Detecting self-similarity in surface microstructures

The relative configurational entropy per cell as a function of length scale is a sensitive detector of spatial self-similarity. For Sierpinski carpets the equally separated peaks of the above function appear at the length scales that depend on the kind of the carpet. These peaks point to the presence of self-similarity even for randomly perturbed initial fractal sets. This is also demonstrated for the model population of particles diffusing over the surface considered by Van Siclen, Phys. Rev. E 56 (1997) 5211. These results allow the subtle self-similarity traces to be explored.Comment: 9 pages, 4 figures, presented at ECOSS18 (Vienna) Sept. 199

Preference programming and inconsistent interval matrices

The problem of derivation of the weights of altematives from pairwise comparison matrices is long standing. In this paper,Lexicographic Goal Programming (LGP) has been used to find out weights from pairwise inconsistent interval judgment matrices. A number of properties and advantages of LGP as a weight determination technique have been explored. An algorithm for identification and modification of inconsistent bounds is also provided. The proposed technique has been illustrated by means of numerical examples.Analytic hierarchy process; Interval judgment; Preferente programming

Kirillov-Reshetikhin crystals B^{7,s} for type E_7^1

We construct a combinatorial crystal structure on the Kirillov-Reshetikhin crystal B^{7,s} in type E_7^1, where 7 is the unique node in the orbit of 0 in the affine Dynkin diagram

Macdonald Polynomials and level two Demazure modules for affine sln+1\mathfrak{sl}_{n+1}

We define a family of symmetric polynomials $G_{\nu,\lambda}(z_1,\cdots, z_{n+1},q)$ indexed by a pair of dominant integral weights. The polynomial $G_{\nu,0}(z,q)$ is the specialized Macdonald polynomial and we prove that $G_{0,\lambda}(z,q)$ is the graded character of a level two Demazure module associated to the affine Lie algebra $\widehat{\mathfrak{sl}}_{n+1}$. Under suitable conditions on $(\nu,\lambda)$ (which includes the case when $\nu=0$ or $\lambda=0$) we prove that $G_{\nu,\lambda}(z,q)$ is Schur positive and give explicit formulae for them in terms of Macdonald polynomials

Spectral characterization and biological studies of some ternary complexes with molecular docking investigations against MERS and SARS type coronaviruses

ABSTRACT. A series of ternary complexes with a Schiff base (HL1) derived from 2-hydrazinobenzimidazole and o-hydroxybenzophenone (primary ligand) have been prepared. Here, 1,10-phenanthroline acts as secondary ligand (L2). These metal complexes were investigated by UV-Vis, IR, 1H NMR and thermal techniques. The spectral data confirmed tridentate nature of the SB ligand with NNO type coordination, whereas the secondary ligand L2 (1,10-phenanthroline) coordinated through its two nitrogen atoms (NN type). These compounds possess distorted octahedral geometry. Moreover, these compounds were screened against B. subtilis and E. coli to evaluate their antibacterial activity. In addition, molecular docking studies were performed against MERS-CoV and SARS-CoV-2 main protease (Mpro). Moreover, DFT calculations and QSAR studies of the SB ligand were also performed.                     KEY WORDS: Ternary complexes, Spectral, Antibacterial, DFT, QSAR, Molecular docking studies   Bull. Chem. Soc. Ethiop. 2021, 35(3), 525-535. DOI: https://dx.doi.org/10.4314/bcse.v35i3.