We consider Kemp’s q-analogue of the binomial distribution. Several convergence results involving the classical binomial, the Heine, the discrete normal, and the Poisson distribution are established. Some of them are q-analogues of classical convergence properties. From the results about distributions, we deduce some new convergence results for (q-)Krawtchouk and q-Charlier polynomials. Besides...

In this paper, we mainly discuss the nonuniform average sampling and reconstruction in multiply generated shift-invariant subspaces \[ V_{p,q}(\Phi_r) = \bigg\{ \sum_{k_{1} \in \mathbf{Z}} \sum_{k_{2} \mathbf{Z}^{d}} c^T(k_{1},k_{2}) \Phi_r(\,\cdot-k_{1},\,\cdot-k_{2}): (c(k_{1},k_{2}))_{(k_{1},k_{2}) \mathbf{Z} \times \big( \ell^{p,q}(\mathbf{Z} \mathbf{Z}^d) \big)^r \bigg\} \] of mixed Lebesg...

Approximate string matching with k differences is considered. Filtration of the text is a widely adopted technique to reduce the text area processed by dynamic programming. We present sublinear filtration algorithms based on the locations of q-grams in the pattern. Samples of q-grams are drawn from the text at fixed periods, and only if consecutive samples appear in the pattern approximately in...

An algorithm is described for finding the maximal weight chain between two points in a locally finite partial order under the restriction that all but • (or fewer) successive pairs in the chain belong to a given subset of the partial order relation. Applications of the method in molecular genetics, critical path scheduling, and other fields are discussed. Let P be a set with two locally finite ...

The notion of stratified (L, M)-semiuniform convergence tower spaces is introduced, which extends the notions ofprobabilistic semiuniform convergence spaces and lattice-valued semiuniform convergence spaces. The resulting categoryis shown to be a strong topological universe. Besides, the relations between our category and that of stratified (L, M)-filter tower spaces are studied.

We introduce the notion of ideal, prime ideal, lter, fuzzy ideal, fuzzy prime ideal, fuzzy lter of ordered $Gamma$-semiring and study their properties and relations between them. We characterize the prime ideals and lters of ordered $Gamma$-semiring with respect to fuzzy ideals and fuzzy l- ters respectively.

Let f be a 2π periodic function in L[0, 2π] and ∑∞ k=−∞ f̂(nk)e inkx be its Fourier series with ‘small’ gaps nk+1 − nk ≥ q ≥ 1. Here we have obtained sufficiency conditions for the absolute convergence of such series if f is of ∧ BV (p) locally. We have also obtained a beautiful interconnection between lacunary and non-lacunary Fourier series.

In this Bachelor thesis, the problem of determining the coefficient q ∈ Q := {q ∈ L∞(Ω) : 0 < q ≤ q(x) ≤ q a.e. in Ω} such that it satisfies the Poisson equation −∇ · (q∇u) = f in Ω u = 0 on ∂Ω for given inexact data uδ (instead of exact data u) with ‖u−u‖H1(Ω) ≤ δ is analyzed and solved numerically. It is implemented in c++ using the Distributed and Unified Numerics Environment (DUNE). The ori...