On time regularity and related conditions for power-bounded operators

Let T be a bounded linear operator in a complex Banach space.Our main result gives various characterizations of the condition:T is power-bounded and an estimate ||(I – T)Tⁿ || cn^–1/2 holds for all positive integers n. In particular, this conditionholds if and only if T = β S + (1 – β)I, forsome β (0, 1) and some power-bounded operator S; or ifand only if T is power-bounded and the discrete semigroup (Tⁿ)is dominated by the continuous semigroup (e^{– t(I –T)})_{t 0} in a natural sense. As a consequence of our main results,for 1/2 < 1 we characterize the condition that T is power-boundedand ||(I – T)Tⁿ || c n^– for all n, in terms ofestimates on the semigroup e^{–t(I – T)}.     

Growth in solvable subgroups of {{\mathrm{GL}}}_r({\mathbb {Z}}/p{\mathbb {Z}})

Let \(K={\mathbb {Z}}/p{\mathbb {Z}}\) and let \(A\) be a subset of \({{\mathrm{GL}}}_r(K)\) such that \(\langle A \rangle \) is solvable. We reduce the study of the growth of \(A\) under the group operation to the nilpotent setting. Fix a positive number \(C\ge 1\) ; we prove that either \(A\) grows (meaning \(|A_3|\ge C|A|\) ), or else there are groups \(U_R\) and \(S\) , with \(U_R\unlhd S \unlhd \langle A\rangle \) , such that \(S/U_R\) is nilpotent, \(A_k\cap S\) is large and \(U_R\subseteq A_k\) , where \(k\) depends only on the rank \(r\) of \({{\mathrm{GL}}}_r(K)\) . Here \(A_k = \{x_1 x_2 \cdots x_k : x_i \in A \cup A^{-1} \cup \{1\}\}\) . When combined with recent work by Pyber and Szabó, the main result of this paper implies that it is possible to draw the same conclusions without supposing that \(\langle A \rangle \) is solvable.     

Structure Elucidation and Activity of Kolossin A,the D‐/L‐Pentadecapeptide Product of a Giant Nonribosomal Peptide Synthetase

The largest continuous bacterial nonribosomal peptide synthetase discovered so far is described. It consists of 15 consecutive modules arising from an uninterrupted, fully functional gene in the entomopathogenic bacterium Photorhabdus luminescens. The identification of its cryptic biosynthesis product was achieved by using a combination of genome analysis, promoter exchange, isotopic labeling experiments, and total synthesis of a focused collection of peptide candidates. Although it belongs to the growing class of D ‐/ L ‐peptide natural products, the encoded metabolite kolossin A was found to be largely devoid of antibiotic activity and is likely involved in interspecies communication. A stereoisomer of this peculiar natural product displayed high activity against Trypanosoma brucei rhodesiense, a recalcitrant parasite that causes the deadly disease African sleeping sickness.     

Headgroup effect on silane structures at buried polymer/silane and polymer/polymer interfaces and their relations to adhesion

Sum frequency generation (SFG) vibrational spectroscopy was used to study the effect of silane headgroups on the molecular interactions that occur between poly(ethylene terephthalate) (PET) and various epoxy silanes at the PET/silane and PET/silicone interfaces. Three different silanes were investigated: (3-glycidoxypropyl) trimethoxysilane (γ-GPS), (3-glycidoxypropyl) methyl-dimethoxysilane (γ-GPMS), and (3-glycidoxypropyl) dimethyl-methoxysilane (γ-GPDMS). These silanes share the same backbone and epoxy end group but have different headgroups. SFG was used to examine the interfaces between PET and each of these silanes, as well as silanes mixed with methylvinylsiloxanol (MVS). We also examined the interfaces between PET and uncured or cured silicone with silanes or silane-MVS mixtures. Silanes with different headgroups were found to exhibit a variety of methoxy group interfacial segregation and ordering behaviors at various interfaces. The effect of MVS was also dependent upon silane headgroup choice, and the interfacial molecular structures of silane methoxy headgroups were found to differ at PET/silane and PET/silicone interfaces. Epoxy silanes have been widely used as adhesion promoters for polymer adhesives; therefore, the molecular structures probed using SFG were correlated to adhesion testing results to understand the molecular mechanisms of silicone-polymer adhesion. Our results demonstrated that silane methoxy headgroups play important roles in adhesion at the PET/silicone interfaces. The presence of MVS can change interfacial methoxy segregation and ordering, leading to different adhesion strengths.     

Factors Affecting the Production of Aromatic Immonium Ions in MALDI 157 nm Photodissociation Studies

Immonium ions are commonly observed in the high energy fragmentation of peptide ions. In a MALDI-TOF/TOF mass spectrometer, singly charged peptides photofragmented with 157 nm VUV light yield a copious abundance of immonium ions, especially those from aromatic residues. However, their intensities may vary from one peptide to another. In this work, the effect of varying amino acid position, peptide length, and peptide composition on immonium ion yield is investigated. Internal immonium ions are found to have the strongest intensity, whereas immonium ions arising from C-terminal residues are the weakest. Peptide length and competition among residues also strongly influence the immonium ion production. Quantum calculations provide insights about immonium ion structures and the fragment ion conformations that promote or inhibit immonium ion formation.

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On the Stability of Pt-Based Catalysts in HBr/Br2 Solution

Stability studies on supported metal nanoparticles are essential for gaining insight into the design and optimization of high-performance materials. In this work, the dissolutions of Pt-based catalysts in HBr/Br₂ mixture of various concentration regimes were studied and correlated with material structural properties. The dissolution of metal nanoparticles was enhanced by adding Br₂ to the HBr solution. Comparing with commercial Pt/C catalyst, the well-alloyed PtIr/C catalyst was observed to exhibit high resistance towards dissolution. In addition, regulating the accessibility of the metal sites to dissolution-inducing species contributed to the marked stability of the nanoparticles in HBr/Br₂ solutions, as shown for the surface-modified PtIr/C catalysts with organic diamine molecules.     

Stabilisation of [Fe2(CO)9] and [Ru2(CO)9] bu substitution with bridging diphosphorus ligands

Reaction of [Fe₂(CO)₉] with a half molar amount of R₂PYPR₂ (Y = CH₂, R = Ph, Me, OMe or OPrⁱ; Y = N(Et), R = OPh, OMe or OCH₂; Y = N(Me), R = OPrⁱ or OEt) leads to the ready formation of a product which on irradiation with ultraviolet light rapidly decarbonylates to the heptacarbonyl derivative [Fe₂(μ-CO)(CO)₆{μ-R₂PYPR₂}]. Treatment of the latter with a slight excess of the appropriate ligand results, under photochemical conditions, in the formation of the dinuclear pentacarbonyl complex [Fe₂(μ-CO)(C))₄{μ-R₂PYPR₂}₂] but under thermal conditions in the formation of the mononuclear species [Fe(CO)₃{R₂PYPR₂}]. Reaction of [Ru₃(CO)₁₂] with an equimolar amount of (RO)₂PN(R′)P(OR)₂ (R′ = Me, R = Prⁱ or Et; R′ = Et, R = Ph or Me) under either thermal or photochemical conditions produces [Ru₃(CO)₁₀{μ-(RO)₂PN(OR)₂}] which reacts further with excess (RO)₂PN(R′)P(OR)₂ on irradiation with ultraviolet light to afford the dinuclear compound [Ru₂(μ-CO)(CO₄{μ-(RO)₂PN(R′)P(OR)₂}₂]. The molecular structure of [Ru₂(μ-CO)(CO)₄{μ-(MeO)₂PN(Et)P(OMe)₂}₂], which has been determined by X-ray crystallography, is described.     

Damaging Effects of Ultraviolet Radiation on the Cornea

The cornea sits at the anterior aspect of the eye and, like the skin, is highly exposed to ultraviolet radiation (UVR). The cornea blocks a significant proportion of UVB from reaching the posterior structures of the eye. However, UVA can penetrate the full thickness of the cornea, even reaching the anterior portion of the lens. Epidemiological data indicate that UVR is a contributing factor for a multitude of diseases of the cornea including pterygium, photokeratitis, climatic droplet keratopathy and ocular surface squamous neoplasia (OSSN), although the pathogenic mechanisms of each require further elucidation. UVR is a well‐known genotoxic agent, and its effects have been well characterized in organs such as the skin. However, we are only beginning to identify its effects on the cornea, such as the UVR signature C → T and CC → TT transversions identified by sequencing and increased proliferative and shedding rates in response to UVR exposure. Alarmingly, a single low‐dose exposure of UVR to the cornea is sufficient to elicit genetic, molecular and cellular changes, supporting the consideration of using protective measures, such as wearing sunglasses when outdoors. The aim of this review was to describe the adverse effects of UVR on the cornea.