On the supersymmetric nonlinear evolution equations

Supersymmetrization of a nonlinear evolution equation in which the bosonic equation is independent of the fermionic variable and the system is linear in fermionic field goes by the name B-supersymmetrization. We provide B-supersymmetric extension of a number of quasilinear and fully nonlinear evolution equations and demonstrate that the supersymmetric system follows from the usual action principle. We observe that B-supersymmetrization can also be realized using a generalized Noetherian symmetry such that the resulting set of Lagrangian symmetries coincides with symmetries of the field equations. Following this viewpoint we derive conservation laws for the supersymmetric pair of equations. We attempt to realize the bosonic and fermionic fields in terms of bright and dark solitons. The interpretation sought by us has its origin in the classic work of Bateman who introduced a reverse-time system with negative friction to bring linear dissipative systems within the framework of variational principle.     

Syntheses,characterizations, crystal structures,DFT/TD-DFT,luminescence behaviors and cytotoxic effect of bicompartmental Zn (II)-dicyanamide Schiff base coordination polymers: An approach to apoptosis,autophagy and necrosis type classical cell death

Two new Zn (II)-dicyanamide (dca) 1-D chain coordination polymers (CPs), [Zn (L^OMe)(μ₁-dca)(μ_1,5-dca)]_n (1) and [Zn (L^OEt)(μ₁-dca)(μ_1,5-dca)]_n (2) have been successfully synthesized from bicompartmental Schiff base ligands N,N^′-Bis(3-methoxysalicylidenimino)-1,3-diaminopropane (H₂L^OMe), N,N^′-Bis(3-ethoxysalicylidenimino)-1,3-diaminoproane (H₂L^OEt) respectively and structurally characterized using various spectroscopic protocols like ¹H NMR, IR, Raman, UV–Vis, fluorescence as well as elemental analysis, TGA, PXRD and SCXRD studies. X-ray single crystal study revealed that both the complexes have two different geometrical arrangement of Zn metal centres with distorted square pyramidal Zn(2) and trigonal prismatic geometry Zn(1). Ab-initio DFT (Density functional theory) has been executed at B3LYP (Becke, 3-parameter, Lee-Yang-Parr) using DGDVP (Diffuse gradient double valence polarised) basis set to explain FMO (Frontier molecular orbital), TD-DFT (Time-dependent density functional theory) and photovoltaic efficiency in Dye Sensitized Solar Cell (DSSC). Hirshfeld surface (HS) and 2D fingerprint plot analyses are shed more light on the non-covalent supramolecular interactions. The steady state and time-resolved fluorescence measurements have been conducted in DMSO and solid-state. CPs exhibited bi-exponential decay in DMSO as well as solid-state where fluorescence behaviors are mainly intra-ligand (π → π^*) in nature with lifetimes in the range (1.11–1.06 ns). In particular, in vitro cytotoxic activities were evaluated towards MCF7 (breast cancer) cell line, MDA-MB-231 (breast carcinoma) cell line and MCF10A (breast epithelial) cell line using MTT assay. CP 1 had lower cytotoxic effect against MCF7 (20 μM), MDA-MB-231 (15 μM) cell lines in comparison with cisplatin (42.2 ± 8, 128.2 ± 7 μM). CP 1 induced classical cell death apoptosis, autophagy and necrosis. Lower IC₅₀ value of CP 1 against MDA-MB-231 cell line provide new insights in the development of cancer therapeutics.     

Heteroleptic transition metal complexes of Schiff‐base‐derived ligands exert their antifungal activity by disrupting membrane integrity

Development of new treatment strategies and chemotherapeutic agents is urgently needed to combat the growing multidrug resistant species of Candida. In this direction, a new series of Cu (II), Co (II), Ni (II) and Zn (II) heteroleptic complexes were synthesized, characterized and evaluated for antifungal activity. Based on spectral characterization and physical measurements, an octahedral geometry was assigned to [Co(L1)(L2)ClH₂O] ( C2 ), [Ni(L1)(L2)ClH₂O] ( C3 ), [Zn(L1)(L2)ClH₂O] ( C4 ) complexes, while a distorted octahedral geometry was assigned to [Cu(L1)(L2)ClH₂O] ( C1 ) complex. All the synthesized compounds were tested for antifungal activity against 11 Candida albicans isolates, including fluconazole (FLC)‐resistant isolates, by determining minimum inhibitory concentrations (MIC) and minimum fungicidal concentrations (MFC), following CLSI guidelines. The mechanism of their antifungal activity was assessed by studying their effect on the plasma membrane using flow cytometry and quantifying the ergosterol contents. All the test compounds showed varying levels of antifungal activity. Both the ligands showed moderate antifungal activity with a median MIC value of 100 μg/mL with no fungicidal activity. Compound C3 was the most potent compound with median MIC and MFC values of 0.10 and 1.60 μg/mL, respectively. Flow cytometry analysis revealed that these compounds at MFC values disrupt the cell membrane, resulting in propidium iodide entering the cells. These compounds also reduced a considerable amount of ergosterol content after treating the cells with MIC and sub‐MIC values. This study indicates that these compounds have high antifungal activity against C. albicans, and have the potential to be developed as novel antifungal drugs.     

O-Nucleoside, S-nucleoside, and N-nucleoside probes of lumazine synthase and riboflavin synthase

Lumazine synthase catalyzes the penultimate step in the biosynthesis of riboflavin, while riboflavin synthase catalyzes the last step. O-Nucleoside, S-nucleoside, and N-nucleoside analogues of hypothetical lumazine biosynthetic intermediates have been synthesized in order to obtain structure and mechanism probes of these two enzymes, as well as inhibitors of potential value as antibiotics. Methods were devised for the selective cleavage of benzyl protecting groups in the presence of other easily reduced functionality by controlled hydrogenolysis over Lindlar catalyst. The deprotection reaction was performed in the presence of other reactive functionality including nitro groups, alkenes, and halogens. The target compounds were tested as inhibitors of lumazine synthase and riboflavin synthase obtained from a variety of microorganisms. In general, the S-nucleosides and N-nucleosides were more potent than the corresponding O-nucleosides as lumazine synthase and riboflavin synthase inhibitors, while the C-nucleosides were the least potent. A series of molecular dynamics simulations followed by free energy calculations using the Poisson-Boltzmann/surface area (MM-PBSA) method were carried out in order to rationalize the results of ligand binding to lumazine synthase, and the results provide insight into the dynamics of ligand binding as well as the molecular forces stabilizing the intermediates in the enzyme-catalyzed reaction.     

The Projection Median of a Set of Points in ℝ<Superscript><Emphasis Type="Italic">d</Emphasis></Superscript>

The projection median of a finite set of points in ℝ² was introduced by Durocher and Kirkpatrick [Computational Geometry: Theory and Applications, Vol. 42 (5), 364–375, 2009]. They proved that the projection median in ℝ² provides a better approximation of the two-dimensional Euclidean median than the center of mass or the rectilinear median, while maintaining a fixed degree of stability. In this paper we study the projection median of a set of points in ℝ ^d for d≥2. Using results from geometric measure theory we show that the d-dimensional projection median provides a (d/π)B(d/2,1/2)-approximation to the d-dimensional Euclidean median, where B(α,β) denotes the Beta function. We also show that the stability of the d-dimensional projection median is at least \frac1(d/p)B(d/2, 1/2)\frac{1}{(d/\pi)B(d/2, 1/2)}, and its breakdown point is 1/2. Based on the stability bound and the breakdown point, we compare the d-dimensional projection median with the rectilinear median and the center of mass, as a candidate for approximating the d-dimensional Euclidean median. For the special case of d=3, our results imply that the three-dimensional projection median is a (3/2)-approximation of the three-dimensional Euclidean median, which settles a conjecture posed by Durocher.     

BODIPY based ‘click on’ fluorogenic dyes: application in live cell imaging

The design, synthesis, and photophysical properties of new BODIPY-based fluorogenic ‘click on’ dyes are reported. CuAAC reaction of non-fluorescent BODIPY azide with a series of non-fluorescent alkyne molecules resulted in fluorescent triazoles which displayed up to 532-fold enhancement of fluorescence in the red region. Imaging studies confirmed the general trend of cell permeability and a cholesterol linked derivative exhibited selective localization into intracellular membranes.     

Rate coefficients for the reactions of OH with n‐propanol and iso‐propanol between 237 and 376 K

The rate coefficients for the reaction OH + CH₃CH₂CH₂OH → products (k₁) and OH + CH₃CH(OH)CH₃ → products (k₂) were measured by the pulsed‐laser photolysis–laser‐induced fluorescence technique between 237 and 376 K. Arrhenius expressions for k₁ and k₂ are as follows: k₁ = (6.2 ± 0.8) × 10^?12 exp[?(10 ± 30)/T] cm³ molecule^?1 s^?1, with k₁(298 K) = (5.90 ± 0.56) × 10^?12 cm³ molecule^?1 s^?1, and k₂ = (3.2 ± 0.3) × 10^?12 exp[(150 ± 20)/T] cm³ molecule^?1 s^?1, with k₂(298) = (5.22 ± 0.46) × 10^?12 cm³ molecule^?1 s^?1. The quoted uncertainties are at the 95% confidence level and include estimated systematic errors. The results are compared with those from previous measurements and rate coefficient expressions for atmospheric modeling are recommended. The absorption cross sections for n‐propanol and iso‐propanol at 184.9 nm were measured to be (8.89 ± 0.44) × 10^?19 and (1.90 ± 0.10) × 10^?18 cm² molecule^?1, respectively. The atmospheric implications of the degradation of n‐propanol and iso‐propanol are discussed. © 2009 Wiley Periodicals, Inc. Int J Chem Kinet 42: 10–24, 2010     

On the Bi-Hamiltonian Structure of the KdV Hierarchy

A construction procedure is derived to obtain expressions for Hamiltonian densities which characterize the bi-Hamiltonian structure of the equations in the KdV hierarchy. All results are obtained by Hamiltonizing the appropriate Lagrangian densities recently found by us. The method is seento work for both real and complex fields.