Geometric structures on loop and path spaces

Is is known that the loop space associated to a Riemannian manifold admits a quasi-symplectic structure. This article shows that this structure is not likely to recover the underlying Riemannian metric by proving a result that is a strong indication of the "almost" independence of the quasi-symplectic structure with respect to the metric. Finally conditions to have contact structures on these spaces are studied.Comment: Final version. To appear in Proceedings of Math. Sci. Indian Academy of Science

The use of disjunct eddy sampling methods for the determination of ecosystem level fluxes of trace gases

The concept of disjunct eddy sampling (DES) for use in measuring ecosystem-level micrometeorological fluxes is re-examined. The governing equations are discussed as well as other practical considerations and guidelines concerning this sampling method as it is applied to either the disjunct eddy covariance (DEC) or disjunct eddy accumulation (DEA) techniques. A disjunct eddy sampling system was constructed that could either be combined with relatively slow sensors (response time of 2 to 40 s) to measure fluxes using DEC, or could also be used to accumulate samples in stable reservoirs for later laboratory analysis (DEA technique). Both the DEC and DEA modes of this sampler were tested against conventional eddy covariance (EC) for fluxes of either CO2 (DEC) or isoprene (DEA). Good agreement in both modes was observed relative to the EC systems. However, the uncertainty in a single DEA flux measurement was considerable (40%) due to both the reduced statistical sampling and the analytical precision of the concentration difference measurements. We have also re-investigated the effects of nonzero mean vertical wind velocity on accumulation techniques as it relates to our DEA measurements. Despite the higher uncertainty, disjunct eddy sampling can provide an alternative technique to eddy covariance for determining ecosystem-level fluxes for species where fast sensors do not currently exist

Vector Coherent State Realization of Representations of the Affine Lie Algebra sl^(2)\hat{sl}(2)

The method of vector coherent states is generalized to study representations of the affine Lie algebra $\hat{sl}(2)$. A large class of highest weight irreps is explicitly constructed, which contains the integrable highest weight irreps as special cases.Comment: 8 pages plain latex. To appear in J. Phys.

Schubert Polynomials for the affine Grassmannian of the symplectic group

We study the Schubert calculus of the affine Grassmannian Gr of the symplectic group. The integral homology and cohomology rings of Gr are identified with dual Hopf algebras of symmetric functions, defined in terms of Schur's P and Q-functions. An explicit combinatorial description is obtained for the Schubert basis of the cohomology of Gr, and this is extended to a definition of the affine type C Stanley symmetric functions. A homology Pieri rule is also given for the product of a special Schubert class with an arbitrary one.Comment: 45 page

Representations of affine Lie algebras, elliptic r-matrix systems, and special functions

There were some errors in paper hep-th/9303018 in formulas 6.1, 6.6, 6.8, 6.11. These errors have been corrected in the present version of this paper. There are also some minor changes in the introduction.Comment: 33 pages, no figure

Symmetry Algebras of Large-N Matrix Models for Open Strings

We have discovered that the gauge invariant observables of matrix models invariant under U($N$) form a Lie algebra, in the planar large-N limit. These models include Quantum Chromodynamics and the M(atrix)-Theory of strings. We study here the gauge invariant states corresponding to open strings (`mesons'). We find that the algebra is an extension of a remarkable new Lie algebra ${\cal V}_{\Lambda}$ by a product of more well-known algebras such as $gl_{\infty}$ and the Cuntz algebra. ${\cal V}_{\Lambda}$ appears to be a generalization of the Lie algebra of vector fields on the circle to non-commutative geometry. We also use a representation of our Lie algebra to establish an isomorphism between certain matrix models (those that preserve `gluon number') and open quantum spin chains. Using known results on quantum spin chains, we are able to identify some exactly solvable matrix models. Finally, the Hamiltonian of a dimensionally reduced QCD model is expressed explicitly as an element of our Lie algebra.Comment: 44 pages, 8 eps figures, 3 tables, LaTeX2.09; this is the published versio

Open-closed string correspondence: D-brane decay in curved space

This paper analyzes the effect of curved closed string backgrounds on the stability of D-branes within boundary string field theory. We identify the non-local open string background that implements shifts in the closed string background and analyze the tachyonic sector off-shell. The renormalization group flow reveals some characteristic properties, which are expected for a curved background, like the absence of a stable space-filling brane. In 3-dimensions we describe tachyon condensation processes to lower-dimensional branes, including a curved 2-dimensional brane. We argue that this 2-brane is perturbatively stable. This is in agreement with the known maximally symmetric WZW-branes and provides further support to the bulk-boundary factorization approach to open-closed string correspondence.Comment: 23 pages, harvma

Eddy covariance flux measurements of pollutant gases in urban Mexico City

Eddy covariance (EC) flux measurements of the atmosphere/surface exchange of gases over an urban area are a direct way to improve and evaluate emissions inventories, and, in turn, to better understand urban atmospheric chemistry and the role that cities play in regional and global chemical cycles. As part of the MCMA-2003 study, we demonstrated the feasibility of using eddy covariance techniques to measure fluxes of selected volatile organic compounds (VOCs) and CO2 [CO subscript 2] from a residential district of Mexico City (Velasco et al., 2005a, b). During the MILAGRO/MCMA-2006 field campaign, a second flux measurement study was conducted in a different district of Mexico City to corroborate the 2003 flux measurements, to expand the number of species measured, and to obtain additional data for evaluation of the local emissions inventory. Fluxes of CO2 [CO subscript 2] and olefins were measured by the conventional EC technique using an open path CO2 [CO subscript 2] sensor and a Fast Isoprene Sensor calibrated with a propylene standard. In addition, fluxes of toluene, benzene, methanol and C2-benzenes [C subscript 2 - benzenes] were measured using a virtual disjunct EC method with a Proton Transfer Reaction Mass Spectrometer. The flux measurements were analyzed in terms of diurnal patterns and vehicular activity and were compared with the most recent gridded emissions inventory. In both studies, the results showed that the urban surface of Mexico City is a net source of CO2 [CO subscript 2] and VOCs with significant contributions from vehicular traffic. Evaporative emissions from commercial and other anthropogenic activities were significant sources of toluene and methanol. The data show that the emissions inventory is in reasonable agreement with measured olefin and CO2 [CO subscript 2] fluxes, while C2-benzenes [C subscript 2 - benzenes] and toluene emissions from evaporative sources are overestimated in the inventory. It appears that methanol emissions from mobile sources occur, but are not present in the mobile emissions inventory.National Science Foundation (U.S.) (Grant ATM-0528227)United States. Dept. of Energy (Award DE-FG02-05ER63980)Mexico. Comisión Ambiental MetropolitanaMolina Center for Energy and the Environmen

Going beyond defining: Preschool educators\u27 use of knowledge in their pedagogical reasoning about vocabulary instruction

Previous research investigating both the knowledge of early childhood educators and the support for vocabulary development present in early childhood settings has indicated that both educator knowledge and enacted practice are less than optimal, which has grave implications for children\u27s early vocabulary learning and later reading achievement. Further, the nature of the relationship between educators\u27 knowledge and practice is unclear, making it difficult to discern the best path towards improved knowledge, practice, and children\u27s vocabulary outcomes. The purpose of the present study was to add to the existing literature by using stimulated recall interviews and a grounded approach to examine how 10 preschool educators used their knowledge to made decisions about their moment-to-moment instruction in support of children\u27s vocabulary development. Results indicate that educators were thinking in highly context-specific ways about their goals and strategies for supporting vocabulary learning, taking into account important knowledge of their instructional history with children and of the children themselves to inform their decision making in the moment. In addition, they reported thinking about research-based goals and strategies for supporting vocabulary learning that went beyond simply defining words for children. Implications for research and professional development are discussed

Noncyclic geometric phase and its non-Abelian generalization

We use the theory of dynamical invariants to yield a simple derivation of noncyclic analogues of the Abelian and non-Abelian geometric phases. This derivation relies only on the principle of gauge invariance and elucidates the existing definitions of the Abelian noncyclic geometric phase. We also discuss the adiabatic limit of the noncyclic geometric phase and compute the adiabatic non-Abelian noncyclic geometric phase for a spin 1 magnetic (or electric) quadrupole interacting with a precessing magnetic (electric) field.Comment: Plain Latex, accepted for publication in J. Phys. A: Math. Ge