Visual Culture Project: Confederate War Etchings: Searching for Arms by Adalbert Johann Volck

Adalbert Johann Volck’s 1861 sketch of Union soldiers, “Searching for Arms,” represents a substantial contribution to the narrative about gender relations during the American Civil War. This simple, small sketch offers the observer a window into the past. It is a collision of symbols and meaning—from gender to war to the household—all wrapped up in one image. This is a portrait sketch of a woman being invaded in her domestic, private sphere, revealing so much about gender relations during the time. The mistress herself seemed to embody a vast range of sentiments such as anger, fear, frailty, and strength, proving the tension in her role as a wife, a mother, and guardian of the home. This inner conflict is something that all women faced during this time as they strove to remain loyal to the cause for which their husbands fought

The Raman Spectra of CH3CF3 and CCl2CF2

Because of the interest attached to ethane and ethane-like molecules in connection with the question of free rotation of the CX3 groups with respect to each other, it was considered that the Raman spectrum of CH3CF3 might yield additional information on this point. Inasmuch as the spectrum of the liquid can be conveniently photographed only at low temperatures (b.p. about -40°), the determination of the polarization of the scattered light would be experimentally very difficult and was not attempted. The fact that the frequencies associated with the CF3 group will be considerably different in magnitude from those of the CH3 group may, in the analysis, compensate for the lack of data on polarization. Only the results of the experiments are presented here; the assignment of the frequencies will be given when completed. The Raman spectrum of the ethylene-like molecule CCl2=CF2 was photographed at room temperature with the substance in the liquid state, and the observed shifts are presented here

Minimal kernels of Dirac operators along maps

Let $M$ be a closed spin manifold and let $N$ be a closed manifold. For maps $f\colon M\to N$ and Riemannian metrics $g$ on $M$ and $h$ on $N$, we consider the Dirac operator $D^f_{g,h}$ of the twisted Dirac bundle $\Sigma M\otimes_{\mathbb{R}} f^*TN$. To this Dirac operator one can associate an index in $KO^{-dim(M)}(pt)$. If $M$ is $2$-dimensional, one gets a lower bound for the dimension of the kernel of $D^f_{g,h}$ out of this index. We investigate the question whether this lower bound is obtained for generic tupels $(f,g,h)$

Letter from Frances B. Hatcher

Letter concerning a position in the mathematics department at Utah Agricultural College

Intra- and Extra-articular Features of Temporomandibular Joint Ankylosis in the Cat (Felis catus).

Temporomandibular joint (TMJ) ankylosis is an uncommon clinical entity in human and veterinary medicine. However, the condition is severely debilitating and is life-limiting if not treated. This study sought to characterize the intra- and extra-articular features of naturally occurring TMJ ankylosis in cats. TMJs from client-owned cats (n = 5) that underwent bilateral TMJ gap arthroplasty were examined and compared with TMJs from healthy, age-matched feline cadavers (n = 2) by cone-beam computed tomography (CBCT), micro-computed tomography (μCT) and histologically. Features of bilateral intra- and extra-articular ankylosis compounded by degenerative joint lesions were identified radiographically and histologically in all affected cats. Features of TMJ 'true' ankylosis included variable intracapsular fibro-osseous bridging, degeneration of the disc and the articular surfaces, narrowing of the joint space and flattening of the condylar process of the mandible. Extra-articular features of TMJ ankylosis included periarticular bone formation and fibro-osseous bridging between the mandible, zygomatic arch and coronoid process. In addition, subchondral bone loss or sclerosis, irregular and altered joint contours and irregularly increased density of the medullary bone characterized the degenerative changes of the osseous components of the TMJ. Complex radiological and histological features of both ankylosis and pseudoankylosis were identified that clinically manifested in complete inability to open the mouth

Volume and homology of one-cusped hyperbolic 3-manifolds

Let M be a complete, finite-volume, orientable hyperbolic manifold having exactly one cusp. If we assume that pi_1(M) has no subgroup isomorphic to a genus-2 surface group, and that either (a) H_1(M;Z_p) has dimension at least 5 for some prime p, or (b) H_1(M;Z_2) has dimension at least 4, and the subspace of H^2(M;Z_2) spanned by the image of the cup product has dimension at most 1, then vol M > 5.06 If we assume that H_1(M;Z_2) has dimension at least 7, and that the compact core of M does not contain a genus-2 closed incompressible surface, then vol M > 5.06.Comment: 31 pages. This version agrees with the published version of the paper, except that an error in the published abstract has been corrected. In particular, the result which applies to manifolds with mod 2 homology of dimension at least 7 is stronger and has a shorter proof than the corresponding result in version

Letters between Frances B. Hatcher and William Kerr

Letters concerning a position in the mathematics department at Utah Agricultural College

The diameter of the set of boundary slopes of a knot

Let K be a tame knot with irreducible exterior M(K) in a closed, connected, orientable 3--manifold Sigma such that pi_1(Sigma) is cyclic. If infinity is not a strict boundary slope, then the diameter of the set of strict boundary slopes of K, denoted d_K, is a numerical invariant of K. We show that either (i) d_K >= 2 or (ii) K is a generalized iterated torus knot. The proof combines results from Culler and Shalen [Comment. Math. Helv. 74 (1999) 530-547] with a result about the effect of cabling on boundary slopes.Comment: This is the version published by Algebraic & Geometric Topology on 29 August 200

More Torsion in the Homology of the Matching Complex

A matching on a set $X$ is a collection of pairwise disjoint subsets of $X$ of size two. Using computers, we analyze the integral homology of the matching complex $M_n$, which is the simplicial complex of matchings on the set $\{1, >..., n\}$. The main result is the detection of elements of order $p$ in the homology for $p \in \{5,7,11,13\}$. Specifically, we show that there are elements of order 5 in the homology of $M_n$ for $n \ge 18$ and for $n \in {14,16}$. The only previously known value was $n = 14$, and in this particular case we have a new computer-free proof. Moreover, we show that there are elements of order 7 in the homology of $M_n$ for all odd $n$ between 23 and 41 and for $n=30$. In addition, there are elements of order 11 in the homology of $M_{47}$ and elements of order 13 in the homology of $M_{62}$. Finally, we compute the ranks of the Sylow 3- and 5-subgroups of the torsion part of $H_d(M_n;Z)$ for $13 \le n \le 16$; a complete description of the homology already exists for $n \le 12$. To prove the results, we use a representation-theoretic approach, examining subcomplexes of the chain complex of $M_n$ obtained by letting certain groups act on the chain complex.Comment: 35 pages, 10 figure

Letters between Frances B. Hatcher and W. J. Kerr

Letters concerning a position in the mathematics department at Utah Agricultural College