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.     

Enantioconvergent Biohydrolysis of Racemic Styrene Oxide to R-phenyl-1, 2-ethanediol by a Newly Isolated Filamentous Fungus Aspergillus tubingensis TF1

An effort was made to isolate biocatalysts hydrolyzing epoxides from various ecological niches of northeast India, a biodiversity hot spot zone of the world and screened for epoxide hydrolase activity to convert different racemic epoxides to the corresponding 1, 2-vicinal diols. Screening of a total of 450 microorganisms isolated was carried out using NBP colorimetric assay. One of the strains TF1, after internal transcribed spacer sequence analysis, identified as Aspergillus tubingensis, showed promising enantioconvergent epoxide hydrolase activity. The hydrolysis of unsubstituted styrene oxide (1) occurred to give 97 % ee of R-(?)-1-phenylethane-1, 2-diol (6) with more than 99 % conversion within 45 min incubation. It is shown to be a cheap and practical biocatalyst for one step asymmetric synthesis of chiral R-diol. The other representative substrates (2–5), although underwent hydrolysis with more than 99 % conversion beyond 15 h, exhibited poor enantioselectivity.     

Kinetic studies of the reactions of O2(b 1sigma(g)+) with several atmospheric molecules

Thermal rate coefficients for the removal (reaction + quenching) of O2(1sigma(g)+) by collision with several atmospheric molecules were determined to be as follows: O3, k3(210-370 K) = (3.63 +/- 0.86) x 10(-11) exp((-115 +/- 66)/T); H2O, k4(250-370 K) = (4.52 +/- 2.14) x 10(-12) exp((89 +/- 210)/T); N2, k5(210-370 K) = (2.03 +/- 0.30) x 10(-15) exp((37 +/- 40)/T); CO2, k6(298 K) = (3.39 +/- 0.36) x 10(-13); CH4, k7(298 K) = (1.08 +/- 0.11) x 10(-13); CO, k8(298 K) = (3.74 +/- 0.87) x 10(-15); all units in cm3 molecule(-1) s(-1). O2(1sigma(g)+) was produced by directly exciting ground-state O2(3sigma(g)-) with a 762 nm pulsed dye laser. The reaction of O2(1sigma(g)+) with O3 was used to produce O(3P), and temporal profiles of O(3P) were measured using VUV atomic resonance fluorescence in the presence of the reactant to determine the rate coefficients for removal of O2(1sigma(g)+). Our results are compared with previous values, where available, and the overall trend in the O2(1sigma(g)+) removal rate coefficients and the atmospheric implications of these rate coefficients are discussed. Additionally, an upper limit for the branching ratio of O2(1sigma(g)+) + CO to give O(3P) + CO2 was determined to be < or = 0.2% and this reaction channel is shown to be of negligible importance in the atmosphere.     

CF3CF=CH2 and (Z)-CF3CF=CHF: temperature dependent OH rate coefficients and global warming potentials

Rate coefficients over the temperature range 206-380 K are reported for the gas-phase reaction of OH radicals with 2,3,3,3-tetrafluoropropene (CF(3)CF=CH(2)), k(1)(T), and 1,2,3,3,3-pentafluoropropene ((Z)-CF(3)CF=CHF), k(2)(T), which are major components in proposed substitutes for HFC-134a (CF(3)CFH(2)) in mobile air-conditioning units. Rate coefficients were measured under pseudo-first-order conditions in OH using pulsed-laser photolysis to produce OH and laser-induced fluorescence to detect it. Rate coefficients were found to be independent of pressure between 25 and 600 Torr (He, N(2)). For CF(3)CF=CH(2), the rate coefficients, within the measurement uncertainty, are given by the Arrhenius expression k(1)(T)=(1.26+/-0.11) x 10(-12) exp[(-35+/-10)/T] cm(3) molecule(-1) s(-1) where k(1)(296 K)=(1.12+/-0.09) x 10(-12) cm(3) molecule(-1) s(-1). For (Z)-CF(3)CF=CHF, the rate coefficients are given by the non-Arrhenius expression k(2)(T)=(1.6+/-0.2) x 10(-18)T(2) exp[(655+/-50)/T] cm(3) molecule(-1) s(-1) where k(2)(296 K)=(1.29+/-0.06) x 10(-12) cm(3) molecule(-1) s(-1). Over the temperature range most relevant to the atmosphere, 200-300 K, the Arrhenius expression k(2)(T)=(7.30+/-0.7) x 10(-13) exp[(165+/-20)/T] cm(3) molecule(-1) s(-1) reproduces the measured rate coefficients very well and can be used in atmospheric model calculations. The quoted uncertainties in the rate coefficients are 2sigma (95% confidence interval) and include estimated systematic errors. The global warming potentials for CF(3)CF=CH(2) and (Z)-CF(3)CF=CHF were calculated to be <4.4 and <3.6, respectively, for the 100 year time horizon using infrared absorption cross sections measured in this work, and atmospheric lifetimes of 12 and 10 days that are based solely on OH reactive loss.     

Synthesis of terminal disaccharide unit of Klebsiella pneumoniae ssp. R20

Synthesis of the terminal disaccharide unit of a novel α-(1→2) linked heptoglycan of K. pneumoniae ssp. strain R20 from methyl α-d-mannopyranoside has been presented. Central to the strategy is the application of Sharpless asymmetric dihydroxylation to introduce a new center at C-6 position of mannopyranoside. The coupling of two heptoglycans (12 and 13) was accomplished by a Lewis acid catalyst.     

Noether-Symmetry Analysis using Alternative Lagrangian Representations

We have sought to work with an approach to Noether symmetry analysis which uses the properties of infinitesimal point transformations in the space-time (q, t) variable to establish the association between symmetries and conservation laws of a dynamical system. In this approach symmetries are expressed in the form of generators. We have studied the variational or Noether symmetries of two uncoupled Harmonic oscillators and two such oscillators coupled by an interaction. Both these systems can have alternative Lagrangian representations. We have studied in detail how the association between symmetries and conservation laws changes as one alters the analytic or Lagrangian representation. This analysis is carried out with a view to explicitly demonstrate that the correlation between symmetry transformation and corresponding invariant quantity depends crucially on the choice of the analytic representation. PACS 45.20.Jj, 45.20.df, 45.20.dh     

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.     

Synthesis and structure-activity relationship study of isoglobotrihexosylceramide analogues

Invariant natural killer T (iNKT) cells are innate T lymphocytes that express T cell receptors binding to exogenous and endogenous glycosphingolpid antigens presented by a nonpolymorphic, non-MHC antigen presenting molecule, CD1d. The endogenous glycosphingolipid metabolite, isoglobotrihexosylceramide (iGb3), is the first known natural ligand for both human and mouse iNKT cells, whose activity has been confirmed in a variety of iNKT cell clones generated by different investigators, representing the majority of the iNKT cell population. The signaling pathway mediated by T cell receptor is largely influenced by the structural variation of glycosphingolpid antigens, leading to multiple and varied biological functions of iNKT cells. In order to investigate the structural requirements behind iGb3 triggered iNKT cell activation, the structure-activity relationship (SAR) of iGb3 needs to be characterized. In this study, iGb3 analogues containing 2' ', 3' ', 4' ' and 6' ' deoxy terminal galactose were synthesized for probing the SAR between iGb3 and TCR. The biological assays on the synthetic iGb3 analogues were performed with use of the murine iNKT cell hybridoma DN32.D3. The results showed that the 2' ' and 3' ' hydroxyl groups of terminal galactose play more important roles for the recognition of iGb3 by TCR; while 4' ' and 6' ' hydroxyl groups were not as crucial for this recognition. These studies might help to understand the general structural requirements for natural endogenous ligands recognized by iNKT cells.