Quantum-Mechanical Investigation of Large Water Clusters

The PM3 quantum-mechanical method has been used to study large water clusters ranging from 8 to 42 water molecules. These large clusters are built from smaller building blocks. The building blocks include cyclic tetramers, pentamers, octamers, and a pentagonal dodecahedron cage. The correlations between the strain energy resulting from bending of the hydrogen bonds formed by different cluster motifs and the number of waters involved in the cluster are discussed. The PM3 results are compared with TIP4P potential and ab initio results. The number of net hydrogen bonds per water increases with the cluster size. This places a limit on the size of clusters that would fit the Benson model of liquid water. Many of the 20-mer clusters fit the Benson model well. Calculations of the ion cluster (H20)4o(H30+)2 reveal that the m/e ratio obtainable by mass spectrometry experiments can uniquely indicate the conformation of the 20 water pentagonal dodecahedron cage present in the larger clusters.

Prediction of Accurate Anharmonic Experimental Vibrational Frequencies for Water Clusters, (H2O)n, n = 2−5

Accurate anharmonic experimental vibrational frequencies for water clusters consisting of 2−5 water molecules have been predicted on the basis of comparing different methods with MP2/aug-cc-pVTZ calculated and experimental anharmonic frequencies. The combination of using HF/6-31G* scaled frequencies for intramolecular modes and anharmonic frequencies for intermolecular modes gives excellent agreement with experiment for the water dimer and trimer and are as good as the expensive anharmonic MP2 calculations. The water trimer, the cyclic Ci and S4 tetramers, and the cyclic pentamer all have unique peaks in the infrared spectrum between 500 and 800 cm-1 and between 3400 and 3700 cm-1. Under the right experimental conditions these different clusters can be uniquely identified using high-resolution IR spectroscopy.

Ancient Calendars and Bolivian Modernity: Tiwanaku’s Gateway of the Sun, Arthur Posnansky, and the World Calendar Movement of the 1930s

Tourists to the archaeological site of Tiwanaku are presented with ancient calendars, of which the Gateway of the Sun is the most important, famous, and beautiful. Arthur Posnansky and other early 20th-century archaeologists claimed that its inscriptions constituted a written calendar. These claims were intimately connected to narratives of Tiwanaku as a central source of knowledge in both pre-Columbian times and the contemporary world. Posnansky presented his interpretation of Tiwanaku’s calendars as a response to the debates of the World Calendar Movement, which in the 1930s was attempting to rationalize the Gregorian calendar. In the Gateway, Posnansky found a uniquely Bolivian response to the international, North Atlantic-dominated scientific community’s search for a rational way to keep time in the world economy. Bolivian intellectuals merged their interest in the indigenous past with their concerns about the role of the modernist Bolivian state in the global system.

New Results Concerning Probability Distributions with Increasing Generalized Failure Rates

The generalized failure rate of a continuous random variable has demonstrable importance in operations management. If the valuation distribution of a product has an increasing generalized failure rate (that is, the distribution is IGFR), then the associated revenue function is unimodal, and when the generalized failure rate is strictly increasing, the global maximum is uniquely specified. The assumption that the distribution is IGFR is thus useful and frequently held in recent pricing, revenue, and supply chain management literature. This note contributes to the IGFR literature in several ways. First, it investigates the prevalence of the IGFR property for the left and right truncations of valuation distributions. Second, we extend the IGFR notion to discrete distributions and contrast it with the continuous distribution case. The note also addresses two errors in the previous IGFR literature. Finally, for future reference, we analyze all common (continuous and discrete) distributions for the prevalence of the IGFR property, and derive and tabulate their generalized failure rates.

A General Approach Towards the Synthesis of Amido-Functionalized Biodegradable Polyesters

The thesis presented here describes methodologies to produce pendant group functionalized polyesters from amido-functionalized α-hydroxy acids. The synthetic methods used to produce the functionalized α-hydroxy acids are compatible with a wide array of functional groups, making this technique highly versatile. The synthesis of functionalized polyesters was investigated to develop polymers with properties that may improve the capabilities of existing biodegradable polyesters for applications in controlled release pharmaceuticals. Chemically modified a-hydroxy acids were synthesized by reacting glyoxylic acid with a primary or secondary amide. To demonstrate the utility of this reaction, fourstructurally dissimilar amide substituents were examined including 2-pyrrolidione, benzamide, acetamide and acrylamide. The reaction is synthetically simple, provides high yields and is uniquely flexible, functionalized monomer. The compatibility of this procedure with the collection of functional groups mentioned circumvents the need for syntheses. The amido-functionalized monomers were polymerized by two different techniques: melt polycondensation and solution polymerization. Melt polycondensation was conducted by heating the monomer past its melting temperature under reduced pressure. Oligomeric functionalized polyesters (= 800 g/mol) with low PDIs (= 1.05) were obtained by melt polycondensation. Melt polycondensation was not compatible with all of the synthesized monomers. Two of the monomers (containing benzamide and acrylamide functionalities) degraded before the polycondensation reaction occurred. Thermal gravimetric analysis confirmed that a process other than polyesterification was occurring, indicating that some amido-functionalized α-hydroxy acids cannot be synthesized in the melt.Solution polymerization was conducted to polymerize functionalized α-hydroxy acids that were incompatible with melt polycondensation. Several modified Steglich polyesterifications were tested including p-toluenesulfonic acid mediated and scandium (III) triflate catalyzed. Only oligomeric functionalized polyesters were formed bythis method. A number of possible side reactions including the formation of an N-acylurea and a cyclic polymer ring were possible. The utility of this procedure appears to be limited due to the complexity of the reaction and its inability to produce high molecular weight polymer.