The Relative Lie Algebra Cohomology of the Weil Representation

We study the relative Lie algebra cohomology of $\mathfrak{so}(p,q)$ with values in the Weil representation $\varpi$ of the dual pair $\mathrm{Sp}(2k, \mathbb{R}) \times \mathrm{O}(p,q)$. Using the Fock model we filter this complex and construct the associated spectral sequence. We then prove that the resulting spectral sequence converges to the relative Lie algebra cohomology and has $E_0$ term, the associated graded complex, isomorphic to a Koszul complex. It is immediate that the construction of the spectral sequence of Chapter 3 can be applied to any reductive subalgebra $\mathfrak{g} \subset \mathfrak{sp}(2k(p+q), \mathbb{R})$. In case the symplectic group is large relative to the orthogonal group ($k \geq pq$), the $E_0$ term is isomorphic to a Koszul complex defined by a regular sequence, see 3.4. Thus, the cohomology vanishes except in top degree. This result is obtained without calculating the space of cochains and hence without using any representation theory. On the other hand, in case $k < p$, we know the Koszul complex is not that of a regular sequence from the existence of the class $\varphi_{kq}$ of Kudla and Millson, see [KM2], a nonzero element of the relative Lie algebra cohomology of degree $kq$. For the case of $\mathrm{SO}_0(p,1)$ we compute the cohomology groups in these remaining cases, namely $k < p$. We do this by first computing a basis for the relative Lie algebra cochains and then splitting the complex into a sum of two complexes, each of whose $E_0$ term is then isomorphic to a Koszul complex defined by a regular sequence. This thesis is adapted from the paper, [BMR], this author wrote with his advisor John Millson and Nicolas Bergeron of the University of Paris.Comment: 96 pages, 1 figure. arXiv admin note: text overlap with arXiv:1411.406

The Relative Lie Algebra Cohomology of the Weil Representation of SO(n,1)

In Part 1 of this paper we construct a spectral sequence converging to the relative Lie algebra cohomology associated to the action of any subgroup $G$ of the symplectic group on the polynomial Fock model of the Weil representation, see Section 7. These relative Lie algebra cohomology groups are of interest because they map to the cohomology of suitable arithmetic quotients of the symmetric space $G/K$ of $G$. We apply this spectral sequence to the case $G = \mathrm{SO}_0(n,1)$ in Sections 8, 9, and 10 to compute the relative Lie algebra cohomology groups $H^{\bullet} \big(\mathfrak{so}(n,1), \mathrm{SO}(n); \mathcal{P}(V^k) \big)$. Here $V = \mathbb{R}^{n,1}$ is Minkowski space and $\mathcal{P}(V^k)$ is the subspace of $L^2(V^k)$ consisting of all products of polynomials with the Gaussian. In Part 2 of this paper we compute the cohomology groups $H^{\bullet}\big(\mathfrak{so}(n,1), \mathrm{SO}(n); L^2(V^k) \big)$ using spectral theory and representation theory. In Part 3 of this paper we compute the maps between the polynomial Fock and $L^2$ cohomology groups induced by the inclusions $\mathcal{P}(V^k) \subset L^2(V^k)$.Comment: 64 pages, 5 figure

Validation of the NASA Dryden X-31 simulation and evaluation of mechanization techniques

This paper shall discuss the evaluation of the original Dryden X-31 aerodynamic math model, processes involved in the justification and creation of the modified data base, and comparison time history results of the model response with flight test

Counterflow dielectrophoresis for trypanosome enrichment and detection in blood

Human African trypanosomiasis or sleeping sickness is a deadly disease endemic in sub-Saharan Africa, caused by single-celled protozoan parasites. Although it has been targeted for elimination by 2020, this will only be realized if diagnosis can be improved to enable identification and treatment of afflicted patients. Existing techniques of detection are restricted by their limited field-applicability, sensitivity and capacity for automation. Microfluidic-based technologies offer the potential for highly sensitive automated devices that could achieve detection at the lowest levels of parasitemia and consequently help in the elimination programme. In this work we implement an electrokinetic technique for the separation of trypanosomes from both mouse and human blood. This technique utilises differences in polarisability between the blood cells and trypanosomes to achieve separation through opposed bi-directional movement (cell counterflow). We combine this enrichment technique with an automated image analysis detection algorithm, negating the need for a human operator

Angular Conditions,Relations between Breit and Light-Front Frames, and Subleading Power Corrections

We analyze the current matrix elements in the general collinear (Breit) frames and find the relation between the ordinary (or canonical) helicity amplitudes and the light-front helicity amplitudes. Using the conservation of angular momentum, we derive a general angular condition which should be satisfied by the light-front helicity amplitudes for any spin system. In addition, we obtain the light-front parity and time-reversal relations for the light-front helicity amplitudes. Applying these relations to the spin-1 form factor analysis, we note that the general angular condition relating the five helicity amplitudes is reduced to the usual angular condition relating the four helicity amplitudes due to the light-front time-reversal condition. We make some comments on the consequences of the angular condition for the analysis of the high-$Q^2$ deuteron electromagnetic form factors, and we further apply the general angular condition to the electromagnetic transition between spin-1/2 and spin-3/2 systems and find a relation useful for the analysis of the N-$\Delta$ transition form factors. We also discuss the scaling law and the subleading power corrections in the Breit and light-front frames.Comment: 24 pages,2 figure

Three-Quark Light-Cone Amplitudes of The Proton And Quark-Orbital-Motion Dependent Observables

We study the three-quark light-cone amplitudes of the proton including quarks' transverse momenta. We classify these amplitudes using a newly-developed method in which light-cone wave functions are constructed from a class of light-cone matrix elements. We derive the constraints on the amplitudes from parity and time-reversal symmetries. We use the amplitudes to calculate the physical observables which vanish when the quark orbital angular momentum is absent. These include transverse-momentum dependent parton distributions $\Delta q_T(x, k_\perp)$, $q_T(x, k_\perp)$, $\delta q(x, k_\perp)$, and $\delta q_L(x,k_\perp)$, twist-three parton distributions $g_T(x)$ and $h_L(x)$, helicity-flip generalized parton distributions $E(x, \xi=0, Q^2)$ and its associates, and the Pauli form factor $F_2(Q^2)$.Comment: 20 pages, no figur

The pollination of the pomaceous fruits

Published July 1913. Facts and recommendations in this publication may no longer be valid. Please look for up-to-date information in the OSU Extension Catalog: http://extension.oregonstate.edu/catalo

Epithelialization of hydrogels achieved by amine functionalization and co-culture with stromal cells

The aim of this study was to develop a hydrogel which would be suitable for corneal cell re-epithelialization when used as a corneal implant. To achieve this, a series of hydrogels were functionalized with primary amines by post-polymerization reactions between amine compounds and glycidyl ether groups attached to the hydrogels. We report a strong correlation between the structure of the amine and the viability of stromal cells and epithelial cells cultured on these hydrogels. Subsequent co-culture of epithelial and stromal cells on the amine modified hydrogels allowed successful expansion of epithelial cells on surfaces functionalized with alkyl α–ω diamines with carbon chain lengths of between 3 and 6. Analysis of variance showed that corneal epithelial cells had a strong preference for surfaces functionalized by the reaction of excess 1,3 diaminopropane with units of glycidyl methacrylate compared to the reaction products of other amines (ammonia; 1,2-diaminoethane; 1,4-diaminobutane or 1,6-diaminohexane). We suggest this approach of amine functionalization combined with stromal/epithelial co-culture offers a promising new approach to achieving a secure corneal epithelium. Keywords: Epithelial cell

Structure functions in the polarized Drell-Yan processes with spin-1/2 and spin-1 hadrons: I. general formalism

We discuss general formalism for the structure functions which can be investigated in the polarized Drell-Yan processes with spin-1/2 and spin-1 hadrons. To be specific, the formalism can be applied to the proton-deuteron Drell-Yan processes. Because of the spin-1 nature, there are new structure functions which cannot be studied in the proton-proton reactions. Imposing Hermiticity, parity conservation, and time-reversal invariance, we find that 108 structure functions exist in the Drell-Yan processes. However, the number reduces to 22 after integrating the cross section over the virtual-photon transverse momentum Q_T or after taking the limit Q_T->0. There are 11 new structure functions in addition to the 11 ones in the Drell-Yan processes of spin-1/2 hadrons. The additional structure functions are associated with the tensor structure of the spin-1 hadron, and they could be measured by quadrupole spin asymmetries. For example, the structure functions exist for "intermediate" polarization although their contributions vanish in the longitudinal and transverse polarization reactions. We show a number of spin asymmetries for extracting the polarized structure functions. The proton-deuteron reaction may be realized in the RHIC-Spin project and other future ones, and it could be a new direction of next generation high-energy spin physics.Comment: 16 pages, REVTeX, amsmath.sty, epsfig.sty, revtex.cls, 6 eps figures. Submitted for publication. Complete postscript file is available at http://www2.cc.saga-u.ac.jp/saga-u/riko/physics/quantum1/structure.html Email: [email protected], [email protected]

Establishment and characterization of turtle liver organoids provides a potential model to decode their unique adaptations

Painted turtles are remarkable for their freeze tolerance and supercooling ability along with their associated resilience to hypoxia/anoxia and oxidative stress, rendering them an ideal biomedical model for hypoxia-induced injuries (including strokes), tissue cooling during surgeries, and organ cryopreservation. Yet, such research is hindered by their seasonal reproduction and slow maturation. Here we developed and characterized adult stem cell-derived turtle liver organoids (3D self-assembled in vitro structures) from painted, snapping, and spiny softshell turtles spanning ~175My of evolution, with a subset cryopreserved. This development is, to the best of our knowledge, a first for this vertebrate Order, and complements the only other non-avian reptile organoids from snake venom glands. Preliminary characterization, including morphological, transcriptomic, and proteomic analyses, revealed organoids enriched in cholangiocytes. Deriving organoids from distant turtles and life stages demonstrates that our techniques are broadly applicable to chelonians, permitting the development of functional genomic tools currently lacking in herpetological research. Such platform could potentially support studies including genome-to-phenome mapping, gene function, genome architecture, and adaptive responses to climate change, with implications for ecological, evolutionary, and biomedical research