Loop Expansion in Light-Cone ϕ4\phi^4 Field Theory

A loop expansion is implemented based on the path integral quantization of the light-cone $\phi^4$ field theory in 1+1 dimensions. The effective potential as a function of the zero-mode field $\omega$ is calculated up to two loop order and its derivative with respect to $\omega$ is used to determine the vacuum expectation value of the field $\phi$. The critical coupling constant at the spontaneous symmetry breakdown is consistent with that obtained in the ordinary instant-form field theory. The critical exponents which describe the behavior of the susceptibility and the vacuum expectation value of $\phi$ near the critical point are evaluated from the effective potential. The one loop diagrams for the connected Green's function are calculated in momentum space. The relevant equal-time correlation function is shown to be closely related.Comment: 12 pages, plain Tex, 1 table, 3 figures available from [email protected] , accepted by Phys. Rev.

Constant-Competitive Prior-Free Auction with Ordered Bidders

A central problem in Microeconomics is to design auctions with good revenue properties. In this setting, the bidders' valuations for the items are private knowledge, but they are drawn from publicly known prior distributions. The goal is to find a truthful auction (no bidder can gain in utility by misreporting her valuation) that maximizes the expected revenue. Naturally, the optimal-auction is sensitive to the prior distributions. An intriguing question is to design a truthful auction that is oblivious to these priors, and yet manages to get a constant factor of the optimal revenue. Such auctions are called prior-free. Goldberg et al. presented a constant-approximate prior-free auction when there are identical copies of an item available in unlimited supply, bidders are unit-demand, and their valuations are drawn from i.i.d. distributions. The recent work of Leonardi et al. [STOC 2012] generalized this problem to non i.i.d. bidders, assuming that the auctioneer knows the ordering of their reserve prices. Leonardi et al. proposed a prior-free auction that achieves a $O(\log^* n)$ approximation. We improve upon this result, by giving the first prior-free auction with constant approximation guarantee.Comment: The same result has been obtained independently by E. Koutsoupias, S. Leonardi and T. Roughgarde

Field Induced Jet Micro-EDM

Electrical discharge machining (EDM) is of the potential of micro/nano meter scale machining capability. However, electrode wear in micro-EDM significantly deteriorates the machining accuracy, thus, it needs to be compensated in process. To solve this problem, a novel micromachining method, namely field induced jet micro-EDM, is proposed in this paper, in which the electrical field induced jet is used as the micro tool electrode. A series of experiments were carried out to investigate the feasibility of proposed method. Due to the electrolyte can be supplied automatically by the capillary effect and the electrostatic field, it is not necessary to use pump or valves. The problem of electrode wear does not exist at all in the machining process because of the field induced jet will be generated periodically. It is also found that the workpiece material can be effectively removed with a crater size of about 2 micrometer in diameter. The preliminary experimental results verified that the field induced jet micro-EDM is an effective micromachining method