Scale properties in data envelopment analysis

Recently there has been some discussion in the literature concerning the nature of scale properties in the Data Envelopment Model (DEA). It has been argued that DEA may not be able to provide reliable estimates of the optimal scale size. We argue in this paper that DEA is well suited to estimate optimal scale size, if DEA is augmented with two additional maintained hypotheses which imply that the DEA-frontier is consistent with smooth curves along rays in input and in output space that obey the Regular Ultra Passum (RUP) law (Frisch 1965). A necessary condition for a smooth curve passing through all vertices to obey the RUP-law is presented. If this condition is satisfied then upper and lower bounds for the marginal product at each vertex are presented. It is shown that any set of feasible marginal products will correspond to a smooth curve passing through all points with a monotonic decreasing scale elasticity. The proof is constructive in the sense that an estimator of the curve is provided with the desired properties. A typical DEA based return to scale analysis simply reports whether or not a DMU is at the optimal scale based on point estimates of scale efficiency. A contribution of this paper is that we provide a method which allows us to determine in what interval optimal scale is located.DEA; efficiency

bbˉb\bar b Description with a Screened Potential

Recent lattice QCD calculations suggest a rather abrupt transition in the confinig potential from a linear to a constant behavior. We analyze the effects of such a fast deconfinement in the simplest non-relativistic system, bottomonium.Comment: 4 pages. Presented at MENU04, Beijing 2004. To be published by IJMP

⇔ (A ⇔ B means A is true if B is true and A is false if B is false)

⇔ Bartram and O'Neill Negotiating a collaborative relationship has enormous benefits: a sense of comradery, when the making of art can be an isolating process; the ongoing dialogue and critique that can add confidence to a work when it has been tested by two minds rather than one; the knowledge of shared responsibility. There are also huge risks that can be so great they often remain unspoken: trust, ownership, authorship. In a new work developed for In Dialogue Bartram & O'Neill will explore some of the complications of collaboration in a performance dialogue which will take place on a series of blackboards over the course of a day. This durational work will allow both artists and viewers to reflect on the issues raised by collaborative working through a visual dialogue. The work will take as it starting point a statement make by Bartram & O'Neill which will appear in a forthcoming issue of TAJ Q How is the collaborative relationship of Angela Bartram and Mary O’Neill negotiated? What is the aim? Who initiates, and who is the instigator in developing the work? Does it matter? Bartram: The collaboration transcends the boundaries between performance and its legacy, between the performer and observer, between author and interpreter. Rather than the documentation being produced by an onlooker outside the performance, the generation of an accompanying texts becomes integral to the performance itself. Thereby creating a text that is embedded in the physical experience of the performance. In the case of Oral / Response the repetition and rhythm of the action of crushing the sticks of charcoal and blowing the dust is echoed in the tat-tat-tat thud of inscribing the text on the shared surface. O’Neill: Communication and development are negotiated through a dialogue. The partnership is equal in its response to the varying methods and processes that make up its sum parts. Integral to this performance is the distinction between cooperation and collaboration as defined by Pierre Dillenbourg (1996). According to Dillenbourg, “cooperative work is accomplished by the division of labour among participants, as an activity where each person is responsible for a portion of the problem solving...” whereas collaboration involves the “mutual engagement of participants in a coordinated effort to solve the problem together.” (Dillenbourg, 1996) In collaboration the disciplinary ghettos of performance and documentation are abandoned in favour of a mode of practice that allows for a greater level of mutual critique. Performers work together towards a shared goal, the success of the performance, rather than focus on the individual contribution. To this end auto/ethnography enhances the processes of give and take, self-critique, and improvement that enhance the collaborative synergy

Monoids Mon⟨a,b:aαbβaγbδaεbφ=b⟩\mathrm{Mon}\langle a,b:a^{\alpha}b^{\beta}a^{\gamma}b^{\delta}a^{\varepsilon}b^{\varphi}=b\rangle admit finite complete rewriting systems

The aim of this note is to prove that monoids $\mathrm{Mon}\langle a,b:aUb=b\rangle$, with $aUb$ of relative length 6, admit finite complete rewriting systems. This is some advance in the understanding the long-standing open problem whether the word problem for one-relator monoids is soluble

Survival probabilities in the double trapping reaction A +B -> B, B + C -> C

We consider the double trapping reaction A + B -> B, B + C -> C in one dimension. The survival probability of a given A particle is calculated under various conditions on the diffusion constants of the reactants, and on the ratio of initial B and C particle densities. The results are of more general form than those obtained in previous work on the problem.Comment: 5 page

A matrix subadditivity inequality for f(A+B) and f(A)+f(B)

Let f be a non-negative concave function on the positive half-line. Let A and B be two positive matrices. Then, for all symmetric norms, || f(A+B) || is less than || f(A)+f(B) ||. When f is operator concave, this was proved by Ando and Zhan. Our method is simpler. Several related results are presented.Comment: accepted in LA