Lifting connections to the r-jet prolongation of the cotangent bundle

We show that the problem of finding all Mfm -natural operators C : Q "M QJ r T ∗ lifting classical linear connections ∇ on m-manifolds M into classical linear connections CM (∇) on the r-jet prolongation J r T ∗M of the cotangent bundle T ∗M p of M can be reduced to that of finding all Mfm -natural operators D : Q "M® T ⊗ q ® T ∗ sending classical linear connections ∇ on M into tensor fields DM (∇) of type (p, q) on M

Government and Online Data: Creation, Access, Preservation

From the 1790 Census to the present, the US government has been a major user, producer, and distributor of data. Through its agencies and departments, it creates data; through funding, grants, and data sharing mandates, it makes research data accessible; through the FDLP and various agency platforms, it circulates and stores data online. This presentation discusses the implications of Government’s role in data creation, online access, and preservation. What are the potential strengths and weaknesses of this relationship, and how can librarians prepare for the future of data creation, preservation, and access? Special attention given to: Federal Data Mandates; Online Sources of Government Data; Challenges to Preservation and Access

Natural operators lifting functions to cotangent bundles of linear higher order tangent bundles

summary:The author studies the problem how a map L:M\to\bbfR on an $n$-dimensional manifold $M$ can induce canonically a map A_M(L):T^* T^{(r)}M\to \bbfR for $r$ a fixed natural number. He proves the following result: ``Let $A: T^{(0,0)}\to T^{(0,0)}(T^* T^{(r)})$ be a natural operator for $n$-manifolds. If $n\ge 3$ then there exists a uniquely determined smooth map H: \bbfR^{S(r)}\times \bbfR\to\bbfR such that $A= A^{(H)}$.''\par The conclusion is that all natural functions on $T^* T^{(r)}$ for $n$-manifolds $(n\ge 3)$ are of the form $\{H\circ(\lambda^{\langle 0,1\rangle}_M,\dots, \lambda^{\langle r,0\rangle}_M)\}$, where H\in C^\infty(\bbfR^r) is a function of $r$ variables

The canonical constructions of connections on total spaces of fibred manifolds

summary:We classify classical linear connections $A(\Gamma ,\Lambda ,\Theta )$ on the total space $Y$ of a fibred manifold $Y\rightarrow M$ induced in a natural way by the following three objects: a general connection $\Gamma$ in $Y\rightarrow M$, a classical linear connection $\Lambda$ on $M$ and a linear connection $\Theta$ in the vertical bundle $VY\rightarrow Y$. The main result says that if $\mathrm{dim}(M)\ge 3$ and $\mathrm{dim}(Y)-\mathrm{dim}(M) \ge 3$ then the natural operators $A$ under consideration form the $17$ dimensional affine space

Natural liftings of foliations to the rr-tangent bunde

summary:Let $F$ be a $p$-dimensional foliation on an $n$-manifold $M$, and $T^r M$ the $r$-tangent bundle of $M$. The purpose of this paper is to present some reltionship between the foliation $F$ and a natural lifting of $F$ to the bundle $T^r M$. Let $L^r_q (F)$ $(q=0, 1, \dots, r)$ be a foliation on $T^r M$ projectable onto $F$ and $L^r_q= \{L^r_q (F)\}$ a natural lifting of foliations to $T^r M$. The author proves the following theorem: Any natural lifting of foliations to the $r$-tangent bundle is equal to one of the liftings $L^r_0, L^r_1, \dots, L^r_n$. \par The exposition is clear and well organized

Product preserving bundle functors on fibered manifolds

summary:The complete description of all product preserving bundle functors on fibered manifolds in terms of natural transformations between product preserving bundle functors on manifolds is given

The natural affinors on (JrT∗)∗(J^rT^*)^*

summary:For natural numbers $r$ and $n\ge 2$ a complete classification of natural affinors on the natural bundle $(J^rT^*)^*$ dual to $r$-jet prolongation $J^rT^*$ of the cotangent bundle over $n$-manifolds is given

Aesthetic Exclusion Within American Capitalist Culture: LGBTQ Students at Gettysburg College and the Creative Reappropriation of Clothing to Forge Personal and Communal Identity

For LGBTQ individuals whose identity expression transgresses heteronormative aesthetic values, mass production and its prioritization of a heteronormative consumer base for profit create feelings of otherness and ostracism. Previous anthropological theory on mass production and advertising recognizes the transference of meaning onto material culture through marketing and identifies the generic symbolic meaning that carbon-copy, mass-produced products hold. Theory and research surrounding colonial encounters attest to power imbalances wherein material culture is imposed on a powerless group, and marginalized individuals react through rejection or creative reappropriation of the material culture, which provides a basis for examining the power imbalance between corporations and marginalized individuals in American retail spaces. Formulated from ethnographic research conducted among members of an LGBTQ living space on Gettysburg College\u27s campus, this Honors Thesis project examines the reaction of LGBTQ individuals to the lack of products in retail spaces designed and advertised with queer identity in consideration. The members of the LGBTQ living space recounted their resistance to the imposition of heteronormative material culture in retail stores primarily attesting to rejection of these spaces and their products: seeking out alternatives such as second hand stores. They posited that retail environments with less clear binary gender divisions allow for freer ability to reappropriate products that were originally advertised to a binary-gender market via styling. Where LGBTQ identity was taken into consideration in marketing, often termed rainbow capitalism, informants spoke to the positive visibility queer-focused marketing provides and the negative pandering that often accompanies it

Canonical 1-forms on higher order adapted frame bundles

summary:Let $(M,\mathcal{F})$ be a foliated $m+n$-dimensional manifold $M$ with $n$-dimensional foliation $\mathcal{F}$. Let $V$ be a finite dimensional vector space over $\mathbf{R}$. We describe all canonical ({\mathcal{F}}\mbox {\it ol}_{m,n}-invariant) $V$-valued $1$-forms $\Theta \colon TP^r(M,{\mathcal{F}}) \rightarrow V$ on the $r$-th order adapted frame bundle $P^r(M,\mathcal{F})$ of $(M,\mathcal{F})$