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This paper deals with some special integral transforms in the setting of quaternionic valued slice polyanalytic functions. In particular, using the polyanalytic Fueter mappings, it is possible to construct a new family of polynomials which are called the generalized Appell polynomials. Furthermore, the range of the polyanalytic Fueter mappings on two different polyanalytic Fock spaces is characterized. Finally, we study the polyanalytic Fueter–Bargmann transforms. [ABSTRACT FROM AUTHOR]

Let n∈ℤ with n≥3. Let Sn and An denote, respectively, the symmetric group and alternating group on n letters. Let m be an indeterminate, and define fm(x):=xn+a(m,n)x+b(m,n), where a(m,n),b(m,n) are certain prescribed forms in m. For a certain set of these forms, we show unconditionally that there exist infinitely many primes p such that fp(x) is irreducible over ℚ, Galℚ(fp)=Sn, and the fields K=ℚ(𝜃) are distinct and monogenic, where fp(𝜃)=0. Using a different set of forms, we establish a similar result for all square-free values of n≡1(mod4), with 5≤n≤401, and any positive integer value of m for which a(m,n) is square-free. Additionally, in this case, we prove that Galℚ(fp)=An. Finally, we show that these results can be extended under the assumption of the abc-conjecture. Our methods make use of recent results of Helfgott and Pasten. [ABSTRACT FROM AUTHOR]

An algebraic number ring is monogenic, or one-generated, if it has the form for a single algebraic integer . It is a problem of Hasse to characterize, whether an algebraic number ring is monogenic or not. In this note, we prove that if is a square-free rational integer, and , then the pure sextic field is not monogenic. Our results are illustrated by examples. [ABSTRACT FROM AUTHOR]

The only quadrature operator of order two on L2(ℝ2) which covaries with orthogonal transforms, in particular rotations is (up to the sign) the Riesz transform. This property was used for the construction of monogenic wavelets and curvelets. Recently, shearlets were applied for various signal processing tasks. Unfortunately, the Riesz transform does not correspond with the shear operation. In this paper, we propose a novel quadrature operator called linearized Riesz transform which is related to the shear operator. We prove properties of this transform and analyze its performance vs. the usual Riesz transform numerically. Furthermore, we demonstrate the relation between the corresponding optical filters. Based on the linearized Riesz transform we introduce finite discrete quasi-monogenic shearlets and prove that they form a tight frame. Numerical experiments show the good fit of the directional information given by the shearlets and the orientation obtained from the quasi-monogenic shearlet coefficients. Finally, we provide experiments on the directional analysis of textures using our quasi-monogenic shearlets. [ABSTRACT FROM AUTHOR]

Morais has recently introduced certain complete orthogonal sets of monogenic polynomials over 3D prolate spheroids with remarkable properties. The underlying functions take on either values in the reduced and full quaternions (identified, respectively, with ℝ3 and ℝ4), and are generally assumed to be nullsolutions of the well known Riesz and Moisil-Théodoresco systems in ℝ3. In continuation of these studies, we recall some fundamental properties of the polynomials, and prove some recursive formulae between them. As a consequence, we obtain a two-term type recurrence relation satisfied by those basis polynomials. These results are then employed to investigate a rather wide class of approximation properties for monogenic functions over 3D prolate spheroids in terms of spheroidal monogenics. [ABSTRACT FROM AUTHOR]

In the Clifford analysis context a specific type of solution for the higher spin Dirac operators $\mathcal{Q}_{k,l} (k \geq l \in \mathbb{N})$ is studied; these higher spin Dirac operators can be seen as generalizations of the classical Rarita-Schwinger operator. To that end subspaces of the space of triple monogenic polynomials are introduced and their algebraic structure is investigated. Also a dimensional analysis is carried out. [ABSTRACT FROM AUTHOR]

In this paper, we provide complete classification of classes of bipartite graphs defined by a single forbidden induced bipartite subgraph with respect to bounded/unbounded clique-width. [ABSTRACT FROM AUTHOR]

We describe commutative rings of prime characteristic with the property indicated in the title of the paper. [ABSTRACT FROM AUTHOR]