Control and Stabilization of the Korteweg-de Vries Equation on a Periodic Domain

In [38 Russell , D.L. , Zhang , B.-Y. ( 1996 ). Exact controllability and stabilizability of the Korteweg-de Vries equation . Trans. Amer. Math. Soc. 348 : 3643 – 3672 . [Google Scholar]], Russell and Zhang showed that the Korteweg-de Vries equation posed on a periodic domain  with an internal control is locally exactly controllable and locally exponentially stabilizable when the control acts on an arbitrary nonempty subdomain of . In this paper, we show that the system is in fact globally exactly controllable and globally exponentially stabilizable. The global exponential stabilizability is established with the aid of certain properties of propagation of compactness and regularity in Bourgain spaces for the solutions of the associated linear system. With Slemrod's feedback law, the resulting closed-loop system is shown to be locally exponentially stable with an arbitrarily large decay rate. A time-varying feedback law is further designed to ensure a global exponential stability with an arbitrarily large decay rate.     

The development of a comprehensive toolbox based on multi-level,high-throughput screening of MOFs for CO/N2 separations

The separation of CO/N₂ mixtures is a challenging problem in the petrochemical sector due to the very similar physical properties of these two molecules, such as size, molecular weight and boiling point. To solve this and other challenging gas separations, one requires a holistic approach. The complexity of a screening exercise for adsorption-based separations arises from the multitude of existing porous materials, including metal–organic frameworks. Besides, the multivariate nature of the performance criteria that needs to be considered when designing an optimal adsorbent and a separation process – i.e. an optimal material requires fulfillment of several criteria simultaneously – makes the screening challenging. To address this, we have developed a multi-scale approach combining high-throughput molecular simulation screening, data mining and advanced visualization, as well as process system modelling, backed up by experimental validation. We have applied our recent advances in the engineering of porous materials'' morphology to develop advanced monolithic structures. These conformed, shaped monoliths can be used readily in industrial applications, bringing a valuable strategy for the development of advanced materials. This toolbox is flexible enough to be applied to multiple adsorption-based gas separation applications.

The separation of challenging mixtures through adsorption is a multidimensional problem that requires a holistic approach. Our toolbox combines experiments, molecular and process simulations with data visualization to find optimal, porous materials.     

Comparative Metabolomic Analysis of Four Fabaceae and Relationship to In Vitro Nematicidal Activity against Xiphinema index

The grapevine fanleaf virus (GFLV), responsible for fanleaf degeneration, is spread in vineyards by the soil nematode Xiphinema index. Nematicide molecules were used to limit the spread of the disease until they were banned due to negative environmental impacts. Therefore, there is a growing interest in alternative methods, including plant-derived products with antagonistic effects to X. index. In this work, we evaluated the nematicidal potential of the aerial parts and roots of four Fabaceae: sainfoin (Onobrychis viciifolia), birdsfoot trefoil (Lotus corniculatus), sweet clover (Melilotus albus), and red clover (Trifolium pratense), as well as that of sainfoin-based commercial pellets. For all tested plants, either aerial or root parts, or both of them, exhibited a nematicidal effect on X. index in vitro, pellets being as effective as freshly harvested plants. Comparative metabolomic analyses did not reveal molecules or molecule families specifically associated with antagonistic properties toward X. index, suggesting that the nematicidal effect is the result of a combination of different molecules rather than associated with a single compound. Finally, scanning electron microscope observations did not reveal the visible impact of O. viciifolia extract on X. index cuticle, suggesting that alteration of the cuticle may not be the primary cause of their nematicidal effect.     

Efficient Fmoc-Protected Amino Ester Hydrolysis Using Green Calcium(II) Iodide as a Protective Agent

In order to modify amino acids, the C-terminus carboxylic acid usually needs to be protected, typically as a methyl ester. However, standard cleavage of methyl esters requires either highly basic or acidic conditions, which are not compatible with Fmoc or acid-labile protecting groups. This highlights the need for orthogonal conditions that permit selective deprotection of esters to create SPPS-ready amino acids. Herein, mild orthogonal ester hydrolysis conditions are systematically explored using calcium(II) iodide as a protective agent for the Fmoc protecting group and optimized for a broad scope of amino esters. Our optimized reaction improved on the already known trimethyltin hydroxide, as it produced better yields with greener, inexpensive chemicals and a less extensive energy expenditure.     

Nucleophilic Additions to Unactivated Carbon-Carbon Double Bonds. Base-Catalysed Ether Formation. Preliminary Communication

Several examples (3 → 5, 4 → 7, 6 → 7, 9 → 10) of base-catalysed intramolecular ether formation involving nucleophilic attack on an unactivated carbon-carbon double bond are described.     

1,7-Trimethylenenorbornane. A novel member of the ‘adamantaneland’. Preliminary communication

A synthesis of the novel C₁₀H₁₆ hydrocarbon 1,7-trimethylenenorbornane ( 13 ), one of the 19 members of the adamantane family, is described.     

An ab initio study of O2 and CO2 transport by perfluorocarbons

Fluorocarbons have been successfully applied as oxygen carriers replacing blood. In order to understand the nature of the interaction between fluorocarbons and hydrocarbons on the one hand and O₂, N₂ and CO₂ on the other, STO-3G calculations have been performed on their complexes. The very slight energies of interaction that were obtained seem to substantiate the contention that O₂, N₂ and CO₂ are physically dissolved in fluorocarbons. This energy of interaction is, however, distinctly larger for fluorocarbons than for hydrocarbons. Electrostatic potentials have been computed around several fluorocarbons. They make it possible to predict the geometries of the complexes that are formed.     

Two-dimensional electrophoresis investigation of short-term response of flax seedlings to a cold shock

The flax, Linum usitatissimum L., is particularly suitable for studying the transduction and long-term signal storage of environmental signals. To investigate the underlying molecular mechanisms, we have focused on the initial changes in the proteome since these offer the possibility of reflecting the plant's history of exposure to stress. In principle, this 'proteome signature' might be revealed by two-dimensional electrophoresis (2-DE). We have therefore determined the potential of 2-DE to study the kinetics of changes to the proteome of flax induced by a 1 min cold shock. Protein identification is difficult with flax because of the lack of knowledge of gene sequences. Nevertheless, 2-DE analysis can be informative providing the significance of changes can be evaluated. We have developed a stringent threshold method to determine the significance of changes in gels obtained with proteins extracted from hypocotyls at different times after cold shock. This allowed us to reliably detect and characterize the kinetics of a set of seven spots that responded to cold shock and that constitute candidates for a proteome signature of long-term signal storage.     

Heterodiamantane und strukturell verwandte Verbindungen. III.. Pentacyclische diäther der C11-reihe. 5, 13-Dioxapentacyclo-[6.5.0.02,6.03,12.04,9]tridecan, 4, 13-dioxapentacyclo [6.4.1.02,7.03,10.05,9]tridecan und 3, 10-dioxapentacyclo [7.3.1.02,7.04,12.06,11]tridecan

Heterodiamantanes and Structurally Related Compounds. Part III. The Pentacyclic C₁₁-Diethers 5, 13-Dioxapentacyclo [6.5.0.0^2,6.0^3,12.0^4,9]tridecane, 4, 13-Dioxapentacyclo [6.4.1.0^2,7.0^3,10.0^5,9]tridecane, and 3, 10-Dioxapentacyclo [7.3.1.0^2,7.0^4,12.0^6,11]tridecane In connection with the studies on heterodiamantanes and structurally related compounds the three novel pentacyclic diethers 3 – 5 were prepared starting from the cyclopentadienone dimer 6 . All four compounds have as common features a central carbocyclic 6-membered ring with four axial alkyl substituents and two oxygen functions in 1, 4 position. The required eleventh C-atom was introduced by dichlorocarbene addition either to 6 ( → 7 ) (Scheme 2) or to 29 ( → 28 ) (Scheme 4). Diether 3 was obtained by reduction of 26 (Scheme 2), a suitable precursor prepared either by intramolecular addition ( 24 → 26 ; Scheme 2) or substitution ( 30 → 26 , 31 → 26 ; Scheme 4), as well as by direct substitution ( 44 → 3 , 42 → 3 ; Scheme 5). Diether 4 was the product of a direct substitution ( 39 → 4 , 36 → 4 ; Scheme 5). The synthesis of diether 5 was achieved from the addition product 51 (resulting from the alcohols 47 and 48 ; Scheme 6). Diether 4 is the thermodynamically least stable of the three diethers 3 – 5 . It was easily isomerized to 5 on treatment with concentrated sulfuric acid in benzene whereas 3 and 5 remained unchanged under these conditions.