The double algebraic view of finite quantum groupoids

This is an introduction to double algebras which is the structure modelled by the properties of the convolution product in Hopf algebras, weak Hopf algebras and in Hopf algebroids. We show that Hopf algebroids with a Frobenius integral can be characterized as the double algebras in which the two multiplications satisfy distributivity. We discuss questions of duality, antipode, Maschke theorem and examples.Comment: 48 pages, AMS-Late

Quantum Chains of Hopf Algebras with Quantum Double Cosymmetry

Given a finite dimensional C^*-Hopf algebra H and its dual H^ we construct the infinite crossed product A=... x H x H^ x H ... and study its superselection sectors in the framework of algebraic quantum field theory. A is the observable algebra of a generalized quantum spin chain with H-order and H^-disorder symmetries, where by a duality transformation the role of order and disorder may also appear interchanged. If H=\CC G is a group algebra then A becomes an ordinary G-spin model. We classify all DHR-sectors of A --- relative to some Haag dual vacuum representation --- and prove that their symmetry is described by the Drinfeld double D(H). To achieve this we construct localized coactions \rho: A \to (A \otimes D(H)) and use a certain compressibility property to prove that they are universal amplimorphisms on A. In this way the double D(H) can be recovered from the observable algebra A as a universal cosymmetrty.Comment: Latex, 48 pages, no figures, extended version of hep-th/9507174, but without the field algebra construction, contains full proofs of the slightly shortened article published in Commun.Math.Phys., the revision only concerns some misprints and an update of the literatur

Non-trivial fixed points of the scalar field theory

The phase structure of the scalar field theory with arbitrary powers of the gradient operator and a local non-analytic potential is investigated by the help of the RG in Euclidean space. The RG equation for the generating function of the derivative part of the action is derived. Infinitely many non-trivial fixed points of the RG transformations are found. The corresponding effective actions are unbounded from below and do probably not exhibit any particle content. Therefore they do not provide physically sensible theories

Preloaded latching device

A latching device is disclosed which is lever operated sequentially to actuate a set of collet fingers to provide a radial expansion and to actuate a force mechanism to provide a compressive gripping force for attaching first and second devices to one another. The latching device includes a body member having elongated collet fingers which, in a deactuated condition, is insertable through bores on the first and second devices so that gripping terminal portions on the collet fingers are proximate to the end of the bore of the first device while a spring assembly on the body member is located proximate to the outer surface of a second device. A lever is rotatable through 90 deg to move a latching rod to sequentially actuate and expand collet fingers and to actuate the spring assembly by compressing it. During the first 30 deg of movement of the lever, the collet fingers are actuated by the latching rod to provide a radial expansion and during the last 60 deg of movement of the lever, the spring assembly acts as a force mechanism and is actuated to develop a compressive latching force on the devices. The latching rod and lever are connected by a camming mechanism. The amount of spring force in the spring assembly can be adjusted; the body member can be permanently attached by a telescoping assembly to one of the devices; and the structure can be used as a pulling device for removing annular bearings or the like from blind bores

The Optimal Design of Trade Policy Flexibility in the WTO

This paper is a contribution to the literature on rational design of trade agreements. The World Trade Organization (WTO) is an incomplete contract among sovereign states. Incomplete contracts contain gaps. Ex post, contractual gaps may leave gains from trade unrealized; they may create “regret” in signatories once unanticipated contingencies or sudden protectionist backlashes have occurred. Trade policy flexibility mechanisms, such as the “safeguards clause” under Art. XIX GATT, are geared towards seizing ex post regret by allowing parties affected by a protectionist shock to partially and temporarily withdraw from previously made trade liberalization concessions – given that they compensate the victim(s) of such backtracking behavior. This paper examines the somewhat understudied issue of optimal trade policy flexibility design in the WTO: In particular, we analyze whether ex post escape should be organized by means of a unilateral opt-out clause (a “liability rule” of escape), or a bilateral renegotiation provision (a “property rule” of escape). Modeling the WTO as a fully non-contingent tariff liberalization contract with contingencies (or “states of nature”) asymmetrically revealed, we find that a liability rule backed by expectation remedies payable to the affected victim Pareto-dominates both a renegotiation clause, as well as any other remedy arrangement connected to a liability rule. Only the remedial design of liability-cum-expectation damages yields the desirable incentives to liberalize ex ante, and to default ex post and therewith is able to replicate the outcomes of the hypothetical contracting ideal of the complete contingent contract.Incomplete contracts, remedies, enforcement, WTO, trade renegotiations, WTO Dispute Settlement,

Outsourcing and Competition Policy

We analyze optimal competition policy by a Competition Agency (CA) in a model with two countries, North and South, where a final good is produced by Northern oligopolistic firms using an input that can either be produced within the firm (vertical integration) or outsourced to Southern oligopolistic producers with lower labor costs (outsourcing). In the case where the final good is only consumed in the North and there is free entry in the South, we find that optimal competition policy in the North is the adoption of a tougher stance. However, with a CA in the South, the Southern CA would optimally appropriate outsourcing rents through restrictions on the degree of competition among domestic firms. In this case the optimal response of the Northern CA would be inaction. In the case where the final good is consumed in both countries, we find that optimal competition policy is marginally affected by the share of Southern consumption, leaving relatively important incentives to engage in rent-shifting. However, for a high enough share of Southern consumption, the interaction between the Northern and Southern CA is shown to be of the Prisoner's Dilemma type, whereby the Nash equilibrium is Pareto-suboptimal and mutual cooperation on competition policy is globally desirable.Competition policy, outsourcing, vertical integration

Weak Hopf Algebras and Reducible Jones Inclusions of Depth 2. I: From Crossed products to Jones towers

We apply the theory of finite dimensional weak C^*-Hopf algebras A as developed by G. B\"ohm, F. Nill and K. Szlach\'anyi to study reducible inclusion triples of von-Neumann algebras N \subset M \subset (M\cros\A). Here M is an A-module algebra, N is the fixed point algebra and \M\cros\A is the crossed product extension. ``Weak'' means that the coproduct \Delta on A is non-unital, requiring various modifications of the standard definitions for (co-)actions and crossed products. We show that acting with normalized positive and nondegenerate left integrals l\in\A gives rise to faithful conditional expectations E_l: M-->N, where under certain regularity conditions this correspondence is one-to-one. Associated with such left integrals we construct ``Jones projections'' e_l\in\A obeying the Jones relations as an identity in M\cros\A. Finally, we prove that N\subset M always has finite index and depth 2 and that the basic Jones construction is given by the ideal M_1:=M e_l M \subset M\cros\A, where under appropriate conditions M_1 = M\cros\A. In a subsequent paper we will show that converseley any reducible finite index and depth-2 Jones tower of von-Neumann factors (with finite dimensional centers) arises in this way.Comment: Latex, 63 page

High-speed Fabrication of Micro-channels using Line-based Laser Induced Plasma Micromachining (L-LIPMM)

Micro-texturing of surfaces has various applications that often involve texturing over large (macro-scale) areas with high precision and resolution. This demands scalability and speed of texturing while retaining feature sizes on the order of a few ?m. Moreover, micro-channels are a versatile micro-feature that are often used in microfluidic devices and can be arrayed or joined to form patterns and free-form geometries. We present a technique to fabricate micro-channels on surfaces with high-speed and by using a multi-materials process, namely Laser Induced Plasma Micromachining (LIPMM). The process has the potential to machine metals, ceramics, polymers and other transparent, brittle and hard-to-machine materials. The presented technique uses an optical system to modify the laser spot into the shape of a line, to fabricate micro-channels directly without scanning as in the case of a regular circular spot. The process schematics are shown, and micro-machining experiments on polished Aluminum are discussed. Moreover, it is shown that the depth and width of the channels may be varied by changing the process parameters like the pulse energy, pulse frequency and number of exposures