Production of Metabolites with Antioxidant and Emulsifying Properties by Antarctic Strain Sporobolomyces salmonicolor AL1

The Sporobolomyces salmonicolor AL₁ Antarctic strain was cultivated and two bioproducts were obtained: exopolysaccharide and biomass. The biologically active substances ergosterol, torularhodin, torulene, β-carotene and CoQ₁₀ were extracted from the biomass and were quantified as follows: ergosterol 5.2?±?0.2 mg/g, torularhodin 458.3?±?24.5 μg/g, torulene 273.7?±?14.5 μg/g, β-carotene 129.2?±?7.3 μg/g and coenzyme Q₁₀ (CoQ₁₀) 236.1?±?12.1 μg/g. Their antioxidant activity was estimated according to the cathode voltammetry method. The most pronounced antioxidant activity (according to trolox) was exhibited by β-carotene 3.78, followed by CoQ₁₀ 3.60, both of them being the main contributors to the total extract activity of 3.19. The biologically active metabolites in combination with exoglucomannan as emulsifier were used for the creation of model emulsion systems characterised by great stability. The absorption of UVA rays by the model emulsions was studied.     

Methoxy-derivatization of alkyl chains increases the in vivo efficacy of cationic Mn porphyrins. Synthesis, characterization, SOD-like activity, and SOD-deficient E. coli study of meta Mn(III) N-methoxyalkylpyridylporphyrins

Cationic Mn(III) N-alkylpyridylporphyrins (MnPs) are potent SOD mimics and peroxynitrite scavengers and diminish oxidative stress in a variety of animal models of central nervous system (CNS) injuries, cancer, radiation, diabetes, etc. Recently, properties other than antioxidant potency, such as lipophilicity, size, shape, and bulkiness, which influence the bioavailability and the toxicity of MnPs, have been addressed as they affect their in vivo efficacy and therapeutic utility. Porphyrin bearing longer alkyl substituents at pyridyl ring, MnTnHex-2-PyP(5+), is more lipophilic, thus more efficacious in vivo, particularly in CNS injuries, than the shorter alkyl-chained analog, MnTE-2-PyP(5+). Its enhanced lipophilicity allows it to accumulate in mitochondria (relative to cytosol) and to cross the blood-brain barrier to a much higher extent than MnTE-2-PyP(5+). Mn(III) N-alkylpyridylporphyrins of longer alkyl chains, however, bear micellar character, and when used at higher levels, become toxic. Recently we showed that meta isomers are ～10-fold more lipophilic than ortho species, which enhances their cellular accumulation, and thus reportedly compensates for their somewhat inferior SOD-like activity. Herein, we modified the alkyl chains of the lipophilic meta compound, MnTnHex-3-PyP(5+) via introduction of a methoxy group, to diminish its toxicity (and/or enhance its efficacy), while maintaining high SOD-like activity and lipophilicity. We compared the lipophilic Mn(III) meso-tetrakis(N-(6'-methoxyhexyl)pyridinium-3-yl)porphyrin, MnTMOHex-3-PyP(5+), to a hydrophilic Mn(III) meso-tetrakis(N-(2'-methoxyethyl)pyridinium-3-yl)porphyrin, MnTMOE-3-PyP(5+). The compounds were characterized by uv-vis spectroscopy, mass spectrometry, elemental analysis, electrochemistry, and ability to dismute O(2)˙(-). Also, the lipophilicity was characterized by thin-layer chromatographic retention factor, R(f). The SOD-like activities and metal-centered reduction potentials for the Mn(III)P/Mn(II)P redox couple were similar-to-identical to those of N-alkylpyridyl analogs: log k(cat) = 6.78, and E(1/2) = +68 mV vs. NHE (MnTMOHex-3-PyP(5+)), and log k(cat) = 6.72, and E(1/2) = +64 mV vs. NHE (MnTMOE-3-PyP(5+)). The compounds were tested in a superoxide-specific in vivo model: aerobic growth of SOD-deficient E. coli, JI132. Both MnTMOHex-3-PyP(5+) and MnTMOE-3-PyP(5+) were more efficacious than their alkyl analogs. MnTMOE-3-PyP(5+) is further significantly more efficacious than the most explored compound in vivo, MnTE-2-PyP(5+). Such a beneficial effect of MnTMOE-3-PyP(5+) on diminished toxicity, improved efficacy and transport across the cell wall may originate from the favorable interplay of the size, length of pyridyl substituents, rotational flexibility (the ortho isomer, MnTE-2-PyP(5+), is more rigid, while MnTMOE-3-PyP(5+) is a more flexible meta isomer), bulkiness and presence of oxygen.     

Homological Mirror Symmetry for manifolds of general type

In this paper we outline the foundations of Homological Mirror Symmetry for manifolds of general type. Both Physics and Categorical prospectives are considered.     

Uniformly Convergent Multigrid Methods for Convection–Diffusion Problems without Any Constraint on Coarse Grids

We construct a class of multigrid methods for convection–diffusion problems. The proposed algorithms use first order stable monotone schemes to precondition the second order standard Galerkin finite element discretization. To speed up the solution process of the lower order schemes, cross-wind-block reordering of the unknowns is applied. A V-cycle iteration, based on these algorithms, is then used as a preconditioner in GMRES. The numerical examples show that this method is convergent without imposing any constraint on the coarsest grid and the convergence of the preconditioned method is uniform.     

Derived categories of Keum's fake projective planes

We conjecture that derived categories of coherent sheaves on fake projective n  -spaces have a semi-orthogonal decomposition into a collection of n+1$n+1$ exceptional objects and a category with vanishing Hochschild homology. We prove this for fake projective planes with non-abelian automorphism group (such as Keum's surface). Then by passing to equivariant categories we construct new examples of phantom categories with both Hochschild homology and Grothendieck group vanishing.     

CONVERGENCE ANALYSIS ON ITERATIVE METHODS FOR SEMIDEFINITE SYSTEMS

The convergence analysis on the general iterative methods for the symmetric and positive semidefinite problems is presented in this paper. First, formulated are refined necessary and sumcient conditions for the energy norm convergence for iterative methods. Some illustrative examples for the conditions are also provided. The sharp convergence rate identity for the Gauss-Seidel method for the semidefinite system is obtained relying only on the pure matrix manipulations which guides us to obtain the convergence rate identity for the general successive subspace correction methods. The convergence rate identity for the successive subspace correction methods is obtained under the new conditions that the local correction schemes possess the local energy norm convergence. A convergence rate estimate is then derived in terms of the exact subspace solvers and the parameters that appear in the conditions. The uniform convergence of multigrid method for a model problem is proved by the convergence rate identity. The work can be regradled as unified and simplified analysis on the convergence of iteration methods for semidefinite problems [8, 9].     

Improving the rate of convergence of ‘high order finite elements’ on polygons and domains with cusps

Summary. Let u and u_V V be the solution and, respectively, the discrete solution of the non-homogeneous Dirichlet problem u=f on , u|=0. For any m and any bounded polygonal domain , we provide a construction of a new sequence of finite dimensional subspaces V_n such that where f H^m–1() is arbitrary and C is a constant that depends only on and not on n (we do not assume u H^m+1()). The existence of such a sequence of subspaces was first proved in a ground–breaking paper by Babuka [8]. Our method is different; it is based on the homogeneity properties of Sobolev spaces with weights and the well–posedness of non-homogeneous Dirichlet problem in suitable Sobolev spaces with weights, for which we provide a new proof, and which is a substitute of the usual shift theorems for boundary value problems in domains with smooth boundary. Our results extended right away to domains whose boundaries have conical points. We also indicate some of the changes necessary to deal with domains with cusps. Our numerical computation are in agreement with our theoretical results.The authors were supported in part by the NSF grant DMS 02-09497. Victor Nistor was also partially supported by NSF grant DMS 02-00808.     

Local Fourier Analysis of Multigrid Methods with Polynomial Smoothers and Aggressive Coarsening

We focus on the study of multigrid methods with aggressive coarsening and polynomial smoothers for the solution of the linear systems corresponding to finite difference/element discretizations of the Laplace equation. Using local Fourier analysis we determine automatically the optimal values for the parameters involved in defining the polynomial smoothers and achieve fast convergence of cycles with aggressive coarsening. We also present numerical tests supporting the theoretical results and the heuristic ideas. The methods we introduce are highly parallelizable and efficient multigrid algorithms on structured and semi-structured grids in two and three spatial dimensions.