4,987 research outputs found
A terminal molybdenum carbide prepared by methylidyne deprotonation
The carbide anion [CMo{N(R)Ar}_3]– [R = C(CD_3)_2CH_3, Ar = C_6H_3Me_2-3,5], is obtained by deprotonation of the corresponding methylidyne compound, [HCMo{N(R)Ar}_3], and is characterized by X-ray diffraction as its {K(benzo-15-crown-5)_2}+ salt, thereby providing precedent for the carbon atom as a terminal substituent in transition-metal chemistry
Generating-function method for fusion rules
This is the second of two articles devoted to an exposition of the
generating-function method for computing fusion rules in affine Lie algebras.
The present paper focuses on fusion rules, using the machinery developed for
tensor products in the companion article. Although the Kac-Walton algorithm
provides a method for constructing a fusion generating function from the
corresponding tensor-product generating function, we describe a more powerful
approach which starts by first defining the set of fusion elementary couplings
from a natural extension of the set of tensor-product elementary couplings. A
set of inequalities involving the level are derived from this set using Farkas'
lemma. These inequalities, taken in conjunction with the inequalities defining
the tensor products, define what we call the fusion basis. Given this basis,
the machinery of our previous paper may be applied to construct the fusion
generating function. New generating functions for sp(4) and su(4), together
with a closed form expression for their threshold levels are presented.Comment: Harvmac (b mode : 47 p) and Pictex; to appear in J. Math. Phy
Generating-function method for tensor products
This is the first of two articles devoted to a exposition of the
generating-function method for computing fusion rules in affine Lie algebras.
The present paper is entirely devoted to the study of the tensor-product
(infinite-level) limit of fusions rules.
We start by reviewing Sharp's character method. An alternative approach to
the construction of tensor-product generating functions is then presented which
overcomes most of the technical difficulties associated with the character
method. It is based on the reformulation of the problem of calculating tensor
products in terms of the solution of a set of linear and homogeneous
Diophantine equations whose elementary solutions represent ``elementary
couplings''. Grobner bases provide a tool for generating the complete set of
relations between elementary couplings and, most importantly, as an algorithm
for specifying a complete, compatible set of ``forbidden couplings''.Comment: Harvmac (b mode : 39 p) and Pictex; this is a substantially reduced
version of hep-th/9811113 (with new title); to appear in J. Math. Phy
A precise CNOT gate in the presence of large fabrication induced variations of the exchange interaction strength
We demonstrate how using two-qubit composite rotations a high fidelity
controlled-NOT (CNOT) gate can be constructed, even when the strength of the
interaction between qubits is not accurately known. We focus on the exchange
interaction oscillation in silicon based solid-state architectures with a
Heisenberg Hamiltonian. This method easily applies to a general two-qubit
Hamiltonian. We show how the robust CNOT gate can achieve a very high fidelity
when a single application of the composite rotations is combined with a modest
level of Hamiltonian characterisation. Operating the robust CNOT gate in a
suitably characterised system means concatenation of the composite pulse is
unnecessary, hence reducing operation time, and ensuring the gate operates
below the threshold required for fault-tolerant quantum computation.Comment: 9 pages, 8 figure
Radical anionic versus neutral 2,2′-bipyridyl coordination in uranium complexes supported by amide and ketimide ligands
The synthesis and characterization of (bipy)₂U(N[t-Bu]Ar)₂ (1-(bipy)₂, bipy = 2,2′-bipyridyl, Ar = 3,5-C₆H₃Me₂), (bipy)U(N[1Ad]Ar)₃ (2-bipy), (bipy)₂U(NC[t-Bu]Mes)₃ (3-(bipy)2, Mes = 2,4,6-C₆H₂Me₃), and IU(bipy)(NC[t-Bu]Mes)₃ (3-I-bipy) are reported. X-ray crystallography studies indicate that bipy coordinates as a radical anion in 1-(bipy)₂ and 2-bipy, and as a neutral ligand in 3-I-bipy. In 3-(bipy)₂, one of the bipy ligands is best viewed as a radical anion, the other as a neutral ligand. The electronic structure assignments are supported by NMR spectroscopy studies of exchange experiments with 4,4′-dimethyl-2,2′-bipyridyl and also by optical spectroscopy. In all complexes, uranium was assigned a +4 formal oxidation state.National Science Foundation (U.S.) (Grant CHE-9988806
Berenstein-Zelevinsky triangles, elementary couplings and fusion rules
We present a general scheme for describing su(N)_k fusion rules in terms of
elementary couplings, using Berenstein-Zelevinsky triangles. A fusion coupling
is characterized by its corresponding tensor product coupling (i.e. its
Berenstein-Zelevinsky triangle) and the threshold level at which it first
appears. We show that a closed expression for this threshold level is encoded
in the Berenstein-Zelevinsky triangle and an explicit method to calculate it is
presented. In this way a complete solution of su(4)_k fusion rules is obtained.Comment: 14 page
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