Let $$\underline{S}$$ be an arbitrary subset of $$R^n$$ where R is a domain with the field fractions $$\mathbb {K}$$ . Denote ring polynomials in n variables over by {K}[\underline{x}] $$ The integer-valued , denoted Int $$(\underline{S},R)$$ defined as set which maps to R. In this article, we study irreducibility for first time case when Unique Factorization Domain. We also show that our resul...

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Let L2(R,H) denote the space of all square integrable quaternionic-valued functions. In this article, let Φ∈L2(R,H). We consider perturbation problems wavelet frame {Φm,n,a0,b0,m,n∈Z} about translation parameter b0 and dilation a0. particular, we also research stability irregular {SmΦ(Smx−nb),m,n∈Z} for sampling.