The aim of this work is to prove new results on a class of digital functions with special emphasis on shifted primes as arguments. Our method lies on the estimate of exponential sums of the form n x Λ(n) exp(2iπf (n + cn) + βn) where f a digital function, c = (cn) is an almostperiodic sequence in Z and β is a real parameter, which extend the works of and to the case of the shifted prime numbers satisfying a digital constraint.
This paper examines the transfer of the almost valuation property to various constructions of ring extensions such as bi-amalgamations and pairs of rings. Namely, Sec. 2 studies the transfer of this property to bi-amalgamation rings. Our results cover previous known results on duplications and amalgamations, and provide the construction of various new and original examples satisfying this property. Section 3 investigates pairs of integral domains where all intermediate rings are almost valuation rings. As a consequence of our results, we provide necessary and sufficient conditions for a pair (R, T), where R arises from a (T, M, D) construction, to be an almost valuation pair. Furthermore, we study the class of maximal non-almost valuation subrings of their quotient field.
This paper studies the transfer of pseudo-almost valuation property
(PAVR property for short) to various context of commutative ring
extensions such as power series ring, trivial ring extension and amalgamation. Our
work is motivated by an attempt to generate new original classes of
rings satisfying this property. The obtained results are backed with
new and illustrative examples arising as trivial ring extensions,
amalgamations and pullback constructions.
In this paper, we discuss new results related to the generalized discrete q-Hermite II polynomialsh n,α (x; q), introduced by Mezlini et al. in 2014. Our aim is to give a continuous orthogonality relation, a q-integral representation and an evaluation at unity of the Poisson kernel, for these polynomials. Furthermore, we introduce q-Schrödinger operators and give the raising and lowering operator algebra corresponding to these polynomials. Our results generate a new explicit realization of the quantum algebra su q (1, 1), using the generators associated with a q-deformed generalized para-Bose oscillator. keywords: q-orthogonal polynomials, q-deformed algebras, harmonic oscillators. MSC(2010): 33D45; 81R30; 81R50.
In this paper, we study the almost Bézout property in different commutative ring extensions, namely, in bi-amalgamated algebras and pairs of rings. In Section 2, we deal with almost Bézout domains issued from bi-amalgamations. Our results capitalize well known results on amalgamations and pullbacks as well as generate new original class of rings satisfying this property. Section 3 investigates pairs of rings where all intermediate rings are almost Bézout domains. As an application of our results, we characterize pairs of rings (R, T), where R arises from a (T, M, D) construction to be an almost Bézout domain.
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