Dynamic interactive membranes with pressure-driven tunable porosity and self-healing ability

When pressure is applied to dynamic interactive membranes consisting of micelles composed of a triblock copolymer, their morphologies can be fine-tuned. Membranes with a range of porosities are accessible which can regulate and thereby control filtration performance and also display effective autonomous healing.     

RuII Multinuclear Metallosupramolecular Rack‐Type Architectures of Polytopic Hydrazone‐Based Ligands: Synthesis,Structural Features,Absorption Spectra,Redox Behavior,and Near‐Infrared Luminescence

A novel class of polytopic hydrazone‐based ligands was synthesized. They gave heteroleptic Ru^II polynuclear rack‐like complexes of formula [Ru_nterpy_n(bridging molecular strand)]²ⁿ⁺ (terpy=2,2′:6′,2′′‐terpyridine). The new rack‐like systems can be viewed as being made of two identical or roughly identical peripheral subunits separated by several similar metal‐containing spacer subunits. The presence of pyrazine or pyrimidine units within the molecular multitopic strands introduces additional chemical diversity: whereas a pyrimidine unit leads to appended orthogonal subunits that are on the same side with regard to the main molecular strand, a pyrazine unit leads to orthogonal subunits that lie on different sides. Mixing pyrazine and pyrimidine units within the same (bridging) molecular strand also allows peculiar and topographically controlled geometries to be obtained. Redox studies provided evidence that each species undergoes reversible redox processes at mild potentials, which can be assigned to specific subunits of the multicomponent arrays. Non‐negligible electronic coupling takes place among the various subunits, and some electron delocalization extending over the overall bridging molecular strand takes place. In particular, oxidation data suggest that the systems can behave as p‐type “molecular wires” and reduction data indicate that n‐type electron conduction can occur within the multimetallic framework. All the multinuclear racks exhibit ³MLCT emission, both at 77 K in rigid matrix and at 298 K in fluid solution, which takes place in the near‐infrared region (emission maxima in the 1000–1100 nm region), and is quite structured. Rigidity of the molecular structures and delocalization within the large bridging ligands are proposed to contribute to the occurrence of the rather uncommon MLCT infrared emission, which is potentially interesting for optical communication devices.     

Lewis Acids as Mild and Effective Catalysts for the Synthesis of 3,5‐Bis[(hetero)arylidene]piperidin‐4‐ones

The aldol‐crotonic condensation reactions of N‐alkyl‐ and NH‐piperidin‐4‐one derivatives with (hetero)aromatic aldehydes promoted by Lewis acids or bases were examined. This comparative study has revealed three effective catalytic systems based on Lewis acids, i.e., LiClO₄ and MgBr₂ (in the presence of tertiary amine), and BF₃⋅Et₂O, for the synthesis of N‐alkyl‐substituted 3,5‐bis(heteroarylidene)piperidin‐4‐ones, including those bearing acid‐ or base‐labile groups both in the (hetero)aromatic groups and in the alkyl substituent at the N‐atom. The highest reaction rate was observed for LiClO₄‐mediated synthesis. Both MgBr₂‐ and LiClO₄‐mediated syntheses were inefficient in the case of NH‐piperidin‐4‐one, while BF₃⋅Et₂O provided the final compounds in high yields. This catalyst is especially advantageous as it allows simultaneous condensation and deprotection in the case of O‐protected piperidin‐4‐one.     

Effect of Cr and Pt promoters on the surface properties of tungstated zirconia: FTIR spectroscopy of probe molecules (CO and NO)

Adsorption of IR probe molecules (CO and NO) has been used for characterization of a Pt-Cr(2)O(3)/WO(3)-ZrO(2) sample. For better assignments of the results obtained 'blank' experiments with WO(3)-ZrO(2), Pt/WO(3)-ZrO(2) and Cr(2)O(3)/WO(3)-ZrO(2) were also performed. The Cr(2)O(3)/WO(3)-ZrO(2) sample was prepared via sulfate route and surface sulfates were detected on the activated sample. These species keep ca. 50% of their initial concentration even after reduction by hydrogen at 773 K. The amount of Lewis acid sites on the activated sample, as measured by CO adsorption, is relatively low and is associated mainly with coordiantively unsaturated (c.u.s.) Zr(4+) cations. Reduction of the sample generates Cr(3+) ions and the concentration of the Lewis acid sites continuously increases with the reduction temperature up to 773 K. At this reduction temperature, however, the strength of the acid sites decreases due to partial removal of the sulfates. While CO is not an efficient probe to discriminate between Zr(4+) and Cr(3+) sites, NO is selectively strongly adsorbed on Cr(3+) cations which allows a more precise monitoring of the evolution of the Cr(3+) sites during reduction. The activated Pt-Cr(2)O(3)/WO(3)-ZrO(2) sample also shows presence of sulfates but these species are practically absent after reduction with hydrogen at 773 K. It was found that platinum promotes the reduction of chromium and tungsten species as well. CO adsorption on activated sample reveals the existence of cationic platinum. However, reduction with hydrogen even at room temperature generates metallic Pt. Its amount continuously increases with the reduction temperature up to 573 K and then, due to the SMSI effect and/or agglomeration, the amount of platinum accessible to adsorption decreases. Comparison with the results obtained with the Pt/WO(3)-ZrO(2) sample shows that chromium and/or sulfates stabilize the cationic form of platinum.     

Reduction of bowl-shaped hydrocarbons: dianions and tetraanions of annelated corannulenes

[structure: see text] The reduction of several annelated corannulene derivatives was undertaken using lithium and potassium metals. It was found that annelation affects the annulenic character of corannulene by changing its charge distribution; the dianions of derivatives that are annelated with six-membered rings have less annulenic character and are less paratropic than corannulene dianion. This effect is even more pronounced in corannulenes that are peri-annelated with five-membered rings. The alkali metal used in the reduction process has a great influence on the outcome, especially on the degree of reduction. Most derivatives get reduced to tetraanions only with potassium, and not with lithium, the exception being systems that can stabilize the tetraanion with lithium by special means, such as aggregation or dimerization. One such system is cyclopenta[bc]corannulene (acecorannulylene), which gives a coordinative dimer that consists of two cyclopentacorannulene tetraanions, bound together in a convex-convex fashion by lithium cations. The points of contact in this dimer are two rehybridized carbons from each cyclopentacorannulene unit, which are bridged together by two lithium cations.     

TURAN'S EXTREMAL PROBLEM FOR POSITIVE DEFINITE FUNCTIONS ON GROUPS

We study the following question: given an open set , symmetricabout 0, and a continuous, integrable, positive definite functionf, supported in and with f(0) = 1, how large can f be? Thisproblem has been studied so far mostly for convex domains inEuclidean space. In this paper we study the question in arbitrarylocally compact abelian groups and for more general domains.Our emphasis is on finite groups as well as Euclidean spacesand ^d. We exhibit upper bounds for f assuming geometric propertiesof of two types: (a) packing properties of and (b) spectralproperties of . Several examples and applications of the maintheorems are shown. In particular, we recover and extend severalknown results concerning convex domains in Euclidean space.Also, we investigate the question of estimating f over possiblydispersed sets solely in dependence of the given measure m :=||of . In this respect we show that in and the integral is maximalfor intervals.     

Periodicity of the Spectrum of a Finite Union of Intervals

A set Ω, of Lebesgue measure 1, in the real line is called spectral if there is a set Λ of real numbers such that the exponential functions e _λ (x)=exp (2πiλx), λ∈Λ, form a complete orthonormal system on L ²(Ω). Such a set Λ is called a spectrum of Ω. In this note we present a simplified proof of the fact that any spectrum Λ of a set Ω which is finite union of intervals must be periodic. The original proof is due to Bose and Madan.     

A short, rigid, structurally pure carbon nanotube by stepwise chemical synthesis

The inaccessibility of uniform-diameter, single-chirality carbon nanotubes (CNTs) in pure form continues to thwart efforts by scientists to use these ultrathin materials in innovative applications that could revolutionize nanoscale electronics. Stimulated by the challenge to address this long-standing problem, we and other organic chemists have envisioned a new production strategy involving the controlled elongation of small hydrocarbon templates, such as hemispherical nanotube end-caps, prepared by bottom-up chemical synthesis; the diameter and rim structure encoded in the template would dictate the diameter and chirality of the resulting CNT. Toward that objective, a short [5,5] CNT has now been synthesized by stepwise chemical methods. This C(50)H(10) geodesic polyarene has been isolated, purified, crystallized, and fully characterized by NMR spectroscopy, UV-vis absorption spectroscopy, high resolution mass spectrometry, and X-ray crystallography.     

Universal mechanism of dissipation in Fermi superfluids at ultralow temperatures

We show that the vortex dynamics in Fermi superfluids at ultralow temperatures is governed by the local heating of the vortex cores creating the heat flux carried by nonequilibrium quasiparticles emitted by moving vortices. This mechanism provides a universal zero temperature limit of dissipation in Fermi superfluids. For the typical experimental conditions realized by the turbulent motion of ^{3}He-B, the temperature of the vortex cores is estimated to be of the order 0.2 T(c). The dispersion of Kelvin waves is derived, and the heat flow generated by Kelvin cascade is shown to have a value close to that experimentally observed.     

An investment model with switching costs and the option to abandon

We develop a complete analysis of a general entry–exit–scrapping model. In particular, we consider an investment project that operates within a random environment and yields a payoff rate that is a function of a stochastic economic indicator such as the price of or the demand for the project’s output commodity. We assume that the investment project can operate in two modes, an “open” one and a “closed” one. The transitions from one operating mode to the other one are costly and immediate, and form a sequence of decisions made by the project’s management. We also assume that the project can be permanently abandoned at a discretionary time and at a constant sunk cost. The objective of the project’s management is to maximise the expected discounted payoff resulting from the project’s management over all switching and abandonment strategies. We derive the explicit solution to this stochastic control problem that involves impulse control as well as discretionary stopping. It turns out that this has a rather rich structure and the optimal strategy can take eight qualitatively different forms, depending on the problems data.