Structure theory for maximally monotone operators with points of continuity

In this paper, we consider the structure of maximally monotone operators in Banach space whose domains have nonempty interior and we present new and explicit structure formulas for such operators. Along the way, we provide new proofs of the norm-to-weak$^{*}$ closedness and of property (Q) for these operators (as recently proven by Voisei). Various applications and limiting examples are given.Comment: 25 page

AS-808-15 Resolution on Revising the Criteria for the Distinguished Scholarship Awards

Streamlines the Distinguished Scholarship Awards description and criteri

Distinguished Pre-Nichols algebras

We formally define and study the distinguished pre-Nichols algebra $\widetilde{\mathcal{B}}(V)$ of a braided vector space of diagonal type $V$ with finite-dimensional Nichols algebra $\mathcal{B}(V)$. The algebra $\widetilde{\mathcal{B}}(V)$ is presented by fewer relations than $\mathcal{B}(V)$, so it is intermediate between the tensor algebra $T(V)$ and $\mathcal{B}(V)$. Prominent examples of distinguished pre-Nichols algebras are the positive parts of quantized enveloping (super)algebras and their multiparametric versions. We prove that these algebras give rise to new examples of Noetherian pointed Hopf algebras of finite Gelfand-Kirillov dimension. We investigate the kernel (in the sense of Hopf algebras) of the projection from $\widetilde{\mathcal{B}}(V)$ to $\mathcal{B}(V)$, generalizing results of De Concini and Procesi on quantum groups at roots of unity.Comment: 32 page

Distinguished Gallantry in Action

Among the many paintings of Abraham Lincoln hanging in the Civil War Institute, there is one face that may not be as familiar. Peering out from a small wooden frame in the main office sits Philip Goettel, a Civil War soldier. His posture is relaxed as he sits in a chair proudly displaying his Union uniform. A caption with the mere word “Father” appears below him, along with a significant date: 1863. Truly, the year 1863 would be a pivotal year in Philip Goettel’s life. He would be wounded, scale a mountain under fire, and earn a Medal of Honor. [excerpt] Course Information: Course Title: HIST 300: Historical Method Academic Term: Fall 2006 Course Instructor: Dr. Michael J. Birkner \u2772 Hidden in Plain Sight is a collection of student papers on objects that are hidden in plain sight around the Gettysburg College campus. Topics range from the Glatfelter Hall gargoyles to the statue of Eisenhower and from historical markers to athletic accomplishments. You can download the paper in pdf format and click View Photo to see the image in greater detail.https://cupola.gettysburg.edu/hiddenpapers/1033/thumbnail.jp

Polynomials defining distinguished varieties

Using a sums of squares formula for two variable polynomials with no zeros on the bidisk, we are able to give a new proof of a representation for distinguished varieties. For distinguished varieties with no singularities on the two-torus, we are able to provide extra details about the representation formula and use this to prove a bounded extension theorem.Comment: 26 page

AS-772-13 Resolution on Increasing the Number of Annual Distinguished Scholarship Awards From Two to Three

Increases the number of DSA awards from two to three starting in 2014-2015

Distinguished minimal topological lassos

The ease with which genomic data can now be generated using Next Generation Sequencing technologies combined with a wealth of legacy data holds great promise for exciting new insights into the evolutionary relationships between and within the kingdoms of life. At the sub-species level (e.g. varieties or strains) certain edge weighted rooted trees with leaf set the set $X$ of organisms under consideration are often used to represent them. Called Dendrograms, it is well-known that they can be uniquely reconstructed from distances provided all distances on $X$ are known. More often than not, real biological datasets do not satisfy this assumption implying that the sought after dendrogram need not be uniquely determined anymore by the available distances with regards to topology, edge-weighting, or both. To better understand the structural properties a set \cL\subseteq {X\choose 2} has to satisfy to overcome this problem, various types of lassos have been introduced. Here, we focus on the question of when a lasso uniquely determines the topology of a dendrogram, that is, it is a topological lasso for it's underlying tree. We show that any set-inclusion minimal topological lasso for such a tree $T$ can be transformed into a structurally nice minimal topological lasso for $T$. Calling such a lasso a distinguished minimal topological lasso for $T$ we characterize them in terms of the novel concept of a cluster marker map for $T$. In addition, we present novel results concerning the heritability of such lassos in the context of the subtree and supertree problems