An improved algorithm for computing topological entropy

A new algorithm is presented for computing the topological entropy of a unimodal map of the interval. The accuracy of the algorithm is discussed and some graphs of the topological entropy which are obtained using the algorithm are displayed.     

The semidirect products of finite cyclic groups that areI-E groups

AnI-E group is a group in which the endomorphism near-ring generated by the group's inner automorphisms equals the endomorphism near-ring generated by its endomorphisms. In this paper we shall completely determine the finite groups that are semidirect products of cyclic groups and areI-E groups.     

Anticancer agent development: X-ray crystal structure and keto-enol tautomerism of dimethyl 1-hydroxy-6,7-methylenedioxy-4-(3′,4′,5′-trimethoxyphenyl-trans-3,4-dihydronaphthalene-2,3-dicarboxylate

Structural and conformational information obtained from the crystal structure and solution¹H nmr investigations of the title compound are compared. The 4-aryltetralone, C₂₄H₂₄O₁₀, crystallizes as a chloroform solvate in the monoclinic space group, P2₁/n, witha=12.519(4),b=17.938(6),c=12.534(9)Å,=111.90(5)°, and D_calc=1.51 g cm^–3 forZ=4. The data for this compound were collected at –150°C. Least-squares refinement of 2796 observed [F _o5(F _o)] reflections led to the final agreement index ofR=0.062. A threefold static disorder was observed for one of the carboxyl groups. The second carboxyl group participates in an intramolecular hydrogen bond and is thus ordered. The¹H nmr spectrum revealed the title compound to exist as a keto-enol tautomeric mixture in solution. Vicinal hydrogen coupling constant analysis proved reliable in ascertaining B-ring stereochemistry of 2,3-disubstituted-4-aryltetralones.     

Microwave chemical processing

The chemical industry admits to minimal use of microwave power because of its high capital and operating costs relative to steam, combustion, electrical, and other traditional sources of energy. Other valid historical and persistent reasons for their lack of proper use include: a poor conceptual understanding of microwaves by chemical professionals, their unwillingness to replace existing adequate methods with radically new technology, the infancy of the microwave industrial power supply, and unfamiliarity of microwave power systems manufacturers with the chemical industry. In years past, the North American chemical industry had few competitors and profits were generally large. Environmental regulations were few and product quality was less a concern than production volume. The microwave power industry relied on the government and communications for lucrative sales. Those days appear over. Chemical manufacturers must probe every technology to achieve the edge necessary to stay competitive while meeting environmental stewardship demands. Microwave power has always offered unique advantages in heating materials selectively and/or quickly to high or preselected temperatures with fast control response. In the cases discussed in this paper, novel applications of microwave power afford: faster production, a reduction in product contaminants, reduced downtime, reduced waste, product quality improvements, and better pollution control.     

Solid supports for micro analytical systems

The development of micro analytical systems requires that fluids are able to interact with the surface of the microfluidic chip in order to perform analysis such as chromatography, solid phase extraction, and enzymatic digestion. These types of analyses are more efficient if there are solid supports within the microfluidic channels. In addition, solid supports within microfluidic chips are useful in producing devices with multiple functionalities. In recent years there have been many approaches introduced for incorporating solid supports within chips. This review will explore several state of the art methods and applications of introducing solid supports into chips. These include packing chips with beads, incorporating membranes into chips, creating supports using microfabrication, and fabricating gels and polymer monoliths within microfluidic channels.     

A hierarchical family of three-dimensional potential energy surfaces for He-CO

A hierarchical family of five three-dimensional potential energy surfaces has been developed for the benchmark He-CO system. Four surfaces were obtained at the coupled cluster singles and doubles level of theory with a perturbational estimate of triple excitations, CCSD(T), and range in quality from the doubly augmented double-zeta basis set to the complete basis set (CBS) limit. The fifth corresponds to an approximate CCSDT/CBS surface (CCSD with iterative triples/CBS, denoted CBS+corr). The CBS limit results were obtained by pointwise basis set extrapolations of the individual counterpoise-corrected interaction energies. For each surface, over 1000 interaction energies were accurately interpolated using a reproducing kernel Hilbert space approach with an R-6+R-7 asymptotic form. In each case, both three-dimensional and effective two-dimensional surfaces were developed. In standard Jacobi coordinates, the final CBS+corr surface has a global minimum at rCO=2.1322a0,R=6.418a0, and gamma=70.84 degrees with a well depth of -22.34 cm-1. The other four surfaces have well depths ranging from -14.83 cm-1 [CCSD(T)/d-aug-cc-pVDZ] to -22.02 cm-1 [CCSD(T)/CBS]. For each of these surfaces the infrared spectrum has been accurately calculated and compared to experiment, as well as to previous theoretical and empirical surfaces. The final CBS+corr surface exhibits root-mean-square and maximum errors compared to experiment (4He) of just 0.03 and 0.04 cm-1, respectively, for all 42 transitions and is the most accurate ab initio surface to date for this system. Other quantities investigated include the interaction second virial coefficient, the integral cross sections, and thermal rate coefficients for rotational relaxation of CO by He, and rate coefficients for CO vibrational relaxation by He. All the observable quantities showed a smooth convergence with respect to the quality of the underlying interaction surface.