PANI-Fe3O4@ZnO nanocomposite as magnetically recoverable organometallic nanocatalyst promoted synthesis of new Azo chromene dyes and evaluation of their antioxidant and antimicrobial activities

Molecular Diversity - A new series of azo chromene dyes were synthesized via a facile cyclocondensation reaction of (E)-1,2-diphenyl-1-diazene and 4-aminocoumarin with 1:2 molar ratio catalyzed by...     

Formal proofs of operator identities by a single formal computation

A formal computation proving a new operator identity from known ones is, in principle, restricted by domains and codomains of linear operators involved, since not any two operators can be added or composed. Algebraically, identities can be modelled by noncommutative polynomials and such a formal computation proves that the polynomial corresponding to the new identity lies in the ideal generated by the polynomials corresponding to the known identities. In order to prove an operator identity, however, just proving membership of the polynomial in the ideal is not enough, since the ring of noncommutative polynomials ignores domains and codomains. We show that it suffices to additionally verify compatibility of this polynomial and of the generators of the ideal with the labelled quiver that encodes which polynomials can be realized as linear operators. Then, for every consistent representation of such a quiver in a linear category, there exists a computation in the category that proves the corresponding instance of the identity. Moreover, by assigning the same label to several edges of the quiver, the algebraic framework developed allows to model different versions of an operator by the same indeterminate in the noncommutative polynomials.     

Relations on the period mapping giving extensions of mixed hodge structures on compact Riemann surfaces

We consider a period map from Teichmüller space to , which is a real vector bundle over the Siegel upper half space. This map lifts the Torelli map. We study the action of the mapping class group on this period map. We show that the period map from Teichmüller space modulo the Johnson kernel is generically injective. We derive relations that the quadratic periods must satisfy. These identities are generalizations of the symmetry of the Riemann period matrix. Using these higher bilinear relations, we show that the period map factors through a translation of the subbundle and is completely determined by the purely holomorphic quadratic periods. We apply this result to strengthen some theorems in the literature. One application is that the quadratic periods, along with the abelian periods, determine a generic marked compact Riemann surface up to an element of the kernel of Johnson's homomorphism. Another application is that we compute the cocycle that exhibits the mapping class group modulo the Johnson kernel as an extension of the group SP _g () by the group .     

High-performance liquid chromatography and capillary supercritical-fluid chromatography separation of vegetable carotenoids and carotenoid isomers

Carotenoids from carrots and tomatoes were separated with high-performance liquid chromatography (HPLC) and capillary supercritical fluid chromatography (SFC). All trans alpha- and beta-carotene were separated from their respective cis-isomers with capillary SFC. Carotenoids extracted from tomatoes included xanthophyll, lycopene and beta-carotene, while alpha- and beta-carotene were extracted from carrots. The HPLC separations were accomplished isocratically with a 25-cm column containing 5-microns ODS and methanol-acetonitrile-chloroform (47:47:6) or acetonitrile-dichloromethane (80:20). beta-Carotene cis-isomers were separated with SFC with a SB-cyanopropyl-25-polymethylsiloxane column, while alpha-carotene isomers were separated with two SB-cyanopropyl-50-polymethylsiloxane columns. Carotenoids from carrots and tomatoes were separated with a SB-phenyl-50-polymethylsiloxane column. Carbon dioxide with 1% ethanol was the SFC mobile phase. The eluent was monitored at 461 nm for HPLC and either 453 or 461 nm for SFC.     

Synthesis,characterization and application of alumina/ vanadium pentoxide nanocomposit by sol–gel method

In this work, we report the preparation of Al₂O₃/V₂O₅ nanocomposit using vanadium and aluminum nitrate by sol–gel method. Characterization of nanocomposit was carried out by powder X‐ray diffractometry (XRD), Fourier transform infrared (FT‐IR), scanning electron microscopy (SEM), Energy‐Dispersive X‐ray (EDX) and UV spectroscopy. Then, applicability of the synthesized nanocomposit was tested as a nanocatalyst for the synthesis of diindolyl oxindole derivatives, an important class of potentially bioactive compounds. The products were obtained in good to high yields from one‐pot three‐component condensation of isatin with indole. Also, this nanocatalyst has been reused several times, without observable loss of activity.     

Efficient Synthesis of 4H-Pyran and Spiro-Oxindole Derivatives Based on Al2O3/V2O5 Nanocomposite as Catalyst

Russian Journal of Organic Chemistry - A simple and eco-friendly catalytic alternative has been proposed for one-pot three-component synthesis of 4H-pyrane and spiro-oxindole derivatives, as two...     

l-Proline-catalysed one-pot synthesis of tetrahydrobenzo[c]acridin-8(7H)-ones at room temperature

Only 10 mol% of l-Proline in ethanol proved to be a very efficient catalyst for the one-pot synthesis of a wide variety of highly substituted tetrahydrobenzo[c]acridin-8(7H)-ones at room temperature. The key advantages of this process are high yields, cost effectiveness of the catalyst, easy work-up and the products can be directly recrystallized from hot ethanol.     

The extreme core

For a Siegel modular cusp formf of weightk letv(f) be the closure of the convex ray hull of the support of the Fourier series inside the cone of semidefinite forms. We show the existence of the extreme core,C _ext, which satisfiesv(f) ⊇k C_ext for all cusp forms. This is a generalization of the Valence Inequality to Siegel modular cusp forms. We give estimations of the extreme core for general n. For n ≤5 we use noble forms to improve these estimates. Forn = 2 we almost specify the extreme core but fall short. We supply improved estimates for all relevant constants and show optimality in some cases. The techniques are mainly from the geometry of numbers but we also use IGUSA’s generators for the ring of Siegel modular forms in degree two.     

Dimensions of cusp forms for Γ0(p) in degree two and small weights

We investigate degree two Siegel cusp forms of small weight for Γ₀(p). Using the Restriction Technique we compute some dimensions and verify the conjectures ofHashimoto in some examples of weights three and four. For weight two we determine the dimension for primesp ≤ 41 and find only lifts. We explain in general how to compute spaces of Siegel cusp forms for subgroups of finite index in Γ _n .     

Improved Information-Theoretic Generalization Bounds for Distributed,Federated, and Iterative Learning

We consider information-theoretic bounds on the expected generalization error for statistical learning problems in a network setting. In this setting, there are K nodes, each with its own independent dataset, and the models from the K nodes have to be aggregated into a final centralized model. We consider both simple averaging of the models as well as more complicated multi-round algorithms. We give upper bounds on the expected generalization error for a variety of problems, such as those with Bregman divergence or Lipschitz continuous losses, that demonstrate an improved dependence of 1/K on the number of nodes. These “per node” bounds are in terms of the mutual information between the training dataset and the trained weights at each node and are therefore useful in describing the generalization properties inherent to having communication or privacy constraints at each node.