Cauchy, Ferrers-Jackson and Chebyshev polynomials and identities for the powers of elements of some conjugate recurrence sequences

In this paper some decompositions of Cauchy polynomials, Ferrers-Jackson polynomials and polynomials of the form x ²ⁿ + y ²ⁿ , n ∈ ℕ, are studied. These decompositions are used to generate the identities for powers of Fibonacci and Lucas numbers as well as for powers of the so called conjugate recurrence sequences. Also, some new identities for Chebyshev polynomials of the first kind are presented here.     

On the Adams–Riemann–Roch theorem in positive characteristic

Let p > 0 be a prime number. We give a short proof of the Adams–Riemann–Roch theorem for the p-th Adams operation, when the involved schemes live in characteristic p. We also answer a question of B. Köck.     

W-shaped mesogens and variations of their molecular structure

New bent-core liquid crystalline dimers with W-shaped molecular geometry have been prepared and studied. We have modified the dimer shape by variation of the connecting part between two bent-core units and changing the terminal chains (perfluoroalkyl, siloxanealkyl). Additionally, we have altered the inner bend angle value (120°, 60° and 148°) by utilization of different aromatic units. Mesomorphic properties of new dimers were established based on the texture observation in the polarizing microscope and DSC measurements. Moreover, x-ray structural analysis has been performed for selected dimers to confirm phase identification. For most of the studied dimers, nematic or columnar phases have been detected, for several compounds appearing in a nematic-columnar phase sequence on cooling from the isotropic phase. The studied dimers showed richer polymorphism than their monomeric counterparts.     

Single versus poly-crystalline layered oxide cathode materials for solid-state battery applications - a short review article

The recent developments in the application of single-crystalline (SC) cathode materials in solid-state batteries are discussed in this mini-review. The characteristics of SC and poly-crystalline (PC) cathode materials are explored, with emphasis on the kinetic and mechanical properties. The critical factors influencing their performance in liquid electrolyte and solid-state battery cells are investigated. Finally, the advantages and disadvantages of both morphologies are discussed and considerations to ensure a fair comparison between SC and PC cathodes in different systems are raised.     

Fast and Reliable Automated Synthesis of RNA and Partially 2′-O- Protected Precursors (`Caged RNA') Based on Two Novel,Orthogonal 2′-O-Protecting Groups,Preliminary Communication

Two sets of RNA phosphoramidites, carrying the (fluoride-labile) 2′-O-[(triisopropylsilyl)oxy]methyl (=tom) group and the (photolabile) [(R)-1-(2-nitrophenyl)ethoxy]methyl (=(R)-npeom) group, were prepared (see 1 – 4 and 5 – 8 , resp.). The two protecting groups were completely orthogonal to each other. Three ribozyme-substrate constructs, protected each by a (R)-npeom group, were synthesized; on photolysis, efficient cleavage of this remaining protecting group occurred (Scheme 3). It could be demonstrated that the presence of one (R)-npeom group within a RNA strand has only a minor influence on the pairing properties of corresponding duplexes.     

Cucurbituril binding of trans-[{PtCl(NH3)2}2(micro-NH2(CH2)8NH2)]2+ and the effect on the reaction with cysteine

The effect of encapsulation by cucurbiturils Q[7] and Q[8] on the rate of reaction of the anti-cancer dinuclear platinum complex trans-[{PtCl(NH3)2}2(micro-NH2(CH2)8NH2)]2+ with the model biological nucleophiles glutathione and cysteine has been examined by NMR spectroscopy. It was expected that the octamethylene linking chain would fold inside the cucurbituril host and hence position the reactive platinum centres close to the cucurbituril portals, and thereby, confer resistance to degradation by biological nucleophiles. The upfield shifts of the resonances from the methylene protons in the linking ligand observed in 1H NMR spectra of the platinum complex upon addition of either Q[7] or Q[8] indicate that the cucurbituril is positioned over the linking ligand, with the Pt(II) centres projecting out of the portal. Furthermore, the relative changes in chemical shift of the methylene resonances suggest that the octamethylene linking chain folds within the cucurbituril cavity, particularly in Q[8]. Simple molecular models, based on the observed relative changes in chemical shift, could be constructed that were consistent with the proposed folding of the linking ligand within the cucurbituril cavity. Encapsulation by Q[7] was found to reduce the rate of reaction of the platinum complex with glutathione. Encapsulation by Q[7] and Q[8] was also found to reduce the rate of reaction of the platinum complex with cysteine, with Q[8] slowing the reaction to a greater extent than Q[7], consistent with the inferred encapsulation geometries. Encapsulation of dinuclear platinum complexes within the cucurbituril cavity may provide a novel way of reducing the reactivity and degradation of these promising chemotherapeutic agents with blood plasma proteins.     

Sodium trichloro­methane­sulfonate monohydrate

Sodium trichloro­methane­sulfonate monohydrate, Na⁺·CCl₃SO₃⁻·H₂O, crystallizes in P2₁/a with all the atoms located in general positions. The trichloro­methane­sulfonate (trichlate) anion consists of pyramidal SO₃ and CCl₃ groups connected via an S—C bond in a staggered conformation with approximate C_3v symmetry. The water mol­ecule is hydrogen bonded to the sulfonate O atoms, with one water H atom forming weak bifurcated O—H⋯O hydrogen bonds to two different trichlate ions. Two water O atoms and three O atoms from different SO₃ groups form a square‐pyramidal arrangement around the sodium ion.     

Bond dissociation energies and radical stabilization energies associated with model peptide-backbone radicals

Bond dissociation energies (BDEs) and radical stabilization energies (RSEs) have been calculated for a series of models that represent a glycine-containing peptide-backbone. High-level methods that have been used include W1, CBS-QB3, U-CBS-QB3, and G3X(MP2)-RAD. Simpler methods used include MP2, B3-LYP, BMK, and MPWB1K in association with the 6-311+G(3df,2p) basis set. We find that the high-level methods produce BDEs and RSEs that are in good agreement with one another. Of the simpler methods, RBMK and RMPWB1K achieve good accuracy for BDEs and RSEs for all the species that were examined. For monosubstituted carbon-centered radicals, we find that the stabilizing effect (as measured by RSEs) of carbonyl substituents (CX=O) ranges from 24.7 to 36.9 kJ mol(-1), with the largest stabilization occurring for the CH=O group. Amino groups (NHY) also stabilize a monosubstituted alpha-carbon radical, with the calculated RSEs ranging from 44.5 to 49.5 kJ mol(-1), the largest stabilization occurring for the NH2 group. In combination, NHY and CX=O substituents on a disubstituted carbon-centered radical produce a large stabilizing effect ranging from 82.0 to 125.8 kJ mol(-1). This translates to a captodative (synergistic) stabilization of 12.8 to 39.4 kJ mol(-1). For monosubstituted nitrogen-centered radicals, we find that the stabilizing effect of methyl and related (CH2Z) substituents ranges from 25.9 to 31.7 kJ mol(-1), the largest stabilization occurring for the CH3 group. Carbonyl substituents (CX=O) destabilize a nitrogen-centered radical relative to the corresponding closed-shell molecule, with the calculated RSEs ranging from -30.8 to -22.3 kJ mol(-1), the largest destabilization occurring for the CH=O group. In combination, CH2Z and CX=O substituents at a nitrogen radical center produce a destabilizing effect ranging from -19.0 to -0.2 kJ mol(-1). This translates to an additional destabilization associated with disubstitution of -18.6 to -7.8 kJ mol(-1).     

Nonequilibrium melting and crystallization of a model Lennard-Jones system

Nonequilibrium melting and crystallization of a model Lennard-Jones system were investigated with molecular dynamics simulations to quantify the maximum superheating/supercooling at fixed pressure, and over-pressurization/over-depressurization at fixed temperature. The temperature and pressure hystereses were found to be equivalent with regard to the Gibbs free energy barrier for nucleation of liquid or solid. These results place upper bounds on hysteretic effects of solidification and melting in high heating- and strain-rate experiments such as shock wave loading and release. The authors also demonstrate that the equilibrium melting temperature at a given pressure can be obtained directly from temperatures at the maximum superheating and supercooling on the temperature hysteresis; this approach, called the hysteresis method, is a conceptually simple and computationally inexpensive alternative to solid-liquid coexistence simulation and thermodynamic integration methods, and should be regarded as a general method. We also found that the extent of maximum superheating/supercooling is weakly pressure dependent, and the solid-liquid interfacial energy increases with pressure. The Lindemann fractional root-mean-squared displacement of solid and liquid at equilibrium and extreme metastable states is quantified, and is predicted to remain constant (0.14) at high pressures for solid at the equilibrium melting temperature.