(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.     

内爆驱动式超高速发射技术的初步研究

为获得10 km/s左右的超高速发射能力,以内爆发射器为研究对象,利用AUTODYN 2D软件对口径为8 mm的内爆发射器进行有限元仿真分析,获得了典型状态下的弹丸发射速度。研制了口径为8 mm的内爆发射器,并在压缩管中填充5 MPa氦气进行实验,分别获得了0.55 g铝合金弹丸7.95 km/s和0.37 g镁合金弹丸10.28 km/s的发射速度,与有限元仿真计算结果的速度偏差分别为15.3%和3.7%。结果表明,设计的内爆发射器具备10 km/s发射能力,满足空间碎片撞击和防护研究的超高速发射需求。     

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.     

A new algorithm for computing modified z-transforms

A new method of computing modified z-tranforms is introduced,which is easy to implement and use. The new algorithm is explainedin detail, and a compact listing is included. Six examples aregiven to demonstrate different uses of the algorithm. Assumptionsused to develop the basic algorithm are explained, and proceduresto overcome the restrictions of these assumptions are explainedand demonstrated. How to solve multirate digital systems problemsusing the introduced algorithm is demonstrated with an example.Time-saving and memory-saving modifications of the algorithmfor multirate problems are also explained.     

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.