On the rigidity theorems for Lagrangian translating solitons in pseudo-Euclidean space II

Let $u$ be a smooth convex function in $\mathbb{R}^{n}$ and the graph $M_{\nabla u}$ of $\nabla u$ be a space-like translating soliton in pseudo-Euclidean space $\mathbb{R}^{2n}_{n}$ with a translating vector $\frac{1}{n}(a_{1}, a_{2}, \cdots, a_{n}; b_{1}, b_{2}, \cdots, b_{n})$, then the function $u$ satisfies $$\det D^{2}u=\exp \left\{ \sum_{i=1}^n- a_i\frac{\partial u}{\partial x_{i}} +\sum_{i=1}^n b_ix_i+c\right\} \qquad \hbox{on}\qquad\mathbb R^n$$ where $a_i$, $b_i$ and $c$ are constants. The Bernstein type results are obtained in the course of the arguments.Comment: 9 page

The molecular gas in the supernova remnant IC443

Although a few highly perturbed regions characterized by gas motions with velocities larger than 20 km/s have been discovered during the last several years in the supernova remnant (SNR) IC 443, the nature of these perturbed clumps and their relationship to the quiescent molecular gas near the SNR remains unknown. In part, this is due to a lack of large-scale, high angular resolution observations. Therefore, a systematic survey of this SNR in the CO (J=1 yields 0) line has been conducted, covering a roughly 50' x 50' region spaced by 2'. The observations were made with the 14 m telescope of the Five College Radio Astronomy Observatory (FCRAO), which has a resolution of 45" and a single sideband receiver temperature of 200 K at 2.6 mm wavelength. Five new clumps were discovered, bringing the total number of known perturbed regions to eight. To study the physical structure of these clumps in more detail, more complete maps of the clumps have been made in both the CO(J=1 yields 0) and (J=2 yields 1) transitions with the FCRAO telescope. These maps show that the extent of perturbed gas in a typical clump is several arcmin, or a few pc at a distance of 1.5 kpc

The Dark Side of Bank Wholesale Funding

Commercial banks increasingly use short-term wholesale funds to supplement traditional retail deposits. Existing literature mainly points to the "bright side" of wholesale funding: sophisticated financiers can monitor banks, disciplining bad ones but refinancing solvent ones. This paper models a "dark side" of wholesale funding. In an environment with a costless but imperfect signal on bank project quality (e.g., credit ratings, performance of peers), short-term wholesale financiers have lower incentives to conduct costly information acquisition, and instead may withdraw based on negative but noisy public signals, triggering inefficient liquidations. We show that the "dark side" of wholesale funding dominates the "bright side" when bank assets are more arm's length and tradable (leading to more relevant public signals and lower liquidation costs): precisely the attributes of a banking sector with securitizations and risk transfers. The results shed light on the recent financial turmoil, explaining why some wholesale financiers did not provide market discipline ex-ante and exacerbated liquidity risks ex-post.Banks;Crises;Funding;Deposits;Bank Runs;Monitoring;Market Discipline

Solutions of special asymptotics to the Einstein constraint equations

We construct solutions with prescribed asymptotics to the Einstein constraint equations using a cut-off technique. Moreover, we give various examples of vacuum asymptotically flat manifolds whose center of mass and angular momentum are ill-defined.Comment: 13 pages; the error in Lemma 3.5 fixed and typos corrected; to appear in Class. Quantum Gra

Study of a homotopy continuation method for early orbit determination with the Tracking and Data Relay Satellite System (TDRSS)

A recent mathematical technique for solving systems of equations is applied in a very general way to the orbit determination problem. The study of this technique, the homotopy continuation method, was motivated by the possible need to perform early orbit determination with the Tracking and Data Relay Satellite System (TDRSS), using range and Doppler tracking alone. Basically, a set of six tracking observations is continuously transformed from a set with known solution to the given set of observations with unknown solutions, and the corresponding orbit state vector is followed from the a priori estimate to the solutions. A numerical algorithm for following the state vector is developed and described in detail. Numerical examples using both real and simulated TDRSS tracking are given. A prototype early orbit determination algorithm for possible use in TDRSS orbit operations was extensively tested, and the results are described. Preliminary studies of two extensions of the method are discussed: generalization to a least-squares formulation and generalization to an exhaustive global method

Impacts of Fire Emissions and Transport Pathways on the Interannual Variation of CO In the Tropical Upper Troposphere

This study investigates the impacts of fire emission, convection, various climate conditions and transport pathways on the interannual variation of carbon monoxide (CO) in the tropical upper troposphere (UT), by evaluating the field correlation between these fields using multi-satellite observations and principle component analysis, and the transport pathway auto-identification method developed in our previous study. The rotated empirical orthogonal function (REOF) and singular value decomposition (SVD) methods are used to identify the dominant modes of CO interannual variation in the tropical UT and to study the coupled relationship between UT CO and its governing factors. Both REOF and SVD results confirm that Indonesia is the most significant land region that affects the interannual variation of CO in the tropical UT, and El Nino-Southern Oscillation (ENSO) is the dominant climate condition that affects the relationships between surface CO emission, convection and UT CO. In addition, our results also show that the impact of El Nino on the anomalous CO pattern in the tropical UT varies strongly, primarily due to different anomalous emission and convection patterns associated with different El Nino events. In contrast, the anomalous CO pattern in the tropical UT during La Nina period appears to be less variable among different events. Transport pathway analysis suggests that the average CO transported by the "local convection" pathway (Delta COlocal) accounts for the differences of UT CO between different ENSO phases over the tropical continents during biomass burning season. Delta COlocal is generally higher over Indonesia-Australia and lower over South America during El Nino years than during La Nina years. The other pathway ("advection within the lower troposphere followed by convective vertical transport") occurs more frequently over the west-central Pacific during El Nino years than during La Nina years, which may account for the UT CO differences over this region between different ENSO phases.NASA Aura Science Team (AST) program NNX09AD85GJackson School of Geosciences at the University of Texas at AustinJet Propulsion Laboratory, California Institute of Technology, under NASAGeological Science

Coupled structural/thermal/electromagnetic analysis/tailoring of graded composite structures

Accomplishments are described for the third years effort of a 5-year program to develop a methodology for coupled structural/thermal/electromagnetic analysis/tailoring of graded composite structures. These accomplishments include: (1) structural analysis capability specialized for graded composite structures including large deformation and deformation position eigenanalysis technologies; (2) a thermal analyzer specialized for graded composite structures; (3) absorption of electromagnetic waves by graded composite structures; and (4) coupled structural thermal/electromagnetic analysis of graded composite structures