Data Collection and Elementary School Mathematics

The curriculum standards of the National Council of Teachers of Mathematics advocate the inclusion of data collection activities throughout the middle school. This paper presents activities that implement these recommendations. Activities include data collection in the home, school and community and encourage students to summarize, interpret, and draw inferences from the data they collect individually and in cooperative groups. Four types of data collection activities are presented - observations, surveys, experiments and sampling. Every activity requires minimal planning/preparation by the teacher yet involves students in a variety of roles. Further, each activity can be adapted to different classroom settings.     

SeqFold – fully automated fold recognition and modeling software – evaluation and application

SeqFold is a fold recognition program based on sequence-similarity detection aided by predicted secondary structure [1–3]. Critical validation and evaluation of SeqFold fold recognition performance based on the latest Critical Assessment of protein Structure Prediction (CASP2) targets has been performed. It has revealed that four out of seven CASP2 threading targets were assigned a correct fold using this method. SeqFold has also been applied to the problem of fold recognition for leptin. Mice with a defective leptin gene are extremely obese and diabetic. Leptin does not exhibit clear sequence homology to any protein with known structure. SeqFold predicts that leptin belongs to the class of short-chain four-helical cytokines. The structure of leptin, which has recently been solved by X-ray crystallography, reveals that leptin is a long-chain four-helical cytokine. The 3D model of leptin demonstrates that SeqFold alignment-based homology modeling captures essential features of the leptin structure. Received: 25 May 1998 / Accepted: 4 August 1998 / Published online: 2 November 1998     

Communities in Italian corporate networks

The community structure of two real-world financial networks, namely the board network and the ownership network of the firms of the Italian Stock Exchange, is analyzed by means of the maximum modularity approach. The main result is that both networks exhibit a strong community structure and, moreover, that the two structures overlap significantly. This is due to a number of reasons, including the existence of pyramidal groups and directors serving in several boards. Overall, this means that the “small world” of listed companies is actually split into well identifiable “continents” (i.e., the communities).     

Optical spectra of sodium phosphate glasses

The visible, infrared, and ultraviolet spectra of seven glasses in the Na₂OP₂O₅ binary system were obtained. Changes in spectra were related to structural changes occurring the glass. Dopant ions Co²⁺, Cu²⁺, and Pb²⁺ were used to infer structural changes occurring as the metaphosphate composition was crossed going from pyrophosphate compositions into ultraphosphate compositions. The presence of chemically bound water was found to cause the overall modifier-to-former ratio to remain constant for glasses containing greater than 65 mol.% P₂O₅.     

Thermal (1,3)-allylic rearrangements in sulfoxides and sulfones

Rates and activation parameters for thermal (1,3)-allylic rearrangement have been determined for the systems β-methylallyl phenyl sulfoxide ($\text{2}$) and the corresponding sulfone ($\text{3}$), with evidence presented for a dissociative reaction mechanism.     

Substitution of the terminal chloride ligands of [Re(6)S(8)Cl(6)](4-) with triethylphosphine: photophysical and electrochemical properties of a new series of [Re(6)S(8)](2+) based clusters

A systematic substitution of the terminal chlorides coordinated to the hexanuclear cluster [Re(6)S(8)Cl(6)](4-) has been conducted. The following complexes: [Re(6)S(8)(PEt(3))Cl(5)](3-) (1), cis- (cis-2) and trans-[Re(6)S(8)(PEt(3))(2)Cl(4)](2-) (trans-2), mer- (mer-3) and fac-[Re(6)S(8)(PEt(3))(3)Cl(3)](-) (fac-3), and cis- (cis-4) and trans-[Re(6)S(8)(PEt(3))(4)Cl(2)] (trans-4) were synthesized and fully characterized. Compared to the substitution of the halide ligands of the related [Re(6)S(8)Br(6)](4-) and [Re(6)Se(8)I(6)](3-) clusters, the chloride ligands are slower to substitute which allowed us to prepare the first monophosphine cluster (1). In addition, the synthesis of fac-3 was optimized by using cis-2 as the starting material, which led to a significant increase in the overall yield of this isomer. Notably, we observed evidence of phosphine isomerization taking place during the preparation of the facial isomer; this was unexpected based on the relatively inert nature of the Re-P bond. The structures of Bu(4)N(+) salts of trans-2, mer-3, and fac-3 were determined using X-ray crystallography. All compounds display luminescent behavior. A study of the photophysical properties of these complexes includes measurement of the excited state lifetimes (which ranged from 4.1-7.1 μs), the emission quantum yields, the rates of radiative and non-radiative decay, and the rate of quenching with O(2). Quenching studies verify the triplet state nature of the excited state.     

An efficient and scalable one-pot double Michael addition-Dieckmann condensation for the synthesis of 4,4-disubstituted cyclohexane beta-keto esters

A simple, scalable, and efficient one-pot methodology for the synthesis of 4,4-disubstituted cyclohexane beta-keto esters from benzylic nitriles or esters and methyl acrylate promoted by potassium tert-butoxide is described. The process relies on a tandem double Michael addition-Dieckmann condensation reaction, which results in the formation of three discrete carbon-carbon bonds in a single pot, including a quaternary center. The method allows for the convenient and rapid synthesis of a variety of 4-aryl-4-cyano-2-carbomethoxycyclohexanone and 4-aryl-2,4-biscarbomethoxycyclohexanone building blocks for use in natural products synthesis and medicinal chemistry.     

Binuclear complexes for aerobic oxidation of primary alcohols and carbohydrates

The influence of electron-donating and electron-accepting properties of three pentadentate ligands was determined in connection with the aerobic oxidation ability of the corresponding binuclear copper(II) complexes for benzyl and allyl alcohols; additionally, the catalytic performance of their palladium and platinum analogs was characterized under comparable conditions. Quantitative aerobic oxidation of benzyl alcohol at 40 °C was achieved with a binuclear copper(II) complex—TEMPO catalyst in 2.5 h, while the regioselective aerobic oxidation of underivatized methyl-β-d-glucopyranoside was accomplished in about 35% yield at 60 °C after 24 h.     

Coordination Chemistry of Low-Valent Rhenium Polypyridyl Complexes: Synthesis, Reactivity, and Electrochemistry

The complex Re(III)(benzil)(PPh(3))Cl(3) (2) is used to synthesize a variety of Re(III) and Re(II) polypyridyl complexes of the type cis-[Re(III)(L(2))(2)Cl(2)](+), [Re(II)(L(2))(3)](2+), Re(III)(L(3))Cl(3), [Re(III)(L(3))(2)Cl](2+), and [Re(III)(L(4))Cl(2)](+), where L(2) = bpy (3and 6), tbpy (4 and 7), phen (5 and 8); L(3) = terpy (9and 10); L(4) = TMPA (11). The complex cis-[Re(III)(bpy)(2)Cl(2)](+) (3) is a useful synthon in the formation of complexes of the type [Re(bpy)(2)L(x)()](n)()(+) that are six- or seven-coordinate Re(III) complexes (13, 16, and 18) or octahedral Re(II) or Re(I) complexes (12 and 17). The [Re(III)(terpy)(2)Cl](2+) (10) complex can be reduced to form the Re(I) complex, [Re(I)(terpy)(2)](+) (21) and then electrochemically reoxidized to form new complexes of the type [Re(III)(terpy)(2)L](n)()(+). Similar behavior is observed for the [Re(II)(bpy)(3)](2+) (6) complex where [Re(III)(bpy)(3)((t)BuNC)](3+) (20) and [Re(I)(bpy)(3)](+) (19) may be formed. The electrochemistry of these complexes is discussed in relation to their reactivity and the observed pi-acidity of the polypyridyl ligands. In addition, X-ray crystal structures for cis-[Re(III)(bpy)(2)Cl(2)]PF(6) (3) and [Re(I)(bpy)(3)]PF(6) (19) are reported. cis-[Re(III)(bpy)(2)Cl(2)]PF(6) (3, ReC(20)H(16)N(4)Cl(2)F(6)P) crystallizes in the monoclinic space group C2/c with Z = 4 and lattice parameters a = 15.043(5) ?, b = 13.261(4) ?, c = 12.440(4) ?, and beta = 108.86(2) degrees at -100 degrees C. [Re(I)(bpy)(3)]PF(6) (19, ReC(30)H(24)N(6)F(6)P) crystallizes in the rhombohedral space group R&thremacr;c(h) (No. 167) with Z = 12 and lattice parameters a = 13.793(3) ? and c = 51.44(3) ? at -100 degrees C.     

Novel Copper(II) Thiodibenzoic Acid Coordination Polymers by in situ Extrusion of Sulfur from 2,2′‐Dithiodibenzoic Acid and the Unique Oxidation of Disulfide to Sulfate

Slow diffusion reaction of 2,2′‐dithiodibenzoic acid (dtdb) with CuCl₂ in the presence of N‐donor ligands results in the formation of different coordination polymers where both S–S and C–S scission and oxidation of S is observed. X‐ray diffraction analysis of [Cu(tdb)(phen)(H₂O)]₂ · 2H₂O.2DMF] ( 1 ), [Cu(tdb)(py)₂(H₂O)]₂ ( 3 ), and [Cu(tdb)(bipy)(H₂O)]₂ · 0.5H₂O ( 4 ) (tdb = thiodibenzoic acid, phen = phenanthroline, py = pyridine, bipy = 2,2′‐bipyridine) show that the metal ions are coordinated to the carboxylate oxygen atoms of the in situ generated tdb ligand in a monodenate fashion. In [Cu(phen)(SO₄)₂(H₂O)₂]_n ( 2 ) and [Cu(bipy)(SO₄)₂(H₂O)₂]_n ( 5 ), the sulfur is oxidized to sulfate ions prior to coordination with the metal. Complex 1 has a dimeric structure with π–π interactions between the phen ligands, whereas 3 and 4 form 1D polymeric chains.