Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: Abstract The aim of this contribution is to give, through the third degree character, a complete description of a large family of quasi-symmetric semiclassical forms of class two. In fact, by using the Stieltjes function and the moments of those forms, we give necessary and sufficient conditions for a regular form to be at the same time of the strict third degree quasi-symmetric and semiclassical of class two. We focus our attention not only on the link between all these forms and the Jacobi forms \({\mathcal {V}}_{q}^{k, l}={\mathcal {J}}(k+q/3,l-q/3)\) , \(k+l\ge -1,~ k, l \in {\mathbb {Z}},~q\in \{1,2\}\) , but also on their connection with the form \({{\mathcal {V}}}={{\mathcal {J}}}\left( -2/3, -1/3\right) \) . PubDate: 2023-03-01

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Abstract: Abstract Let \( (G_n)_{n=0}^{\infty } \) be a polynomial power sum, i.e. a simple linear recurrence sequence of complex polynomials with power sum representation \( G_n = f_1\alpha _1^n + \cdots + f_k\alpha _k^n \) and polynomial characteristic roots \( \alpha _1,\ldots ,\alpha _k \) . For a fixed polynomial p, we consider sets \( \left\{ a,b,c \right\} \) consisting of three non-zero polynomials such that \( ab+p, ac+p, bc+p \) are elements of \( (G_n)_{n=0}^{\infty } \) . We will prove that under a suitable dominant root condition there are only finitely many such sets if neither \( f_1 \) nor \( f_1 \alpha _1 \) is a perfect square. PubDate: 2023-03-01

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Abstract: 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: 2023-03-01

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Abstract: Abstract Let \(n\ge 1, e\ge 1, k\ge 2\) and c be integers. An integer u is called a unit in the ring \({\mathbb {Z}}_n\) of residue classes modulo n if \(\gcd (u, n)=1\) . A unit u is called an exceptional unit in the ring \({\mathbb {Z}}_n\) if \(\gcd (1-u,n)=1\) . We denote by \({\mathcal {N}}_{k,c,e}(n)\) the number of solutions \((x_1,\ldots ,x_k)\) of the congruence \(x_1^e+\cdots +x_k^e\equiv c \pmod n\) with all \(x_i\) being exceptional units in the ring \({\mathbb {Z}}_n\) . In 2017, Mollahajiaghaei presented a formula for the number of solutions \((x_1,\ldots ,x_k)\) of the congruence \(x_1^2+\cdots +x_k^2\equiv c\pmod n\) with all \(x_i\) being the units in the ring \({\mathbb {Z}}_n\) . Meanwhile, Yang and Zhao gave an exact formula for \({\mathcal {N}}_{k,c,1}(n)\) . In this paper, by using Hensel’s lemma, exponential sums and quadratic Gauss sums, we derive an explicit formula for the number \({\mathcal {N}}_{k,c,2}(n)\) . Our result extends Mollahajiaghaei’s theorem and that of Yang and Zhao. PubDate: 2023-03-01

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Abstract: Abstract The purpose of this paper is to propose an inertial extrapolation method for solving a certain class of variational inequality problems more general than the classical variational inequality problems in real Hilbert spaces. Our proposed method is of viscosity-type and converges strongly to a solution of the aforementioned problem when the underlying/cost operator is pseudo-monotone and uniformly continuous; this makes our method to be potentially more applicable than most existing methods in the literature. To support our results numerically, we considered some examples in both finite and infinite dimensional Hilbert spaces and compared our results with other existing results in the literature. PubDate: 2023-03-01

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Abstract: Abstract We construct examples of centrally harmonic spaces by generalizing work of Copson and Ruse. We show that these examples are generically not centrally harmonic at other points. We use this construction to exhibit manifolds which are not conformally flat but such that their density function agrees with Euclidean space. PubDate: 2023-03-01

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Abstract: Abstract We give an alternative proof of a result of Babai, that there exists a constant c such that any finite group G can be realized as the automorphism group of a poset with at most c G points. We also provide bounds for the minimum number of points of a poset with cyclic automorphism group of a given prime power order. PubDate: 2023-03-01

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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: 2023-03-01

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Abstract: Abstract A semigroup S is said to be left equalizer simple if, for all elements a, b, x, y of S, \(xa=xb\) implies \(ya=yb\) . It is known that left equalizer simplicity is a necessary condition for a semigroup to be embedded in a left simple semigroup. A semigroup satisfying the identity \(axyb=ayxb\) is called a medial semigroup. In this paper we show how to construct left equalizer simple medial semigroups, especially, medial semigroups which can be embedded in idempotent-free left simple semigroups. PubDate: 2023-03-01

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Abstract: Abstract Let X be a Banach space over the field \(\mathbb F\) ( \(\mathbb R\) or \(\mathbb C)\) . Denote by B(X) the set of all bounded linear operators on X and by F(X) the set of all finite rank operators on X. A subalgebra \(\mathcal A\subseteq B(X)\) is called a standard operator algebra if \(F(X)\subseteq \mathcal A\) . Suppose that \(\delta \) is a mapping from \(\mathcal A\) into B(X). First, we prove that if \(\delta \) is a Lie triple derivation, then \(\delta \) is standard. Next, we show that if \(\delta \) is a local Lie triple derivation and \(\mathrm {dim}(X)\ge 3\) , then \(\delta \) is a Lie triple derivation. Finally, we prove that if \(\delta \) is a 2-local Lie triple derivation, then \(\delta =d+\tau \) , where d is a derivation, and \(\tau \) is a homogeneous mapping from \(\mathcal A\) into \(\mathbb {F}I\) such that \(\tau (A+B)=\tau (A)\) for each A, B in \(\mathcal A\) where B is a sum of double commutators. PubDate: 2023-03-01

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Abstract: Abstract Dartyge and Sárközy (partly with other coauthors) introduced pseudorandom measures of subsets. In this paper, we further study the symmetry measure of subsets by employing Gyarmati’s method. In addition, we study the symmetry measure of some subsets constructed by using power residues, additive characters and primitive roots. PubDate: 2023-03-01

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Abstract: Abstract The purpose of this article is to study the characteristics of static perfect space-time metrics on contact metric manifolds. At first we prove that if a complete K-contact metric manifold is the spatial factor of static perfect space-time, then it is isometric to a round sphere. For a three dimensional contact metric manifold, which is the spatial factor of static perfect space-time, we show that it is Einstein if its Ricci tensor is commuting. Next we consider static perfect space-time \((\kappa ,\mu ,\nu )\) -contact metric manifolds and give some characteristics under certain conditions. PubDate: 2023-03-01

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Abstract: Abstract Let D be a fixed nonsquare positive integer, and let \(\{u_n\}_{n=1}^{\infty }\) denote the X-coordinates of the Pell equation \(u^2-Dv^2=1\) . Further, for any fixed nonnegative integer r, let \(S(D,r)=\{n n\in {\mathbb {N}}, 2^r n\) and \( u_n=px^2\) for some odd prime p and positive integer \(x \}\) . In this paper, using some elementary number theory methods, we give a necessary and sufficient condition for the existence of S(D, r) and an upper bound for the number of elements n in S(D, r). PubDate: 2023-03-01

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Abstract: Abstract For delay-differential equations with piecewise constant delay, we construct center invariant manifolds with the optimal regularity. More precisely, we consider perturbations that are either globally Lipschitz or of class \(C^1\) . More generally, we consider Lipschitz and \(C^1\) perturbations of evolution families that need not be invertible and need not have bounded growth. Nevertheless, the solutions in the center invariant manifold are always unique and global. PubDate: 2023-03-01

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Abstract: Abstract Write \(\mathrm {ord}_p(\cdot )\) for the multiplicative order in \({\mathbb {F}}_p^{\times }\) . Recently, Matthew Just and the second author investigated the problem of classifying pairs \(\alpha , \beta \in {\mathbb {Q}}^{\times }\setminus \{\pm 1\}\) for which \(\mathrm {ord}_p(\alpha ) > \mathrm {ord}_p(\beta )\) holds for infinitely many primes p. They called such pairs order-dominant. We describe an easily-checkable sufficient condition for \(\alpha ,\beta \) to be order-dominant. Via the large sieve, we show that almost all integer pairs \(\alpha ,\beta \) satisfy our condition, with a power savings on the size of the exceptional set. PubDate: 2023-03-01

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Abstract: Abstract This paper investigates the deformations of Riemannian metrics, in particular Hessian metrics, by Zermelo’s navigation under the action of the weak gradient winds. Various descriptions of the resulting Randers metrics are given in relation to other special classes of Finsler metrics, e.g., projectively flat, locally dually flat. We prove that the resulting Randers metric obtained from perturbation by a conformal gradient wind is locally dually flat if and only if the background Riemannian metric is homothetic with the Euclidean metric. The inverse problem answers the question, when a given Randers metric comes from a Hessian metric and a gradient vector field through the Zermelo deformation. Some relevant examples are indicated at the end. PubDate: 2023-03-01

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Abstract: Abstract The main objective of this paper is to present a new extension of the familiar Mathieu series and the alternating Mathieu series S(r) and \({{\widetilde{S}}}(r)\) which are denoted by \({\mathbb {S}}_{\mu ,\nu }(r)\) and \(\widetilde{{\mathbb {S}}}_{\mu ,\nu }(r)\) , respectively. The computable series expansions of their related integral representations are obtained in terms of the exponential integral \(E_1\) , and convergence rate discussion is provided for the associated series expansions. Further, for the series \({\mathbb {S}}_{\mu ,\nu }(r)\) and \(\widetilde{{\mathbb {S}}}_{\mu ,\nu }(r)\) , related expansions are presented in terms of the Riemann Zeta function and the Dirichlet Eta function, also their series built in Gauss’ \({}_2F_1\) functions and the associated Legendre function of the second kind \(Q_\mu ^\nu \) are given. Our discussion also includes the extended versions of the complete Butzer–Flocke–Hauss Omega functions. Finally, functional bounding inequalities are derived for the investigated extensions of Mathieu-type series. PubDate: 2023-03-01

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Abstract: Abstract In this paper, we consider Sasakian metric as a proper \(\eta \) -Ricci almost soliton and prove that it is isometric to a unit sphere \(S^{2n+1}\) , provided the dimension of the manifold is greater than 3. Next, we prove that if a Sasakian manifold admitting a generalized \(\eta \) -Ricci soliton whose potential vector field is a contact vector field is \(\eta \) -Einstein and the potential vector field is Killing. Finally, we prove that a complete Sasakian manifold of dimension greater than 3 is isometric to a unit sphere if it admits a non-trivial gradient generalized \(\eta \) -Ricci soliton. PubDate: 2023-03-01