Unified Galerkin- and DAE-Based Approximation of Fractional Order Systems

We consider numerical solutions of nonlinear multiterm fractional integrodifferential equations, where the order of the highest derivative is fractional and positive but is otherwise arbitrary. Here, we extend and unify our previous work, where a Galerkin method was developed for efficiently approximating fractional order operators and where elements of the present differential algebraic equation (DAE) formulation were introduced. The DAE system developed here for arbitrary orders of the fractional derivative includes an added block of equations for each fractional order operator, as well as forcing terms arising from nonzero initial conditions. We motivate and explain the structure of the DAE in detail. We explain how nonzero initial conditions should be incorporated within the approximation. We point out that our approach approximates the system and not a specific solution. Consequently, some questions not easily accessible to solvers of initial value problems, such as stability analyses, can be tackled using our approach. Numerical examples show excellent accuracy. DOI: 10.1115/1.4002516]

A norbornadiene–cyclobutadiene cycloaddition cascade: novel intramolecular σ2+π2 trapping of a cyclobutane ring

Norbornadiene and 1,2-bismethoxycarbonylcyclobutadiene furnish a novel heptacyclic system 3(whose X-ray crystal structure has been determined)and an annulated pterodactylane derivative 4 in a single step.

A porphyrin bearing tetrahydrothiophene pickets; co-ordination behaviour and electron transfer

A novel ‘picket-fence’ porphyrin, 5,10,15,20-tetrakis[o-(tetrahydro-2-thenoylamino)phenyl]porphyrin (H2L) with ligating tetrahydrothiophene rings disposed perpendicular to the porphyrin plane has been synthesised. Its zinc(II) derivative, [ZnL], binds two silver(I) ions co-operatively with a dissociation constant of 4.8 × 10–8 dm3 mol–1. Time-resolved fluorescence lifetime measurements reveal the presence of intramolecular photoexcited electron transfer in this donor–acceptor system.

Potassamide induced in situ alkylation of 5,6-dihydroisoquinolines: Structure of products

Potassamide induced in situ alkylation of 1-alkyl- 4-cyano-3-methoxy-5,6-dihydroisoquinolines (2a & 2b) with alkyl iodides (CH3I, CH3CH2I & cyclohexyl iodide) gave the 5-alkyl- and 5,9-dialkyl-5,6-dihydroisoquinolines (4–ad & 3a–e), isoquinoline derivatives, (5a–b) and diastereomeric mixture of 4- alkyl-1,2,3,4-tetrahydroisoquinolin-3(2H)-ones (6a–e & 6′a–e). Structures were assigned on the basis of spectral data [Mass, 1H & 13C NMR, 2D NOESY & HC-COLOC]. Amide induced in situ alkylation of compounds 3a and 4a with CH3I gave in almost quantitative yield the dimethylated compounds 3d and 3a respectively. While KNH2/liq.NH3 methylation of 1,2- dihydroisoquinoline, 1 with CH3I gave the mixture of compounds, 6a & 6′a and the isoquinoline derivative 5a, NaH/benzene reaction of 1 with CH3I gave exclusively 5a. N-methylation of the mixture of compounds 6a & 6′a with NaH/CH3I gave the methylated derivatives, 7 & 8. A suitable mechanism has been proposed for the formation of products.

Maximum-entropy calculation of the electron density at 4 A resolution of Pf1 filamentous bacteriophage

A 4 A electron-density map of Pf1 filamentous bacterial virus has been calculated from x-ray fiber diffraction data by using the maximum-entropy method. This method produces a map that is free of features due to noise in the data and enables incomplete isomorphous-derivative phase information to be supplemented by information about the nature of the solution. The map shows gently curved (banana-shaped) rods of density about 70 A long, oriented roughly parallel to the virion axis but slewing by about 1/6th turn while running from a radius of 28 A to one of 13 A. Within these rods, there is a helical periodicity with a pitch of 5 to 6 A. We interpret these rods to be the helical subunits of the virion. The position of strongly diffracted intensity on the x-ray fiber pattern shows that the basic helix of the virion is right handed and that neighboring nearly parallel protein helices cross one another in an unusual negative sense.

Syntheses, spectroscopy, structures, and conformations of .lambda.3-cyclotriphosphazanes: role of negative hyperconjugation

The reactions of As-chlorocyclotriphosphazane [EtNPCl], with phenols or trifluoroethanol yield the respective aryloxy- or trifluoroethoxy-containingX 3-cyclotriphosphazanes [EtNP(OR)]3 (R = C6H4Br-4 (2),C 6H5 (3C,6 H3-Mez-3,5 (4), C6H3Mez-2,6 (5), CH2CF3 (6)) as their cis-transisomericmixtures. The products have beencharacterized by IRand NMRspectroscopy. Thecrystalstructuresofboth thecis (2a) and trans(2b) isomer_softhep-bromophenoxy derivative have been determined by X-ray diffraction. Crystal data for 2a: triclinic, P1, a = 9.872(4) A, b = 13.438(6) A, c = 13.548(8) A, CY = 117.02(5)', 0 = 96.00(6)', y = 105.38(4)O, Z = 2, final R = 0.080. Crystal data for 2b: monoclinic, P21/n, a = 12.721(6) A, b = 13.468(7) A, c = 17.882(5) A, /3 = 101.62(3)O, Z = 4, final R = 0.066. The cis isomer exhibits a chair-triaxial conformation and the trans isomer a boat-triaxial conformation. Conformational preferences of X3-cyclotriphosphazanes have been probed by both MNDO and ab initio calculations on model systems [HNPXIp (X = H, F). In addition to vicinal lone pair repulsions, negative hyperconjugative interactions involving the nitrogen lone pairs and adjacent P-X Q* orbitals are found to be important (especially when X is an electronegative substituent) in determining the conformational preferences of X3-cyclotriphosphazanes. The calculations also show that the axial - equatorial conversion at phosphorus has a large activation barrier in these systems

Grinding abrasive wear and associated particle size effect

The type of abrasion that the grinding medium experiences inside a ball mill is classified as high stress or grinding abrasion, because the stress levels at the surface of the medium exceed the yield stress of the metal when hard abrasives are crushed. During dry grinding of ores the medium undergoes not only abrasion but also erosion and impact. As all three mechanisms of wear occur simultaneously, it is difficult to follow the individual components of wear. However, it is possible to show that the overall kinetics of wear follows a simple power law of the type w = at(b), where w is the weight loss of the grinding medium for a specified grinding time t and a and b are constants. Experimental data, obtained from dry grinding of quartz for a wide range of times using AISI 52100 steel balls having various microstructures in a laboratory scale batch mill, are fitted to the proposed equation and the wear rate w is calculated from the first derivative of the equation. The mean particle sizes of the quartz charge DBAR corresponding to 50 and 80% retained size are determined by mechanical sieving of the ground product after a grinding time t and thus the relationship between wear rate and particle size of the abrasive is established. It is found that w increases rapidly with DBAR up to some critical size and then increases at a much lower rate.

Recognition of Polycyclic Aromatic Hydrocarbons and Their Derivatives by the 1,3-Dinaphthalimide Conjugate of Calix4]arene: Emission, Absorption, Crystal Structures, and Computational Studies

Polycyclic aromatic hydrocarbons (PAHs) are environmental pollutants as well as well-known carcinogens. Therefore, it is important to develop an effective receptor for the detection and quantification of such molecules in solution. In view of this, a 1,3-dinaphthalimide derivative of calix4]arene (L) has been synthesized and characterized, and the structure has been established by single crystal XRD. In the crystal lattice, intermolecular arm-to-arm pi center dot center dot center dot pi overlap dominates and thus L becomes a promising receptor for providing interactions with the aromatic species in solution, which can be monitored by following the changes that occur in its fluorescence and absorption spectra. On the basis of the solution studies carried out with about 17 derivatives of the aromatic guest molecular systems, it may be concluded that the changes that occur in the fluorescence intensity seem to be proportional to the number of aromatic rings present and thus proportional to the extent of pi center dot center dot center dot pi interaction present between the naphthalimide moieties and the aromatic portion of the guest molecule. Though the nonaromatic portion of the guest species affects the fluorescence quenching, the trend is still based on the number of rings present in these. Four guest aldehydes are bound to L with K-ass of 2000-6000 M-1 and their minimum detection limit is in the range of 8-35 mu M. The crystal structure of a naphthaldehyde complex, L.2b, exhibits intermolecular arm-to-arm as well as arm-to-naphthaldehyde pi center dot center dot center dot pi interactions. Molecular dynamics studies of L carried out in the presence of aromatic aldehydes under vacuum as well as in acetonitrile resulted in exhibiting interactions observed in the solid state and hence the changes observed in the fluorescence and absorption spectra are attributable for such interactions. Complex formation has also been delineated through ESI MS studies. Thus L is a promising receptor that can recognize PAHs by providing spectral changes proportional to the aromatic conjugation of the guest and the extent of aromatic pi center dot center dot center dot pi interactions present between L and the guest.

Effect of Substrate Binding Loop Mutations on the Structure, Kinetics, and Inhibition of Enoyl Acyl Carrier Protein Reductase from Plasmodium falciparum

Enoyl acyl carrier protein reductase (ENR), which catalyzes the final and rate limiting step of fatty acid elongation, has been validated as a potential drug target. Triclosan is known to be an effective inhibitor for this enzyme. We mutated the substrate binding site residue Ala372 of the ENR of Plasmodium falciparum (PfENR) to Methionine and Valine which increased the affinity of the enzyme towards triclosan to almost double, close to that of Escherichia coli ENR (EcENR) which has a Methionine at the structurally similar position of Ala372 of PfENR. Kinetic studies of the mutants of PfENR and the crystal structure analysis of the A372M mutant revealed that a more hydrophobic environment enhances the affinity of the enzyme for the inhibitor. A triclosan derivative showed a threefold increase in the affinity towards the mutants compared to the wild type, due to additional interactions with the A372M mutant as revealed by the crystal structure. The enzyme has a conserved salt bridge which stabilizes the substrate binding loop and appears to be important for the active conformation of the enzyme. We generated a second set of mutants to check this hypothesis. These mutants showed loss of function, except in one case, where the crystal structure showed that the substrate binding loop is stabilized by a water bridge network. (C) 2011 IUBMB mum Life, 63(1): 30-41,2011

Extended gravitational action and novel consequences

It is found that the inclusion of higher derivative terms in the gravitational action along with concepts of phase transition and spontaneous symmetry breaking leads to some novel consequence. The Ricci scalar plays the dual role, like a physical field as well as a geometrical field. One gets Klein-Gordon equation for the emerging field and the corresponding quanta of geometry are called Riccions. For the early universe the model removes singularity along with inflation. In higher dimensional gravity the Riccions can break into spin half particle and antiparticle along with breaking of left-right symmetry. Most tantalizing consequences is the emergence of the physical universe from the geometry in the extreme past. Riccions can Bose condense and may account for the dark matter.

High-pressure studies on the critical composition in Ge—As—Te glasses

High-pressure resistivity measurements have been performed on G37.5AsxTe92.5-x (x = 20, 40, 45, 50 and 55) and Ge10AsxTe90-x (x = 15, 20, 35, 40, 45 and 50) glasses. The glasses show reversible metallization behaviour under pressure. The pressure derivative of the logarithm of the resistivity of the glasses is a minimum at glass compositions corresponding to the average coordination number [r] = 2.60. This behaviour is interpreted on the basis of the existence of a critical composition in glasses with a layered structure.

Crystal structure of a daturalactone - a withanolide

The crystal structure of a daturalactone derivative has been determined by X-ray structural analysis. The compound crystallizes in orthorhomic space group P2(1)2(1)2(1) with cell parameters a = 15.141(1) angstrom, b = 18.425(1) angstrom, c = 19.251(2) angstrom. The structure was solved by direct methods and refined to R = 0.082. The asymmetric unit contains two non-equivalent molecules. Extensive hydrogen bonding is present. The conformations of the rings are A: a distorted half-chair, B: a perfect half-chair, C: a chair, D: an envelope-half chair and E: a twist boat. Ring junctions A/B, B/C, C/D are all trans fused. Methyl carbons C(18), C(19), C(27) and the lactone moiety is beta-oriented whereas the methyl carbons C(21) and C(28) are alpha-oriented.

Effect of substitution of Y on the structural, magnetic, and thermal properties of hexagonal DyMnO3 single crystals

We investigate the structural, magnetic, and specific heat behavior of the hexagonal manganite Dy0.5Y0.5MnO3 in order to understand the effect of dilution of Dy magnetism with nonmagnetic yttrium. In this compound, the triangular Mn lattice orders antiferromagnetic at T-N(Mn) approximate to 68 K observed experimentally in the derivative of magnetic susceptibility as well as in specific heat. In addition, a low-temperature peak at T-N(Dy) similar to 3 K is observed in specific heat which is attributed to rare earth order. The T-N(Mn) increases by 9 K compared to that of hexagonal (h) DyMnO3 while T-N(Dy) is unchanged. A change in slope of thermal evolution of lattice parameters is observed to occur at temperature close to T-N(Mn). This hints at strong magnetoelastic coupling in this geometric multiferroic. In magnetization measurements, steplike features are observed when the magnetic field is applied along the c axis which shift to higher fields with temperature and vanish completely above 40 K. The presence of different magnetic phases at low temperature and strong magnetoelastic effects can lead to such field-induced transitions which resemble metamagnetic transitions. This indicates the possibility of strong field-induced effects in dielectric properties of this material, which is unexplored to date.

Thiol-ene Clickable Hyperscaffolds Bearing Peripheral Allyl Groups

Radical catalyzed thiol-ene reaction has become a useful alternative to the Huisgen-type click reaction as it helps to expand the variability in reaction conditions as well as the range of clickable entities. Thus, direct generation of hyper-branched polymers bearing peripheral allyl groups that could be clicked using a variety of functional thiols would be of immense value. A specifically designed AB(2) type monomer, that carries two allyl benzyl ethers groups and one alcohol functionality, was shown to undergo self-condensation under acid-catalyzed melt-transetherification to yield a hyperbranched polyether that carries numerous allyl end-groups. Importantly, it was shown that the kinetics of polymerization is not dramatically affected by the change of the ether unit from previously studied methyl benzyl ether to an allyl benzyl ether. The peripheral allyl groups were readily clicked quantitatively, using a variety of thiols, to generate an hydrocarbon-soluble octadecyl-derivative, amphiphilic systems using 2-mercaptoethanol and chiral amino acid (N-benzoyl cystine) derivatized hyperbranched structures; thus demonstrating the versatility of this novel class of clickable hyperscaffolds. (C) 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 49:1735-1744, 2011

Transformation of 16-dehydroprogesterone and 17?-hydroxyprogesterone by Mucor piriformis

Mucor piriformis was used to study the mode of transformation of 16-dehydroprogesterone (I, pregna-4, 16-diene-3, 20-dione) and 17 alpha-hydroxyprogesterone (II, 17 alpha-hydroxypregn-4-ene-3, 20-dione). Biotransformation products formed from I were 14 alpha-hydroxypregna-4, 16-diene-3, 20-dione (Ia), 7 alpha, 14 alpha-dihydroxypregna-4 16-diene-3, 20-dione (Ib), 3 beta, 7 alpha, 14 alpha-trihydroxy-5 alpha-pregn-16-en-20-one (Ic), and 3 alpha, 7 alpha, 14 alpha-trihydroxy-5 alpha-pregn-16-en-20-one (Id). Metabolites Ic and Id appear to be hitherto unknown. Timecourse studies suggested that the transformation is initiated by hydroxylation at the 14 alpha-position (Ia) followed by hydroxylation at the 7 alpha-position (Ib). Microsomes (105,000 g sediment) prepared from 16-dehydroprogesterone-induced cells hydroxylate I to its 14 alpha-hydroxy derivative (Ia) in the presence of NADPH. Incubation of Ia with the organism resulted in the formation of Ib, Ic and Id. Biotransformation products formed from compound II were 17 alpha, 20 alpha-dihydroxypregn-4-en-3-one (IIa), 7 alpha, 17 alpha-dihydroxypregn-4-ene-3, 20-dione (IIb), 6 beta, 17 alpha, 20 alpha-trihydroxypregn-4-en-3-one (IIc) and 11 alpha, 17 alpha, 20 alpha-trihydroxypregn-4-en-3-one (IId). Time-course studies indicated that IIa is the initial product formed, which is further hydroxylated either at the 6 beta or 11 alpha position. Incubation of IIa with the organism resulted in the formation of IIc and IId. Reduction of the 4-en-3-one system and 20-keto group has not been observed before in organisms of the order Mucorales. In addition, M. piriformis has been shown to carry out hydroxylation at the C-6, C-7, C-11 and C-14 positions in the steroid molecules tested.