In the present paper combinatorial identities involving q-dual sequences or polynomials with coefficients q-dual sequences are derived. Further, combinatorial identities for q-binomial coefficients(Gaussian coefficients), q-Stirling numbers and q-Bernoulli numbers and polynomials are deduced.

Highest weight representations of Uq(su(1, 1)) with q = expπi/N are investigated. The structures of the irreducible hieghesat weight modules are discussed in detail. The Clebsch-Gordan decomposition for the tensor product of two irreducible representations is discussed. By using the results, a representation of SL(2,R) ⊗ Uq(su(2)) is also presented in terms of holomorphic sections which also ha...

We consider the quantum double D(G) of a compact group G, following an earlier paper. We use the explicit comultiplication on D(G) in order to build tensor products of irreducible ∗-representations. Then we study their behaviour under the action of the R-matrix, and their decomposition into irreducible ∗-representations. The example of D(SU(2)) is treated in detail, with explicit formulas for d...

The irreducible representations of the cubic space group are described and used to determine the mapping of continuum states to lattice states with non-zero linear momentum. The Clebsch-Gordan decomposition is calculated from the character table for the cubic space group. These results are used to identify multiparticle states which appear in the hadron spectrum on the lattice.

We consider Apollonian circle packings of a half Euclidean plane. We give necessary and sufficient conditions for two such packings to be related by a Euclidean similarity (that is, by translations, reflections, rotations and dilations) and describe explicitly the group of self-similarities of a given packing. We observe that packings with a non-trivial self-similarity correspond to positive re...

the genus hyoscyamus belongs to the tribe hyoscyameae miers of solanaceae family. variation in protein bands elaborates the relationship among the collections from various geographical regions. in this study the seed storage protein diversity of 19 accessions of hyoscyamus (h. niger, h. reticulatus and  h. pusillus) from west azerbaijan (iran) was investigated according to the sodium dodecyl su...

walnut is an important nut crop worldwide. iran is one of the walnut centers of diversity and cultivation. morphological traits and rapd primers were applied to determine genetic diversity among 31 iranian and four foreign walnut genotypes. from 14 rapd primers, 180 bands were amplified among which 174 were polymorphic. the lowest and highest similarity coefficients were 0.37 and 0.89 respectiv...

We propose a generic algorithm for computation of similarity measures for sequential data. The algorithm uses generalized suffix trees for efficient calculation of various kernel, distance and non-metric similarity functions. Its worst-case run-time is linear in the length of sequences and independent of the underlying embedding language, which can cover words, k-grams or all contained subseque...

Abstract The development of a model to quantify semantic similarity and relatedness between words has been the major focus many studies in various fields, e.g. psychology, linguistics, natural language processing. Unlike measures proposed by most previous research, this article is aimed at estimating automatically strength associative that can be semantically related or not. We demonstrate perf...