The complexity of the word problems for commutative semigroups and polynomial ideals

AbstractAny decision procedure for the word problems for commutative semigroups and polynomial deals inherently requires computational storage space growing exponentially with the size of the problem instance to which the procedure is applied. This bound is achieved by a simple procedure for the semigroup problem

Australian whistlers

22 p. ; 24 cm.Includes bibliographical references (p. 22)

New birds from New Guinea

7 p. ; 24 cm.Includes bibliographical references

New geometric representations and domination problems on tolerance and multitolerance graphs

Tolerance graphs model interval relations in such a way that intervals can tolerate a certain amount of overlap without being in conflict. In one of the most natural generalizations of tolerance graphs with direct applications in the comparison of DNA sequences from different organisms, namely multitolerance graphs, two tolerances are allowed for each interval – one from the left and one from the right side. Several efficient algorithms for optimization problems that are NPhard in general graphs have been designed for tolerance and multitolerance graphs. In spite of this progress, the complexity status of some fundamental algorithmic problems on tolerance and multitolerance graphs, such as the dominating set problem, remained unresolved until now, three decades after the introduction of tolerance graphs. In this article we introduce two new geometric representations for tolerance and multitolerance graphs, given by points and line segments in the plane. Apart from being important on their own, these new representations prove to be a powerful tool for deriving both hardness results and polynomial time algorithms. Using them, we surprisingly prove that the dominating set problem can be solved in polynomial time on tolerance graphs and that it is APX-hard on multitolerance graphs, solving thus a longstanding open problem. This problem is the first one that has been discovered with a different complexity status in these two graph classes. Furthermore we present an algorithm that solves the independent dominating set problem on multitolerance graphs in polynomial time, thus demonstrating the potential of this new representation for further exploitation via sweep line algorithms

Australian bowerbirds

18 p. : ill. ; 24 cm.Includes bibliographical references

Bahama snails

48 p. : ill., map ; 24 cm.Includes bibliographical references (p. 46-48)."A survey was made of the Cerion snails in the Bimini group, Bahama Islands. Samples were obtained of every colony on North, East, and South Bimni, and the location and extent of the colonies were mapped. Samples from Gun Cay, North Cat Cay, and South Cat Cay were also studied. Subfossil dead shells of Cerion were collected in several areas where Cerion has become extinct. 2. Each colony has its own diagnostic characteristics of size, shape, sculpture, and coloration, but three groups of colonies are distinguishable: the lerneri group, the biminiense group, and the Cat Cay group (pillsburyi). Even though superficially each group appears to be a separate species, each is allopatric, and adjacent colonies show signs of gene exchange. Two colonies are apparently hybrid populations. 3. Hybrid colonies show high variability (C.V.) with respect to sculpture (amount of costation) and coloration, but size and shape are not more variable than in other colonies. 4. Colony size is very variable, ranging from a few hundred individuals to several hundred thousands. 5. Some colonies are isolated from one another by stretches of from 1 to 5 kilometers of unsuitable or unoccupied terrain; in other areas the colonies form an uninterrupted band parallel to the beach. 6. The colonies are similar to one another in basic ecology, but differ in preference for substrate (coral rock or sand), preferred plants, and exposure. 7. Geographic variation is pronounced, but irregular. The facts are best explained by one's assuming two antagonistic tendencies: a high degree of sedentariness and infrequent long-distance dispersal by hurricanes. 8. Differences in shell characteristics evolve more rapidly than reproductive isolation. As a consequence, some populations which had become morphologically very distinct during a period of isolation were still able to interbreed freely when they again came into contact. 9. The characteristics that adapt Cerion so superbly to its continuously changing habitat make it exceedingly difficult to classify the populations of this genus in the conventional categories of species and subspecies"--P. 45-46

Why are vinyl cations sluggish electrophiles?

The kinetics of the reactions of the vinyl cations 2 [Ph2C═C+–(4-MeO–C6H4)] and 3 [Me2C═C+–(4-MeO–C6H4)] (generated by laser flash photolysis) with diverse nucleophiles (e.g., pyrroles, halide ions, and solvents containing variable amounts of water or alcohol) have been determined photometrically. It was found that the reactivity order of the nucleophiles toward these vinyl cations is the same as that toward diarylcarbenium ions (benzhydrylium ions). However, the reaction rates of vinyl cations are affected only half as much by variation of the nucleophiles as those of the benzhydrylium ions. For that reason, the relative reactivities of vinyl cations and benzhydrylium ions depend strongly on the nature of the nucleophiles. It is shown that vinyl cations 2 and 3 react, respectively, 227 and 14 times more slowly with trifluoroethanol than the parent benzhydrylium ion (Ph)2CH+, even though in solvolysis reactions (80% aqueous ethanol at 25 °C) the vinyl bromides leading to 2 and 3 ionize much more slowly (half-lives 1.15 yrs and 33 days) than (Ph)2CH-Br (half-life 23 s). The origin of this counterintuitive phenomenon was investigated by high-level MO calculations. We report that vinyl cations are not exceptionally high energy intermediates, and that high intrinsic barriers for the sp2 ⇌ sp rehybridizations account for the general phenomenon that vinyl cations are formed slowly by solvolytic cleavage of vinyl derivatives, and are also consumed slowly by reactions with nucleophiles

An organometallic chimie douce approach to new Re(x)W(1-x)O3 phases

Re(x)W(1-x)O3.H2O and Re(x)W(1-x)O3 phases are prepared by a new organometallic chimie douce concept employing the organometallic precursor methyltrioxorhenium.Comment: 3 pages, 6 figures, submitted to Chem. Com