In this paper, we establish a WP-Bailey lattice. By iterating this method, we obtain a transformation formula for WP-Bailey pairs. By considering the unit WP-Bailey pair, several new transformation formulas are given. In particular, we give a new Andrews-Gordon identity.
Liu, Qi
Zhang, Yanhui
Liu, Benjuan
Amonette, James E.
Lin, Zhibin
Liu, Gang
Ambus, Per
Xie, Zubin
Background and aims Modern agriculture is driving the release of excessive amounts of reactive nitrogen (N) from the soils to the environment, thereby threatening ecological balances and functions. The amendment of soils with biochar has been suggested as a promising solution to regulate the soil N cycle and reduce N effluxes. However, a comprehensive and quantitative understanding of biochar impacts on soil N cycle remains elusive. Methods A meta-analysis was conducted to assess the influence of biochar on different variables involved in soil N cycle using data compiled across 208 peer-reviewed studies. Results On average, biochar beneficially increases symbiotic biological N-2 fixation (63%), improves plant N uptake (11%), reduces soil N2O emissions (32%), and decreases soil N leaching (26%), but it poses a risk of increased soil NH3 volatilization (19%). Biochar-induced increase in soil NH3 volatilization commonly occurs in studies with soils of low buffering capacity (soil pH <=3D 5, organic carbon <=3D 10 g kg(-1), or clay texture), the application of high alkaline biochar (straw- or manure-derived biochar), or biochar at high application rate (> 40 t ha(-1)). Besides, if the pyrolytic syngas is not purified, the biochar production process may be a potential source of N2O and NOx emissions which correspond to 2-4% and 3-24% of the feedstock-N, respectively. Conclusions This study suggests that to make biochar beneficial for decreasing soil N effluxes, clean advanced pyrolysis technique and adapted use of biochar are of great importance.
Recently, we have identified a randomized quartet phylogeny algorithm that has O(n log n) runtime with high probability, which is asymptotically optimal. Our algorithm has high probability of returning the correct phylogeny when quartet errors are independent and occur with known probability, and when the algorithm uses a guide tree on O(log log n) taxa that is correct with high probability. In practice, none of these assumptions is correct: quartet errors are positively correlated and occur with unknown probability, and the guide tree is often error prone. Here, we bring our work out of the purely theoretical setting. We present a variety of extensions which, while only slowing the algorithm down by a constant factor, make its performance nearly comparable to that of Neighbour Joining, which requires Theta (n(3)) runtime in existing implementations. Our results suggest a new direction for quartet-based phylogenetic reconstruction that may yield striking speed improvements at minimal accuracy cost. An early prototype implementation of our software is available at http://www.cs.uwaterloo.ca/similar to jmtruszk/qtree.tar.gz.
This note contains a combinatorial construction of symmetries arising in symplectic geometry (partially wrapped or infinitesimal Fukaya categories), algebraic geometry (derived categories of singularities), and K-theory (Waldhausen's S-construction). Our specific motivation (in the spirit of expectations of Kontsevich) is a combinatorial construction of categorical quantizations of Lagrangian skeleta of symplectic manifolds. The main result of this paper gives an immediate solution in the one-dimensional case of ribbon graphs. (C) 2014 Elsevier Inc. All rights reserved.
The article presents John Deely's philosophical critique of Martin Heidegger's Being and Time from the perspective of Catholic theology defined by the work of Thomas Aquinas, John Poinsot, and Jacques Maritain. Deely's analysis centers on the philosophical definition of esse intentionale. A biographical context for the critique stems from the life-long friendship of John Deely and the author. The moral force of Deely's critique is now confirmed by the recent publication of Heidegger's personal diaries, the Black Notebooks.
The hybrid HF/DFT method B3LYP has been employed to investigate the geometrical and electronic structures of AuC (n) (n = 1-11) clusters. The properties such as geometrical parameters and electronic energies are determined for open-chain and cyclic species. Our results indicate that the open-chain structures with low spin states (doublet) are more stable than the cyclic ones for the small sizes clusters (n a parts per thousand currency sign 9), as the cluster sizes increase (n = 10, 11), the cyclic species are more stable. The incremental binding energies show a smooth even-odd alternation phenomenon for open-chain species, n-even (n is the numbers of C atom in the clusters) species have the stronger stabilities relative to the adjacent odd-numbered ones. In addition, the most favorable dissociation channels are determined by calculating the fragmentation energies accompanying various possible pathways. The studied clusters incline to be dissociated to Au + C (n) and AuC (n-3) + C-3 fragments.
Bodlaender, Hans L.
Drange, Pal Gronas
Dregi, Markus S.
Fomin, Fedor V.
Lokshtanov, Daniel
Pilipczuk, Micha L.
We give an algorithm that for an input n-vertex graph G and integer k > 0, in time 2(O(k))n, either outputs that the treewidth of G is larger than k, or gives a tree decomposition of G of width at most 5k + 4. This is the first algorithm providing a constant factor approximation for treewidth which runs in time single exponential in k and linear in n. Treewidth-based computations are subroutines of numerous algorithms. Our algorithm can be used to speed up many such algorithms to work in time which is single exponential in the treewidth and linear in the input size.
A straightforward and environment-friendly protocol for the synthesis of valuable chiral N-(tert-butylsulfinyl)imines has been developed. Different from traditional process with benzaldehydes as substrates, arylmethyl alcohols, benzylthiol, dibenzyl ether, thioether, and disulfide are used as alternative substrates to react with tert-butanesulfinamide in the presence of (KOBu)-Bu-t under air for the synthesis of chiral N-(tert-butylsulfinyl)imines. This is a transition metal-free, mild, cost-effective, and simple process.
The finite-dimensional irreducible representations of Yangian of Lie Superalgebra of A(n, n) type is described in terms of Drinfel'd polynomials. The necessarily and sufficient conditions of finite-dimensionality of irreducible representation are formulated and proved. The Poincare-Birkoff-Witt theorem for Yangian of A(n, n) Lie Superalgebra is proved also.