded further by samples generated through clinical research. Stable isotope ¹³C-labelled LCPUFA standards offer many advantages as research tools because they may be distinguished from their naturally abundant counterparts by mass spectrometry and directly incorporated as internal standards into analytical procedures. Further, ¹³C-labelled LCPUFAs are safe to use as metabolic tracers to study uptake and metabolism in humans. Currently, ¹³C-labelled LCPUFAs are expensive, available in limited supply and not in triglyceride form. To resolve these issues, marine heterotrophic microorganisms are being isolated and screened for LCPUFA production with a view to the efficient biosynthetic production of U-¹³C-labelled fatty acids using U-¹³C glucose as a carbon source. Of 37 isolates obtained, most were thraustochytrids, and either DHA or omega-6 docosapentaenoic acid (22:5n-6) were produced as the major LCPUFA. The marine protist Hyalochlorella marina was identified as a novel source of EPA and omega-3 docosapentaenoic acid (22:5n-3). As proof of principle, gram-level production of ¹³C-labelled DHA has been achieved with high chemical purity ( >99%) and high ¹³C incorporation levels (>90%), as confirmed by NMR and MS analyses. Finally, U-¹³C-DHA was enzymatically re-esterified to glycerol to yield a ¹³C-labelled tridocosahexaenoin.     

Free vibration of axially loaded thin-walled composite Timoshenko beams

Based on shear-deformable beam theory, free vibration of thin-walled composite Timoshenko beams with arbitrary layups under a constant axial force is presented. This model accounts for all the structural coupling coming from material anisotropy. Governing equations for flexural-torsional-shearing coupled vibrations are derived from Hamilton’s principle. The resulting coupling is referred to as sixfold coupled vibrations. A displacement-based one-dimensional finite element model is developed to solve the problem. Numerical results are obtained for thin-walled composite beams to investigate the effects of shear deformation, axial force, fiber angle, modulus ratio on the natural frequencies, corresponding vibration mode shapes and load–frequency interaction curves.     

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.     

Applying a fixed point theorem of Krasnosel’skii type to the existence of asymptotically stable solutions for a Volterra-Hammerstein integral equation

Using a fixed point theorem of Krasnosel’skii type, the paper proves the existence of asymptotically stable solutions for a Volterra-Hammerstein integral equation.     

Dugundji’s theorem for cone metric spaces

In this work, we will prove the Dugundji extension theorem for the cone metric space. It is heavily reliant on the paracompactness of the cone topology that is proved by Ayse Sönmez in the paper Sönmez (2010) [11].     

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.     

Hydrolytic Activity of Vanadate toward Serine-Containing Peptides Studied by Kinetic Experiments and DFT Theory

Hydrolysis of dipeptides glycylserine (Gly-Ser), leucylserine (Leu-Ser), histidylserine (His-Ser), glycylalanine (Gly-Ala), and serylglycine (Ser-Gly) was examined in vanadate solutions by means of (1)H, (13)C, and (51)V NMR spectroscopy. In the presence of a mixture of oxovanadates, the hydrolysis of the peptide bond in Gly-Ser proceeds under the physiological pH and temperature (37 °C, pD 7.4) with a rate constant of 8.9 × 10(-8) s(-1). NMR and EPR spectra did not show evidence for the formation of paramagnetic species, excluding the possibility of V(V) reduction to V(IV) and indicating that the cleavage of the peptide bond is purely hydrolytic. The pD dependence of k(obs) exhibits a bell-shaped profile, with the fastest hydrolysis observed at pD 7.4. Combined (1)H, (13)C, and (51)V NMR experiments revealed formation of three complexes between Gly-Ser and vanadate, of which only one complex, designated Complex 2, formed via coordination of amide oxygen and amino nitrogen to vanadate, is proposed to be hydrolytically active. Kinetic experiments at pD 7.4 performed by using a fixed amount of Gly-Ser and increasing amounts of Na(3)VO(4) allowed calculation of the formation constant for the Gly-Ser/VO(4)(3-) complex (K(f) = 16.1 M(-1)). The structure of the hydrolytically active Complex 2 is suggested also on the basis of DFT calculations. The energy difference between Complex 2 and the major complex detected in the reaction mixture, Complex 1, is calculated to be 7.1 kcal/mol in favor of the latter. The analysis of the molecular properties of Gly-Ser and their change upon different modes of coordination to the vanadate pointed out that only in Complex 2 the amide carbon is suitable for attack by the hydroxyl group in the Ser side chain, which acts as an effective nucleophile. The origin of the hydrolytic activity of vanadate is most likely a combination of the polarization of amide oxygen in Gly-Ser due to the binding to vanadate, followed by the intramolecular attack of the Ser hydroxyl group.     

Local {W^{2,m(\cdot)}_{loc}}regularity for p(.)-Laplace equations

We study ${W^{2,m(\cdot)}_{loc}}$ regularity for local weak solutions of p(·)-Laplace equations where ${p\in C^1(\Omega) \cap C(\overline{\Omega})}$ and ${\min_{x\in \overline{\Omega}} p(x) > 1}$ .