Boundary null-controllability of linear diffusion–reaction equations

This Note deals with the boundary null-controllability of linear diffusion–reaction equations in a 2D bounded domain. We transform the determination of the sought HUM boundary control into the minimization of a continuous and strictly convex functional. In the case of a rectangular domain where the diffusion tensor is represented by a diagonal matrix, we establish a procedure based on the inner product method that uses a complete orthonormal family of Sturm–Liouville's eigenfunctions to express explicitly the sought control.     

Electrochemical and Theoretical Investigations of the Role of the Appended Base on the Reduction of Protons by [Fe(2) (CO)(4) (κ(2) -PNP(R) )(μ-S(CH(2) )(3) S] (PNP(R) ={Ph(2) PCH(2) }(2) NR, R=Me, Ph)

The behavior of [Fe(2) (CO)(4) (κ(2) -PNP(R) )(μ-pdt)] (PNP(R) =(Ph(2) PCH(2) )(2) NR, R=Me (1), Ph (2); pdt=S(CH(2) )(3) S) in the presence of acids is investigated experimentally and theoretically (using density functional theory) in order to determine the mechanisms of the proton reduction steps supported by these complexes, and to assess the role of the PNP(R) appended base in these processes for different redox states of the metal centers. The nature of the R substituent of the nitrogen base does not substantially affect the course of the protonation of the neutral complex by CF(3) SO(3) H or CH(3) SO(3) H; the cation with a bridging hydride ligand, 1?μH(+) (R=Me) or 2?μH(+) (R=Ph) is obtained rapidly. Only 1?μH(+) can be protonated at the nitrogen atom of the PNP chelate by HBF(4) ?Et(2) O or CF(3) SO(3) H, which results in a positive shift of the proton reduction by approximately 0.15?V. The theoretical study demonstrates that in this process, dihydrogen can be released from a η(2) -H(2) species in the Fe(I) Fe(II) state. When R=Ph, the bridging hydride cation 2?μH(+) cannot be protonated at the amine function by HBF(4) ?Et(2) O or CF(3) SO(3) H, and protonation at the N atom of the one-electron reduced analogue is also less favored than that of a S atom of the partially de-coordinated dithiolate bridge. In this situation, proton reduction occurs at the potential of the bridging hydride cation, 2?μH(+) . The rate constants of the overall proton reduction processes are small for both complexes 1 and 2 (k(obs) ≈4-7?s(-1) ) because of the slow intramolecular proton migration and H(2) release steps identified by the theoretical study.     

LW-compact operators and domination problem

Positivity - This paper introduces a ‘new’ class of operators. An operator T from a Banach lattice E into a Banach space Y will be called an LW-compact if T carries L-weakly compact...     

Nanocellulose as a novel nanostructured adsorbent for environmental remediation: a review

Nanocellulose is a lightweight material with strong mechanical strength, inexpensive production costs and safe handling compared to synthetic nanoparticles. Thanks to the high specific surface area, broad possibility of surface modification and high mechanical strength, nanocellulose has emerged as a new class of biobased adsorbent with promising potential application in environmental remediation. Many classes of pollutants could be adsorbed by nanocellulose, including heavy metals, dissolved organic pollutants, dyes, oil and undesired effluents. The possibility for the regeneration of the nanocellulose adsorbent is another benefit driving attempts to fully exploit this new class of nanostructured biobased material. In this review, an update of the most relevant uses of nanocellulose as a new class of adsorbents for environmental remediation is outlined. An emphasis on the key advancement of surface modifications of nanocellulose to enhance the adsorption efficiency according to the pollutant class is highlighted.     

Electrochemical and Theoretical Investigations of the Role of the Appended Base on the Reduction of Protons by [Fe2(CO)4(κ2‐PNPR)(μ‐S(CH2)3S] (PNPR={Ph2PCH2}2NR,R=Me,Ph)

The behavior of [Fe₂(CO)₄(κ²‐PNP^R)(μ‐pdt)] (PNP^R=(Ph₂PCH₂)₂NR, R=Me ( 1 ), Ph ( 2 ); pdt=S(CH₂)₃S) in the presence of acids is investigated experimentally and theoretically (using density functional theory) in order to determine the mechanisms of the proton reduction steps supported by these complexes, and to assess the role of the PNP^R appended base in these processes for different redox states of the metal centers. The nature of the R substituent of the nitrogen base does not substantially affect the course of the protonation of the neutral complex by CF₃SO₃H or CH₃SO₃H; the cation with a bridging hydride ligand, 1 μH⁺ (R=Me) or 2 μH⁺ (R=Ph) is obtained rapidly. Only 1 μH⁺ can be protonated at the nitrogen atom of the PNP chelate by HBF₄?Et₂O or CF₃SO₃H, which results in a positive shift of the proton reduction by approximately 0.15 V. The theoretical study demonstrates that in this process, dihydrogen can be released from a η²‐H₂ species in the Fe^IFe^II state. When R=Ph, the bridging hydride cation 2 μH⁺ cannot be protonated at the amine function by HBF₄?Et₂O or CF₃SO₃H, and protonation at the N atom of the one‐electron reduced analogue is also less favored than that of a S atom of the partially de‐coordinated dithiolate bridge. In this situation, proton reduction occurs at the potential of the bridging hydride cation, 2 μH⁺ . The rate constants of the overall proton reduction processes are small for both complexes 1 and 2 (k_obs≈4–7 s^?1) because of the slow intramolecular proton migration and H₂ release steps identified by the theoretical study.