Neumann-like integrable models

A countable class of integrable dynamical systems, with four-dimensional phase space and conserved quantities in involution (Hn,In)$(H_n,I_n)$ are exhibited. For n=1$n=1$ we recover Neumann system on T^∗S²$T^{\ast }{S}^2$. All these systems are also integrable at the quantum level.     

Phosphorylated cellulose for water purification: a promising material with outstanding adsorption capacity towards methylene blue

Cellulose - Enhancing the sorption properties of cellulose is a prerequisite for its efficient use in water purification as an alternative to costly activated carbon. Here, solvent-free...     

Magnetic Coupling Constants of Self‐Assembled CuII [3×3] Grids: Alternative Spin Model from Theoretical Calculations

This paper reports a theoretical analysis of the electronic structure and magnetic properties of a ferromagnetic Cu^II [3×3] grid. A two‐step strategy, combining calculations on the whole grid and on binuclear fragments, has been employed to evaluate all the magnetic interactions in the grid. The calculations confirm an S=7/2 ground state, which is in accordance with the magnetisation versus field curve and the thermal dependence of the magnetic moment data. Only the first‐neighbour coupling terms present non‐negligible amplitudes, all of them in agreement with the structure and arrangement of the Cu 3d magnetic orbitals. The results indicate that the dominant interaction in the system is the antiferromagnetic coupling between the ring and the central Cu sites (J₃=J₄≈?31 cm^?1). In the ring two different interactions can be distinguished, J₁=4.6 cm^?1 and J₂=?0.1 cm^?1, in contrast to the single J model employed in the magnetic data fit. The calculated J values have been used to determine the energy level distribution of the Heisenberg magnetic states. The effective magnetic moment versus temperature plot resulting from this ab initio energy profile is in good agreement with the experimental curve and the fitting obtained with the simplified spin model, despite the differences between these two spin models. This study underlines the role that the theoretical evaluations of the coupling constants can play on the rationalisation of the magnetic properties of these complex polynuclear systems.     

Preparation of Stereoregular Isotactic Poly(mandelic acid) through Organocatalytic Ring‐Opening Polymerization of a Cyclic O‐Carboxyanhydride

Poly(mandelic acid) (PMA) is an aryl analogue of poly(lactic acid) (PLA) and a biodegradable analogue of polystyrene. The preparation of stereoregular PMA was realized using a pyridine/mandelic acid adduct (Py?MA) as an organocatalyst for the ring‐opening polymerization (ROP) of the cyclic O‐carboxyanhydride (manOCA). Polymers with a narrow polydispersity index and excellent molecular‐weight control were prepared at ambient temperature. These highly isotactic chiral polymers exhibit an enhancement of the glass‐transition temperature (T_g) of 15 °C compared to the racemic polymer, suggesting potential future application as high‐performance commodity and biomedical materials.     

New complex macromolecular architectures based on organosilicon chemistry

Polycarbosilane networks were prepared from well-defined α, ω-difunctional oligomers: X-[Si(CH₃)₂-CH₂-CH₂]_n-X with X = H ( 1 ) and X = CH=CH₂ ( 2 ). Crosslinking reactions were performed by hydrosilylation of tetramethyltetravinylcyclotetrasiloxane (V₄) or of tetravinylsilane with SiH end groups of 1 . Hydrosilylation of Si-CH=CH₂ end groups of 2 with tetramethyltetrahydrocyclotetrasiloxane (D₄H) was also successfully tried. Some physicochemical properties of these new networks will be presented.¹⁾ Interpenetrating networks based on polysiloxanes and polycarbonates were synthesized by the in situ method: a polysiloxane bearing various proportions of room temperature crosslinkable -Si(OEt)₃ side groups was mixed with bis(allyl ethylene glycol) biscarbonate and a free-radical initiator. After the formation of the first network at room temperature, the cross-linking of the polycarbonate network was performed by raising the temperature up to 80°C. Various chemical modifications of the polysiloxane component in the IPN were performed in order to improve the degree of interpenetration as estimated from turbidity, density, refractive index and DSC measurements.²⁾     

A Comparative Study of Various Pretreatment Approaches for Bio-Ethanol Production from Willow Sawdust,Using Co-Cultures and Mono-Cultures of Different Yeast Strains

The effect of different pretreatment approaches based on alkali (NaOH)/hydrogen peroxide (H₂O₂) on willow sawdust (WS) biomass, in terms of delignification efficiency, structural changes of lignocellulose and subsequent fermentation toward ethanol, was investigated. Bioethanol production was carried out using the conventional yeast Saccharomyces cerevisiae, as well as three non-conventional yeasts strains, i.e., Pichia stipitis, Pachysolen tannophilus, Wickerhamomyces anomalus X19, separately and in co-cultures. The experimental results showed that a two-stage pretreatment approach (NaOH (0.5% w/v) for 24 h and H₂O₂ (0.5% v/v) for 24 h) led to higher delignification (38.3 ± 0.1%) and saccharification efficiency (31.7 ± 0.3%) and higher ethanol concentration and yield. Monocultures of S. cerevisiae or W. anomalus X19 and co-cultures with P. stipitis exhibited ethanol yields in the range of 11.67 ± 0.21 to 13.81 ± 0.20 g/100 g total solids (TS). When WS was subjected to H₂O₂ (0.5% v/v) alone for 24 h, the lowest ethanol yields were observed for all yeast strains, due to the minor impact of this treatment on the main chemical and structural WS characteristics. In order to decide which is the best pretreatment approach, a detailed techno-economical assessment is needed, which will take into account the ethanol yields and the minimum processing cost.     

Towards a unified recurrent neural network theory: The uniformly pseudo-projection-anti-monotone net

In the past decades, various neural network models have been developed for modeling the behavior of human brain or performing problem-solving through simulating the behavior of human brain. The recurrent neural networks are the type of neural networks to model or simulate associative memory behavior of human being. A recurrent neural network (RNN) can be generally formalized as a dynamic system associated with two fundamental operators: one is the nonlinear activation operator deduced from the input-output properties of the involved neurons, and the other is the synaptic connections (a matrix) among the neurons. Through carefully examining properties of various activation functions used, we introduce a novel type of monotone operators, the uniformly pseudo-projectionanti-monotone (UPPAM) operators, to unify the various RNN models appeared in the literature. We develop a unified encoding and stability theory for the UPPAM network model when the time is discrete. The established model and theory not only unify but also jointly generalize the most known results of RNNs. The approach has lunched a visible step towards establishment of a unified mathematical theory of recurrent neural networks.     

可见区分光光度法测量水体色度

针对目前水质色度测量方法的局限性,采用分光光度法测量相关色度学参数,通过色度学参数与国家标准方法的色度值建立数值关系,从而测定水体的色度值.该方法不仅保证测量结果与现行国家标准测量结果一致,而且客观性强,稳定可靠,灵敏度更高,也更准确.克服了目视比色法需要水体与标准溶液色调一致的局限性,可以推广到其他色调的废水色度测量...     

Quantum Transport in Crystals: Effective Mass Theorem and K·P Hamiltonians

In this paper the effective mass approximation and the k·p multi-band models, describing quantum evolution of electrons in a crystal lattice, are discussed. Electrons are assumed to move in both a periodic potential and a macroscopic one. The typical period e{\epsilon} of the periodic potential is assumed to be very small, while the macroscopic potential acts on a much bigger length scale. Such homogenization asymptotic is investigated by using the envelope-function decomposition of the electron wave function. If the external potential is smooth enough, the k·p and effective mass models, well known in solid-state physics, are proved to be close (in the strong sense) to the exact dynamics. Moreover, the position density of the electrons is proved to converge weakly to its effective mass approximation.     

Random bipartite entanglement from W and W-like states

We describe a protocol for distilling maximally entangled bipartite states between random pairs of parties from those sharing a tripartite W state |W=(1/sqrt[3])(|100+|010+|001)(ABC), and show that the total distillation rate E(t)(infinity) [the total number of Einstein-Podolsky-Rosen (EPR) pairs distilled per W, irrespective of who shares them] may be done at a higher rate than EPR distillation between specified pairs of parties. Specifically, the optimal rate for distillation to specified parties has been previously shown to be 0.92 EPR pairs per W, while our protocol can asymptotically distill 1 EPR pair per W between random pairs of parties, which we conjecture to be optimal. We thus demonstrate a tradeoff between overall distillation rate and final distribution of EPR pairs. We further show that there exist states with fixed lower-bounded E(t)(infinity), but arbitrarily small distillable entanglement for specified parties.