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.     

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.     

The thermal effect of urethral warming during cryosurgery

The heating effect of urethral warming during cryosurgery has been investigated theoretically, via heat transfer simulations. Two warmer configurations have been considered: (i). the clinically available urethral warmer, which has a configuration of a counter flow fluid heat exchanger; (ii). a newly designed urethral warmer, based on a temperature controlled electrical heater, termed a "cryoheater". A dramatic effect of thermal resistance to heat transfer through the heat exchanger wall has been identified, which is absent in the cryoheater. It follows that the cryoheater is expected to be more efficient in generating an unfrozen region around the urethra. It is shown that the conventional heat exchanger may fail to prevent freezing around the urethra in a significant number of prostate cases, depending on the layout of cryoprobes around the urethra. On the other hand, clinical reports exist which suggest that the heat exchanger improves in many cases the outcome of cryosurgery, in terms of long term complications. It is speculated in the current report that the cryoheater can further improve the outcome of cryosurgery, by providing protection from freezing in a wider range of cases. It is suggested that a future study be conducted to examine the correlation between the layout of cryoprobes and surgical outcome.     

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.     

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     

TGA–MS degradation studies of some new aliphatic–aromatic polybenzimidazoles

The degradation of a series of polybenzimidazoles containing metylene groups in the chain was studied by TGA and MS. On heating the polymer derived from m-phenylenediacetic acid and 3,3′-diaminobenzidine to about 560°C in argon, partial fast decomposition into a solid sublimate was observed. The sublimate consisted of a mixture of fractions derived from the breaking of the chain at the methylene bonds. These methylene groups can be preoxidized at 250°C to carbonyl groups, eliminating thereby this mode of decomposition. At temperature higher than 560°C, gaseous products similar to those of the corresponding all-aromatic PBI are obtained.     

Improved algorithms for the random cluster graph model

We model noisy clustering data using random graphs: Clusters correspond to disjoint sets of vertices. Two vertices from the same set (resp., different sets) share an edge with probability p (resp., r < p). We give algorithms that reconstruct the clusters from the graph with high probability. Compared to previous studies, our algorithms have lower time complexity and apply under wider parameter range. © 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2007     

ENDANGERED SPECIES AND NATURAL RESOURCE EXPLOITATION: EXTINCTION VS. COEXISTENCE

A model of renewable resource exploitation under event uncertainty is formulated. The model is applied to analyze the situation in which excessive water diversion for human needs can lead to the extinction of an animal population. Special attention is given to uncertainty regarding the conditions that lead to extinction. The manner in which the potential benefit foregone due to the species' extinction (the “extinction penalty”) induces more conservative exploitation policies is studied in detail. When the extinction penalty is ignored, the optimal policy is to drive the resource stock to a particular equilibrium level from any initial state. When the extinction penalty is accounted for and the conditions that lead to extinction are not fully understood (i.e., involve uncertainty), an interval of equilibrium states is identified, which depends on the penalty and on the immediate extinction risk.