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.     

Throughput of a satellite channel communication

Summary The throughput of a satellite channel communication is depending upon the link protocol. It is well known that the classical HDLC protocol is inadequate when applied to satellite links instead of short terrestrial links. Several modifications have been proposed to overcome this problem. The present paper gives an analysis and evaluation of a new class of protocols called Virtual Subchannel schemes which splits the satellite link into several components; these subchannels are assigned for transmission in cyclic order and are controlled independently of each other by the classical HDLC procedure.     

Improving the performance of Invertible Bloom Lookup Tables

Invertible Bloom Lookup Tables (IBLTs) have been recently introduced as an extension of traditional Bloom filters. IBLTs store key-value pairs. Unlike traditional Bloom filters, IBLTs support both a lookup operation (given a key, return a value) and an operation that lists out all the key-value pairs stored. One issue with IBLTs is that there is a probability that a lookup operation will return “not found” for a key. In this paper, a technique to reduce this probability without affecting the storage requirement and only moderately increasing the search time is presented and evaluated. The results show that it can significantly reduce the probability of not returning a value that is actually stored in the IBLT. The overhead of the modified search procedure, compared to the standard IBLT search procedure, is small and has little impact on the average search time.     

The Role of Cations in Some Inorganic Hydrolysis Reactions

Cations which shift certain equilibria from left to right by forming a compound with one of the reaction products were investigated with respect to their kinetic role in the process. Silver ions have no influence on the rate of the hydrolysis of cyanogen iodide. Similarly, cations which form sparingly soluble carbonates do not influence the rate of hydration of carbon dioxide. On the other hand, the hydrolysis of chlorine is accelerated by Ag⁺ and, to a lesser extent, by Cd²⁺ and Fe(III). It is shown that the effect is not due simply to a bimolecular reaction between chlorine and the cation. In the case of Ag⁺, heterogeneous catalysis may play some role, in analogy with the solvolysis of organic halides. In the case of Cd²⁺, there is spectrophotometric evidence for compounds between Cl₂ and HOCl on the one hand, and the cation on the other. It is suggested that these compounds interconvert more rapidly than do the parent substances. A similar mechanism may be operative in the case of Fe(III), and, possibly, also in the case of Ag⁺.     

Palmqvist Crack Extension and the Center-Loaded Penny Crack Analogy

Palmqvist crack extension in WC-Co can be described using the center-loaded penny crack analogy. When Palmqvist cracks are represented by semicircles of diameter l (l=crack length measured from an impression corner), the stress intensity factor which controls crack extension differs from that of a half-penny crack of radius l+a (2a = impression size) by only a slowly varying factor m=2^1/2 (l/a)^1/2; m≅1.0 to 2.4 for WC-Co and m≅0.8 to 1.4 for ceramics.     

Sintering TiO2 in HCl Atmospheres

TiO₂ was sintered in HCl atmospheres to enhance the effects of vapor transport. Little or no densification is observed for temperatures between 1000° and 1300°C. Particle coarsening occurs at temperatures above 1200°C. The apparent activation energy for particle growth is 114 kJ/mol. It is concluded that the primary mass-transport mechanism is vapor transport while the particle growth rate is limited by grain-boundary mobility .     

Effects of Particle Size on the Fusion of Soda–Lime–Silicate Glass Containing NaCl

The coupled effects of particle size and 1 wt% NaCl additions on the sequence of melting reactions in a multicomponent system (sand–soda ash–calcite–dolomite–feldspar) were studied using data from DTA, DTGA, and XRD interactively. Glass batches varied in average particle size from 250 μm to finer than 45 μm. Milestone events in the fusion process of the coarse particle base glass were elucidated. The termination temperature of the last significant reaction associated with CO₂ release was 35°C lower in the fine particle size batch than with the coarsest batch. Liquid-phase formation at ∼523°C in the batch with 1 wt% NaCl occurred to an increasingly sizable extent with decreasing particle size. This contrasts with a similar effect at ∼630°C for a comparable batch without NaCl via eutectic melting between soda ash and dolomite. Sodium chloride additions significantly enhanced dissolution of CaO relic.     

Surface Chemistry of Lead Titanate and Its Impact on Binder Removal

Carbon residue after binder burnout was characterized for several nonstoichiometric lead titanate powders. Thermal decomposition of the poly(methyl methacrylate) (PMMA) binder was performed in nitrogen at 600°C. A drastic decrease in carbon retention was obtained in the case of the titanium-rich samples. The amount of carbon retention varies from 0.2 mg/m² to 1.2 mg/m² by changing the Pb/Ti molar ratio from 0.92 to 1.08. The surface reaction between PMMA and lead titanate particles was studied by diffuse reflectance Fourier transform infrared spectroscopy (DRIFTS). Surface hydroxyls reacted with ester groups in the PMMA or the methylmethacrylate monomer produced upon pyrolysis. The DRIFTS results showed that titaniumrich samples are less reactive and produce less surfacebound organic groups. Interestingly, titanium-rich samples contained more surface hydroxyls. Isoelectric point measurements, however, show that titanium-rich samples are more acidic. Thus, the reactivity of the surface hydroxyls is determined primarily by their acid-base characteristics rather than their concentration. Lead titanate powder was exposed to MMA vapor in a tube furnace at the indicated temperatures using nitrogen carrier gas as a model experiment. DRIFTS difference spectroscopy and Raman spectroscopy were performed on these samples after the exposure. MMA reacts with lead titanate powder in manner similar to PMMA. Analysis for sp ² and sp ³ absorbance of Raman spectra of these exposed powders at 400°–600°C showed pyrolysis behavior of surface-reacted species. The relative amount of sp ² bonded carbon decreases with increasing exposure temperature.     

Autoxidation of saturated fatty acids. II. The determination of the site of hydroperoxide groups in autoxidizing methyl palmitate

The monohydroperoxides of methyl palmitate oxidized at 150C were concentrated, purified, and reduced to yield a mixture of isomers of monohydroxy palmitate. No evidence of unsaturation in these molecules could be obtained, and no direct method for the resolution or identification of the individual isomers was found. Nuclear magnetic resonance (NMR) spectroscopy of the reduced esters suggested that the hydroxy groups were not located at either end of the chain of the fatty ester. To establish the location of the initial oxidative attack on saturated esters, the reduced esters of oxidized methyl palmitate were chemically cleaved at the location of the hydroxy group by means of chromium trioxide oxidation and by the Beckmann transformation. The resulting mono- and dibasic fatty acids were methylated and analyzed by gas chromatography. This analysis indicated that the oxidation of methyl palmitate did not occur selectively at one location along the ester. Although all carbon atoms can apparently be oxidized, preferential oxidation was observed toward the center of the molecule.