A short practical synthesis of 2′-deoxymugineic acid

A short and practical synthesis of 2′-deoxymugineic acid (DMA) has been developed via reductive alkylation with the aldehyde intermediates. No protection of azetidine-2-carboxylic acid was required and the presence of free carboxylic acid function facilitated purification by simple acid and base extractions. Furthermore, the intermediates were conveniently purified by HPLC due to the presence of chromophoric benzyl ester protecting group(s). Hydrogenolysis of the benzyl protecting groups in the final step furnished DMA in overall good yield.     

An elementary proof of a theorem of Johnson and Lindenstrauss

A result of Johnson and Lindenstrauss [13] shows that a set of n points in high dimensional Euclidean space can be mapped into an O(log n/?²)‐dimensional Euclidean space such that the distance between any two points changes by only a factor of (1 ± ?). In this note, we prove this theorem using elementary probabilistic techniques. © 2002 Wiley Periodicals, Inc. Random Struct. Alg., 22: 60–65, 2002     

Diastereoselective one-pot Wittig olefination-Michael addition and olefin cross metathesis strategy for total synthesis of cytotoxic natural product (+)-varitriol and its higher analogues

A stereoselective route for the total synthesis of anticancer marine natural product (+)-varitriol (1) is detailed herein. The impressive biological activity and interesting structural features of natural (+)-varitriol fuelled us to undertake the synthesis of some higher analogues (1a-j) of this molecule. The key features of the synthetic strategy include one-pot Wittig olefination followed by a highly diastereoselective oxa-Michael addition to assemble stereochemically pure tetrasubstituted THF moiety of the natural varitriol and olefin cross metathesis to couple the aromatic part with tetrasubstituted THF moiety. The total synthesis of title natural product is efficient with 21.8% overall yield for 9 linear steps from D-ribose and thus facilitates the more scaled-up practical route for the synthesis of 1 and its analogues as well. The synthetic (+)-varitriol (1) and its analogues were screened for their cytotoxicity. The present synthetic approach paves the way for preparation of numerous analogues of the title natural product for drug development.     

Spectral analysis for radial sections of some homogeneous vector bundles on certain noncompact Riemannian symmetric spaces

We prove an analogue of Schwartz’s theorem on spectral analysis for radial sections of some homogeneous vector bundles on noncompact Riemannian symmetric spaces. We include some results and observations regarding mean periodic functions in this case. We also observe failure of spectral analysis for various Lorentz spaces and Lebesgue spaces of radial sections and relate it with the failure of the Wiener-Tauberian theorems in this setup.     

Optimal control of effort of a stage structured prey–predator fishery model with harvesting

This paper describes a prey–predator fishery model with stage structure for prey. The adult prey and predator populations are harvested in the proposed system. The dynamic behavior of the model system is discussed. It is observed that singularity induced bifurcation phenomenon is appeared when variation of the economic interest of harvesting is taken into account. We have incorporated state feedback controller to stabilize the model system in the case of positive economic interest. Fishing effort used to harvest the adult prey and predator populations is used as a control to develop a dynamic framework to investigate the optimal utilization of the resource, sustainability properties of the stock and the resource rent earned from the resource. Pontryagin’s maximum principle is used to characterize the optimal control. The optimal system is derived and then solved numerically using an iterative method with Runge–Kutta fourth-order scheme. Simulation results show that the optimal control scheme can achieve sustainable ecosystem.     

Complementarity with complete but P-acyclic preferences

This paper extends the formulation of complementarity in Milgrom and Shannon (1994) to the case of complete but P-acyclic preferences. In such a case, quasi-supermodularity and the single-crossing property on their own do not guarantee monotone comparative statics or equilibrium existence: an additional condition, monotone closure, is required.     

Coumarin Based Fluorescent Probe for Colorimetric Detection of Fe<Superscript>3+</Superscript> and Fluorescence Turn On-Off Response of Zn<Superscript>2+</Superscript> and Cu<Superscript>2+</Superscript>

A new coumarin based Schiff-base chemosensor-(E)-7-(((8-hydroxyquinolin-2-yl)methylene) amino)-4-methyl-2H-chromen-2-one (H ₁₁ L) was synthesized and evaluated as a colorimetric sensor for Fe³⁺ and fluorescence “turn on-off” response of Zn²⁺ and Cu²⁺ using absorption and fluorescence spectroscopy. Upon treatment with Fe³⁺ and Zn²⁺, the absorption intensity as well as the fluorescence emission intensity increases drastically compared to other common alkali, alkaline earth and transition metal ions, with a distinct color change which provide naked eye detection. Formation of 1:1 metal to ligand complex has been evaluated using Benesi-Hildebrand relation, Job’s plot analyses, ¹H NMR titration as well as ESI-Mass spectral analysis. The complex solution of H ₁₁ L with Zn²⁺ ion exhibited reversibility with EDTA and regenerate free ligand for further Zn²⁺ sensing. H ₁₁ L exhibits two INHIBIT logic gates with two different chemical inputs (i) Zn²⁺ (IN1) and Cu²⁺ (IN2) and (ii) Zn²⁺ (IN1) and EDTA (IN2) and the emission as output. Again, an IMPLICATION logic gate is obtained with Cu²⁺ and EDTA as chemical inputs and emission as output mode. Both free ligand as well as metal-complexes was optimized using density functional theory to interpret spectral properties. The corresponding energy difference between HOMO-LUMO energy gap for H ₁₁ L, H₁₁L-Zn²⁺ and H₁₁L-Cu²⁺ are 2.193, 1.834 and 0.172 eV, respectively.     

Structure and orientation of an intermetallic phase in a W-Ni-Co alloy

The aim of this investigation is crystal structure determination of an intermetallic phase formed in a W-Ni-Co alloy during a heat-treatment carried out at a temperature of 800°C. This intermetallic phase is expected to play a critical role on the final microstructure (fine tungsten particles in an FCC matrix that is present in between large tungsten grains) and thereby, on the properties of the alloy. 92W-5.3Ni-2.7Co alloy was prepared through powder metallurgy route (liquid phase sintering) followed by heat-treatment at 800°C for 5?h. The intermetallic phase formed at this temperature was characterised using transmission and scanning electron microscopes. The intermetallic phase was found to have orthorhombic crystal structure with Pnam (62) space group as determined using automated diffraction tomography along with precession electron diffraction. Chemical analysis in TEM suggested that the intermetallic phase is based on stoichiometry (Co,Ni)₂W. Orientation imaging of the phase was also carried out in TEM and EBSD to understand its evolution. Equiaxed or lath morphology of the intermetallic phase was found to depend on the crystallographic orientation relationship of the phase with the tungsten grains and the matrix phase.