Trade in Goods and Factors with International Differences in Technology

A general model of trade caused by international differences in production technology is developed using techniques of duality theory. For the caseof product-augmenting differences in technology, it is shown that there is a positive correlation between net export and technological superiority, such that a country will "on average" export goods for which the country has superior technolor. If some factors are permitted to be internationally traded, it is demonstrated via this correlation that the volume of trade must increase. Thus unlike trade caused by factor endowment differences, goods trade caused by product-augmenting differences in production technolody is always in this sense complementary with factor trade. For factor-augmenting technology differences, in the absence of factor trade the goods trade pattern is as if it was caused by factor endowment differences. With factor trade, goods trade and factor trade can then be either complements or substitutes.

Steep Slopes and Preferred Breaks in GRB Spectra: the Role of Photospheres and Comptonization

The role of a photospheric component and of pair breakdown is examined in the internal shock model of gamma-ray bursts. We discuss some of the mechanisms by which they would produce anomalously steep low energy slopes, X-ray excesses and preferred energy breaks. Sub-relativistic comptonization should dominate in high comoving luminosity bursts with high baryon load, while synchrotron radiation dominates the power law component in bursts which have lower comoving luminosity or have moderate to low baryon loads. A photosphere leading to steep low energy spectral slopes should be prominent in the lowest baryon loadComment: ApJ'00, in press; minor revs. 10/5/99; (uses aaspp4.sty), 15 pages, 3 figure

Closure Relations for Electron-Positron Pair-Signatures in Gamma-Ray Bursts

We present recipes to diagnose the fireball of gamma-ray bursts (GRBs) by combining observations of electron-positron pair-signatures (the pair-annihilation line and the cutoff energy due to the pair-creation process). Our recipes are largely model-independent and extract information even from the non-detection of either pair-signature. We evaluate physical quantities such as the Lorentz factor, optical depth and pair-to-baryon ratio, only from the observable quantities. In particular, we can test whether the prompt emission of GRBs comes from the pair/baryonic photosphere or not. The future-coming Gamma-Ray Large Area Space Telescope (GLAST) satellite will provide us with good chances to use our recipes by detecting or non-detecting pair-signatures.Comment: 7 pages, 4 figures, accepted for publication in ApJ, with extended discussions. Conclusions unchange

Quasi-thermal Comptonization and gamma-ray bursts

Quasi-thermal Comptonization in internal shocks formed between relativistic shells can account for the high energy emission of gamma-ray bursts. This is in fact the dominant cooling mechanism if the typical energy of the emitting particles is achieved either through the balance between heating and cooling or as a result of electron-positron pair production. Both processes yield sub or mildly relativistic energies. In this case the synchrotron spectrum is self-absorbed, providing the seed soft photons for the Comptonization process, whose spectrum is flat [F(v) ~ const], ending either in an exponential cutoff or a Wien peak, depending on the scattering optical depth of the emitting particles. Self-consistent particle energy and optical depth are estimated and found in agreement with the observed spectra.Comment: 10 pages, ApJ Letters, accepted for publicatio

Radiation Front Sweeping the Ambient Medium of Gamma-Ray Bursts

Gamma-ray bursts (GRBs) are emitted by relativistic ejecta from powerful cosmic explosions. Their light curves suggest that the gamma-ray emission occurs at early stages of the ejecta expansion, well before it decelerates in the ambient medium. If so, the launched gamma-ray front must overtake the ejecta and sweep the ambient medium outward. As a result a gap is opened between the ejecta and the medium that surfs the radiation front ahead. Effectively, the ejecta moves in a cavity until it reaches a radius R_{gap}=10^{16}E_{54}^{1/2} cm where E is the isotropic energy of the GRB. At R=R_{gap} the gap is closed, a blast wave forms and collects the medium swept by radiation. Further development of the blast wave is strongly affected by the leading radiation front: the front plays the role of a precursor where the medium is loaded with e+- pairs and preaccelerated just ahead of the blast. It impacts the emission from the blast at R < R_{load}=5R_{gap} (the early afterglow). A spectacular observational effect results: GRB afterglows should start in optical/UV and evolve fast (< min) to a normal X-ray afterglow. The early optical emission observed in GRB 990123 may be explained in this way. The impact of the front is especially strong if the ambient medium is a wind from a massive progenitor of the GRB. In this case three phenomena are predicted: (1) The ejecta decelerates at R<R_{load} producing a lot of soft radiation. (2) The light curve of soft emission peaks at t_{peak}=40(1+z)E_{54}^{1/2}(Gamma_{ej}/100)^{-2} s where Gamma_{ej} is the Lorentz factor of the ejecta. Given measured redshift z and t_{peak}, one finds Gamma_{ej}. (3) The GRB acquires a spectral break at 5 - 50 MeV because harder photons are absorbed by radiation scattered in the wind.Comment: 20 pages, accepted to Ap

Infinite Factorial Finite State Machine for Blind Multiuser Channel Estimation

New communication standards need to deal with machine-to-machine communications, in which users may start or stop transmitting at any time in an asynchronous manner. Thus, the number of users is an unknown and time-varying parameter that needs to be accurately estimated in order to properly recover the symbols transmitted by all users in the system. In this paper, we address the problem of joint channel parameter and data estimation in a multiuser communication channel in which the number of transmitters is not known. For that purpose, we develop the infinite factorial finite state machine model, a Bayesian nonparametric model based on the Markov Indian buffet that allows for an unbounded number of transmitters with arbitrary channel length. We propose an inference algorithm that makes use of slice sampling and particle Gibbs with ancestor sampling. Our approach is fully blind as it does not require a prior channel estimation step, prior knowledge of the number of transmitters, or any signaling information. Our experimental results, loosely based on the LTE random access channel, show that the proposed approach can effectively recover the data-generating process for a wide range of scenarios, with varying number of transmitters, number of receivers, constellation order, channel length, and signal-to-noise ratio.Comment: 15 pages, 15 figure

A fit to the simultaneous broadband spectrum of Cygnus X-1 using the transition disk model

We have used the transition disk model to fit the simultaneous broad band ($2-500$ keV) spectrum of Cygnus X-1 from OSSE and Ginga observations. In this model, the spectrum is produced by saturated Comptonization within the inner region of the accretion disk, where the temperature varies rapidly with radius. In an earlier attempt, we demonstrated the viability of this model by fitting the data from EXOSAT, XMPC balloon and OSSE observations, though these were not made simultaneously. Since the source is known to be variable, however, the results of this fit were not conclusive. In addition, since only once set of observations was used, the good agreement with the data could have been a chance occurrence. Here, we improve considerably upon our earlier analysis by considering four sets of simultaneous observations of Cygnus X-1, using an empirical model to obtain the disk temperature profile. The vertical structure is then obtained using this profile and we show that the analysis is self- consistent. We demonstrate conclusively that the transition disk spectrum is a better fit to the observations than that predicted by the soft photon Comptonization model. Since the temperature profile is obtained by fitting the data, the unknown viscosity mechanism need not be specified. The disk structure can then be used to infer the viscosity parameter $\alpha$, which appears to vary with radius and luminosity. This behavior can be understood if $\alpha$ depends intrinsically on the local parameters such as density, height and temperature. However, due to uncertainties in the radiative transfer, quantitative statements regarding the variation of $\alpha$ cannot yet be made.Comment: 8 figures. uses aasms4.sty, accepted by ApJ (Mar 98