Vibrational spectroscopy of Cm-C/Cb-Cb stretching vibrations of copper tetramesityl porphyrin: An algebraic approach

Using Lie algebraic techniques and simpler expressions of the matrix elements of Majorana and Casimir operators given by us, we obtain an effective Hamiltonian operator which conveniently describes stretching vibrations of biomolecules. For a copper tetramesityl porphyrin molecule, the higher excited vibrational levels are calculated by applying the U(2) algebraic approach.     

Problems on matchings and independent sets of a graph

Let $G$ be a finite simple graph. For $X?V\left(G\right)$, the difference of $X$, $d\left(X\right)?\left|X\right|?\left|N\left(X\right)\right|$ where $N\left(X\right)$ is the neighborhood of $X$ and $max\{d\left(X\right):X?V\left(G\right)\}$ is called the critical difference of $G$. $X$ is called a critical set if $d\left(X\right)$ equals the critical difference and $\ker \left(G\right)$ is the intersection of all critical sets. $\mathrm{diadem}\left(G\right)$ is the union of all critical independent sets. An independent set $S$ is an inclusion minimal set with$d\left(S\right)>0$ if no proper subset of $S$ has positive difference.A graph $G$ is called a König–Egerváry graph if the sum of its independence number $\alpha \left(G\right)$ and matching number $\mu \left(G\right)$ equals $\left|V\left(G\right)\right|$.In this paper, we prove a conjecture which states that for any graph the number of inclusion minimal independent set $S$ with $d\left(S\right)>0$ is at least the critical difference of the graph.We also give a new short proof of the inequality $\left|\ker \left(G\right)\right|+\left|\mathrm{diadem}\left(G\right)\right|\le 2\alpha \left(G\right)$.A characterization of unicyclic non-König–Egerváry graphs is also presented and a conjecture which states that for such a graph $G$, the critical difference equals $\alpha \left(G\right)?\mu \left(G\right)$, is proved.We also make an observation about $\ker \left(G\right)$ using Edmonds–Gallai Structure Theorem as a concluding remark.     

An algebraic approach to the comparative study of the vibrational spectra of monofluoroacetylene (HCCF) and deuterated acetylene (HCCD)

Using the Lie algebraic method the vibrational energy levels of HCCF and HCCD are calculated for 102 and 110 vibrational bands, respectively, using the local Hamiltonian. A comparative study is made between the two. Better results are obtained than those published earlier from local mode analysis.     

Imino Diels-Alder Reactions: Efficient Synthesis of Pyrano- and Furanoquinolines Catalyzed by 4-Nitrophthalic Acid

Summary. 4-Nitrophthalic acid was found to be an effective catalyst for the imino Diels-Alder reaction of N-benzylideneanilines with 3,4-dihydro-2H-pyran and 2,3-dihydrofuran to afford pyrano- and furanoquinolines in good yields. It was also found that aryl amines react smoothly with 3,4-dihydro-2H-pyran and 2,3-dihydrofuran under the same condition to afford the corresponding pyrano- and furanoquinolines in high yields. This catalyst is inexpensive, easily available, water soluble, and stable to aqueous reaction conditions.     

Strain-stiffening response in transient networks formed by reverse wormlike micelles

Strain-stiffening, that is, an increase in material stiffness at large deformations, is a property of many biological materials. Currently, model systems for the study of this phenomenon are elastic networks (gels) of semiflexible filamentous biopolymers such as actin, keratin, or fibrin. Here, we demonstrate strain-stiffening in a class of viscoelastic solutions, comprising reverse wormlike micelles. These structures are formed by the coassembly of the physiological surfactants, lecithin and bile salt, in an organic solvent, cyclohexane. In contrast to the biopolymer gels, the networks here are transient and are formed by the physical entanglement of relatively flexible worms. Our results suggest that neither a permanent network nor a high filament rigidity is required for strain-stiffening. We suggest a different origin, based on a temporary strain-induced increase in the volume fraction of entangled worms. Our system can also serve as a convenient synthetic model for future studies into this phenomenon.     

New mesogenic compounds possessing a biphenyl ester and ether moiety comprising 1,3-dimethylbarbituric acid: synthesis,characterisation and mesomorphic studies

New substituted derivatives of 5-vinyl-1,3-dimethylbarbituric acid were synthesised and evaluated for liquid crystal properties. Two sets of molecules were prepared. One end of all the molecules possesses the 1,3-dimethylbarbituric core. The first set comprises biphenyl ethers, 4a–n and the second set biphenyl esters, 5a–g. Liquid crystalline properties were investigated by POM and DSC techniques. All the compounds exhibited enantiotropic smectic A and nematic mesophases. The LC properties were found to depend on the spacer and terminal alkoxy- chain and alkoxy- ester moiety of the molecules. Smaller alkyl chain members showed a smectic phase, while higher alkyl chain members showed a nematic phase.     

Synthesis of a new class of glycolipids and the evaluation of their immunogenicity using murine splenocytes

A new class of glycolipids were generated by the incorporation of lipid entities at the C-6 position of D-glucose through oxidation of the primary hydroxyl group of tetrabenzylated D-glucose to form corresponding aldehyde, which in turn was subjected to Grignard reaction with C8 and C16 alkyl magnesium halides. The resulting lipidated secondary alcohol was further subjected to esterification with long-chain carboxylic acids to afford novel glycolipids. All of the derivatives 4a–b, 6a–d, and 8a–b exhibited low cytotoxicity and induced strong T and B cell proliferation and IL-2, IL-4, and IFN-γ expression from stimulated splenocyte culture, signifying their potent immunostimulating activity.     

Formation of left-handed helices in hybrid peptide oligomers with cis beta-sugar amino acid and L-Ala as building blocks

Residue based control of specific helical folding is explored in hybrid peptide oligomers consisting of alternating L-Ala and cis-beta-furanoid sugar amino acid (FSAA) residues as building blocks; two series of these hybrid oligomers are designed, synthesized and extensively characterized by using NMR, CD, FT-IR and MD simulation studies; results show the co-existence of left-handed 11- and 14/15-helical conformations in these short oligomers of Boc-(alpha/beta) and Boc-(beta/alpha) series.