Metal‐Chelated Polymer Nanodiscs for NMR Studies

Paramagnetic relaxation enhancement (PRE) is commonly used to speed up spin lattice relaxation time (T₁) for rapid data acquisition in NMR structural studies. Consequently, there is significant interest in novel paramagnetic labels for enhanced NMR studies on biomolecules. Herein, we report the synthesis and characterization of a modified poly(styrene‐co‐maleic acid) polymer which forms nanodiscs while showing the ability to chelate metal ions. Cu²⁺‐chelated nanodiscs are demonstrated to reduce the T₁ of protons for both polymer and lipid‐nanodisc components. The chelated nanodiscs also decrease the proton T₁ values for a water‐soluble DNA G‐quadruplex. These results suggest that polymer nanodiscs functionalized with paramagnetic tags can be used to speed‐up data acquisition from lipid bilayer samples and also to provide structural information from water‐soluble biomolecules.     

Characterization of Tm doped mixed alkali borate glasses—spectroscopic investigations

The effect of mixed alkalis on the optical absorption spectra of Tm³⁺ in xNa₂O·(30−x)K₂O·70B₂O₃ glasses has been studied. The optical band gap values (E_opt) for both direct and indirect transitions have been obtained using Davis and Mott theory. Spectroscopic parameters like Racah (E¹, E² and E³), spin-orbit (ξ_4f) and Judd-Ofelt intensity parameters (, and ) have been calculated for different x values. Radiative transition probabilities (A_rad), radiative lifetimes (τ_R), branching ratios (β), integrated absorption cross sections (Σ) and multiphonon relaxation rates (W_MPR) are calculated for certain excited states of Tm³⁺ ion. The observed trends in the above parameters as a function of x in these borate glasses have been discussed keeping in view the effect of mixed alkalies in borate glasses. Certain potential lasing transitions have been identified for laser action among the various transitions of Tm³⁺ in these mixed alkali borate glasses.     

Scaling group analysis of bioconvective micropolar fluid flow and heat transfer in a porous medium

Journal of Thermal Analysis and Calorimetry - The current and potential applications of bioconvection renewed drive for theoretical research on synthesis and process control in biofuel cells and...     

<Emphasis Type="Italic">hp</Emphasis>-Discontinuous Galerkin methods for strongly nonlinear elliptic boundary value problems

In this paper, we have analyzed a one parameter family of hp-discontinuous Galerkin methods for strongly nonlinear elliptic boundary value problems with Dirichlet boundary conditions. These methods depend on the values of the parameter , where θ = + 1 corresponds to the nonsymmetric and θ = −1 corresponds to the symmetric interior penalty methods when and f(u,∇u) = −f, that is, for the Poisson problem. The error estimate in the broken H ¹ norm, which is optimal in h (mesh size) and suboptimal in p (degree of approximation) is derived using piecewise polynomials of degree p ≥ 2, when the solution . In the case of linear elliptic problems also, this estimate is optimal in h and suboptimal in p. Further, optimal error estimate in the L ² norm when θ = −1 is derived. Numerical experiments are presented to illustrate the theoretical results. Supported by DST-DAAD (PPP-05) project.     

An -local discontinuous Galerkin method for some quasilinear elliptic boundary value problems of nonmonotone type

In this paper, an -local discontinuous Galerkin method is applied to a class of quasilinear elliptic boundary value problems which are of nonmonotone type. On -quasiuniform meshes, using the Brouwer fixed point theorem, it is shown that the discrete problem has a solution, and then using Lipschitz continuity of the discrete solution map, uniqueness is also proved. A priori error estimates in broken norm and norm which are optimal in , suboptimal in are derived. These results are exactly the same as in the case of linear elliptic boundary value problems. Numerical experiments are provided to illustrate the theoretical results.

     

Synthesis, reactivity studies, structural aspects, and solution behavior of half sandwich ruthenium(II) N,N',N'-triarylguanidinate complexes

[(η(6)-C(10)H(14))RuCl(μ-Cl)](2) (η(6)-C(10)H(14) = η(6)-p-cymene) was subjected to a bridge-splitting reaction with N,N',N'-triarylguanidines, (ArNH)(2)C═NAr, in toluene at ambient temperature to afford [(η(6)-C(10)H(14))RuCl{κ(2)(N,N')((ArN)(2)C-N(H)Ar)}] (Ar = C(6)H(4)Me-4 (1), C(6)H(4)(OMe)-2 (2), C(6)H(4)Me-2 (3), and C(6)H(3)Me(2)-2,4 (4)) in high yield with a view aimed at understanding the influence of substituent(s) on the aryl rings of the guanidine upon the solid-state structure, solution behavior, and reactivity pattern of the products. Complexes 1-3 upon reaction with NaN(3) in ethanol at ambient temperature afforded [(η(6)-C(10)H(14))RuN(3){κ(2)(N,N')((ArN)(2)C-N(H)Ar)}] (Ar = C(6)H(4)Me-4 (5), C(6)H(4)(OMe)-2 (6), and C(6)H(4)Me-2 (7)) in high yield. [3 + 2] cycloaddition reaction of 5-7 with RO(O)C-C≡C-C(O)OR (R = Et (DEAD) and Me (DMAD)) (diethylacetylenedicarboxylate, DEAD; dimethylacetylenedicarboxylate, DMAD) in CH(2)Cl(2) at ambient temperature afforded [(η(6)-C(10)H(14))Ru{N(3)C(2)(C(O)OR)(2)}{κ(2)(N,N')((ArN)(2)C-N(H)Ar)}]·xH(2)O (x = 1, R = Et, Ar = C(6)H(4)Me-4 (8·H(2)O); x = 0, R = Me, Ar = C(6)H(4)(OMe)-2 (9), and C(6)H(4)Me-2 (10)) in moderate yield. The molecular structures of 1-6, 8·H(2)O, and 10 were determined by single crystal X-ray diffraction data. The ruthenium atom in the aforementioned complexes revealed pseudo octahedral "three legged piano stool" geometry. The guanidinate ligand in 2, 3, and 6 revealed syn-syn conformation and that in 4, and 10 revealed syn-anti conformation, and the conformational difference was rationalized on the basis of subtle differences in the stereochemistry of the coordinated nitrogen atoms caused by the aryl moiety in 3 and 4 or steric overload caused by the substituents around the ruthenium atom in 10. The bonding pattern of the CN(3) unit of the guanidinate ligand in the new complexes was explained by invoking n-π conjugation involving the interaction of the NHAr/N(coord)Ar lone pair with C═Nπ* orbital of the imine unit. Complexes 1, 2, 5, 6, 8·H(2)O, and 9 were shown to exist as a single isomer in solution as revealed by NMR data, and this was ascribed to a fast C-N(H)Ar bond rotation caused by a less bulky aryl moiety in these complexes. In contrast, 3 and 10 were shown to exist as a mixture of three and five isomers in about 1:1:1 and 1·0:1·2:2·7:3·5:6·9 ratios, respectively in solution as revealed by a VT (1)H NMR, (1)H-(1)H COSY in conjunction with DEPT-90 (13)C NMR data measured at 233 K in the case of 3. The multiple number of isomers in solution was ascribed to the restricted C-N(H)(o-tolyl) bond rotation caused by the bulky o-tolyl substituent in 3 or the aforementioned restricted C-NH(o-tolyl) bond rotation as well as the restricted ruthenium-arene(centroid) bond rotation caused by the substituents around the ruthenium atom in 10.     

Solution- and solid-phase, modular approaches for obtaining different natural product-like polycyclic architectures from an aminoindoline scaffold for combinatorial chemistry

With the goal of developing a modular approach leading to different indoline alkaloid natural-product-like tricyclic derivatives having an unsaturated lactam (see compounds 13, 14, and 16), an aminoindoline-based bicyclic scaffold 10 was obtained from 9. The selective deprotection of the indoline NTeoc or benzylic NHAlloc in compound 10, followed by N-acryloylation and then subjection to a ring-closing metathesis reaction, successfully led to obtaining two different architectures (13/14 and 16) having an unsaturated lactam functionality. This modular solution-phase methodology was then developed on solid phase. To achieve this objective, the aminoindoline bicyclic scaffold having an additional hydroxyl group could be immobilized onto the solid support using alkylsilyl linker-based polystyrene macrobeads, giving 18. By applying a ring-closing metathesis approach, 20 (tricyclic derivative with seven-membered-ring unsaturated lactam) and 23 (tricyclic derivative with eight-membered-ring unsaturated lactam) were then obtained from 18 in a number of steps.     

Synthesis and photoelectron spectroscopic studies of N(CH2CH2NMe)3P=E (E = O, S, NH, CH2)

The synthesis and the crystal and molecular structure of N(CH(2)CH(2)NMe)(3)P=CH(2) is reported. The P-N(ax) distance is rather long in N(CH(2)CH(2)NMe)(3)P=CH(2). The ylide N(CH(2)CH(2)NMe)(3)P=CH(2) proved to be a stronger proton acceptor than proazaphosphatrane N(CH(2)CH(2)NMe)(3)P, since it was shown to deprotonate N(CH(2)CH(2)NMe)(3)PH(+). The extremely strong basicity of the ylide is in accordance with its low ionization energy (6.3 eV), which is the lowest in the presently investigated series N(CH(2)CH(2)NMe)(3)P=E (E: CH(2), NH, lone pair, O and S), and to the best of our knowledge it is the smallest value observed for a non-conjugated phosphorus ylide. Computations reveal the existence of two bond strech isomers, and the stabilization of the phosphorus centered cation by electron donation from the equatorial and the axial nitrogens. Similar stabilizing effects operate in the case of protonation of E. A fine balance of these different interactions determines the P-N(ax) distance, which is thus very sensitive to the level of the theory applied. According to the quantum mechanical calculations, methyl substitution at the equatorial nitrogens flattens the pyramidality of this atom, increasing its electron donor capability. As a consequence, the PN(ax) distance in the short-transannular bonded protonated systems and the radical cations is longer by about 0.5 A in the N(eq)(Me) than in the N(eq)(H) systems. Accordingly, isodesmic reaction energies show that a stabilization of about 25 and 10 kcal/mol is attributable to the formation of the transannular bond in case of N(eq)(H) and the experimentally realizable N(eq)(Me) species, respectively.     

An efficient approach towards three component coupling of one pot reaction for synthesis of functionalized benzopyrans

Three component coupling of one pot reaction which servers as the most convenient route to the synthesis of benzopyran derivatives using the TiCl₄ catalyst (10 mol %) under solvent free conditions is described. The procedure offers a systematic method with a number of advantages including operational simplicity, neat reactions, reduced reaction time, high yields of products and applicability to large scale reactions.     

A unifying theory of a posteriori error control for discontinuous Galerkin FEM

A unified a posteriori error analysis is derived in extension of Carstensen (Numer Math 100:617–637, 2005) and Carstensen and Hu (J Numer Math 107(3):473–502, 2007) for a wide range of discontinuous Galerkin (dG) finite element methods (FEM), applied to the Laplace, Stokes, and Lamé equations. Two abstract assumptions (A1) and (A2) guarantee the reliability of explicit residual-based computable error estimators. The edge jumps are recast via lifting operators to make arguments already established for nonconforming finite element methods available. The resulting reliable error estimate is applied to 16 representative dG FEMs from the literature. The estimate recovers known results as well as provides new bounds to a number of schemes. C. Carstensen and M. Jensen supported by the DFG Research Center MATHEON “Mathematics for key technologies” in Berlin and the Hausdorff Institute of Mathematics in Bonn, Germany. C. Carstensen, T. Gudi, and M. Jensen supported by DST-DAAD (PPP-05) project no. 32307481.