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Abstract: Abstract Spectral theory has become a central area of studies on commutative hypergroups. Spectral analysis and synthesis have been proved for different classes of hypergroups. In their paper (Fechner and Székelyhidi in Ann Univ Sci Budapest Sect Comput), the authors introduced and studied an infinite join of general finite hypergroups. Here we prove that under some general conditions spectral analysis and synthesis hold on that hypergroup. PubDate: 2022-06-01

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Abstract: Abstract A ring R is called a left FGF ring if every finitely generated left R-module can be embedded in a free left R-module. It is proved that a group ring RG is left FGF if and only if R is left FGF and G is a finite group. PubDate: 2022-06-01

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Abstract: Abstract Estimation of the tail index of heavy-tailed distributions and its applications are essential in many research areas. We propose a class of weighted least squares (WLS) estimators for the Parzen tail index. Our approach is based on the method developed by Holan and McElroy (J Stat Plan Inference 140(12):3693–3708, 2010). We investigate consistency and asymptotic normality of the WLS estimators. Through a simulation study, we make a comparison with the Hill, Pickands, DEdH (Dekkers, Einmahl and de Haan) and ordinary least squares (OLS) estimators using the mean square error as criterion. The results show that in a restricted model some members of the WLS estimators are competitive with the Pickands, DEdH and OLS estimators. PubDate: 2022-06-01

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Abstract: Abstract We provide a unique normal form for rank two irregular connections on the Riemann sphere. In fact, we provide a birational model where we introduce apparent singular points and where the bundle has a fixed Birkhoff–Grothendieck decomposition. The essential poles and the apparent poles provide two parabolic structures. The first one only depends on the formal type of the singular points. The latter one determines the connection (accessory parameters). As a consequence, an open set of the corresponding moduli space of connections is canonically identified with an open set of some Hilbert scheme of points on the explicit blow-up of some Hirzebruch surface. This generalizes previous results obtained by Szabó to the irregular case. Our work is more generally related to ideas and descriptions of Oblezin, Dubrovin–Mazzocco, and Saito–Szabó in the logarithmic case. After the first version of this work appeared, Komyo used our normal form to compute isomonodromic Hamiltonian systems for irregular Garnier systems. PubDate: 2022-06-01

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Abstract: Abstract The aim of this paper is to continue the work started in Pavlović (Filomat 30(14):3725–3731, 2016) . We investigate further the properties of the local closure function and the spaces defined by it using common ideals, like ideals of finite sets, countable sets, closed and discrete sets, scattered sets and nowhere dense sets. Also, closure compatibility between the topology and the ideal, idempotency, and cases when the local closure of the whole space X is X or a proper subset of X, are closely investigated. In the case of closure compatibility and idempotency of the local closure function, the topology obtained by the local closure function is completely described. PubDate: 2022-06-01

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Abstract: Abstract In this note, an upper bound for the sum of fractional parts of certain smooth functions is given. Such sums arise naturally in numerous problems of analytic number theory. The main feature is here an improvement of the main term due to the use of Weyl’s bound for exponential sums and a device used by Popov. PubDate: 2022-06-01

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Abstract: Abstract In this paper, first we study surjective isometries (not necessarily linear) between completely regular subspaces A and B of \(C_0(X,E)\) and \(C_0(Y,F)\) where X and Y are locally compact Hausdorff spaces and E and F are normed spaces, not assumed to be either strictly convex or complete. We show that for a class of normed spaces F satisfying a newly defined property related to their T-sets, such an isometry is a (generalized) weighted composition operator up to a translation. Then we apply the result to study surjective isometries between A and B whenever A and B are equipped with certain norms rather than the supremum norm. Our results unify and generalize some recent results in this context. PubDate: 2022-06-01

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Abstract: Abstract In this paper, the authors have obtained \(L_1\) -approximations of functions f in \( {{\,\mathrm{Lip}\,}}(\alpha ,1) \) \( (0 < \alpha \le 1) \) by trigonometrical polynomials \( N_n (f;x)\) whenever the nonnegative and nonincreasing sequence \( (p_n )\) satisfies certain conditions. This enables the authors to approximate \( f \in {{\,\mathrm{Lip}\,}}(\alpha ,p) \) \((0< \alpha \le 1,1\le p < \infty )\) in \( L_p\) -norm by trigonometrical polynomials \( \sigma _n^\beta (f;x)\) \( (\beta > 0)\) . PubDate: 2022-06-01

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Abstract: Abstract Let \({\mathcal {A}}\) be a \(*\) -algebra and \({{\mathcal {M}}}\) be a \(*\) - \({\mathcal {A}}\) -bimodule. We study the local properties of \(*\) -derivations and \(*\) -Jordan derivations from \({\mathcal {A}}\) into \({{\mathcal {M}}}\) under the following orthogonality conditions on elements in \({\mathcal {A}}\) : \(ab^*=0\) , \(ab^*+b^*a=0\) and \(ab^*=b^*a=0\) . We characterize the mappings on zero product determined algebras and zero Jordan product determined algebras. Moreover, we give some applications on \(C^*\) -algebras, group algebras, matrix algebras, algebras of locally measurable operators and von Neumann algebras. PubDate: 2022-06-01

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Abstract: Abstract In this paper, we study how the roots of the Kac polynomials \(W_n(z) = \sum _{k=0}^{n-1} \xi _k z^k\) concentrate around the unit circle when the coefficients of \(W_n\) are independent and identically distributed nondegenerate real random variables. It is well known that the roots of a Kac polynomial concentrate around the unit circle as \(n\rightarrow \infty \) if and only if \({\mathbb {E}}[\log ( 1+ \xi _0 )]<\infty \) . Under the condition \({\mathbb {E}}[\xi ^2_0]<\infty \) , we show that there exists an annulus of width \({\text {O}}(n^{-2}(\log n)^{-3})\) around the unit circle which is free of roots with probability \(1-{\text {O}}({(\log n)^{-{1}/{2}}})\) . The proof relies on small ball probability inequalities and the least common denominator used in [17]. PubDate: 2022-06-01

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Abstract: Abstract Lagrange introduced the notion of Schwarzian derivative and Thurston discovered its mysterious properties playing a role similar to that of curvature on Riemannian manifolds. Here we continue our studies on the development of the Schwarzian derivative on Finsler manifolds. First, we obtain an integrability condition for the Möbius equations. Then we obtain a rigidity result as follows; Let (M, F) be a connected complete Finsler manifold of positive constant Ricci curvature. If it admits non-trivial Möbius mapping, then M is homeomorphic to the n-sphere. Finally, we reconfirm Thurston’s hypothesis for complete Finsler manifolds and show that the Schwarzian derivative of a projective parameter plays the same role as the Ricci curvature on theses manifolds and could characterize a Bonnet–Mayer-type theorem. PubDate: 2022-06-01

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Abstract: Abstract Let \(p\equiv -q \equiv 5\pmod 8\) be two prime integers. In this paper, we investigate the unit groups of the fields \( L_1 =\mathbb {Q}(\sqrt{2}, \sqrt{p}, \sqrt{q}, \sqrt{-1} )\) and \( L_1^+=\mathbb {Q}(\sqrt{2}, \sqrt{p}, \sqrt{q} )\) . Furthermore , we give the second 2-class groups of the subextensions of \(L_1\) as well as the 2-class groups of the fields \( L_n =\mathbb {Q}( \sqrt{p}, \sqrt{q}, \zeta _{2^{n+2}} )\) and their maximal real subfields. PubDate: 2022-06-01

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Abstract: Abstract We study the Galvin property. We show that various square principles imply that the cofinality of the Galvin number is uncountable (or even greater than \(\aleph _1\) ). We prove that the proper forcing axiom is consistent with a strong negation of the Glavin property. PubDate: 2022-06-01

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Abstract: Abstract In this paper, we first prove the existence and uniqueness of the solutions for a delayed hyperbolic partial differential equation by applying the progressive contraction technique introduced by Burton (Nonlinear Dyn Syst Theory 16(4): 366–371, 2016; Fixed Point Theory 20(1): 107–113, 2019) to the corresponding fixed-point problem. Then we derive a Hyers–Ulam stability result for this differential equation by using a Wendorff-type inequality and the Abstract Gronwall Lemma. PubDate: 2022-06-01

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Abstract: Abstract Let \(\mathcal {A}\) and \(\mathcal {B}\) be abelian categories and \({\mathbf {F}} :\mathcal {A}\rightarrow \mathcal {B}\) an additive and right exact functor which is perfect, and let \(({\mathbf {F}},\mathcal {B})\) be the left comma category. We give an equivalent characterization of Gorenstein projective objects in \(({\mathbf {F}},\mathcal {B})\) in terms of Gorenstein projective objects in \(\mathcal {B}\) and \(\mathcal {A}\) . We prove that there exists a left recollement of the stable category of the subcategory of \(({\mathbf {F}},\mathcal {B})\) consisting of Gorenstein projective objects modulo projectives relative to the same kind of stable categories in \(\mathcal {B}\) and \(\mathcal {A}\) . Moreover, this left recollement can be filled into a recollement when \(\mathcal {B}\) is Gorenstein and \({\mathbf {F}}\) preserves projectives. PubDate: 2022-06-01

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Abstract: Abstract For any fixed integers a and b greater than 1, we study the Diophantine equation \(a^x+(ab+1)^y=b^z\) . First, we describe a heuristic list of the positive integer solutions x, y and z of the equation. Finally, we solve the equation in some particular cases, which supports the validity of our list of solutions. PubDate: 2022-06-01

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Abstract: Abstract We will describe the topological type of the discriminant curve of the morphism \((\ell , f)\) , where \(\ell \) is a smooth curve and f is an irreducible curve (branch) of multiplicity less than five or a branch such that the difference between its Milnor number and Tjurina number is less than 3. We prove that for a branch of these families, the topological type of the discriminant curve is determined by the semigroup, the Zariski invariant and at most two other analytical invariants of the branch. PubDate: 2022-06-01

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Abstract: We determine the maximum number of edges in a \(K_4\) -minor-free n-vertex graph of girth g, when \(g=5\) or g is even. We argue that there are many different n-vertex extremal graphs if n is even and g is odd. PubDate: 2022-05-04

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Abstract: Abstract Our goal is to study the multiplication by a polynomial of a \(H_q\) -Laguerre–Hahn form and its inverse one where \(H_q\) be the q-derivative operator. The class of the obtained form is discussed in detail in the two cases. Some examples in connection with the \(H_{q}\) -semiclassical forms are highlighted. PubDate: 2022-04-30