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Among monoidal categories with finite coproducts preserved by tensoring on the left, we characterise those with finite biproducts as being precisely those in which the initial object and the coproduct of the unit with itself admit right duals. This generalises Houston's result that any compact closed category with finite coproducts admits biproducts.
The Catalan numbers are well known to be the answer to many different counting problems, and so there are many different families of sets whose cardinalities are the Catalan numbers. We show how such a family can be given the structure of a simplicial set. We show how the low-dimensional parts of this simplicial set classify, in a precise sense, the structures of monoid and of monoidal category. This involves aspects of combinatorics, algebraic topology, quantum groups, logic, and category theory.
Critics of U.S. congressional and state legislative redistricting have argued that gerrymandering severely undermines electoral competitiveness to the point of violating constitutional equal protection standards. In this article, we evaluate whether redistricting principles and processes have any measurable consequence on state legislative electoral competition. In addition to their substantive importance, state legislative general election contests provide greater variance than congressional data for empirically assessing theoretical propositions regarding redistricting principles and processes. We find that electoral competitiveness in state legislative races declined throughout the 1990s, even after term limit reforms were implemented. The proportion of uncontested state legislative seats has doubled since the 1970s, and there has also been a slight increase in average margin of election district victory. Our results show that political principles and some traditional, “politically-neutral” redistricting principles significantly decrease the probability of uncontested state legislative elections. In contrast, independent redistricting commissions did not appear to affect state legislative competition. We conclude with a discussion of how our findings relate to the redistricting reform debate.
We explain how any cofibrantly generated weak factorisation system on a category may be equipped with a universally and canonically determined choice of cofibrant replacement. We then apply this to the theory of weak ω-categories, showing that the universal and canonical cofibrant replacement of the operad for strict ω-categories is precisely Leinster's operad for weak ω-categories.
We form tricategories and the homomorphisms between them into a bicategory, whose 2-cells are certain degenerate tritransformations. We then enrich this bicategory into an example of a three-dimensional structure called a locally cubical bicategory, this being a bicategory enriched in the monoidal 2-category of pseudo double categories. Finally, we show that every sufficiently well-behaved locally cubical bicategory gives rise to a tricategory, and thereby deduce the existence of a tricategory of tricategories.
A diamond based insulated gate bipolar transistor is incorporated into a two-dimensional device simulator (MEDICI) to examine the current gain (β) and potential distribution across the device. Initially, work has focused on an important component of IGBT structure, the PNP bipolar transistor, which has been simulated and is reported upon in this paper. Empirical parameters for emitter and collector regions were used. Various carrier concentrations for base region were used to optimize the simulation. It was found that decreasing the thickness of base region leads to an increase in current gain. A buffer layer is needed to prevent the punch-through at low carrier concentration in the base region. Various approaches of increasing the current gain are also discussed in this paper.
I am of two minds in regard to a response to the reviews of Economic Growth and Change in Bourbon Mexico. Although I am gratified by the attention that it has received, I have been disinclined to engage in a debate about its merits and defects. Ultimately a book must stand on its own. Some will find that Economic Growth and Change makes a plausible case, and others will say that it does not. That is how it should be. I have no interest in rewriting those sections of Economic Growth and Change that miss the mark. Still, the invitation to write a reply does allow me the opportunity to re-examine some of the most controversial issues with an eye toward how scholars might move ahead with the agenda on the reconstruction of Latin America's colonial economic history.
Spinel (MgAl2O4) single crystals which had been neutron irradiated at (nominally) 400 and 750°C to high doses (53-250 dpa) were examined using 27Al magic angle spinning (MAS) nuclear magnetic resonance (NMR). The sensitivity of this procedure to a specific cation (Al) residing in different crystallographic environments allowed us to determine the distribution of the Al between the tetrahedral and octahedral cation sites in the spinel structure. Our results indicate that the Al was distributed nearly equally over both cation sites in the spinel, resulting in a nearly inverse structure.
There was a time when the detractors of Bacchylides singled out his eleventh ode as inept even by Bacchylidean standards: it was like the unfortunate tenor who was so stupid that even the other tenors noticed. The time of such criticism is gone, and the unfavourable verdict against Bacchylides' ode has nearly disappeared as well. The mythical journey in time which proceeds from the building of Artemis' altar back to the madness of Proetus' daughters and back further to the quarrel between Proetus and Acrisius is no longer seen as rambling. Instead the ode's structure has been revealed as an elegant set of concentric rings. Proetus' unhappy daughters are no longer unwanted, for Bacchylides has woven images into and around their story which suggest the integration of young women into the structure of the Greek city: the girls' resistance to marriage (Hera) is overcome through the mediation of Artemis, and they are returned to their father at last fit to be wed to the men of Tiryns. The entire ode has now been described as a fitting song for a city delighting in a victory gained with the aid of Artemis.4 The ode's images have been analysed and found coherent. Epithets, once scorned as too plentiful and various to bear true meaning, have now been defended. And finally, for a wonder, the song has been singled out as an example of that very thing so routinely denied to Bacchylides: Pindaric style. But even the most complimentary treatments of the poem seem somehow to fall short of explaining how this song serves as proper and sufficient praise for Alexidamus, the boy from Metapontum who wrestled his way to victory at the Pythian games.