Gadolinium Photocatalysis: Dearomative [2+2] Cycloaddition/Ring-Expansion Sequence with Indoles

Lanthanide photocatalysts are much less investigated in synthetic chemistry than rare and expensive late transition metals. We herein introduce Gd^III photocatalysis of a highly regioselective, intermolecular [2+2] photocycloaddition/ring-expansion sequence with indoles, which could provide divergent access to cyclopenta[b]indoles and indolines. A simple and commercially available Gd(OTf)₃ salt is sufficient for this visible-violet-light-induced transformation. The reaction proceeds either through a transient or start-to-end dearomatization cascade and shows excellent regioselectivity (usually >95:5 r.r.), broad scope (59 examples), good functional group tolerance and facile scale-up under mild, direct visible-light-excitation conditions. Mechanistic investigations reveal that direct excitation of the Gd(OTf)₃/indole mixture gives an excited state intermediate, which undergoes the subsequent [2+2] cycloaddition and cyclobutane-expansion cascade.     

Regioselective synthesis of 5-alkylsalicylates, 5-alkyl-2-hydroxy-acetophenones, and 5-alkyl-2-hydroxy-benzophenones by [3 + 3] cyclization of 1,3-bis(silyl enol ethers) with 2-alkyl-1,1,3,3-tetraethoxypropanes

A variety of 5-alkylsalicylates, 5-alkyl-2-hydroxy-acetophenones, and 5-alkyl-2-hydroxy-benzophenones was regioselectively prepared by TiCl4 mediated formal [3 + 3] cyclization of 1,3-bis(silyl enol ethers) with 2-alkyl-1,1,3,3-tetraethoxypropanes.     

Weak real integral characterizations for exponential stability of semigroups in reflexive spaces

Let (t _n ) be a sequence of nonnegative real numbers tending to ∞, such that 1≤t _n+1?t _n ≤α for all natural numbers n and some positive α. We prove that a strongly continuous semigroup {T(t)} _t≥0, acting on a Hilbert space H, is uniformly exponentially stable if $$\sum_{n=0}^\infty\varphi\bigl(\bigl|\bigl\langle T(t_n)x, y\bigr\rangle\bigr|\bigr)<\infty, $$ for all unit vectors x, y in H. We obtain the same conclusion under the assumption that the inequality $$\sum_{n=0}^\infty\varphi\bigl(\bigl|\bigl\langle T(t_n)x, x^\ast\bigr\rangle\bigr|\bigr)<\infty, $$ is fulfilled for all unit vectors x∈X and x ^?∈X ^?, X being a reflexive Banach space. These results are stated for functions φ belonging to a special class of functions, such as defined in the second section of this paper. We conclude our paper with a Rolewicz’s type result in the continuous case on Hilbert spaces.     

Multitime dynamic programming for multiple integral actions

This paper introduces a new type of dynamic programming PDE for optimal control problems with performance criteria involving multiple integrals. The main novel feature of the multitime dynamic programming PDE, relative to the standard Hamilton-Jacobi-Bellman PDE, is that it is connected to the multitime maximum principle and is of divergence type. Introducing a generating vector field for the maximum value function, we present an interesting and useful connection between the multitime maximum principle and the multitime dynamic programming, characterizing the optimal control by means of a multitime Hamilton-Jacobi-Bellman (divergence) PDE that may be viewed as a feedback law. Section 1 recalls the multitime maximum principle. Section 2 shows how a multitime control dynamics determines the multitime Hamilton-Jacobi-Bellman PDE via a generating vector field of the value function. Section 3 gives an example of two-time dynamics with nine velocities proving that our theory works well. Section 4 shows that the Hamilton PDEs are characteristic PDEs of multitime Hamilton-Jacobi PDE and that the costates in the multitime maximum principle are in fact gradients of the components of the generating vector field.     

Hodge numbers for CICYs with symmetries of order divisible by 4

We compute the Hodge numbers for the quotients of complete intersection Calabi‐Yau three‐folds by groups of orders divisible by 4. We make use of the polynomial deformation method and the counting of invariant Kähler classes. The quotients studied here have been obtained in the automated classification of V. Braun. Although the computer search found the freely acting groups, the Hodge numbers of the quotients were not calculated. The freely acting groups, G, that arise in the classification are either or contain , , or as a subgroup. The Hodge numbers for the quotients for which the group G contains or have been computed previously. This paper deals with the remaining cases, for which or . We also compute the Hodge numbers for 99 of the 166 CICY's which have quotients.     

The Effect of Hydrophilic Bentonite Nanoclay on the Thermogelation Properties of Poly(N-isopropylacrylamide)-poly(ethylene glycol)-poly(N-isopropylacrylamide) Triblock Copolymer Aqueous Solutions

The effect of hydrophilic bentonite addition on the thermogelation properties of aqueous solutions of poly(N-isopropylacrylamide)–poly(ethylene glycol)–poly(N-isopropylacrylamide) (PNIPAM-PEG-PNIPAM) triblock copolymers of various compositions and molecular weights was investigated. Dynamic rheometry and differential scanning calorimetry (DSC) measurements showed that increasing concentrations of clay added to 20 wt.% polymer aqueous solutions caused a decrease of the temperature at which the viscosity starts increasing, while the temperature corresponding to the maximum endothermic effect due to the PNIPAM chain dehydration remained practically unchanged. The storage modulus, G′, increased with clay concentration for shorter PNIPAM chain triblock copolymers, while an opposite situation occurred in the case of the block copolymer with the longest PNIPAM block. For bentonite concentrations above 1 wt.%, G′ was larger than the viscous modulus, G″, at temperatures higher than the phase separation temperature, indicating a predominantly elastic character of the resulting composite hydrogels. These findings were explained through the presence of polymer–clay interactions occurring mainly through the PEG blocks.     

Spatial distribution of 7Be in soils of Lower Austria after heavy rains

The ⁷Be approach in estimating the erosion rates is based on the assumption that the deposition of ⁷Be fallout associated with the erosive event is spatially uniform. The objective of the present work was to verify this assumption by assessing the influence of heavy rainfalls on the ⁷Be spatial distribution in Seibersdorf soils, Austria. Incremental and bulk soil depth profiles were collected from a flat site, undisturbed for the last 9 months prior sampling and with no evidence of erosion or deposition after the occurrence of heavy rains (>30 mm day^?1). The mean value of the ⁷Be areal activities (Bq m^?2) measured at 10 different points from the selected area was 312 Bq m^?2. This value corresponded to a total rainfall of 295 mm within the last 5 months prior sampling, considering that the highest mass activity of ⁷Be at soil surface will decay below the minimum detectable activity after 5 months’ time. The resulted coefficient of variation had a value of 19 % showing acceptable spatial variability of ⁷Be fallout connected with individual storm events on a local scale.     

Synthesis,characterization of SiO2 supported-industrial phosphoric acid catalyst for hydrolysis of NaBH4 solution

Abstract

Tunisian industrial phosphoric acid H₃PO₄ was supported on silica gel SiO₂ (SIPA) to catalyze the hydrolysis reaction of aqueous alkaline sodium borohydride (NaBH₄). The SiO₂ was produced from purified quartz sand using alkali fusion-acidification chemical process. The BET surface area results indicate that the prepared silica gel could reach a specific surface area up to 585 m²/g. The addition of PO₃H₂ functional groups resulted in an increase of surface acidity of SiO₂ catalyst as shown by FT-IR and DTA-DTG spectra. The total acidity of SIPA catalyst was determined by titration to be 2.8?mmol H⁺/g. SEM/EDS maps reveal the distribution of heavy metals on the silica surface. The effect of supported PO₃H₂ functional groups and heavy metals on the NaBH₄ hydrolysis reaction was studied for different ratios of SIPA catalyst to NaBH₄. The sample 12SIPA/NaBH₄ leads to a very high hydrogen generation rate (up to 90%). The activation energy of hydrogen generation by NaBH₄ hydrolysis was 25.7?kJ mol^?1.     

Studies on new hybrid materials prepared by both Diels–Alder and Michael addition reactions

New polyurethane chemically crosslinked networks containing silica were synthesized by both Diels–Alder polymerization and Michael addition reaction. Structural characterization of the products was evidenced by proton nuclear magnetic resonance and attenuated total reflectance in conjunction with Fourier transform infrared spectroscopy techniques. Differential scanning calorimetry was used to demonstrate the thermally remendable character of the materials obtained through Diels–Alder polymerization. The influence of increasing silica content on the glass transition temperatures was studied. It was observed that the glass transition temperatures increased with increasing silica content. Absolute heat capacities and crosslinking densities were determined for the thermoreversible materials. A comparison between materials obtained through Diels–Alder process and Michael addition method was studied. A kinetic study was conducted via an isoconversional method. Morphological studies were conducted by atomic force microscopy technique.     

Ultimate limit of resolution of subwavelength imaging devices formed by metallic rods

It is demonstrated that the ultimate physical limit of resolution of novel imaging devices based on arrays of metallic rods is determined by the skin depth of the metal. Our theoretical and numerical results show that wire medium lenses may provide a unique solution for subwavelength imaging at frequencies up to the terahertz range and may enable image formation at a significant distance from the source plane.