The Protectionist Prescription: Errors in Diagnosis and Cure

macroeconomics, trade protection

A short survey of the environment at the dumping site for Santa Cruz Harbor dredging and A study of seaward dipping internal structures in marine ripple marks at Whaler's Cove, California. Annual report, Part 4, August 1972

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Uniform Approximation of Abhyankar Valuation Ideals in Smooth Function Fields

In this paper we use the theory of multiplier ideals to show that the valuation ideals of a rank one Abhyankar valuation centered at a smooth point of a complex algebraic variety are approximated, in a quite strong sense, by sequences of powers of fixed ideals. Fix a rank one valuation v centered at a smooth point x on an algebraic variety over a field of characteristic zero. Assume that v is Abhyankar, that is, that its rational rank plus its transcendence degree equal the dimension of the variety. Let a_m denote the ideal of elements in the local ring of x whose valuations are at least m. Our main theorem is that there exists e>0 such that a_{mn} is contained in (a_{m-e})^n for all m and n. This can be viewed as a greatly strengthened form of Izumi's Theorem for Abhyankar valuations centered on smooth complex varieties.Comment: 27 pages, late

Trade and Growth: Import-Led or Export-Led? Evidence From Japan and Korea

It is commonly argued that Japanese trade protection has enabled the nurturing and development internationally competitive firms. The results in our paper suggest that when it comes to TFP growth, this view of Japan is seriously erroneous. We find that lower tariffs and higher import volumes would have been particularly beneficial for Japan during the period 1964 to 1973. Our results also lead us to question whether Japanese exports were a particularly important source of productivity growth. Our findings on Japan suggest that the salutary impact of imports stems more from their contribution to competition than to intermediate inputs. Furthermore our results indicate a reason for why imports are important. Greater imports of competing products spur innovation. Our results suggest that competitive pressures and potentially learning from foreign rivals are important conduits for growth. These channels are even more important as industries converge with the market leader. This suggests that further liberalization by Japan and other East Asian countries may result in future dynamic gains. Our results thus call the views of both the World Bank and the revisionists into question and provide support for those who advocate more liberal trade policies.

Stability and Absence of Binding for Multi-Polaron Systems

We resolve several longstanding problems concerning the stability and the absence of multi-particle binding for N\geq 2 polarons. Fr\"ohlich's 1937 polaron model describes non-relativistic particles interacting with a scalar quantized field with coupling \sqrt\alpha, and with each other by Coulomb repulsion of strength U. We prove the following: (i) While there is a known thermodynamic instability for U<2\alpha, stability of matter does hold for U>2\alpha, that is, the ground state energy per particle has a finite limit as N\to\infty. (ii) There is no binding of any kind if U exceeds a critical value that depends on \alpha but not on N. The same results are shown to hold for the Pekar-Tomasevich model.Comment: 23 page

Ground state properties of multi-polaron systems

We summarize our recent results on the ground state energy of multi-polaron systems. In particular, we discuss stability and existence of the thermodynamic limit, and we discuss the absence of binding in the case of large Coulomb repulsion and the corresponding binding-unbinding transition. We also consider the Pekar-Tomasevich approximation to the ground state energy and we study radial symmetry of the ground state density.Comment: Contribution to the proceedings of ICMP12, Aalborg, Denmark, August 6--11, 2012; 8 page

Binding, Stability, and Non-binding of Multi-polaron Systems

The binding of polarons, or its absence, is an old and subtle topic. After defining the model we state some recent theorems of ours. First, the transition from many-body collapse to the existence of a thermodynamic limit for N polarons occurs precisely at U=2\alpha, where U is the electronic Coulomb repulsion and \alpha is the polaron coupling constant. Second, if U is large enough, there is no multi-polaron binding of any kind. We also discuss the Pekar-Tomasevich approximation to the ground state energy, which is valid for large \alpha. Finally, we derive exact results, not reported before, about the one-dimensional toy model introduced by E. P. Gross.Comment: 12 pages; contribution to the proceedings of the conference QMath 11 (Hradec Kralove, September 2010); clarification added after Theorem 4.

A New Generalized Harmonic Evolution System

A new representation of the Einstein evolution equations is presented that is first order, linearly degenerate, and symmetric hyperbolic. This new system uses the generalized harmonic method to specify the coordinates, and exponentially suppresses all small short-wavelength constraint violations. Physical and constraint-preserving boundary conditions are derived for this system, and numerical tests that demonstrate the effectiveness of the constraint suppression properties and the constraint-preserving boundary conditions are presented.Comment: Updated to agree with published versio