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Geodesics and Bounded Harmonic Functions on Infinite GraphsIt is shown there that an infinite connected planar graph with a uniform upper bound on vertex degree and rapidly decreasing Green's function (relative to the simple random walk) has infinitely many pairwise finitelyintersecting geodesic rays starting at each vertex. We then demonstrate the existence of nonconstant bounded harmonic functions on the graph.

Cogrowth of Regular GraphsLet G be a dregular graph and T the covering tree of G. We define a cogrowth constant of G in T and express it in terms of the first eigenvalue of the Laplacian on G. As a corollary, we show that the cogrowth constant is as large as possible if and only if the first eigenvalue of the Laplacian on G is zero. Grigorchuk's criterion for amenability of finitely generated groups follows.

Amenability and superharmonic functionsLet G be a countable group and u a symmetric and aperiodic probability measure on G . We show that G is amenable if and only if every positive superharmonic function is nearly constant on certain arbitrarily large subsets of G. We use this to show that if G is amenable, then the Martin boundary of G contains a fixed point. More generally, we show that G is amenable if and only if each member of a certain family of Gspaces contains a fixed point.

On the Commute Time of Random Walks on GraphsGiven a simple random walk on an undirected connected graph, the commute time of the vertices x and y is defined as C(x,y) = ExTy+EyTx. We give a new proof, based on the optional sampling theorem for martingales, of the formula C(x,y) = 1/(Π(y)e(y,x)) in terms of the escape probability e(y,x ) (the probability that once the random walk leaves x, it hits y before it returns to x) and the stationary distribution Π(·). We use this formula for C(x,y) to show that the maximum commute time among all barbelltype graphs in N vertices is attained for the lollipop graph and its value is O[(4N3)/27]

On the spectrum and Martin boundary of homogeneous spacesGiven a conservative, spatially homogeneous Markov process X on an homogeneous spaces χ, we show that if the bottom of the spectrum of the generator of X is zero then the Martin boundary of contains a unique point fixed by the isometry group of χ.

On Iterates of Moebius transformations on fieldsLet p be a quadratic polynomial over a splitting field K, and S be the set of zeros of p. We define an associative and commutative binary relation on G ≡ K ∪ {∞ } S so that every Moebius transformation with fixed point set S is of the form x plus" c for some c. This permits an easy proof of Aitken acceleration as well as generalizations of known results concerning Newton's method, the secant method, Halley's method, and higher order methods. If K is equipped with a norm, then we give necessary and sufficient conditions for the iterates of a Moebius transformation m to converge (necessarily to one of its fixed points) in the norm topology. Finally, we show that if the fixed points of m are distinct and the iterates of m converge, then Newton's method converges with order 2, and higher order generalizations converge accordingly.

A note on the Zeta Function of a GraphThe number of splanning trees in a finite graph is first expressed as the derivative (at 1) of a determinant and then in terms of a zeta function. This generalizes a result of Hashimoto to nonregular graphs.

WomanAsSymbol: Intersections of Indian Nationalism, Gender, and IdentityThe purpose of this article is to explore the connection between Indian nationalism and gender identity. I provide a critique of Radhakrishnan and Chatterjee's notion of the outer/inner dichotomy of Indian nationalism by stating that religion, in postcolonial India, has emerged as a discursive totality that has subsumed the politics of indigenous or inner identity more so than other rhetoric of caste, tribal, gender, and class. I provide a groundwork for this debate via the writings of Nehru and Gandhi. I conclude, through an analysis of the practices of amniocentesis and Sati, that women and their bodies have been used as representations of the conflicts surrounding national subjectivity.

Associativity of the Secant MethodIterating a function like 1+1/x gives a sequence which converges to the Golden Mean but does so at a much slower rate than those sequences derived from Newton's method or the secant method. There is, however, a surprising relation between all these sequences. This relation, easily explained by the use of good notation, is generalized by means of Pascal's "Mysterium Hexagrammicum". Throughout, we make contact with many areas of mathematics and physics including abstract groups, calculus, continued fractions, differential equations, elliptic curves, Fibonacci numbers, functional equations, fundamental groups, Lie groups, matrices, Moebius transformations, pi, polynomial approximation, relativity, and resistors.

Assessing Outcomes with Nursing Research Assignments and Citation Analysis of Student BibliographiesWhat are the library and information research requirements in a typical undergraduate nursing program? Do distancelearning library services provide undergraduate nursing students with the research materials they require for their academic work? In order to determine how the broad range of reference, instruction, and access services offered by Feinberg Library at Plattsburgh State University of New York, are used by students, the author reviewed selected nursing course syllabi for research requirements and the resulting student research bibliographies as an outcome assessment. The review included 441 bibliographic citations from 78 student research papers from 19981999. Results indicated no significant difference between on and offcampus student bibliography citations with regards to currency, format or number of citations. Results also indicated that the reviewed undergraduate nursing research assignments were indeed designed to promote research integration into nursing practice, and that student access to information was sufficient to allow them to complete their academic assignments.

Those Immersed Resurface: A Follow Up with Track 2 Participants of the First Information Literacy ImmersionSo what happens to all those great ideas and all that motivation that we get when we attend conferences and professional development opportunities? In the case of the first Track 2 participants of ACRL's Institute for Information Literacy's Immersion program, quite a lot. Two years after the first Immersion program, a followup survey pursued this question and found where great ideas and motivation are taking librarians and the institutions they work for.

Effects of an Ice Storm on Fuel Loadings and Potential Fire Behavior in a Pine Barren of Northeastern New YorkEcological effects of natural disturbances depend on the disturbance type, frequency, intensity and spatial scale. Of the major natural disturbances in the Northeast, ice storms are more frequent than fires or wind storms. Affecting nearly ten million hectares, the ice storm of January, 1998 was probably the most intense and widespread natural disturbance in the Northeast during the 20th Century. Some of the areas heavily impacted by this ice storm were sandstone pavement pine barrens of northeastern New York, among the rarest ecological communities in New York State. Jack pine (Pinus banksiana) is the dominant tree species in the barrens. Ice storm damage to pine trees resulted in estimates of woody debris averaging 18 tons/ac (40 tonnes/ha) at the eight sites sampled in this study. These unusually high fuel loadings increase the probability for catastrophic wildfire. Predictions of fire behavior and fire intensity in these ice stormdamaged stands were made using the TSTMDL subsystem of BEHAVE. Estimates of fire behavior in these ice stormdamaged stands include flame lengths between 10 and 17 ft (3 and 5 m) and fireline intensities between 900 and 2600 Btu/ft/sec (3175 and 9400 kW/m). Fires of these intensities would be very difficult to suppress and would cause adverse ecological effects, including destruction of seeds contained in the slash. Further research is necessary to customize fuel models used to predict fire behavior in northeastern forests affected by disturbances.

A Guide to the Zooplankton of Lake ChamplainThis key was developed by undergraduate research students working on a project with NYDEC and the Lake Champlain Monitoring program to develop longterm data sets for Lake Champlain plankton. Funding for development of this key was provided by, the Lake Champlain Basin Program through the U.S. Environmental Protection Agency (EPA) and the New York Department of Environmental Conservation (NYDEC). The key contains couplet keys for the major taxa in Cladocera and Copepoda and a picture key to the major Rotifer plankton in Lake Champlain. All drawings are original by Ian M. Ater. Many thanks to the employees of the Lake Champlain Research Institute and the NYDEC for hours of excellent work in the field and in the lab: Robert Bonham, Adam Bouchard, Trevor Carpenter, Virginia Damuth, Jeff Jones, Marti Kroll, Dustin Lewis, Shannon Margrey, Tracy McGregor, Stephanie Stone and David Welch. We greatly appreciate the time and effort of Paula Woodward and Francis Dumenci in helping to put this guide together.

Decomposition Rates of Typha Spp. in Northern Freshwater Wetlands over a StreamMarshPeatland GradientDecomposition rates in wetlands vary with the composition of the biotic community and the physical and chemical environment. Variations in the process of decomposition in turn affect the overall rate of nutrient cycling within the wetland, affecting both primary productivity and general wetland health. This shortterm study took place in northern New York within the Little Chazy River watershed. The effects of wetland factors including nutrient status, dissolved oxygen, and pH value on decay rate were measured over a freshwater streammarshpeatland gradient. Litterbags were utilized and collected weekly from three separate sites within or near the Altona Flat Rock ecosystem. Soil and water parameters, as well as colonization by macroinvertebrates, were studied in order to link decay rates with specific wetland characteristics. Decomposition rates for Typha spp. were evaluated using the change in dry biomass, and percent nitrogen content of the plant litter. Dry biomass reduction took place most rapidly in the stream site and least rapidly in the peatland site, while fluctuations of percent nitrogen content did not show a distinct trend. A high level of dissolved oxygen corresponded to a higher decay rate, while a low pH value corresponded to a lower decay rate.

Plant Community Succession Following Disturbances in a Pine Barren and Adjacent Hardwood ForestThe sandstone pavement barren and adjacent cobblestone formations in Clinton County, New York were created by the sudden release of water from glacial Lake Iroquois approximately 12000 ybp. Today, the barren is a rare ecological community type in New York State, dominated by jack pine, a species that can tolerate a water and moisturedeficient soil. The soil in the cobblestone deposits supports hardwood trees such as northern red oak, sugar maple, red maple, and American beech. In January 1998, several days of freezing rain in the Northeast blanketed 10 million ha with 2 to 10 cm of ice. Two million ha of forests were severely affected, including the pine barren and adjacent forests in Clinton County, New York. This study investigated the effects of the ice storm and subsequent "restoration cuttings" on plant community succession in the pine barren and adjacent hardwoods. The William H. Miner Agricultural Research Institute, Chazy, New York owns the eight stands sampled in this study. Both disturbance types had dramatic effects on plant community structure. Nearly half of the hardwood trees were severely affected by the ice storm, but most survived through epicormic branching. Understory trees and regeneration proliferated beneath the temporary canopy gaps in the main canopy. Overstory species are represented in the regeneration size classes, with shadetolerant species being most important. In the hardwoods, neither the ice storm or restoration cuttings caused plant community succession in the strict definition; the disturbances caused shifts in importance of species present at the time the disturbances occurred rather than a replacement of one plant community by another. In the pine barren, ice storm damage was especially intense, causing severe crown breakage in more than half of the pine trees. The majority of pine trees were killed by the ice storm and no pine seedlings were observed in the ice stormdamaged stands. Moderate amounts of jack pine regeneration (between 18000 and 24000 stems per hectare) were found in the areas treated with a restoration cutting. This amount of jack pine regeneration was considered sufficient to replace the original stand. The future of ice stormdamaged, uncut stands in the barren is not promising. Here, the majority of pine trees are standing dead stems and the regeneration, while sparse, is primarily red maple. Without silvicultural intervention, ice storm damaged areas of the barren will have a shift from dominance by jack pine to heath shrubs, especially black huckleberry. The restoration cutting showed that mechanical treatment, while not as effective as fire in regenerating jack pine, can bring about adequate amounts of jack pine regeneration, along with red maple, white birch and gray birch.

Reinforcing Information and Technology Literature: The Plattsburg Tip SheetThis article describes a Plattsburgh State University Library and Information Services (LIS) faculty workshop on information and technology literacy. The workshop was developed in response to a call for the redraft ing and submission for academic curriculum review of all courses intended for General Education approval and credit to meet new college General Education requirements. The focus of this article is on the infor mation and technology literacy specifics of the new requirements, the particular style of tip sheet developed for the workshop, and its potential for use by other librarians. The essence of the Plattsburgh Tip Sheet is a practical approach to rethinking lectures, class activities, and assignments to reinforce information and technology literacies.

On integral Apollonian circle packingsThe curvatures of four mutually tangent circles with disjoint interior form what is called a Descartes quadruple. The four smallest curvatures of circles in an Apollonian circle packing form what is called a root Descartes quadruple and, if the curvatures are relatively prime, we say that it is a primitive root quadruple. We prove a conjecture of Mallows by giving a closed formula for the number of primitive root quadruples with minimum curvature n. An Apollonian circle packing is called strongly integral if every circle has curvature times center a Gaussian integer. The set of all such circle packings for which the center of the largest circle is in the unit square and for which curvature plus curvature times center is congruent to 1 modulo 2 is called the standard supergasket. These centers are in onetoone correspondence with the primitive root quadruples and exhibit certain symmetries first conjectured by Mallows. We prove these symmetries; in particular, the centers are symmetric around y = x if n is odd, around x = 1/2 if n is an odd multiple of 2, and around y = 1/2 if n is a multiple of 4.

Variability in troglomorphic adaptations of a Mexican cavefish, Poecilia mexicana, from Tabasco, MexicoThe cavefish Poecilia mexicana, earlier known as Poecilia sphenops, is a livebearing toothcarp or molly found only in Cueva de las Sardinas (also known as Cueva de Villa Luz or El Azufre), in Tabasco, Mexico. The cave ecosystem is based on mixed energy inputs from sulfur springs and chemolithotrophic baceteria, bats, and skylights. The rich food base supports an amazing population density of the cavefish. Earlier studies reported that the fish showed increasing troglomorphic adaptations in physical characteristics and behaviors as you went deeper into the cave. Data presented on eye size reduction show considerable variation and overlap of data by location sampled, and no statistical analyses were done. We sampled from some of the same areas as earlier studies and from the most remote sites in the cave. Our results show considerable variation in troglomorphy of eye reduction from all locations, and no statistical difference with fish from any part of the cave. Evolutionary pressure to develop troglomorphy may be reduced in this cave because of the rich food base, or hybridization with surface forms may not be limited by physical location within the cave.