28,640 research outputs found
Simple Irreducible Subgroups of Exceptional Algebraic Groups
A closed subgroup of a semisimple algebraic group is called irreducible if it
lies in no proper parabolic subgroup. In this paper we classify all irreducible
subgroups of exceptional algebraic groups which are connected, closed and
simple of rank at least . Consequences are given concerning the
representations of such subgroups on various -modules: for example, with one
exception, the conjugacy classes of irreducible simple connected subgroups of
rank at least are determined by their composition factors on the adjoint
module for .Comment: 46 pages; version to appear in J. Al
Irreducible A_1 Subgroups of Exceptional Algebraic Groups
A closed subgroup of a semisimple algebraic group is called irreducible if it
lies in no proper parabolic subgroup. In this paper we classify all irreducible
subgroups of exceptional algebraic groups . Consequences are given
concerning the representations of such subgroups on various -modules: for
example, the conjugacy classes of irreducible subgroups are determined by
their composition factors on the adjoint module of .Comment: 51 pages; published in J. Al
ConSole: using modularity of contact maps to locate solenoid domains in protein structures.
BackgroundPeriodic proteins, characterized by the presence of multiple repeats of short motifs, form an interesting and seldom-studied group. Due to often extreme divergence in sequence, detection and analysis of such motifs is performed more reliably on the structural level. Yet, few algorithms have been developed for the detection and analysis of structures of periodic proteins.ResultsConSole recognizes modularity in protein contact maps, allowing for precise identification of repeats in solenoid protein structures, an important subgroup of periodic proteins. Tests on benchmarks show that ConSole has higher recognition accuracy as compared to Raphael, the only other publicly available solenoid structure detection tool. As a next step of ConSole analysis, we show how detection of solenoid repeats in structures can be used to improve sequence recognition of these motifs and to detect subtle irregularities of repeat lengths in three solenoid protein families.ConclusionsThe ConSole algorithm provides a fast and accurate tool to recognize solenoid protein structures as a whole and to identify individual solenoid repeat units from a structure. ConSole is available as a web-based, interactive server and is available for download at http://console.sanfordburnham.org
On Mubayi's Conjecture and conditionally intersecting sets
Mubayi's Conjecture states that if is a family of -sized
subsets of which, for , satisfies whenever
for all distinct sets , then , with equality occurring only if is the family
of all -sized subsets containing some fixed element. This paper proves that
Mubayi's Conjecture is true for all families that are invariant with respect to
shifting; indeed, these families satisfy a stronger version of Mubayi's
Conjecture. Relevant to the conjecture, we prove a fundamental bijective
duality between -unstable families and -unstable families.
Generalising previous intersecting conditions, we introduce the
-conditionally intersecting condition for families of sets and prove
general results thereon. We conjecture on the size and extremal structures of
families that are -conditionally
intersecting but which are not intersecting, and prove results related to this
conjecture. We prove fundamental theorems on two -conditionally
intersecting families that generalise previous intersecting families, and we
pose an extension of a previous conjecture by Frankl and F\"uredi on
-conditionally intersecting families. Finally, we generalise a
classical result by Erd\H{o}s, Ko and Rado by proving tight upper bounds on the
size of -conditionally intersecting families and by characterising the families that attain these bounds. We extend
this theorem for certain parametres as well as for sufficiently large families
with respect to -conditionally intersecting families
whose members have at most a fixed number
members
Capital Importers Pay More for their Imports
We examine the effects that a countryâs net capital flows have on the (border) prices that a country pays for its imports of goods. Using data from 2000 to 2009 for 11 euro area countries we utilize a pricing-to-market specification to study exportersâ pricing behavior to the rest of the countries in the sample, at the industry level, for 900 goods disseminated at the 4- digit Standard International Trade Classification (SITC- revision 3) level. This allows us to construct a panel dataset which contains observations across exporters, importers, industries and time, ending up with a total of 594,327 observations. We find a strong influence of the importing countryâs net capital inflows on the border prices of its imports of goods. This result is robust across different specifications of the underlying model, as well to different sample dis-aggregations across types of capital flows, product categories, and exporters.capital flows, import prices, pricing to market, globalization, euro area
Turkish Delight for Some, Cold Turkey for Others?: The Effects of the EU-Turkey Customs Union
Following Turkeyâs application for EU membership in 1987, a Customs Union (CU) between Turkey and the EU, mainly covering trade in manufacturing goods and processed agricultural products, came into effect in 1995. In addition to a large agricultural sector, Turkey also specializes in the production and exportation of relatively low-price, low-quality varieties of manufactured products. We use a theoretical framework in order to demonstrate that these features of the Turkish economy imply asymmetric changes in the trade volumes of the incumbent countries of the EU as a result of the EU-Turkey CU. By examining disaggregated trade data we find that the technologically sophisticated EU countries (e.g., mainly the Northern European countries) are also least similar to Turkey in terms of their export structure, whereas the degree of export similarity between the less technologically sophisticated EU members and Turkey is high. Our econometric results indicate that, in contrast to the âNorthernâ groupâs exports to other EU15 countries (which have remained intact), the Southern countriesâs exports to the other EU15 countries have declined as a result of the EU-Turkey CU. Moreover, the extra penetration of the Turkish market by EU countries has not been more favourable to the Southern group. These findings also imply that technologically sophisticated countries may see no significant further benefits from Turkeyâs full accession to the EU (whereas the migration and political influence related costs for these countries may be large).European Union, Turkey, customs union, exports, gravity, differentiated products
Complete Reducibility in Good Characteristic
Let be a simple algebraic group of exceptional type, over an
algebraically closed field of characteristic . A closed subgroup
of is called -completely reducible (-cr) if whenever is contained
in a parabolic subgroup of , it is contained in a Levi subgroup of .
In this paper we determine the -conjugacy classes of non--cr simple
connected subgroups of when is good for . For each such subgroup
, we determine the action of on the adjoint module and the
connected centraliser of in . As a consequence we classify all
non--cr connected reductive subgroups of , and determine their connected
centralisers. We also classify the subgroups of which are maximal among
connected reductive subgroups, but not maximal among all connected subgroups.Comment: 66 pages. To appear in Trans. Amer. Math. So
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