A short review of the use of quantum groups to addition theorems for q-special functions is given. We discuss a general convolution formula for Al-Salam and Chihara polynomials arising from its quantum algebra as transition coeecients. This contribution does not contain new results.

We consider two indeterminate moment problems: One corresponding to a birth and death process with quartic rates and the other corresponding to the Al-Salam-Carlitz q-polynomials. Using the Darboux method, we calculate their Nevanlinna matrices and several families of orthogonality measures.

We study intersecting D6-branes in Calabi-Yau manifolds that are smooth hypersurfaces in weighted projective spaces. We develop the techniques for calculating intersection numbers between special Lagrangian sub-manifolds defined as fixed loci of anti-holomorphic involutions. We present global Pati-Salam and MSSM-like models that are supersymmetric up to a decoupled hidden sector. ∗email: palti@...

Generalized Yang-Mills theories are constructed, that can use fields other than vector as gauge fields. Their geometric interpretation is studied. An application to the Glashow-Weinberg-Salam model is briefly review, and some related mathematical and physical considerations are made.

We describe the q–Engel series expansion for Laurent series discovered by John Knopfmacher and use this algorithm to shed new light on partition identities related to two entries from Slater’s list. In our study Al-Salam/Ismail and Santos polynomials play a crucial rôle. Dedicated to the memory of John Knopfmacher 1937–1999

Samir Kunkri, ∗ Guruprasad Kar, † Sibasish Ghosh, ‡ and Anirban Roy § Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B.T. Road, Kolkata 700 108, India Department of Computer Science , The University of York, Heslington, York, YO10 5DD, United Kingdom The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, Trieste, Italy, 34014 (Dated: February ...