(k, l)-Algebraic Stability of Gauss Methods

It is well known that the s-stage Gauss Runge-Kutta methodsof order 2s are algebraically stable, or equivalently (1, 0)-algebraicallystable. In this paper, we show that there exists some l_s >0 such that the Gauss methods are (k, l) algebraically stablefor l [0, l_s) with k(l)=e^2l+O(l^p+1, where p=2s if s=1 or s=2,and p=2 if s>3.     

The role of water in the design of glycosidic linkage flexibility

In this paper we show how a variety of computational methods are used to understand the role that water plays in the solution conformational dynamics of carbohydrates. A comparison is made between maltose and a designed disaccharide (α-D-Glc-NAc-(1→4)-β-D-Glc-3-NH₂) in which the cross glycosidic linkage hydrogen bonds have been significantly strengthened. However, despite the stronger intramolecular hydrogen bonds in the maltose derivative, the correlation times for glycosidic dihedral angle fluctuations are approximately the same for the two sugars. Upon investigation of the water in the first hydration shells for the two disaccharides, high water probability densities were found between the functional groups straddling the glycosidic linkage that bonds the two monosaccharides together. This probability density corresponds to single water molecules forming bridging hydrogen bonds between the functional groups on either side of the linkage for periods of 3.66 ps in the case of maltose and 8.36 ps in the case of the amine derivative. Ab initio studies of saccharide structure interaction with single water molecules reveal that these intermolecular (sugar-solvent) hydrogen bonds are of similar strength to the intramolecular (sugar-sugar) hydrogen bonds. This combination of molecular dynamics and ab initio computational methods demonstrates that increasing the internal hydrogen bond strength in oligosaccharides does not lead to significantly slower internal molecular motion of these sugars in solution. The intermolecular hydrogen bonds formed with water compete equally with the intramolecular hydrogen bonds in the sugar. This result has important implications when considering hydrophobic versus hydrophilic effects in glycoproteins.     

Buoyancy corrections for the potential of an impurity in a 4He nanodroplet

This paper presents correction terms for the effective potential for the translation and rotation of an impurity atom or molecule solvated in a helium nanodroplet that were previously published (Lehmann, K. K., 1999, Molec. Phys., 97, 645). The correction arises from changes in the total He-He potential energy of the displaced liquid as a function of the solute position within the droplet. For the alkali atoms, this buoyancy type correction removes the large barrier to ejection of the atom from the droplets, which is predicted if this term is neglected.     

Synthesis of Diels—Alder Adducts of Phencyclone and NMR Studies of Hindered Rotations of Unsubstituted Bridgehead Phenyls: Microscale Experiments in Organic Chemistry

Synthesis of Diels—Alder adducts of phencyclone with diverse dienophiles provides the basis for a major extended module in the second-semester laboratory of an organic chemistry course. With many accessible target compounds, students can have individual novel compounds to prepare. Especially attractive for students, the adducts are highly hindered, resulting in slow rotation about the C—C sp²—sp³ single bond to the unsubstituted bridgehead phenyl groups. Slow-exchange-limit NMR spectra (¹H at 300 MHz and ¹³C at 75 MHz) are obtained at ambient temperatures for these phenyl groups. The highly crystalline products are easily prepared and offer excellent opportunities to integrate modern 1-D and 2-D NMR techniques into this synthesis experiment, while introduccing concepts of dynamic NMR spectroscopy. The synthetic reactions are readily carried out at the microscale level.     

UNDERSTANDING MULTIPLE SPECIES ECOSYSTEM DYNAMICS USING A CONSUMER RESOURCE MODEL

Most ecological systems comprise multiple species coexisting and the dynamics of these multiple species can be important for understanding, management, and conservation. One method to study such ecological system dynamics is the use of heterogeneous models. Here we formulate and analyze a multiple species (n patches or groups) consumer resource model. Initial insights are gained by analyzing the special cases and . A threshold consumption number C₀ is used to investigate system stability and hence the long‐term dynamics of the system. It is shown how this threshold consumption number can measure the effects and extent of multiple species coexistence in the system.     

BOTT–BOREL–WEIL THEORY AND BERNSTEIN–GEL’FAND–GEL’FAND RECIPROCITY FOR LIE SUPERALGEBRAS

The main focus of this paper is Bott–Borel–Weil (BBW) theory for basic classical Lie superalgebras. We take a purely algebraic self-contained approach to the problem. A new element in this study is twisting functors, which we use in particular to prove that the top of the cohomology groups of BBW theory for generic weights is described by the recently introduced star action. We also study the algebra of regular functions, related to BBW theory. Then we introduce a weaker form of genericness, relative to the Borel subalgebra and show that the virtual BGG reciprocity of Gruson and Serganova becomes an actual reciprocity in the relatively generic region. We also obtain a complete solution of BBW theory for \( \mathfrak{o}\mathfrak{s}\mathfrak{p} \)(m|2), D(2, 1; α), F(4) and G(3) with distinguished Borel subalgebra. Furthermore, we derive information about the category of finite-dimensional \( \mathfrak{o}\mathfrak{s}\mathfrak{p} \)(m|2)-modules, such as BGG-type resolutions and Kostant homology of Kac modules and the structure of projective modules.     

CHLORIN AND PORPHYRIN DERIVATIVES AS POTENTIAL PHOTOSENSITIZERS IN PHOTODYNAMIC THERAPY

In order to find a photosensitizer with better optical properties and pharmacokinetics than Photofrin II, a series of new photosensitizers related to methyl pheophorbide-a and chlorin-e6 were synthesized. These compounds absorb at substantially longer wavelengths (lambda max 660 nm) than does Photofrin II (630 nm) and show promise for use in photodynamic therapy. Among the porphyrins, we observed that long carbon chain ether derivatives are better photosensitizers than their ester analogs. These sensitizers were tested for in vivo photosensitizing activity vis-a-vis Photofrin II, using the standard screening system of DBA/2 mice bearing transplanted SMT/F tumors. Most of these photosensitizers were found to have better tumoricidal photosensitizing activity than Photofrin II and demonstrated more rapid attenuation of normal tissue photosensitivity with time after administration vis-a-vis Photofrin II.     

SIMULATIONS TO INVESTIGATE ANIMAL MOVEMENT EFFECTS ON POPULATION DYNAMICS

Abstract Movement of organisms will influence their ecology and demographics. Animal movements are often characterized by path structures with directional persistence. The extent to which this impacts on population dynamics is investigated in this paper using theoretical simulations. The effects of different movement strategies on variations in visits to individual patches across a forage area are discussed. Variations in resource biomass across patches are shown to persist after long simulations. Consumer resource equations with movement are used to show how heterogeneity in resources caused by these variations can affect global population dynamics. With directional movements (random or persistent), dynamics change from limit cycles to stable equilibrium solutions. It is suggested that this effect has the potential to increase survival because perturbations from unforeseen factors (like drought) are less likely to crash populations.     

A fraud-alert model for credit cards during the authorization process

^*Correspondence regarding this paper should be addressed to the first author In this paper, we set forth an expert-system model to help alertbanks and other financial institutions to fraudulent usage ofconsumer credit during the authorization process. The paperfirst addresses the model-building process, then briefly describesprototype development, and finally presents results from analysisof real data from a Canadian bank.