Enumerating and decoding perfect linear Lee codes

Using group theory approach, we determine all numbers q for which there exists a linear 1-error correcting perfect Lee code of block length n over Z _q , and then we enumerate those codes. At the same time this approach allows us to design a linear time decoding algorithm.      

Nonplanar Shock Structures in a Relativistic Degenerate Multi-Species Plasma

A nonlinear propagation of cylindrical and spherical modified ion-acoustic (mIA) waves in an unmagnetized, collisionless, relativistic, degenerate multi-species plasma has been investigated theoretically. This plasma system is assumed to contain non-relativistic degenerate light ions, both non-relativistic and ultra-relativistic degenerate electron and positron fluids, and arbitrarily charged static heavy ions. The restoring force is provided by the degenerate pressures of the electrons and positrons, whereas the inertia is provided by the mass of ions. The arbitrarily charged static heavy ions participate only in maintaining the quasi-neutrality condition at equilibrium. The modified Burgers (mB) equation is derived by using reductive perturbation technique and numerically analyzed to identify the basic features of mIA shock structures. The basic characteristics of mIA shock waves are found to be significantly modified by the effects of degenerate pressures of electron, positron, and ion fluids, their number densities, and various charge state of heavy ions. The implications of our results to dense plasmas in astrophysical compact objects (e.g., non-rotating white dwarfs, neutron stars, etc.) are briefly discussed.     

Magnetic Bead Cellulose as a Suitable Support for Immobilization of α-Chymotrypsin

Magnetic bead cellulose was prepared by a suspension method from the mixture of viscose and magnetite using thermal sol?Cgel transition and regeneration of cellulose. The prepared magnetic particles after their activation with divinyl sulfone were shown to be suitable magnetic carrier for immobilization of ??-chymotrypsin and for its application in proteomic studies. The specific activity of the immobilized proteinase was high; its activity did not change in the course of storage. The following properties of the immobilized proteinase were compared with those of the soluble enzyme: pH and temperature dependence of the activity, self-cleavage activity, and possibility of repeated use. ??-Chymotrypsin immobilized to magnetic bead cellulose was used for the proteolytic digestion of porcine pepsin A and human gastric juice and a possibility of direct use of enzyme reaction products for matrix-assisted laser desorption/ionization time of flight mass spectrometry analysis was shown.     

Synthetic macrocyclic receptors in chiral analysis and separation

Chiral synthetic macrocyclic receptors that can achieve chiral discrimination by NMR spectroscopy and/or chiral separation by HPLC are overviewed. Synthetic macrocycles introduced here include crown ethers, calixarenes/calixresorcinarenes/calixpyrroles, macrocyclic amides/amines, and porphyrins. These macrocyclic frameworks are advantageous because intermolecular interactions can take place effectively, such as the ion–dipole interactions in crown ethers, the CH/π and π–π interactions in calixarenes, hydrogen bonding and salt formation in macrocyclic amides and amines, and π–π stacking and metal coordination in porphyrins. Additional functional groups on the periphery of the macrocyclic platforms not only make the whole molecule chiral but also act as the interaction sites. Chiral macrocyclic receptors can show a high degree of chiral recognition/discrimination by using the peripheral functional groups as well as the macrocyclic skeletons (preorganization). Both hosts and guests are shown in the figures to quickly overview the molecular recognition scope of synthetic macrocyclic receptors in chiral analysis and separation.     

Mechanism of BPh3-Catalyzed N-Methylation of Amines with CO2 and Phenylsilane: Cooperative Activation of Hydrosilane

BPh₃ catalyzes the N-methylation of secondary amines and the C-methylenation (methylene-bridge formation between aromatic rings) of N,N-dimethylanilines or 1-methylindoles in the presence of CO₂ and PhSiH₃; these reactions proceed at 30–40 °C under solvent-free conditions. In contrast, B(C₆F₅)₃ shows little or no activity. ¹¹B NMR spectra suggested the generation of [HBPh₃]⁻. The detailed mechanism of the BPh₃-catalyzed N-methylation of N-methylaniline ( 1 ) with CO₂ and PhSiH₃ was studied by using DFT calculations. BPh₃ promotes the conversion of two substrates (N-methylaniline and CO₂) into a zwitterionic carbamate to give three-component species [Ph(Me)(H)N⁺CO₂⁻⋅⋅⋅BPh₃]. The carbamate and BPh₃ act as the nucleophile and Lewis acid, respectively, for the activation of PhSiH₃ to generate [HBPh₃]⁻, which is used to produce key CO₂-derived species, such as silyl formate and bis(silyl)acetal, essential for the N-methylation of 1 . DFT calculations also suggested other mechanisms involving water for the generation of [HBPh₃]⁻ species.     

Synthesis and Chiroptical Properties of Chiral Carbazole-Based BODIPYs

A series of carbazole-based boron dipyrromethenes (BODIPYs) 2 a – g bearing binaphthyl units have been synthesized by the Et₂AlCl-mediated reaction of the corresponding BODIPY difluorides 1 a – g with 1,1′-binaphthalene-2,2′-diol. Substituents such as halogen, nitrile, and amino groups were tolerated under the reaction conditions, and the reaction of the phenylethynyl-substituted 1 h gave (R,R)- 3 h bearing two binaphthyl units. The chiroptical properties of these dyes with different substituents were investigated by UV/Vis, CD, fluorescence, and circularly polarized luminescence (CPL) spectroscopy. The CD spectra showed Cotton effects in the absorption region of the BODIPY moieties. In addition, they showed CPL both in solution and in the solid state. Interestingly, several dyes recorded higher g_lum values in the solid state, probably due to intermolecular interactions. Because (R,R)- 3 h recorded relatively low g_lum values, the diastereomer (R,S)- 3 h was prepared. The (R,S) diastereomer showed intense CPL, which suggests a synergetic effect of the two binaphthyl groups. Finally, chiral carbazole-based BODIPY dimers have been synthesized for the first time and their chiroptical properties were investigated. They showed redshifted fluorescence and CPL, which reached the near-IR (NIR) region in the solid state.     

Third-order optical nonlinearity in regioregular head-to-tail coupled poly(3-Hexylthiophene)

We measured the third-order optical nonlinearity of regioregular head-to-tail coupled poly (3-hexylthiophene) (HT-PHT) and regiorandom poly (3-hexylthiophene) (R-PHT) around exciton resonance using degenerate four wave mixing. The observed value of ∣χ⁽³⁾∣ at the exciton resonance peak of HT-PHT is in the order of 10^-9 esu which is approximately three-fold larger than that of R-PHT. We observed for the first time the enhancement in optical nonlinearity that occurs through the control of regularity of the polymeric structure. Response time of the nonlinearity was also measured using the transient grating method. The decay time of the transient grating in R-PHT and HT-PHT was less than 2 ps.