S_4-symmetry of 6j-symbols and Frobenius-Schur indicators in rigid monoidal C^*-categories

We show that a left-rigid monoidal C^*-category with irreducible monoidal unit is also a sovereign and spherical category. Defining a Frobenius-Schur type indicator we obtain selection rules for the fusion coefficients of irreducible objects. As a main result we prove S_4-invariance of 6j-symbols in such a category.Comment: 21 pages + 16 pages with figures; LaTeX2e plus macro package XYpic; file with included pictures available as http://www.desy.de/~jfuchs/s4/s4.ps.g

A systematic review of reviews on patellofemoral pain syndrome. Exploring the risk factors, diagnostic tests, outcome measurements and exercise treatment

Abstract: Background: Literature has shown a growing number of published studies on Patellofemoral Pain Syndrome every year. The increasing evidence base has revealed a significant number of reviews which makes it confusing for clinicians and researchers to choose from the best evidence. This study aimed to gather the reviews on Patellofemoral Pain Syndrome and provide information about the most common clinical tests, risk factors, exercise treatment and outcome measures. In addition, secondary questions aimed to report the study settings and patient characteristics of the primary included studies. Methods: Studies eligible for this Review of Reviews were those published from 1993 to July 2013. Databases searched included PubMed, CINAHL, SPORTDiscus, Pedro and the Cochrane Library. Four key areas were searched using the words: PFPS, Anterior Knee Pain (AKP) or Chondromalacia patella (CP), plus a keyword. The keywords for the four research topics were a) risk factors; b) exercise treatment; c) diagnostic clinical tests and d) psychometric outcome measurements. Only reviews with clear methodological strategy were included. A two-stage evaluation was performed ineach review assessment. At first, the level of evidence was graded and then the methodological quality of each review was assessed. Results: Full text screening revealed that only 18 reviews were eligible for use. The selected reviews included 213 primary studies. After excluding duplicates, 144 primary studies were screened to answer the secondary questions. A gold standard clinical test for PFPS assessment cannot be reached and the use of functional tasks should be considered. The quadriceps strength deficits are still the only evidence based risk factors along with the dynamic malalignment of the lower limb. More research is still required on strength and flexibility deficits of other lower limb muscles. The quadriceps-based exercises are still the only ones to have strong evidence together with hamstrings, quadriceps, gastrocnemius and anterior hip muscles stretching. Finally, the usage of Activities of Daily Living Scale is recommended as the best outcome measure. Conclusion: There is no evidence on whether the above treatment and assessment methods should be used in sedentarypeople or differently across population groups or gender. More RCTs with large populations, powered correctly, inclinical environments are called for in further research

On Lie groups as quasi-K\"ahler manifolds with Killing Norden metric

A 6-parametric family of 6--dimensional quasi-K\"ahler manifolds with Norden metric is constructed on a Lie group. This family is characterized geometrically.Comment: 11 pages, 2 table

Revisiting the Quantum Group Symmetry of Diatomic Molecules

We propose a q-deformed model of the anharmonic vibrations in diatomic molecules. We analyse the applicability of the model to the phenomenological Dunham's expansion by comparing with experimental data. Our methodology involves a global consistency analysis of the parameters that determine the q-deformed system, when compared with fitted vibrational parameters to 161 electronic states in diatomic molecules. We show how to include both the positive and the negative anharmonicities in a simple and systematic fashion.Comment: 15 pages, 3 Table

Quantization of U_q[so(2n+1)] with deformed para-Fermi operators

The observation that n pairs of para-Fermi (pF) operators generate the universal enveloping algebra of the orthogonal Lie algebra so(2n+1) is used in order to define deformed pF operators. It is shown that these operators are an alternative to the Chevalley generators. On this background Uq[so(2n+1)] and its "Cartan-Weyl" generators are written down entirely in terms of deformed pB operators.Comment: plain TeX, Preprint INRNE-TH-93/7, 6

A classification of the torsion tensors on almost contact manifolds with B-metric

The space of the torsion (0,3)-tensors of the linear connections on almost contact manifolds with B-metric is decomposed in 15 orthogonal and invariant subspaces with respect to the action of the structure group. Three known connections, preserving the structure, are characterized regarding this classification.Comment: 17 pages, exposition clarified, references adde

Hopf algebraic structure of the parabosonic and parafermionic algebras and paraparticle generalization of the Jordan Schwinger map

The aim of this paper is to show that there is a Hopf structure of the parabosonic and parafermionic algebras and this Hopf structure can generate the well known Hopf algebraic structure of the Lie algebras, through a realization of Lie algebras using the parabosonic (and parafermionic) extension of the Jordan Schwinger map. The differences between the Hopf algebraic and the graded Hopf superalgebraic structure on the parabosonic algebra are discussed.Comment: 11 pages, LaTex2e fil

Algebraic structure of the Green's ansatz and its q-deformed analogue

The algebraic structure of the Green's ansatz is analyzed in such a way that its generalization to the case of q-deformed para-Bose and para-Fermi operators is becoming evident. To this end the underlying Lie (super)algebraic properties of the parastatistics are essentially used.Comment: plain TeX, Preprint INRNE-TH-94/4, 13

On the Invariant Theory of Weingarten Surfaces in Euclidean Space

We prove that any strongly regular Weingarten surface in Euclidean space carries locally geometric principal parameters. The basic theorem states that any strongly regular Weingarten surface is determined up to a motion by its structural functions and the normal curvature function satisfying a geometric differential equation. We apply these results to the special Weingarten surfaces: minimal surfaces, surfaces of constant mean curvature and surfaces of constant Gauss curvature.Comment: 16 page

Vanishing Theorems and String Backgrounds

We show various vanishing theorems for the cohomology groups of compact hermitian manifolds for which the Bismut connection has (restricted) holonomy contained in SU(n) and classify all such manifolds of dimension four. In this way we provide necessary conditions for the existence of such structures on hermitian manifolds. Then we apply our results to solutions of the string equations and show that such solutions admit various cohomological restrictions like for example that under certain natural assumptions the plurigenera vanish. We also find that under some assumptions the string equations are equivalent to the condition that a certain vector is parallel with respect to the Bismut connection.Comment: 25 pages, Late