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new algorithm to *compute* fusion coecients By

"... This is a proceedings article reviewing a recent combinatorial construction of the bsu(n)k WZNW fusion ring by C. Stroppel and the author. It contains one novel aspect: the explicit derivation of an algorithm for the computation of fusion coecients dierent from the Kac-Walton formula. The discussion ..."

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This is a

*proceedings*article reviewing a recent combinatorial construction of the bsu(n)k WZNW fusion ring by*C*. Stroppel and the author. It contains one novel aspect: the explicit derivation of an algorithm for the*computation*of fusion coecients dierent from the Kac-Walton formula###
Nuclear Physics B *Proceedings* Supplement – preprint (2014) 1–42 Nuclear Physics B *Proceedings* Supplement Universal Aspects of QCD-like TheoriesI

"... In these lectures I review some basic examples of how the concepts of universality and scaling can be used to study aspects of the chiral and the deconfinement transition, if not in QCD directly but in QCD-like theories. As an example for flavor dynamics I discuss a quark-hadron model to describe th ..."

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the phase diagram of two-color QCD with the functional renormalization group. Universal aspects of deconfinement are illustrated mainly in the

*2*+ 1 dimensional SU(N) gauge theories with second order transition where many exact results from spin models can be exploited.### 1On the Identifiability of Overcomplete Dictionaries via the Minimisation Principle Underlying K-SVD

, 2013

"... This article gives theoretical insights into the performance of K-SVD, a dictionary learning algorithm that has gained significant popularity in practical applications. The particular question studied here is when a dictionary Φ ∈ Rd×K can be recovered as local minimum of the minimisation criterion ..."

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This article gives theoretical insights into the performance of K-SVD, a dictionary learning algorithm that has gained significant popularity in practical applications. The particular question studied here is when a dictionary Φ ∈ Rd×K can be recovered as local minimum of the minimisation criterion underlying K-SVD from a set of N training signals yn = Φxn. A theoretical analysis of the problem leads to two types of identifiability results assuming the training signals are generated from a tight frame with coefficients drawn from a random symmetric distribution. First asymptotic results showing, that in expectation the generating dictionary can be recovered exactly as a local minimum of the K-SVD criterion if the coefficient distribution exhibits sufficient decay. This decay can be characterised by the coherence of the dictionary and the `1-norm of the coefficients. Based on the asymptotic results it is further demonstrated that given a finite number of training samples N, such that N / logN = O(K3d), except with probability O(N−Kd) there is a local minimum of the K-SVD criterion within distance O(KN−1/4) to the generating dictionary. Index Terms dictionary learning, sparse coding, K-SVD, finite sample size, sampling complexity, dictionary identification, minimisation criterion, sparse representation 1

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Applied and *Computational* Harmonic Analysis

"... This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or sel ..."

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This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for

*internal*non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution###
*Proceeding* of The *International* Seminar on Chemistry

"... Abstract Banana stem as waste contains cellulose is interesting as a cheap and available raw material for preparing the ion exchanger resin. Natural cellulose contains several ionizable functional groups, it act as a weak ion exchanger, introducing functional groups can increase the exchange capaci ..."

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in methylene chloride, at 90 O

*C*for*2*.5 hours. Phosphorus cellulose cation exchanger is characterized, and the capacity of cation exchange is determined, Cation exchange efficiency of Gd,*Nd*, Ce, Sm, Pr, and Y ions are observed. The banana stem fiber contains 50% of cellulose, of which containing 91% α### Authors:

, 1997

"... 1 Dedicated to Ludwig Elsner on the occasion of his sixtieth birthday We describe canonical forms for elements of a classical Lie group of matrices under similarity transformations in the group. Matrices in the associated Lie algebra and Jordan algebra of matrices inherit related forms under these s ..."

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1 Dedicated to Ludwig Elsner on the occasion of his sixtieth birthday We describe canonical forms for elements of a classical Lie group of matrices under similarity transformations in the group. Matrices in the associated Lie algebra and Jordan algebra of matrices inherit related forms under these similarity transforma-tions. In general, one cannot achieve diagonal or Schur form, but the form that can be achieved displays the eigenvalues of the matrix. We also discuss matrices in in-tersections of these classes and their Schur-like forms. Such multistructered matrices arise in applications from quantum physics and quantum chemistry. 1