House System

House system

House  System 1

The College has a house system with, as of 16 May 2019,[update] six different houses that compete across a range of sporting codes including cross country running and swimming together with varied cultural activities: Barnicoat-Rutherford Combined (White & Black) Chaytor (Red) Domett (Green) Monro (Blue) Robinson (Orange) Kahurangi (Yellow)The two boarding houses, Rutherford and Barnicoat, recently underwent a five-year refurbishment. A third boarding house, Fell, was closed to boarders at the end of 2018, and is now available for lease, predominantly to sports and community groups.

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Talking System

Talking System is a tribute band to Modern Talking and Blue System, both founded by German producer and composer Dieter Bohlen

House  System 2

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Qualification system

Each nation could send a maximum of 1 boy. The top scoring teams of the Marc Hodler Trophy Ski Jumping at the 2015 Junior Nordic World Ski Championships plus the hosts Norway were allowed to send the maximum of 1 boy. Any remaining quota spots were distributed to nations not already qualified, with a maximum of one boy or girl from one nation. The quota limit was 20. Qualification summary

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Farm system

LEAGUE CHAMPIONS: Rome, GCL Braves

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Root system

A very remarkable feature is that for every Nichols algebra (under sufficient finiteness conditions) there exists a generalized root system with a set of roots displaystyle Phi , which controls the Nichols algebra. This has been discovered in for diagonal Nichols algebras in terms of the bicharacter q i j displaystyle q_ij and in for general semisimple Nichols algebras. In contrast to ordinary crystallographic root systems known from Lie algebras, the same generalized root system displaystyle Phi may possess several be different Weyl chambers, corresponding to non-equivalent choices of sets of positive roots = displaystyle Phi =Phi ^cup -Phi ^ and simple positive roots 1 , ... n displaystyle alpha _1,ldots alpha _n , having different Cartan matrices and different Dynkin diagrams. The different Weyl chambers correspond in fact to different non-isomorphic Nichols algebras which are called Weyl-equivalent. Quantum groups are very special with respect to the fact that here all Borel parts are isomorphic; nevertheless even in this case Lusztig's reflection operator T s displaystyle T_s is again not' a Hopf algebra isomorphism! Definition of Weyl groupoid and generalized roots systemLet I = 1 , ... n displaystyle I=1,ldots n where n displaystyle n is the rank, with formal basis 1 , ... n displaystyle alpha _1,ldots alpha _n . We first discuss generalized Cartan graphs as in: A generalized Cartan matrix c i j , i , j I displaystyle c_ij,;;i,jin I is an integral matrix such that c i i = 2 , c i j eq j with m i j displaystyle m_ij finite ( r i r j ) m i , j a ( a ) = a displaystyle (r_ir_j)^m_i,j^a(a)=a Equivalence to Crystallographic Hyperplane ArrangementsIn it was shown that Weyl groupoids are in 1:1 correspondence to crystallographic hyperplane arrangements. These are a set of hyperplanes in R n displaystyle mathbb R ^n through the origin and choices of normal vectors such that for every simplicial chamber bounded by n displaystyle n hyperplanes with normal vectors 1 , ... n displaystyle alpha _1^perp ,ldots alpha _n^perp all other chosen normal vector displaystyle alpha ^perp can be expressed as integral linear combination of the i displaystyle alpha _i^perp . In the set of all finite crystallographic hyperplane arrangements (and hence finite Weyl groupoids or finite generalized root systems) have been classified. Apart from the reflection arrangements A n , B n , C n , D n , E 6 , E 7 , E 8 , F 4 , G 2 displaystyle A_n,B_n,C_n,D_n,E_6,E_7,E_8,F_4,G_2 there is one more infinite family and altogether 74 exceptionswith rank up to 8 displaystyle 8 . Example of rank 3 (also a super Lie algebra)The smallest crystallographic hyperplane arrangement, Weyl groupoid, generalized root system, which is not of ordinary Lie type, is as follows. It appears for a diagonal Nichols algebra, even a super Lie algebra. The hyperplane arrangement can be constructed from a cuboctahedron (a platonic solid): It has 7 displaystyle 7 roots ( 4 displaystyle 4 resp. 3 displaystyle 3 hyperplanes, in the pictures bounding equilateral triangle resp. diagonals in squares, in the super Lie algebra odd resp. even roots). It visibly has 2 displaystyle 2 different types of Weyl chambers (equilateral triangles resp. right triangles) with different Cartan matrices in which the roots in terms of simple roots are as follows: a = ( 1 , 0 , 0 ) , ( 0 , 1 , 0 ) , ( 0 , 0 , 1 ) , ( 1 , 1 , 0 ) , ( 1 , 0 , 1 ) , ( 0 , 1 , 1 ) , ( 1 , 1 , 1 ) displaystyle Phi _^a=(1,0,0),(0,1,0),(0,0,1),(1,1,0),(1,0,1),(0,1,1),(1,1,1) In the picture the white chamber, e.g with basis 1 , 2 , 3 displaystyle alpha _1,alpha _2,alpha _3 . Clearly, the Dynkin diagram of this type of chamber a A displaystyle ain A is a simply-laced triangle,Reflection on 2 displaystyle alpha _2 brings us to the second type of chamber a = ( 1 , 0 , 0 ) , ( 0 , 1 , 0 ) , ( 0 , 0 , 1 ) , ( 1 , 1 , 0 ) , ( 0 , 1 , 1 ) , ( 1 , 1 , 1 ) , ( 1 , 2 , 1 ) displaystyle Phi _^a'=(1,0,0),(0,1,0),(0,0,1),(1,1,0),(0,1,1),(1,1,1),(1,2,1) In the picture the gray chamber, e.g with basis 1 , 2 , 3 = 12 , 2 , 23 displaystyle alpha _1',alpha _2',alpha _3'=alpha _12,-alpha _2,alpha _23 . The Dynkin diagram of this type of chamber a A displaystyle a'in A is just A 2 displaystyle A_2 (but one more root).This root system is the smallest member of an infinite series. The pictures are from, where the example is also discussed thoroughly.

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What Are Some Ways to Keep My Hair Really Healthy?
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عمليات البحث ذات الصلة
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