Tree-edges deletion problems with bounded diameter obstruction sets

We study the following problem: given a tree G and a finite set of trees H, find a subset O of the edges of G such that G-O does not contain a subtree isomorphic to a tree from H, and O has minimum cardinality. We give sharp boundaries on the tractability of this problem: the problem is polynomial when all the trees in H have diameter at most 5, while it is NP-hard when all the trees in H have diameter at most 6. We also show that the problem is polynomial when every tree in H has at most one vertex with degree more than 2, while it is NP-hard when the trees in H can have two such vertices.The polynomial-time algorithms use a variation of a known technique for solving graph problems. While the standard technique is based on defining an equivalence relation on graphs, we define a quasiorder. This new variation might be useful for giving more efficient algorithm for other graph problems.     

Sensing the physicochemical nature of he and ne in micropores by adsorption measurements

He and Ne in contact with molecular sieves in the form of crystalline A zeolites and amorphous carbon molecular sieves fibers (CMSF) were studied by adsorption measurements. Classification of the effective enclosure of zeolitic apertures and of graphitic constrictions, as determined by recent temperature-programmed desorption mass spectrometry (TPD-MS) studies of adsorption of He and Ne onto these materials, was utilized in making a prudent choice of samples and experimental conditions. In view of the former TPD information, the behaviors of adsorption and volumetric measurements reported herein are straightforwardly interpreted. The combined TPD, adsorption isotherms, and dead volume data deepen the understanding of the physicochemical nature of adsorbed gas, where gas adsorption in the vicinity of pore constrictions and/or apertures as well as on the inner surface areas of pores and/or cages could be resolved. Previous conclusions that the huge activation energies measured for Ne/CMSF at high temperatures are unlikely to characterize chemical desorption but reflect those required for overcoming the barrier of effectively constricted apertures were confirmed by the volumetric data presented here. At 77 K, considerable He adsorption was observed in the porous solids and found to be responsible for abnormal deduced values of dead volumes. The occurrence of significant adsorption of He onto A zeolites and CMSF at 77 K warrants the realization that in cases concerning porous materials, volumetrically deduced quantities should not be taken for granted, but should be carefully considered and uniquely interpreted in relation to the specific experimental conditions under which they are taken.     

Effects of structure on properties of some new aromatic-aliphatic polybenzimidazoles

Polybenzimidazoles were prepared in poly(phosphoric acid) from isophthalic, m- and p-phenylene diacetic, succinic, adipic, suberic, and sebacic acids and 3,3′-diaminobenzidine, 3,3′,4,4′-tetraaminodiphenyl ether and 3,3′,4,4′-tetraaminodiphenylmethane. The thermal, mechanical, and bonding properties were studied. A 3:1 copolymer of isophthalic and m-phenylenediacetic acid with 3,3′-diaminobenzidine showed the best results as far as isothermal oxidation resistance and thermal and processing characteristics.     

A new route of oxygen isotope exchange in the solid phase: demonstration in CuSO4.5H2O

Temperature-programmed desorption mass spectrometry (TPD-MS) measurements on [(18)O]water-enriched copper sulfate pentahydrate (CuSO(4).5H(2)(18)O) reveal an unambiguous occurrence of efficient oxygen isotope exchange between the water of crystallization and the sulfate in its CuSO(4) solid phase. To the best of our knowledge, the occurrence of such an exchange was never observed in a solid phase. The exchange process was observed during the stepwise dehydration (50-300 degrees C) of the compound. Specifically, the exchange promptly occurs somewhere between 160 and 250 degrees C; however, the exact temperature could not be resolved conclusively. It is shown that only the fifth, sulfate-associated, anionic H(2)O molecule participates in the exchange process and that the exchange seems to occur in a preferable fashion with, at the most, one oxygen atom in SO(4). Such an exchange, occurring below 250 degrees C, questions the common conviction of unfeasible oxygen exchange under geothermic conditions. This new oxygen exchange phenomenon is not exclusive to copper sulfate but is unambiguously observed also in other sulfate- and nitrate-containing minerals.     

STOCHASTIC ENERGY DEMAND AND THE STABILIZATION VALUE OF ENERGY STORAGE

The economic value of energy storage to meet peak electricity demand is analyzed with an emphasis on the role of demand uncertainty. The concept of the stabilization value, which measures that part of the benefit of the storage project which is due solely to the stochastic demand components, is defined. The magnitude of the stabilization value, relative to the overall value of energy storage, is evaluated in terms of a simple model that accounts for the relevant characteristics of the electric power utility's production mix. It is found that neglecting the demand uncertainty can seriously bias the benefit assessment of the storage project as well as the determination of the optimal storage capacity.     

On the Dynamics of Knowledge-Based Economic Growth

A geometric approach to characterize the solutions of higher-dimensional dynamic optimization problems is applied to a model of knowledge-based economic growth. The characterization reveals a variety of growth patterns, ranging from sustained growth to stagnation. Growth processes exhibit a turnpike property, reaching as rapidly as possible the path along which human and physical capital are equally productive at the margin and evolving along it thereafter. Some growth processes display overshooting behavior and some are sensitive to threshold capital stocks. This work has been supported by the Paul Ivanier Center of Robotics and Production Management, Ben Gurion University of the Negev, Beer Sheva, Israel.     

Kinetic Considerations in the Formation of Electrical Active Grain Boundaries in Barium Titanate and Similar Perovskites

Grain boundaries in ceramic barium titanate and related materials can be engineered in order to obtain desired transport behavior. Our ability to do so is closely related to kinetic limitations during the preparation. The close-packed structure of perovskites excludes native or foreign interstitials in the bulk. (Interstitial protons are regarded as OH_O , using the Kröger-Vink notation). Antisites are also unlikely due to size, charge and coordination number mismatch. The possible point defects are, therefore, substitutionals and vacancies. The kinetic limitations of these species, and the results in terms of grain boundary engineering, are considered in this contribution.A clear distinction between three different conditions is made. At very high temperatures, it is assumed that all the relevant defects are mobile and can equilibrate, at least locally. Hence, their concentrations are all functions of the degrees of freedom of the system. At lower temperatures, the cation sublattice is frozen. Therefore, the concentrations of metal vacancies and substitutional cations are constants and, from local electrical neutrality point of view, a new parameter becomes important: the concentration of frozen charge. The concentrations of electronic defects and oxygen vacancies in this metastable state are functions of temperature, oxygen partial pressure and frozen charge. The normalized concentration of frozen metal vacancies is calculated as a function of the doping factor, f (defined as the ratio between the electron concentration at a given state and at a reference state), and a nonstoichiometry parameter. Around room temperature, the anion sublattice is also frozen, and only electrons and holes exhibit significant transport properties.     

Elastostatic resonances—a new approach to the calculation of the effective elastic constants of composites

A new method is presented for a systematic evaluation of the effective elastic tensor C^(e) in a two-component composite. Both C^(e) and local strain field are expanded in terms of a complete set of elastostatic resonances. The resonances are found by calculating eigenstates of a certain integral operator, and this can be carried out in stages. First one finds the eigenstates of individual, isolated grains or fibers, and only then does one attempt to calculate eigenstates of the entire composite. We apply this procedure to 2D periodic arrays of cylinders—both hexagonal and square. Using simple matrix perturbation techniques we obtain exact expansions for the elastic constants in powers of p, the volume fraction of the cylinders, that go up to the order p¹¹ in the case of bulk modulus of the hexagonal array.     

Electrical conductivity of Co doped cuprous oxide

The solubility limit of metals in cuprous oxide is very low and it is therefore difficult to form solid solutions of metal oxides with cuprous oxide. In an on going research looking for such solid solutions and their properties we have prepared Co doped Cu₂O. We report here on measurements of the electrical conductivity of Co doped Cu₂O as a function of the oxygen partial pressure. It is found that Co doped material is an n-type semiconductor in the low oxygen partial pressure regime and p-type at higher oxygen pressures (while undoped Cu₂O is a p-type material throughout the whole existence regime). A point defect model is discussed. The ionic transference number is also measured and is found to be less than 2⋅10⁻⁴. Paper presented at the 2nd Euroconference on Solid State Ionics, Funchal, Madeira, Portugal, Sept. 10–16, 1995