Monroe, County of and Monroe County Part-Time Employees, CSEA, Local 1000 AFSCME, AFL-CIO

In the matter of the fact-finding between the County of Monroe, employer, and the CSEA (Monroe County Part-time Employees), union. PERB case no. M2009-239. Before: Stephen P. LaLonde, fact finder

Lyons Central School District and Lyons Teachers Association

In the matter of the fact-finding between the Lyons Central School District, employer, and the Lyons Teachers Association, union. PERB case no. M2013-086. Before: Stephen P. LaLonde, fact finder

West Irondequoit Central School District and West Irondequoit Teachers Association

In the matter of the fact-finding between the West Irondequoit Central School District, employer, and the West Irondequoit Teachers Association, union. PERB case no. M2013-095. Before: Stephen P. LaLonde, fact finder

Wayne, County of & Sheriff of Wayne County and Wayne County Sheriffs Court Officers Association

In the matter of the fact-finding between the County of Wayne & Sheriff of Wayne County, employer, and the Wayne County Sheriff\u27s Court Officers Association, union. PERB case no. M2010-008

Wheatland-Chili Central School District and Wheatland-Chili Federation of Teachers (Bus Drivers, Custodians & Cafeteria Workers Unit)

In the Matter of Fact-Finding Between Wheatland-Chili Central School District and Wheatland-Chili Federation of Teachers (Bus Drivers, Custodians & Cafeteria Workers Unit). PERB Case No. M2007-142. Before: Stephen P. LaLonde, Impartial Fact Finder

Monroe County Sheriff and Monroe County Deputy Sheriffs Association

In the matter of the fact-finding between the Monroe County Sheriff, employer, and the Monroe County Deputy Sheriffs Association, union. PERB case no. M2013-172. Before: Stephen P. LaLonde, fact finder

The Geography of Non-formal Manifolds

We show that there exist non-formal compact oriented manifolds of dimension $n$ and with first Betti number $b_1=b\geq 0$ if and only if $n\geq 3$ and $b\geq 2$, or $n\geq (7-2b)$ and $0\leq b\leq 2$. Moreover, we present explicit examples for each one of these cases.Comment: 8 pages, one reference update

Earth's first snowball event: Evidence from the early Paleoproterozoic Huronian Supergroup

Ever since it was first proposed that the Earth completely froze during glaciations ∼ 640 million years ago evidence supporting this hypothesis has been increasing, primarily from samples of carbonates directly overlying glacial diamictites, termed cap carbonates. However, this was not the first extensive glacial period that affected planet Earth: ∼1750 million years prior to Neoproterozoic glaciations the Earth went through its first major glacial episode, the early Paleoproterozoic Huronian glaciations. The second Huronian ice advance deposited the Bruce Formation, with its overlying cap carbonate, the Espanola Formation. This up to ∼ 300 m thick succession of limestone, siltstone, dolostone and sandstone overlies diamictite containing a dropstone-bearing layer with δ13Ccarb of −10‰. The 12C-enriched interval also has rare earth element (REE) patterns with negative Eu anomalies, radiogenic Sr isotopes, and negative εNd(0) in the carbonate. The first of these observations is probably due to highly reducing conditions in the sediment, and the possible thawing of methane-rich areas, releasing fluids that mixed with the overlying bottom waters; the last two reflect the diagenetic incorporation into the carbonate of radiogenic Sr, and derivation of REEs, including Nd, from abundant silty loess. This infers a stratified water mass with a relatively stagnant bottom layer during disintegration of an ice shelf. Above this REE patterns through the basal Espanola become increasingly more light depleted upwards, C becomes heavier, Sr is less radiogenic, εNd(0) is near 0 and one area has up to ∼ 1300 ppm Ba incorporated into the carbonate, indicating breakdown of water-mass stratification. Vertically over ∼ 200 m δ13Ccarb increases from −4.5 to −2.5‰ as the environment shallowed incorporating gradually increasing amounts of seawater into the freshwater plume, which initially extended to depths below wave base. Strata deposited in the upper Espanola near the strandline contain layers of Fe-Mn-rich dolomite with positive Eu anomalies reflecting Paleoproterozioc seawater composition dominating even the nearshore by this time. These observations are similar to those from Neoproterozoic cap carbonates, and provide new evidence for the possibly snowball Earth-like nature of the ∼ 2.4 Ga Bruce glaciation

Seidel elements and mirror transformations

The goal of this article is to give a precise relation between the mirror symmetry transformation of Givental and the Seidel elements for a smooth projective toric variety $X$ with $-K_X$ nef. We show that the Seidel elements entirely determine the mirror transformation and mirror coordinates.Comment: 36 pages. We corrected several issues as pointed out by the refere