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Electrochemical CO₂ reduction was studied by using a graphite electrode coated with cobalt octacyanophthalocyanine (CoPc(CN)₈) and dipped in an aqueous phase. The most active and selective CO₂ reduction was achieved at −1.20 V (vs Ag/AgCl) with the ratio of the produced CO/H₂ around 10 at pH 9.3. The electrocatalytic CO₂ reduction by CoPc(CN)₈ could be achieved at a more positive applied potential than non-substituted CoPc (CoPc), which can be ascribed to the relatively positive redox potential of CoPc(CN)₈. The catalytic mechanism of the CoPc(CN)₈ in a homogeneous system was investigated by an in situ potential-step chronoamperospectroscopy under argon and under CO₂ as well. In CoPc(CN)₈ the rate-determining step was an intermediate formation step, while in CoPc it was the second reduction of the complex.

A method for the preparation of an α-formylated pyrrole or dipyrromethane which contains an electron-withdrawing β-acetyl is described. Formylation proceeds directly from the corresponding acid pyrrole or dipyrromethane without the need of the usual two-step acid decarboxylation/formylation procedure. The acid is first transformed into its acid chloride with oxalyl chloride, followed by reduction to the aldehyde with the mild reducing agent sodium triacetoxyborohydride, in a one-pot reaction. The non-basic acylating reagent PR₃ is necessary both for acyl chloride formation and for the reduction to succeed.

Octakis(alkoxymethyl) cobalt phthalocyanines with relatively short side chains were synthesized which exhibited no thermotropic liquid crystalline behaviour. The final products as well as the intermediates have been characterized by proton magnetic resonance, infrared and electron spectra and elemental analysis. Cyclic voltammograms were measured for octakis(alkoxymethyl) cobalt phthalocyanines in order to examine their electron transfer properties. The electron transfer properties of octakis (alkoxymethyl) cobalt phthalocyanines depend on the kind and number of substituents and are due to the interaction between the phthalocyanine ring, the central metal which is influenced by the conjugated π electron current of the porphyrazine ring.

This paper starts by setting the ground for a lambda calculus notation that strongly mirrors the two fundamental operations of term construction, namely abstraction and application. In particular, we single out those parts of a term, called items in the paper, that are added during abstraction and application. This item notation proves to be a powerful device for the representation of basic substitution steps, giving rise to different versions of β-reduction including local and global β-reduction. In other words substitution, thanks to the new notation, can be easily formalised as an object language notion rather than remaining a meta language one. Such formalisation will have advantages with respect to various areas including functional application and the partial unfolding of definitions. Moreover our substitution is, we believe, the most general to date. This is shown by the fact that our framework can accommodate most of the known reduction strategies, which range from local to global. Finally, we show how the calculus of substitution of Abadi et al., can be embedded into our calculus. We show moreover that many of the rules of Abadi et al. are easily derivable in our calculus.

The characteristic class of a star product on a symplectic manifold appears as the class of a deformation of a given symplectic connection, as described by Fedosov. In contrast, one usually thinks of the characteristic class of a star product as the class of a deformation of the Poisson structure (as in Kontsevich's work). In this paper, we present, in the symplectic framework, a natural procedure for constructing a star product by directly quantizing a deformation of the symplectic structure. Basically, in Fedosov's recursive formula for the star product with zero characteristic class, we replace the symplectic structure by one of its formal deformations in the parameter ℏ. We then show that every equivalence class of star products contains such an element. Moreover, within a given class, equivalences between such star products are realized by formal one-parameter families of diffeomorphisms, as produced by Moser's argument.

We give an up-to-date overview of geometric and topological properties of cosymplectic and coKähler manifolds. We also mention some of their applications to time-dependent mechanics.

Actions of Lie groups on presymplectic manifolds are analyzed, introducing the suitable comomentum and momentum maps. The subsequent theory of reduction of presymplectic dynamical systems with symmetry is studied. In this way, we give a method of reduction which enables us to remove gauge symmetries as well as non-gauge "rigid" symmetries at once. This method is compared with other step-by-step reduction procedures. As particular examples in this framework, we discuss the reduction of time-dependent dynamical systems with symmetry, the reduction of a mechanical model of field theories with gauge and non-gauge symmetries, and the gauge reduction of the system made of a conformal particle.

Omni-Lie algebroids are generalizations of Alan Weinstein's omni-Lie algebras. A Dirac structure in an omni-Lie algebroid 𝔇E ⊕ 𝔍E is necessarily a Lie algebroid together with a representation on E. We study the geometry underlying these Dirac structures in the light of reduction theory. In particular, we prove that there is a one-to-one correspondence between reducible Dirac structures and projective Lie algebroids in ; we establish the relation between the normalizer N_L of a reducible Dirac structure L and the derivation algebra Der(b (L)) of the projective Lie algebroid b(L); we study the cohomology group H^•(L, _ρL) and the relation between N_L and H¹(L, ρ_L); we describe Lie bialgebroids using the adjoint representation; we study the deformation of a Dirac structure L, which is related with H²(L, ρ_L).

During the past three decades, the advantageous concept of the Green’s function has been extended from linear systems to nonlinear ones. At that, there exists a rigorous and an approximate extension. The rigorous extension introduces the so-called backward and forward propagators, which play the same role for nonlinear systems as the Green’s function plays for linear systems. The approximate extension involves the Green’s formula for linear systems with a Green’s function satisfying the corresponding nonlinear equation. For the numerical evaluation of nonlinear ordinary differential equations, the second approach seems to be more convenient. In this article we study a hierarchy of nonlinear partial differential equations that can be approximated by the second approach. Green’s functions for particular nonlinearities are derived explicitly. Numerical error analysis in the case of exponential nonlinearity for different source functions supports the advantage of the approach.

Recently Akl and al. introduced a new model of parallel computation, called BSR (broadcasting with selective reduction) and showed that it is more powerful than any CRCW PRAM and yet requires no more resources (asymptotically) for implementation than even EREW PRAM [2,3,4]. The model allows constant time solutions to sorting, parallel prefix and other problems. In this paper, we describe constant time solution to the detection of repetitions (with overlapping) problem using the one criterion BSR model. This is the first constant time solution to this problem on any model of computation. If the problem is only to detect the existence of any repetition then n processors suffice, where n is the length of the string. If all repetitions are to be found then processors suffice in our algorithm.

We easily synthesized a pure calcium silicon nitride phosphor powder, Ca₂Si₅N₈:Eu${}^{2+}$ from starting materials stable in air, using a graphite crucible to provide reducing conditions at a comparatively lower calcination temperature (1400${}^{\circ }$C) and shorter reaction time (8 h) under an atmospheric pressure. At 150${}^{\circ }$C, the nitride phosphor still retained 77% of its original emission intensity at room temperature.

In this paper, we derive solutions to the derivative nonlinear Schrödinger equation, which are associated to real and complex discrete eigenvalues of the Kaup–Newell spectral problem. These solutions are obtained by investigating double Wronskian solutions of the coupled Kaup–Newell equations and their reductions by means of bilinear method and a reduction technique. The reduced equations include the derivative nonlinear Schrödinger equation and its nonlocal version. Some obtained solutions allow not only periodic behavior, but also solitons on periodic background. Dynamics are illustrated.

Herein, a concise one-pot method to prepare magnetic yolk–shell composite nanoparticles (MYSCNPs) is developed. Phenolic resin microspheres act as sacrificial templates for depositing SiO₂, and Fe@SiO₂ is used as the shell-forming promoter. The diameters of MYSCNPs are $\sim 180$ nm. MYSCNPs have magnetic performance, and both the yolk and shell of MYSCNPs are mesoporous. LaCl₃ catalysts are loaded onto MYSCNPs to prepare loaded LaCl₃ catalysts (LaCl₃-lo-MYSCNPs). Using sodium borohydride (NaBH${}_4)$ and LaCl₃-lo-MYSCNPs, liquid terminated-carboxyl fluoropolymers (LTCFs) are efficiently reduced to the corresponding liquid terminated-hydroxyl fluoropolymers (LTHFs). The structures of LTCFs and LTHFs are analyzed using FTIR and ¹H-NMR. The results show that C=C and COOH of LTCFs are successfully reduced to C–C and OH.

Redundancy rules in knowledge bases will affect the reasoning process of knowledge bases. And they will take up a lot of unnecessary memory space. So the notions of redundancy rules are briefly introduced. Meanwhile they are classified into four types. This paper studies the redundancy rules based on propositional logic and presents the reduction algorithms of four kinds of redundancy rules. They are equivalent redundancy rules, implication redundancy rules and cycle redundancy rules in explicit redundancy rules and condition redundancy rules in implicit redundancy rules. The reduction in this paper optimizes the structure of rule-based knowledge bases. And it also improves the efficiency of time and space of the reasoning on knowledge bases.

Attribute reduction is a part of the most basic and significant research contents in rough set theory. The so-called attribute reduction is the smallest independent subset that keeps certain properties of information table unchanged. In this paper, four interval-valued intuitionistic fuzzy probabilistic rough set models and their natures are given on the basis of the dominant-, inferior- and interval-valued intuitionistic fuzzy probabilistic rough set models. At the same time, the interval-valued intuitionistic fuzzy numbers are transformed by fuzzy degree, and the approximate accuracy and approximate classification quality under the dominance relation are used for reduction, at last, the feasibility is verified by an example.

We consider the following matrix reachability problem: given r square matrices with entries in a semiring, is there a product of these matrices which attains a prescribed matrix? Similarly, we define the vector (resp. scalar) reachability problem, by requiring that the matrix product, acting by right multiplication on a prescribed row vector, gives another prescribed row vector (resp. when multiplied on the left and right by prescribed row and column vectors, gives a prescribed scalar). We show that over any semiring, scalar reachability reduces to vector reachability which is equivalent to matrix reachability, and that for any of these problems, the specialization to any r ≥ 2 is equivalent to the specialization to r = 2. As an application of these reductions and of a theorem of Krob, we show that when r = 2, the vector and matrix reachability problems are undecidable over the max-plus semiring (ℤ∪{-∞}, max,+). These reductions also improve known results concerning the classical zero corner problem. Finally, we show that the matrix, vector, and scalar reachability problems are decidable over semirings whose elements are "positive", like the tropical semiring (ℤ∪{+∞}, min,+).

Let A be a commutative Noetherian local ring with maximal ideal $𝔪$, and let I be an ideal. The fiber cone is then an image of the polynomial ring over the residue field $A/𝔪$. The kernel of this map is called the defining ideal, and it is natural to ask how to compute it. In this paper, we provide a construction for the defining ideals of Cohen–Macaulay fiber cones.

This note concerns Legendrian cobordisms in one-jet spaces of functions, in the sense of Arnol’d [Lagrange and Legendre cobordisms. I, Funkt. Anal. Prilozhen. 14(3) (1980) 1–13, 96.] — consisting of big Legendrian submanifolds between two smaller ones. We are interested in such cobordisms which fit with generating functions, and wonder which structures and obstructions come with this notion. As a central result, we show that the classes of Legendrian concordances with respect to the generating function equipment can be given a group structure. To this construction, we add one of a homotopy with respect to generating functions.

Veolia Water Solutions & Technologies receives two prizes at AquaTech China for AnoxKaldnes™ MBBR technology and its Carbon Footprint Reduction Program.

International Consortium Led by Chinese Scientists Announce the First Complete Sequencing of Pear Genome.

Eli Lilly Opens Diabetes Research Center in China.

China 'Soaring Ahead' in Nanotechnology Research.

Latest Genomic Studies Shed New Light on Maize Diversity and Evolution.

Insight Genetics and Kindstar Global Partner to Enhance Cancer Care in China.

Two studies from the Institute of Plant and Microbial Biology published in PNAS show how plants respond to changing environments.

China's Pharmaceuticals Sales Force Levels Surpass US for First Time.

Let ξ ≥ 1 be a countable ordinal. We study the Borel subsets of the plane that can be made by refining the Polish topology on the real line. These sets are called potentially . We give a Hurewicz-like test to recognize potentially sets.