Networks and chain coverings in partial orders and their products

For an arbitrary poset P, subposets {P _i : 1ik} form a transitive basis of P if P is the transitive closure of their union. Let u be the minimum size of a covering of P by chains within posets of the basis, s the maximum size of a family of elements with no pair comparable in any basis poset, and a the maximum size of an antichain in P. Define a dense covering to be a collection D of chains within basis posets such that each element belongs to a chain in D within each basis poset and is the top of at least k-1 chains and the bottom of at least k-1 chains in D. Dense coverings generalize ordinary chain coverings of poset. Let d=min {|D|–(k–1)|P|}. For an arbitrary poset and transitive basis, a convenient network model for dense coverings yields the following: Theorem 1: da, with equality iff P has a minimum chain decomposition in which every pair of consecutive elements on each chain are comparable in some basis poset. Theorem 2: usda. Theorem 3: s=d iff s=a. The most interesting special case is where the transitive basis expresses P as the product of two posets, in which case u and s measure the minimum and maximum sizes of unichain coverings and semiantichains.     

A neuro-fuzzy system for X-ray spectra interpretation

A decision scheme for the interpretation of spectra from wavelength dispersive X-ray fluorescence spectrometry is described that encompasses elements from three areas of artificial intelligence: fuzzy logic, rule based expert systems and neural net technology.After transforming the recorded spectra to line spectra by appropriate background correction a reasoning scheme is applied that takes into account not only the observed spectra, but also the recording conditions and prior spectroscopic information regarding the relative emission probabilities and the usefulness of the different lines for the purpose of element identification. The latter is done on the basis of a previously described scheme to compute conditional a posteriori Bayes probabilities for a mean matrix. These different pieces of information are then assembled into a battery of fuzzy rules. The importance of the rules as well as the importance of the X-ray lines is determined in a training process, similar to the one in a feedforward back-propagation network.To further stabilize the results this network is pruned in a second training cycle. This, however, had little effect on the quality of interpretation.The advantages of this approach to the interpretation of X-ray spectra over older ones are numerous: the system adapts itself to better interpret spectra that are of greater importance to a laboratory as these are better represented in the training set; the fuzzy logic is capable of working with incomplete and uncertain knowledge, and the neural network results based on these fuzzy rules is readily interpretable by the X-ray spectroscopist as every rule can be expressed also in natural language as in any classical rule based system.On leave from Silesian University, Katowice, Poland     

Phenomenological and neural-network modeling of cephalosporin C production bioprocess

Cephalosporin C production process withCephalosporium acremonium ATCC 48272 in synthetic medium was investigated and the experimental results allowed the development of a mathematical model describing the process behavior. The model was able to explain fairly well the diauxic phenomenon, higher growth rate during the glucose-consumption phase, and the production occurring only in the sucrose-consumption phase. Moreover, the process was simulated utilizing the neural-networks technique. Two feed-forward neural-networks with one hidden layer were employed. Both models, phenomenological and neural-networks based, satisfactorily describe the bioprocess. The difficulties in determining kinetic parameters are avoided when neural networks are utilized.     

Synthesis,structure, and magnetic properties of the cobalt(<Emphasis Type="SmallCaps">II</Emphasis>) 1,3,5-benzenetricarboxylate layered coordination polymer

The reaction of Co(NO₃)₂·6H₂O with 1,3,5-benzenetricarboxylic acid (H₃btc, trimesic acid) in DMF at 100 °C afforded the coordination polymer [Co₃(dmf)₆(btc)(Hbtc)(H₂btc)]··9H₂O (1) (dmf is N,N′-dimethylformamide, DMF). According to the X-ray diffraction study, the metal-organic coordination polymer is composed of planar honeycomb (6,3) networks, in which the organic benzenetricarboxylate anions and the inorganic Co²⁺ cations play a role of three-connected nodes. Disordered water molecules are intercalated between the layers. A study of the magnetic properties showed the presence of a weak antiferromagnetic coupling between the Co²⁺ ions (S = 3/2). Dedicated to Academician G. A. Abakumov on the occasion of his 70th birthday. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 1719–1723, September, 2007.     

Kinetics of formation of a linear polymer-polymer network system in the presence of 3d metal chelates

For semi-interpenetrating polymer networks (semi-IPNs) based on an incompatible polyurethane network/linear polymethylmethacrylate pair formed in situ in the presence of 3d metal chelates, we have studied the effect of the system composition on the kinetics of formation of the components and the nature of complex formation between the metal compound and the polymer matrix. The ratio of the system components has been shown to have an effect on the selection of the macroligand in formation of complexes of the metal chelate with the polar groups of the semi-IPN, where the general character of the kinetic behavior for the formation of the network and the linear polymer is preserved. __________ Translated from Teoreticheskaya i éksperimental’naya Khimiya, Vol. 42, No. 6, pp. 351–356, November–December, 2006.     

RE3Ga9Ge (RE=Y, Ce, Sm, Gd and Yb): compounds with an open three-dimensional polygallide framework synthesized from liquid gallium

The RE₃Ga₉Ge compounds (RE=Y, Ce, Sm, Gd and Yb) were synthesized at 850°C in quantitative yield from reactions containing excess liquid Ga. The orthorhombic crystal structure is characterized by a unique three-dimensional open Ga framework with parallel straight tunnels. In the tunnels, inserted are arrays of the RE atoms together with interpenetrated monoatomic RE-Ga-Ge planes. A complex disordered arrangement of the RE and Ga atoms is observed in the monoatomic plane. Depending on the extent of disorder, the crystal structure could be presented either in a sub-cell (no ordering) or in a super-cell (partial ordering). Single-crystal X-ray data for Ce₃Ga₉Ge sub-structure: space group Immm, Z=2, cell parameters a=4.3400(12) Å; b=10.836(3) Å; and c=11.545(3) Å; super-structure: space group Cmma, Z=8, cell parameters a=8.680(3) Å; b=23.090(7) Å; and c=10.836(3) Å. The refinement based on the full-matrix least squares on F_o²[I>2σ(I)] converged to final residuals R₁/wR₂=0.0226/0.0528 and 0.0729/0.1569 for the sub- and super-structures, respectively. The relationship between the disordered sub-structure and partially ordered super-structure is discussed. Magnetic susceptibility measurements show Curie-Weiss behavior at the temperatures above 30 K with the negative Weiss constants Θ=−49(1) and−7.7 K for Gd and Ce analogs, respectively. An antiferromagnetic transition is observed in the Gd analog at T_N=26.1 K. The μ_eff obtained for both analogs is close to the RE³⁺ free-ion value.     

交联网络和浓溶液中高分子链运动的NMR研究Ⅲ.质子自旋-晶格弛豫时间与凝胶和浓溶液体系中高分子链段的运动

用自旋－晶格弛豫时间（Ｔ１）研究了溶胀的交联聚丙烯酰胺－丙烯酸网络和线型聚苯乙烯溶液中质子的弛豫行为。交联网络中，随着交联度增大，Ｔ１ＣＨ／Ｔ１ＣＨ２的值由１．１７逐渐趋近于１；而线型聚苯乙烯溶液中，Ｔ１ＣＨ／Ｔ１ＣＨ２的值由最稀浓度下的１．７过渡到１。说明在交联网络中，交联度很低时，链段的运动已经相当受约束；但交联度很大时，充分溶胀的交联网络中链段运动仍有一定自由度。而在线型高分子浓溶液中，链段的运动严重受阻，导致自旋扩散效应非常完全，彻底平均掉了各质子间Ｔ１时间的差异。     

三维聚合物双(三丁基锡)戊二酸酯的合成及晶体结构研究

用三丁基氯化锡与戊二羧酸二钠以2:1摩尔比反应,合成了双（三丁基锡）戊二羧酸酯,并用元素分析、红外光谱、核磁共振氢谱及X-射线单晶衍射进行了表征和结构测定。X-射线单晶衍射法测定表明,化合物属单斜晶系,空间群为Cc,晶胞参数:a=13.984（3）,b=16.164（3）,c=16.894（3）A,β=107.457（3）°,V=3642.9（11）A3,Z=4,C29H60O4Sn2,Dc=1.251g/cm3,μ=1.394 mm-1,R=0.0500,wR=0.0874,F（000）=1416。晶体结构中存在2种化学环境不同的三角双锥构型的锡原子,由于配体中2个羧基在不同方向的交联作用,使化合物呈现三维立体骨架结构,并且在骨架结构中存在沿a、b、c轴3个方向伸展的规则的大环直孔道。     

ANN原子参数法预报合金相晶型及晶格常数

运用人工神经网络方法，以二元合金组成元素的电子结构为基本特征，对二元合金相晶型作了区分，进一步对其晶格常数作了预报，结果令人满意。     

Simulation of aerated lagoon using artificial neural networks and multivariate regression techniques

The aim of this study was to develop an empirical model that provides accurate predictions of the biochemical oxygen demand of the output stream from the aerated lagoon at International Paper of Brazil, one of the major pulp and paper plants in Brazil. Predictive models were calculated from functional link neural networks (FLNNs), multiple linear regression, principal components regression, and partial least-squares regression (PLSR). Improvement in FLNN modeling capability was observed when the data were preprocessed using the PLSR technique. PLSR also proved to be a powerful linear regression technique for this problem, which presents operational data limitations.