Rank reduction of conformal blocks

Let $X$ be a smooth, pointed Riemann surface of genus zero, and $G$ a simple, simply-connected complex algebraic group. Associated to a finite number of weights of $G$ and a level is a vector space called the space of conformal blocks, and a vector bundle of conformal blocks over $\bar{\text{M}}_{0,n}$. We show that, assuming the weights are on a face of the multiplicative eigenvalue polytope, the space of conformal blocks is isomorphic to a product of conformal blocks over groups of lower rank. If the weights are on a degree zero wall, then we also show that there is an isomorphism of conformal blocks bundles, giving an explicit relation between the associated nef divisors. The methods of the proof are geometric, and use the identification of conformal blocks with spaces of generalized theta functions, and the moduli stacks of parahoric bundles recently studied by Balaji and Seshadri.Comment: 30 pages, 11 figures. Changes include corrections and added details to proofs, and improved exposition. Length change is due to change in formattin

Improved recursive Green's function formalism for quasi one-dimensional systems with realistic defects

We derive an improved version of the recursive Green's function formalism (RGF), which is a standard tool in the quantum transport theory. We consider the case of disordered quasi one-dimensional materials where the disorder is applied in form of randomly distributed realistic defects, leading to partly periodic Hamiltonian matrices. The algorithm accelerates the common RGF in the recursive decimation scheme, using the iteration steps of the renormalization decimation algorithm. This leads to a smaller effective system, which is treated using the common forward iteration scheme. The computational complexity scales linearly with the number of defects, instead of linearly with the total system length for the conventional approach. We show that the scaling of the calculation time of the Green's function depends on the defect density of a random test system. Furthermore, we discuss the calculation time and the memory requirement of the whole transport formalism applied to defective carbon nanotubes

Electronic transport in metallic carbon nanotubes with mixed defects within the strong localization regime

We study the electron transport in metallic carbon nanotubes (CNTs) with realistic defects of different types. We focus on large CNTs with many defects in the mesoscopic range. In a recent paper we demonstrated that the electronic transport in those defective CNTs is in the regime of strong localization. We verify by quantum transport simulations that the localization length of CNTs with defects of mixed types can be related to the localization lengths of CNTs with identical defects by taking the weighted harmonic average. Secondly, we show how to use this result to estimate the conductance of arbitrary defective CNTs, avoiding time consuming transport calculations

Vanishing tilt-to-length coupling for a singular case in two-beam laser interferometers with Gaussian beams

The omnipresent tilt-to-length coupling in two-beam laser interferometers, frequently a nuisance in precision measurements, vanishes for the singular case of two beams with identical parameters and complete detection of both beams without clipping. This effect has been observed numerically and is explained in this manuscript by the cancellation of two very different effects of equal magnitude and opposite sign. This paper was published in Applied Optics and is made available as an electronic reprint with the permission of OSA. The paper can be found at the following URL on the OSA website: [http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-54-5-1010]. Systematic or multiple reproduction or distribution to multiple locations via electronic or other means is prohibited and is subject to penalties under law

An Evaluation of the jobsOntario Training Program

This paper examines the effectiveness of the Ontario government’s jobsOntario Training (JOT) program to determine whether it is successful in helping social assistance welfare recipients obtain jobs. A review of provincial documents as well as surveys and interviews with officials responsible for the development and implementation of the program were conducted. The findings reveal that pre-employment training is effective in helping social assistance welfare recipients become employed and the use of local brokers to deliver JOT contributes to the success of the program

„Ins Ohr des Allwissenden schreit auch der letzte Krampf des zertretenen Wurms“. Luise Millerin und der Secretarius Wurm in Friedrich Schillers Kabale und Liebe zwischen christlich-bürgerlichen Wertvorstellungen, Antisemitismus und jüdischer Emanzipation

Friedrich Schiller wielokrotnie angażował się w walkę o wolność, co wpłynęło na jego wielką popularność wśród Żydów z Europy Środkowej. Pod koniec lat osiemdziesiątych XVIII w., gdy sztuki Schillera zyskiwały uznanie, toczyła się burzliwa dyskusja o emancypacji Żydów, a antysemityzm stawał się jednym z najbardziej rozpowszechnionych w społeczeństwie poglądów. Jednak Schiller nigdy jednoznacznie nie sięgnął po temat Żydów, w przeciwieństwie do np. G. E. Lessinga i jego sztuki Nathan der Weise. Tylko jednego z jego bohaterów – zbója Moritza Spiegelberga z dramatu Räuber można by określić jako Żyda, jednak nawet badacze dzieł Schillera nie są w tej kwestii zgodni. W niniejszym artykule chcę pokazać, że temat Żydów odgrywa u Schillera także pewną rolę w jego dramacie Kabale und Liebe, a jeden z bohaterów – sekretarz Wurm, ma wyraźnie żydowskie rysy

Predictability and Patentable Processes: The Federal Circuit's In re Bilski Decision and Its Effect on the Incentive to Invent

Throughout the past two centuries, the U.S. patent system has defined the scope of (potentially) patentable processes by proscribing patents on fundamental principles (including abstract ideas, laws of nature, and natural phenomena). Unfortunately, such a description of patentable subject matter led to ambiguity and unpredictability in the application of the patent laws. In 2008, the Federal Circuit addressed this uncertainty by promulgating a new standard to describe the ambit of patentable processes: a process may constitute patentable subject matter if (1) it utilizes a particular machine or apparatus, or (2) it transforms an object into a different state or thing. This Article describes how the Federal Circuit's new standard furthers the underlying policy goal of all patent laws: the incentivization of innovation. Specifically, this paper argues that this new rule presents a simple and easy to apply standard that will increase the predictability of the patent laws. In the presence of such predictability, prospective inventors and investors are more likely to engage in research and development, thus leading to increased inventive activity