Reversible dispersion of single-walled carbon nanotubes based on a CO2-responsive dispersant

A CO(2)-responsive dispersant, N,N-dimethyl-N'-(pyren-1-ylmethyl) acetimidamidinium (PyAH(+)), which bears both a pyrene moiety and an amidinium cation, has been successfully synthesized. Through strong π-π interaction between the pyrene moiety and single-walled carbon nanotubes (SWNTs), we have demonstrated that PyAH(+) can be modified onto SWNT surfaces to promote the dispersion of SWNTs in water. Furthermore, taking advantage of gas triggered interconversions between the amidinium cation and amidine, reversible control on the solubility of SWNTs has been achieved simply through alternated bubbling of CO(2) and Ar. This work has demonstrated a new method for controlled dispersion and aggregation of SWNTs, and it may contribute to the development of gas responsive carbon materials.     

Lower order terms for the one-level density of elliptic curve L-functions

It is believed that, in the limit as the conductor tends to infinity, correlations between the zeros of elliptic curve L-functions averaged within families follow the distribution laws of the eigenvalues of random matrices drawn from the orthogonal group. For test functions with restricted support, this is known to be the true for the one- and two-level densities of zeros within the families studied to date. However, for finite conductor Miller's experimental data reveal an interesting discrepancy from these limiting results. Here we use the L-functions ratios conjectures to calculate the 1-level density for the family of even quadratic twists of an elliptic curve L-function for large but finite conductor. This gives a formula for the leading and lower order terms up to an error term that is conjectured to be significantly smaller. The lower order terms explain many of the features of the zero statistics for relatively small conductor and model the very slow convergence to the infinite conductor limit. However, our main observation is that they do not capture the behaviour of zeros in the important region very close to the critical point and so do not explain Miller's discrepancy. This therefore implies that a more accurate model for statistics near to this point needs to be developed.     

On a terminal value problem for a generalization of the fractional diffusion equation with hyper-Bessel operator

In this paper, we consider an inverse problem of recovering the initial value for a generalization of time-fractional diffusion equation, where the time derivative is replaced by a regularized hyper-Bessel operator. First, we investigate the existence and regularity of our terminal value problem. Then we show that the backward problem is ill-posed, and we propose a regularizing scheme using a fractional Tikhonov regularization method. We also present error estimates between the regularized solution and the exact solution using two parameter choice rules.     

A new dynamic programming formulation for scheduling independent tasks with common due date on parallel machines

This paper deals with a scheduling problem of independent tasks with common due date where the objective is to minimize the total weighted tardiness. The problem is known to be ordinary NP-hard in the case of a single machine and a dynamic programming algorithm was presented in the seminal work of Lawler and Moore [E.L. Lawler, J.M. Moore, A functional equation and its application to resource allocation and sequencing problems, Management Science 16 (1969) 77–84]. In this paper, this algorithm is described and discussed. Then, a new dynamic programming algorithm is proposed for solving the single machine case. These methods are extended for solving the identical and uniform parallel-machine scheduling problems.     

Electronic Structure Trends in N‐Heterocyclic Carbenes (NHCs) with Varying Number of Nitrogen Atoms and NHC?Transition‐Metal Bond Properties

Carbenes derived from five‐membered heterocycles with different numbers of nitrogen atoms ranging from two to four lead formally either to normal N‐heterocyclic or mesoionic carbenes with, in some cases, the same skeletal structure. The electronic structures of fourteen of these compounds were examined by means of DFT calculations at the B3LYP/aug‐cc‐pVTZ level. The examined parameters include the energies of the σ‐lone pair at C_carbene and the π‐HOMO of the protonated form, which are correlated to the first and second proton affinities. The singlet–triplet energy gap was used as a measure of the stability of the N‐heterocyclic carbene (NHC) towards dimerisation. Natural population analysis provided insight into the variation of the p_π population and the natural charge at C_carbene with NHC structure. Additionally, the transition metal? NHC bond in L‐AuCl and L‐TiCl₄ and the nature of the orbital interactions between the NHC and the transition‐metal fragment were analysed in detail by the extended transition state–natural orbitals for chemical valence (ETS–NOCV) approach at the BP86/TZ2P level. Similarities and differences between the NHC? gold and the NHC? titanium bond are discussed, and trends in key bonding properties can be traced back to the variation of the electronic parameters of the NHC.     

Sequestered alkyllithiums: why phenyllithium alone is suitable for betaine-ylide generation

The key step in the trans-selective modification of the Wittig reaction is the alpha-lithiation of the lithium bromide coordinated ylide-aldehyde adduct (the so-called "P-betaine"). Only phenyllithium effects this deprotonation rapidly and cleanly. Alkyllithiums (in particular, butyl-, sec-butyl-, and tert-butyllithium) react only sluggishly and incompletely, being tied up in very stable mixed aggregates with the lithium alkoxide part of the betaines.     

Pseudo-steady-state solutions for solidification in a wedge

Polubarinova-Kochina's analytical differential equation methodis used to determine the pseudo-steady-state solution to problemsinvolving the freezing (solidification) of wedges of liquidwhich are initially at their fusion temperature. In particular,we consider four distinct problems for wedges which are: freezingwith the same constant boundary temperature, freezing with thesame constant boundary heat fluxes, freezing with distinct constantboundary temperatures and freezing with distinct constant fluxesat the boundaries. For the last two problems, a Heun's differentialequation with an unknown singularity is derived, which in bothcases admits a particularly elegant simple solution for thespecial case when the wedge angle is . The moving boundariesobtained are shown pictorially.     

Synthesis and properties of N,N′-dialkylimidazolium bis(nonafluorobutane-1-sulfonyl)imides: a new subfamily of ionic liquids

A series of N,N′-dialkylimidazolium bis(nonafluorobutane-1-sulfonyl)imides was synthesized in high yields by quaternization of imidazole derivatives with various readily available alkylating reagents, followed by anion exchange with highly stable and non-hygroscopic potassium bis(nonafluorobutane-1-sulfonyl)imide. The latter was obtained by an improved method starting from ammonium chloride and nonafluorobutane-1-sulfonyl fluoride. The quaternary imidazolium salts thus obtained constitute a new subfamily of thermally stable and remarkably hydrophobic ionic liquids with melting points in the range 0-40 °C and solubilities in water and organic solvents (aromatic hydrocarbons, dialkyl ethers) in the range of 0.5-1.5 wt%. The ionic liquids can be easily purified from ionic byproducts (e.g., halogenide salts) by aqueous extraction followed by thorough drying in a high vacuum without loss of yield. Due to the above features, these new ionic fluids may be considered as promising recyclable media in repeated catalytic processes.