Logical analysis of numerical data

“Logical analysis of data” (LAD) is a methodology developed since the late eighties, aimed at discovering hidden structural information in data sets. LAD was originally developed for analyzing binary data by using the theory of partially defined Boolean functions. An extension of LAD for the analysis of numerical data sets is achieved through the process of “binarization” consisting in the replacement of each numerical variable by binary “indicator” variables, each showing whether the value of the original variable is above or below a certain level. Binarization was successfully applied to the analysis of a variety of real life data sets. This paper develops the theoretical foundations of the binarization process studying the combinatorial optimization problems related to the minimization of the number of binary variables. To provide an algorithmic framework for the practical solution of such problems, we construct compact linear integer programming formulations of them. We develop polynomial time algorithms for some of these minimization problems, and prove NP-hardness of others. The authors gratefully acknowledge the partial support by the Office of Naval Research (grants N00014-92-J1375 and N00014-92-J4083).     

N2- and O2-broadening of CO2 for the (301)III ← (000) band at 6231 cm

The N₂- and O₂-broadening effect have been investigated for 10 absorption lines of the CO₂ (30⁰1)_III ← (00⁰0) band centered at 6231 cm⁻¹, in the range from P(28) to R(28) by a near-infrared diode-laser spectrometer. We have analyzed the observed line profiles with the Galatry function, and determined the N₂- and O₂-broadening coefficients precisely. The air-broadening coefficients for these lines have been derived. The present results are compared with those of the previous studies for this band and with some of the other bands.     

Voltammetric study of the transfer of polyammonium ions at nitrobenzene / water interface.

The transfer of polyammonium ions, poly[(dimethylimino)-1,6-hexanediyl] (n = 140, n being the degree of polymerization) ion and poly[(dimethylimino)(2-oxo-1,2-ethanediyl)imino-alpha,omega-alkanediylimino(1-oxo-1,2-ethanediyl)(dimethylimino)-alpha',omega'-alkanediyl] ([-N+ (CH3)2CH2CONH(CH2)x NHCOCH2N+ (CH3)2(CH2)y-]n, x = 2, 3, 4, or 6, y = 3 or 6, and n = 30-130) ions, at a polarizable nitrobenzene / water interface has been studied by normal pulse voltammetry and cyclic voltammetry. Despite the polydispersity of the preparations, by normal pulse voltammetry, an S-shaped current-potential curve with a well-defined limiting current, and, by cyclic voltammetry, a pair of anodic and cathodic peak currents due to the transfer of polyammonium ions across the interface were observed within the potential window. The voltammetric behavior is described. Also, the effect of ion-pair formation of the polyammonium ions with supporting electrolyte anions in nitrobenzene- and water-phases on the half-wave or midpoint potential of the ion-transfer, and the relation between the structure of the polyammonium ions and the transfer potentials are discussed.     

Decompositions of positive self-dual boolean functions

A coterie, which is used to realize mutual exclusion in distributed systems, is a family C of subsets such that any pair of subsets in C has at least one element in common, and such that no subset in C contains any other subset in C. Associate with a family of subsets C a positive Boolean function f_c such that f_c(x) = 1 if the Boolean vector x is equal to or greater than the characteristic vector of some subset in C, and 0 otherwise. It is known that C is a coterie if and only if f_c is dual-minor, and is a non-dominated (ND) coterie if and only if f_c is self-dual. We study in this paper the decomposition of a positive self-dual function into smaller positive self-dual functions, as it explains how to represent and how to construct the corresponding ND coterie. A key step is how to decompose a positive dual-minor function f into a conjunction of positive self-dual functions f₁,f₂,…, f_k. In addition to the general condition for this decomposition, we clarify the condition for the decomposition into two functions f₁, and f₂, and introduce the concept of canonical decomposition. Then we present an algorithm that determines a minimal canonical decomposition, and a very simple algorithm that usually gives a decomposition close to minimal. The decomposition of a general self-dual function is also discussed.     

Study on organic pollution parameters for dyes and dyeing auxiliaries

Analytical and Bioanalytical Chemistry -     

Preparation of a copper ion complex of sterically congested diphenyldiazomethanes having a pyridine ligand and characterization of their photoproducts

To show that persistent high-spin polycarbenes can be realized by utilizing hetero spin systems, two diphenyldiazomethanes having pyridyl groups, i.e., bis{4-(4-pyridyl)-2,6-dimethylphenyl}diazomethane (4,4'-DPy-1-N(2)) and {2,4-di(4-pyridyl)-6-bromophenyl}(2,6-dimethyl-4-tert-butylphenyl)diazomethane (2,4-DPy-1-N(2)), were prepared. Triplet carbenes, 4,4'-DPy-1 and 2,4-DPy-1, generated by photolysis of the corresponding diazomethanes were characterized by spectroscopic means (ESR and UV/vis in matrix at low temperatures and laser flash photolysis in solution at room temperature). The results showed that they were fairly persistent. Magnetic properties of the photoproducts from a 1:1 complex between DPy-1-N(2) and Cu(hfac)(2) (hfac = hexafluoroacetylacetonate) were characterized by ESR and a superconducting quantum interference device (SQUID) magneto/susceptometer. The field dependences of magnetization for the complexes, expressed by using M versus H/T plots, were analyzed in terms of the Brillouin function to be S = 6.80 (F = 0.60) for the 1:1 complex of 4,4'-DPy-1 and Cu(hfac)(2) and S = 3.71 (F = 0.73) for the 1:1 complex of 2,4-DPy-1 and Cu(hfac)(2) at 2.0 K. Thus, it has been demonstrated that a high-spin species is actually generated in the photoproducts and that the complexed carbenes showed significant stability.     

Halogen-free water-immiscible ionic liquids based on tetraoctylammonium cation and dodecylsulfate and dodecylbenzenesulfonate anions, and their application as chelate extraction solvent.

The tetraoctylammonium cation forms water-immiscible room temperature ionic liquids with dodecylsulfate and dodecylbenzenesulfonate anions. The ionic liquids are halogen-free and can be considered environmentally friendly solvents. At 25 degrees C, the solubilities of water in tetraoctylammonium dodecylsulfate and tetraoctylammonium dodecylbenzenesulfonate were 2.8 and 4.0%, respectively, and the densities were 0.92 and 0.93 g cm(-3). The ionic liquids formed stable interfaces with water at 25 degrees C. The possible use of tetraoctylammonium dodecylsulfate as chelate extraction solvent was evaluated by using 4,4,4-trifluoro-1-(2-thienyl)-1,3-butanedione as extractant. Tetraoctylammonium dodecylsulfate showed high extraction performance for divalent transition metal cations.     

Syntheses and reactions of ferrocene-containing polymers. III. Cyclopolymerization of 1,1′-divinylferrocene

1,1′-Divinylferrocene was polymerized with BF₃OEt₂ and AIBN initiators. Polymers were separated into benzene-soluble and benzene-insoluble fractions, the latter probably being crosslinked. The polymers obtained with BF₃OEt₂ were shown by infrared and NMR spectroscopy to contain both cyclized (70–80%) and uncyclized units, whereas the radical polymer consisted of more than 96% cyclized units. The benzene-soluble fraction of the cationically obtained polymer softened at temperatures below 150°C, but the insoluble fraction decomposed at 240°C. The radical polymers were stable up to 250–280°C (dec).     

螺环倍半萜(±)-α-花柏烯-3-酮的全合成

通过萜品油烯 ( Terpinolene)与 2 ,4-二氧代戊酸甲酯的 de Mayo反应得到 [2 +2 ]光加成产物 ,经反aldol重排 ,再环合成具有螺 [5 ,5 ]十一烷结构的花柏烯基本碳架 ,进而对其官能团进行化学修饰 ,完成了螺环倍半萜 (± ) -α-花柏烯 -3 -酮的全合成 .