An algebra related to the fusion rules of Wess-Zumino-Witten models

We introduce a new family of examples of quantum groups. Its irreducible representations are indexed by level l dominant integral weights of affine Lie algebra s(n), and their branching rules with respect to the truncated tensor product is given by the fusion rules of SU(n) _l -Wess-Zumino-Witten model in conformal field theory.     

Non-Abelian fusion rules from an Abelian system

We demonstrate the emergence of non-Abelian fusion rules for excitations of a two dimensional lattice model built out of Abelian degrees of freedom. It can be considered as an extension of the usual toric code model on a two dimensional lattice augmented with matter fields. It consists of the usual C(Z_p)$\mathbb{C}\left({\mathbb{Z}}_p\right)$ gauge degrees of freedom living on the links together with matter degrees of freedom living on the vertices. The matter part is described by a n$n$ dimensional vector space which we call H_n$H_n$. The Z_p${\mathbb{Z}}_p$ gauge particles act on the vertex particles and thus H_n$H_n$ can be thought of as a C(Z_p)$\mathbb{C}\left({\mathbb{Z}}_p\right)$ module. An exactly solvable model is built with operators acting in this Hilbert space. The vertex excitations for this model are studied and shown to obey non-Abelian fusion rules. We will show this for specific values of n$n$ and p$p$, though we believe this feature holds for all n>p$n>p$. We will see that non-Abelian anyons of the quantum double of C(S₃)$\mathbb{C}\left(S_3\right)$ are obtained as part of the vertex excitations of the model with n=6$n=6$ and p=3$p=3$. Ising anyons are obtained in the model with n=4$n=4$ and p=2$p=2$. The n=3$n=3$ and p=2$p=2$ case is also worked out as this is the simplest model exhibiting non-Abelian fusion rules. Another common feature shared by these models is that the ground states have a higher symmetry than Z_p${\mathbb{Z}}_p$. This makes them possible candidates for realizing quantum computation.     

Lie algebra cohomology and the fusion rules

We prove a vanishing theorem for Lie algebra cohomology which constitutes a loop group analogue of Kostant's Lie algebra version of the Borel-Weil-Bott theorem. Consider a complex semi-simple Lie algebra and an integrable, irreducible, negative energy representation of. Givenn distinct pointsz _k in , with a finite-dimensional irreducible representationV _k of assigned to each, the Lie algebra of-valued polynomials acts on eachV _k , via evaluation atz _k . Then, the relative Lie algebra cohomologyH ^* is concentrated in one degree. As an application, based on an idea of G. Segal's, we prove that a certain homolorphic induction map from representations ofG to representations ofLG at a given level takes the ordinary tensor product into the fusion product. This result had been conjectured by R. Bott.     

High-intensity lasers and controlled fusion

The use of high-intensity lasers to cause ignition in inertial confinement fusion is presented, with emphasis on current experimental programs and physical concepts that are at the forefront of the field. In particular, we highlight the issues of fast electron transport through dense materials, an essential element of the Fast Ignitor concept.Received: 22 November 2002, Published online: 5 August 2003PACS: 52.20.Fs Electron collisions - 52.38.Kd Laser-plasma acceleration of electrons and ions     

Automorphisms of the affineSU(3) fusion rules

We classify the automorphisms of the (chiral) level-k affineSU(3) fusion rules, for any value ofk, by looking for all permutations that commute with the modular matricesS andT. This can be done by using the arithmetic of the cyclotomic extensions where the problem is naturally posed. Whenk is divisible by 3, the automorphism group (Z ₂) is generated by the charge conjugationC. Ifk is not divisible by 3, the automorphism group (Z ₂×Z ₂) is generated byC and the Altschüler-Lacki-Zaugg automorphism. Although the combinatorial analysis can become more involved, the techniques used here forSU(3) can be applied to other algebras.     

Application of dipole sum rules to transfer reaction strengths

Equations illustrating the application of dipole sum rules by relating the reaction strengths from single-particle transfer (stripping as well as pick up reactions) to the magnetic dipole moment of the target state (derived earlier) have been rewritten in a more symmetrical and user friendly form. The purpose of the present work is not to calculate the magnetic moment but to provide six different ways --from stripping and pick up reactions as well as from their combination, to study the discrepancies in the measurement of reaction strengths through their relationships with the magnetic moment. Received: 9 November 2000 / Accepted: 16 March 2001     

Surface effects in controlled thermonuclear fusion

The US. fusion power development program is aimed at the first significant production of fusion power on an experimental scale in the early 1980's, and at a demonstration of the commercial production of fusion power between 1995 and 1997, according to a status report by Robert L. Hirsch.¹ In order to achieve this god, four major concepts are being pursued in the U.S. at this time. Three concepts use magnetic fields to confine a plasma for either pulsed or steady-state operation: the tokamak, theta-pinch, and mirror devices. The fourth concept is laser fusion, which utilizes inertia to hold a plasma for a very short period of time (<10^?9 sec).     

Berenstein-Zelevinsky triangles,elementary couplings,and fusion rules

We present a general scheme for describing (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 (4) _k fusion rules is obtained.Work supported by NSERC (Canada).Work supported by NSERC (Canada) and FCAR (Québec).     

On new conformal field theories with affine fusion rules

Some time ago, conformal data with affine fusion rules were found. Our purpose here is to realize some of these conformal data, using systems of free bosons and parafermions. The so constructed theories have extended W algebras which are close analogues of affine algebras. Exact character formulae are given, and the realizations are shown to be full-fledged unitary conformal field theories.     

Characters and fusion rules forW-algebras via quantized Drinfeld-Sokolov reduction

Using the cohomological approach toW-algebras, we calculate characters and fusion coefficients for their representations obtained from modular invariant representations of affine algebras by the quantized Drinfeld-Sokolov reduction.Supported in part by Junior Fellowship from Harvard Society of FellowsSupported in part by NSF grants DMS-8802489 and DMS-9103792Supported in part by RIMS-91 ProjectCommunicated by A. Jaffe     

Status and prospects of controlled thermonuclear fusion

Of all approaches to controlled thermonuclear fusion the tokamak experiments have been most successful. Over the last decade particularly three large devices have achieved plasma density,n, temperature,T, and energy confinement time, _E, in ranges necessary for a fusion reactor plasma. Such maximum values have, however, been obtained not yet simultaneously but only in separate pulses, although the crucial triple product,nT _E, has also been improved by several orders of magnitude. The high temperatures sufficient in a fusion reactor can be produced by injection of neutral atoms or by absorption of radio frequency waves in the ion cyclotron frequency range. The plasma confinement ( _E1s) is still not understood and is handled through empirical scaling laws. Particle densities have usually been on the low side (n5×10¹⁹ m^–3) because increased fuelling rates can easily lead to violent current disruptions. Progress in obtaining peaked density profiles with pellet injection has led to high density plasmas without disruptions. Serious unsolved problems concern the spoiling of the fusion rates by (nonhydrogenic) impurities, the plasma parameter control over longer periods of time and indeed the plasma heating by fusion alpha-particles (ignition, burning). The most urgent technological question refers to the lifetime of the first wall which is in direct contact with the plasma. An important step towards ignition has been made by the recent JET/DT experiments in which, for the first time, the actual reactor fuel component tritium has been used to produce neutrons. The next generation tokamak ITER is, at present, being planned and designed in a world-wide collaborative effort. It should be operating before the year 2010 and is intended to investigate an ignited plasma burning for several minutes.     

Multifocus image fusion and denoising scheme based on homogeneity similarity

A novel image fusion algorithm based on homogeneity similarity is proposed in this paper, aiming at solving the fusion problem of clean and noisy multifocus images. Firstly, the initial fused image is acquired with one multiresolution image fusion method. The pixels of the source images, which are similar to the corresponding initial fused image pixels, are considered to be located in the sharply focused regions. By this method, the initial focused regions are determined. In order to improve the fusion performance, morphological opening and closing are employed for post-processing. Secondly, the homogeneity similarity is introduced and used to fuse the clean and noisy multifocus images. Finally, the fused image is obtained by weighting the neighborhood pixels of the point of source images which are located at the focused region. Experimental results demonstrate that, for the clean multifocus image fusion, the proposed method performs better than some popular image fusion methods in both subjective and objective qualities. Furthermore, it can simultaneously resolve the image restoration and fusion problem when the source multifocus images are corrupted by the Gaussian white noise, and can also provide better performance than the conventional methods.     

Application of similarity laws to the blade passage sound of centrifugal fans

This paper is concerned with similarity laws governing the harmonic components of the sound radiated from centrifugal fans. Measurements are made with two precisely similar fans having impellers of 140 mm and 280 mm diameter. The experimental apparatus used is in accordance with the in-duct method suggested in a recent ISO-proposal [1]. The present experimental results verify Weidemann's [2] formulation of similarity laws, which describes the radiated sound pressure as a product of non-dimensional terms. The experiments also prove that it is possible to extrapolate data from a model fan to other geometrically similar fans of different size.     

Application of QCD-sum rules to the resonance Λ(1405)

We investigate the resonance Λ(1405) in the framework of QCD-sum rules. It is found that in addition to local operators consisting of three quarks also those consisting of three quarks and a quark-antiquark pair both in a color singlet and flavor octet are important.     

基于相似性分类的高光谱主成分融合方法比较

为了提高复杂场景弱小目标高光谱融合图像的质量,提出了基于相似性分类的主成分融合方法。光谱数据像素向量的相似性测度分类产生类矩阵,通过由类矩阵主成分变换的降维投影矩阵来投影变换原有光谱数据,获得降维数据矩阵。对比了传统PCA与基于欧式距离分类的PCA(ED_PCA)、基于光谱角分类的PCA(SA_PCA)、基于光谱信息散度分类的PCA(SID_PCA)和基于正交投影散度分类的PCA(OPD_PCA)四种改进方法的融合性能。实验结果表明:SA_PCA和SID_PCA方法兼具了ED_PCA和OPD_PCA的优点,对比度提升较好,阈值参数不敏感,运行时间较短。     

Application of the similarity method to calculate electronic processes in semiconductor devices

An analytic solution for several problems in the physics of p-n junctions has been obtained by the similarity method [1]. The effect of surface recombination on the distribution of minority-carrier charge density in the base of a semiconductor diode shaped like a rectangular parallelepiped or as a cylinder, upon application of a forward voltage pulse has been evaluated. A formula is obtained to calculate transients in semiconductor diodes having a finite uniform base and ohmic back contact, for any shape of signal applied to the diode and for various initial conditions. The effect that recombination at the free surface about the injector contact has on the transient with instantaneous switching of a diode or transistor are taken into account. All results are generalized for a class of similar semiconductor devices.In conclusion I wish to thank Professor L. I. Kudryashev and Decent L. I. Baranov for much valuable consultation and advice.