On finding optimal and near-optimal lineal spanning trees

The search for good lineal, or depth-first, spanning trees is an important aspect in the implementation of a wide assortment of graph algorithms. We consider the complexity of findingoptimal lineal spanning trees under various notions of optimality. In particular, we show that several natural problems, such as constructing a shortest or a tallest lineal tree, are NP-hard. We also address the issue of polynomial-time, near-optimization strategies for these difficult problems, showing that efficient absolute approximation algorithms cannot exist unlessP = NP.     

On the concept of relative and plastic spins and its implications to large deformation theories. Part II: Anisotropic hardening plasticity

Summary By resorting to both microscopic and macroscopic considerations, including the concept of single slip, dislocation stress, and a scale invariance argument we show that the notion and formalism of the relative spin introduced in Part I reduces to that of plastic spin previously recognized in the literature. The central feature of this reduction is the possibility of obtaining physically based constitutive equations for the plastic spin along with appropriate evolution equations for the dislocation or back stress. When these constitutive models are incorporated in the analysis of existing data on tension-torsion tests, we find satisfactory agreement between theory and experiment. In particular, a theoretical interpretation of the torsionally induced axial strain, as observed for example by Swift, Bailey et al., Hart and Chang, and others, is provided. Moreover, the recent experiments of Montheillet et al. on torsionally induced axial stresses are discussed in the light of the presently proposed models of large inelastic deformation inelasticity accounting for anisotropy and texture effects.

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With 12 Figures     

Digital parallelism, perpendicularity, and rectangles

The slope of digital line segments is defined and an algorithm to evaluate it is presented. Parallelism and perpendicularity of two digital line segments are also defined. Finally, rectangular digital regions are defined and characterized, and an algorithm that determines whether or not a given digital region is a digital rectangle is presented.     

Combined mode I-mode III fracture of a high strength low-alloy steel

Special formulations of theJ integral were used to quantify the combined mode I-mode III fracture behavior of ASTM A710 Grade A steel, a tough material which displays elastic-plastic behavior at room temperature. Experimental fracture initiation loci for two heat-treated conditions were linear inJ _i-J_iii space, agreeing with analytical predictions based on linear elasticity. As commonly observed in mode I fracture behavior, large tearing modulus values accompanied largeJ values for mode I and mode III components, individually as well as for totalJ values. There was a pronounced tendency toward antiplane shear flow in the modified compact tension specimens tested. This may result from the concentration of mode III shear strains in the plane of the propagating crack as predicted by slip line theory. Shear fractures with the crack propagating at inclined angles to both load line and plate free surfaces are favored energetically over pure mode I cracks even though the total surface area formed by the latter is much smaller.     

Squaring down of general MIMO systems to invertible uniform rank systems via pre- and/or post-compensators

Pre- and/or post-compensators are designed to square down a general MIMO system to a uniform rank system, the structure of which is almost similar to a SISO system. The method of squaring down either does not change the finite zero structure of the given MIMO system or simply adds additional finite zeros in the left half s-plane. The significance of such a squaring down lies in the simplicity of the structure of a uniform rank system lending itself for easy analysis and control design.     

Security concepts for the dynamics of autonomous vehicle networks

The secure operation of autonomous vehicle networks in the presence of adversarial observation is examined, in the context of a canonical double-integrator-network (DIN) model. Specifically, we study the ability of a sentient adversary to estimate the full network’s state, from noisy local measurements of vehicle motions. Algebraic, spectral, and graphical characterizations are provided, which indicate the critical role of the inter-vehicle communication topology and control scheme in achieving security.     

Preparation of trehalose and sorbitol fatty acid polyesters by interesterification

Trehalose octaoleate and sorbitol hexaoleate were prepared by a one-stage solvent-free interesterification of methyl oleate with trehalose octaacetate (TOAC) and sorbitol hexaacetate (SOHA), respectively, in the presence of 1–2.5% sodium metal as catalyst. The greatest yield of trehalose octaoleate, 97.5%, and sorbitol hexaoleate, 96.0%, were obtained at a mole ratio of methyl oleate: SOHA of 6:1 and methyl oleate:TOAC of 8:1 at a synthesis time of 2.5 hr, and temperatures of 105–115°C. The structure of both trehalose octaoleate and sorbitol hexaoleate was confirmed by infrared (IR) and nuclear magnetic resonance (C-13 NMR) spectroscopy. Physical properties such as viscosity, HLB, solubility, color, refractive index, specific gravity and density approximated the physical properties of sucrose polyesters (SPE) and vegetable oils. Trehalose octaoleate and sorbitol hexaoleate, as well as sucrose octaoleate, were not susceptible toin vitro lipolysis, suggesting potential application as low calorie oils. Presented at American Oil Chemists’ Society Annual Meeting in New Orleans, LA, in May, 1987.     

Over-production of 5-enolpyruvylshikimate-3-phosphate synthase in Escherichia coli: use of the T7 promoter

5-Enolpyruvylshikimate-3-phosphate (EPSP) synthase, the productof the Escherichia coli aroA gene, has been overproduced inE.coli BL21(DE3) under the control of the T7 gene 10 promoterand ribosome binding site, to a level of {small tilde}50% oftotal cell protein. EPSP synthase is the primary target of thepost-emergence herbicide, glyphosate, commonly known as Roundup^TM.A simple two step purification is described, which results in99% pure homogeneous protein (as determined by PAGE). The integrityof the protein has been compared with previously characterizedprotein from .E.coli AB2829(pKD501) by determination of itskinetic parameters, N-terminal protein and DNA sequences, aminoacid analysis and ¹³C-NMR spectroscopy. This new overproducingstrain readily provides the gram quantities of highly pure proteinrequired for NMR studies of the active site and the developmentof novel time-resolved solid-state NMR techniques currentlyunderway in this laboratory.     

Synchronization in heterogeneous networks of discrete‐time introspective right‐invertible agents

This paper studies output synchronization problem, formation problem, and regulated synchronization problem for a heterogenous network of discrete‐time introspective right‐invertible agents. We first propose a decentralized control scheme to solve the output synchronization problem for a set of communication topologies. Moreover, if the synchronization trajectories are assumed to be bounded, a universal controller can be constructed for all communication topologies, which contain a directed spanning tree. The design can be applied to solve the formation problem with arbitrary formation vectors. In the regulated synchronization problem, we assume only the root receives information from exosystem. We then design a decentralized controller to solve the problem for a set of communication topologies. Copyright © 2013 John Wiley & Sons, Ltd.     

The Effect of Organic Diluent on the Extraction of Eu(III) by HEH[EHP]

ABSTRACT

Because there are fewer tools available to probe the interactions therein, the effect of the fundamental chemistry of the organic diluent on solvent extraction equilibria has been under-characterized relative to the aqueous. As a result, diluents for solvent extraction are often selected for an application not for their utility as a medium for reaction, but for other (often equally) important reasons (like low flammability). To begin to improve this imbalance in the science, twenty different diluents have been used in a study of the extraction of radiotracer ^152/154Eu³⁺ from dilute nitric acid solutions using the extractant 2-ethylhexylphosphonic acid mono-2-ethylhexyl ester (HEH[EHP]). To increase the utility of the study and to honor the memory of Professor Jan Rydberg, this investigation was conducted by a cadre of comparatively inexperienced separation scientists (who are as a result no longer inexperienced separation scientists) as a radioanalytical chemistry and solvent extraction educational exercise. Slope analysis was used to determine the apparent stoichiometry of the extracted metal complex. The results discussed in the following indicate that, while the pH dependence exhibits the expected three H⁺ exchanged per metal ion extracted, the extractant dependence suggests that the number of protonated extractant molecules in the extracted complex changes with the organic diluent. The experimentally observed “extractant dependency” ranges from 2.5 to 3.0 dimer equivalent molecules per extracted metal ion. Ironically, in the diluents exhibiting the highest apparent M:(HA)₃ stoichiometry, HEH[EHP] extracts Eu³⁺ less efficiently. Europium luminescence spectroscopy was used to probe for changes in the first coordination sphere of the complex in different diluents. A model and conceptual framework for understanding these observations is described.