Strand Lines and Chronology of the Glacial Great Lakes in Northwestern New York

Author Institution: Department of Geological Sciences, State University of New York at BuffaloRecent restudy of Glacial Great Lake history in northwestern New York tends to confirm a general sequence of nine to ten major lake stands, predicted from others' work in adjacent areas in the Erie and Huron basins. However, some doubt is raised as to the dating and position of the ice margin at the initiation of this sequence. The evidence suggests that glacial lake waters rose to form Lake Whittlesey between 12,700 and 13,800 years B.P., with advance to either the Lake Escarpment, Gowanda, or Hamburg End Moraines. Lake Whittlesey lowered to the Warren I level about 12,700 B.P., after the ice margin had retreated less than one mile from the main portion of the Hamburg Moraine. A second but brief lake stand (Warren II) is weakly suggested by a lower set of beach ridges. However, such a stand must have been very brief, for it gave way to a much lower lake soon after the ice margin had retreated from the next more northerly (Alden) moraine. This much lower lake stage, probably correlating with Lake Wayne, occurred during construction of the gravelly Buffalo Moraine and before waters rose again to form Lake Warren III. Lake Warren III, evidenced by the strongest beaches in this area, ended following ice-margin retreat from the Batavia Moraine, when lake level dropped 40 feet to the Lake Grassmere level. Evidence for lower and later glacial lake stands is sparce, but includes features which may correlate with the short-lived Lakes Lundy and Early Algonquin, and a much smaller local glacial lake, Dana. Lake Dana, the last glacial lake in this portion of the Erie basin, was extinguished as the terminus of the ice sheet retreated north of the Niagara escarpment and into the present area of Lake Ontario and thus opened the Rome outlet to the Mohawk-Hudson River drainage system. The average of several C14 dates from the Lake Ontario basin suggests that this event occured prior to 12,100 years ago. At least 170 feet of isostatic uplift has taken place on the Buffalo isobase since Lake Whittlesey time

Asymptotic formula for the moments of Minkowski question mark function in the interval [0,1]

In this paper we prove the asymptotic formula for the moments of Minkowski question mark function, which describes the distribution of rationals in the Farey tree. The main idea is to demonstrate that certain a variation of a Laplace method is applicable in this problem, hence the task reduces to a number of technical calculations.Comment: 11 pages, 1 figure (final version). Lithuanian Math. J. (to appear

Conference Report: Gender, Neoliberalism, and Financial Crisis: Gendered impacts and feminist alternatives

The politics of austerity and crisis are deeply gendered and open up a wide range of feminist debates around neoliberalism, resistance, and gender justice. The Gender, Neoliberalism, and Financial Crisis Postgraduate Conference, which took place at the University of York on 27 September 2013, sought to map the multiple impacts of financial crisis, austerity, and neoliberalism on women and to articulate an alternative feminist agenda. It brought together researchers from around the world working on feminist political economy, sociology, development studies, economics, and related disciplines to present their findings and build networks for future research collaboration

Factors of sums and alternating sums involving binomial coefficients and powers of integers

We study divisibility properties of certain sums and alternating sums involving binomial coefficients and powers of integers. For example, we prove that for all positive integers $n_1,..., n_m$, $n_{m+1}=n_1$, and any nonnegative integer $r$, there holds {align*} \sum_{k=0}^{n_1}\epsilon^k (2k+1)^{2r+1}\prod_{i=1}^{m} {n_i+n_{i+1}+1\choose n_i-k} \equiv 0 \mod (n_1+n_m+1){n_1+n_m\choose n_1}, {align*} and conjecture that for any nonnegative integer $r$ and positive integer $s$ such that $r+s$ is odd, $$\sum_{k=0}^{n}\epsilon ^k (2k+1)^{r}({2n\choose n-k}-{2n\choose n-k-1})^{s} \equiv 0 \mod{{2n\choose n}},$$ where $\epsilon=\pm 1$.Comment: 14 pages, to appear in Int. J. Number Theor

Improved bounds for the number of forests and acyclic orientations in the square lattice

In a recent paper Merino and Welsh (1999) studied several counting problems on the square lattice $L_n$. The authors gave the following bounds for the asymptotics of $f(n)$, the number of forests of $L_n$, and $\alpha(n)$, the number of acyclic orientations of $L_n$: $3.209912 \leq \lim_{n\rightarrow\infty} f(n)^{1/n^2} \leq 3.84161$ and $22/7 \leq \lim_{n\rightarrow\infty} \alpha(n) \leq 3.70925$. In this paper we improve these bounds as follows: $3.64497 \leq \lim_{n\rightarrow\infty} f(n)^{1/n^2} \leq 3.74101$ and $3.41358 \leq \lim_{n\rightarrow\infty} \alpha(n) \leq 3.55449$. We obtain this by developing a method for computing the Tutte polynomial of the square lattice and other related graphs based on transfer matrices

What Moser Could Have Asked: Counting Hamilton Cycles in Tournaments

Moser asked for a construction of explicit tournaments on $n$ vertices having at least $(\frac{n}{3e})^n$ Hamilton cycles. We show that he could have asked for rather more

Mean Row Values in (u,v)(u,v)-Calkin-Wilf Trees

We fix integers $u,v \geq 1$, and consider an infinite binary tree $\mathcal{T}^{(u,v)}(z)$ with a root node whose value is a positive rational number $z$. For every vertex $a/b$, we label the left child as $a/(ua+b)$ and right child as $(a+vb)/b$. The resulting tree is known as the $(u,v)$-Calkin-Wilf tree. As $z$ runs over $[1/u,v]\cap \mathbb{Q}$, the vertex sets of $\mathcal{T}^{(u,v)}(z)$ form a partition of $\mathbb{Q}^+$. When $u=v=1$, the mean row value converges to $3/2$ as the row depth increases. Our goal is to extend this result for any $u,v\geq 1$. We show that, when $z\in [1/u,v]\cap \mathbb{Q}$, the mean row value in $\mathcal{T}^{(u,v)}(z)$ converges to a value close to $v+\log 2/u$ uniformly on $z$

Charge distribution in two-dimensional electrostatics

We examine the stability of ringlike configurations of N charges on a plane interacting through the potential $V(z_1,...,z_N)=\sum_i |z_i|^2-\sum_{i<j} ln|z_i-z_j|^2$. We interpret the equilibrium distributions in terms of a shell model and compare predictions of the model with the results of numerical simulations for systems with up to 100 particles.Comment: LaTe