Quasimodularity and large genus limits of Siegel-Veech constants

Quasimodular forms were first studied in the context of counting torus coverings. Here we show that a weighted version of these coverings with Siegel-Veech weights also provides quasimodular forms. We apply this to prove conjectures of Eskin and Zorich on the large genus limits of Masur-Veech volumes and of Siegel-Veech constants. In Part I we connect the geometric definition of Siegel-Veech constants both with a combinatorial counting problem and with intersection numbers on Hurwitz spaces. We introduce modified Siegel-Veech weights whose generating functions will later be shown to be quasimodular. Parts II and III are devoted to the study of the quasimodularity of the generating functions arising from weighted counting of torus coverings. The starting point is the theorem of Bloch and Okounkov saying that q-brackets of shifted symmetric functions are quasimodular forms. In Part II we give an expression for their growth polynomials in terms of Gaussian integrals and use this to obtain a closed formula for the generating series of cumulants that is the basis for studying large genus asymptotics. In Part III we show that the even hook-length moments of partitions are shifted symmetric polynomials and prove a formula for the q-bracket of the product of such a hook-length moment with an arbitrary shifted symmetric polynomial. This formula proves quasimodularity also for the (-2)-nd hook-length moments by extrapolation, and implies the quasimodularity of the Siegel-Veech weighted counting functions. Finally, in Part IV these results are used to give explicit generating functions for the volumes and Siegel-Veech constants in the case of the principal stratum of abelian differentials. To apply these exact formulas to the Eskin-Zorich conjectures we provide a general framework for computing the asymptotics of rapidly divergent power series.Comment: 107 pages, final version, to appear in J. of the AM

Hybrid power semiconductor

The voltage rating of a bipolar transistor may be greatly extended while at the same time reducing its switching time by operating it in conjunction with FETs in a hybrid circuit. One FET is used to drive the bipolar transistor while the other FET is connected in series with the transistor and an inductive load. Both FETs are turned on or off by a single drive signal of load power, the second FET upon ceasing conductions, rendering one power electrode of the bipolar transistor open. Means are provided to dissipate currents which flow after the bipolar transistor is rendered nonconducting

Resonant Interactions in Rotating Homogeneous Three-dimensional Turbulence

Direct numerical simulations of three-dimensional (3D) homogeneous turbulence under rapid rigid rotation are conducted to examine the predictions of resonant wave theory for both small Rossby number and large Reynolds number. The simulation results reveal that there is a clear inverse energy cascade to the large scales, as predicted by 2D Navier-Stokes equations for resonant interactions of slow modes. As the rotation rate increases, the vertically-averaged horizontal velocity field from 3D Navier-Stokes converges to the velocity field from 2D Navier-Stokes, as measured by the energy in their difference field. Likewise, the vertically-averaged vertical velocity from 3D Navier-Stokes converges to a solution of the 2D passive scalar equation. The energy flux directly into small wave numbers in the $k_z=0$ plane from non-resonant interactions decreases, while fast-mode energy concentrates closer to that plane. The simulations are consistent with an increasingly dominant role of resonant triads for more rapid rotation

Network support for integrated design

A framework of network support for utilization of integrated design over the Internet has been developed. The techniques presented also applicable for Intranet/Extranet. The integrated design system was initially developed for local application in a single site. With the network support, geographically dispersed designers can collaborate a design task through out the total design process, quickly respond to clients’ requests and enhance the design argilty. In this paper, after a brief introduction of the integrated design system, the network support framework is presented, followed by description of two key techniques involved: Java Saverlet approach for remotely executing a large program and online CAD collaboration

Positivity Of Equivariant Gromov–Witten Invariants

We show that the equivariant Gromov–Witten invariants of a projective homogeneous space G/P exhibit Graham-positivity: when expressed as polynomials in the positive roots, they have nonnegative coefficients

A mass-balance/photochemical assessment of DMS sea-to-air flux as inferred from NASA GTE PEM-West a and B observations

This study reports dimethyl sulfide (DMS) sea-to-air fluxes derived from a mass-balance/photochemical-modeling approach. The region investigated was the western North Pacific covering the latitude range of 0°-30°N. Two NASA airborne databases were used in this study: PEM-West A in September-October 1991 and PEM-West B in February-March 1994. A total of 35 boundary layer (BL) sampling runs were recorded between the two programs. However, after filtering these data for pollution impacts and DMS lifetime considerations, this total was reduced to 13. Input for each analysis consisted of atmospheric DMS measurements, the equivalent mixing depth (EMD) for DMS, and model estimated values for OH and NO3. The evaluation of the EMD took into account both DMS within the BL as well as that transported into the overlying atmospheric buffer layer (BuL). DMS fluxes ranged from 0.6 to 3.0 μmol m-2d-1 for PEM-West A (10 sample runs) and 1.4 to 1.9 μmol m-2d-1 for PEM-West B (3 sample runs). Sensitivity analyses showed that the photochemically evaluated DMS flux was most influenced by the DMS vertical profile and the diel profile for OH. A propagation of error analysis revealed that the uncertainty associated with individual flux determinations ranged from a factor of 1.3 to 1.5. Also assessed were potential systematic errors. The first of these relates to our noninclusion of large-scale mean vertical motion as it might appear in the form of atmospheric subsidence or as a convergence. Our estimates here would place this error in the range of O to 30%. By far the largest systematic error is that associated with stochastic events (e.g., those involving major changes in cloud coverage). In the latter case, sensitivity tests suggested that the error could be as high as a factor of 2. With improvements in such areas as BL sampling time, direct observations of OH, improved DMS vertical profiling, direct assessment of vertical velocity in the field, and preflight (24 hours) detailed meteorological data, it appears that the uncertainty in this approach could be reduced to ±25%. Copyright 1999 by the American Geophysical Union

Symmetries and Lie algebra of the differential-difference Kadomstev-Petviashvili hierarchy

By introducing suitable non-isospectral flows we construct two sets of symmetries for the isospectral differential-difference Kadomstev-Petviashvili hierarchy. The symmetries form an infinite dimensional Lie algebra.Comment: 9 page