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Results in Mathematics
Journal Prestige (SJR): 0.582

Citation Impact (citeScore): 1
Number of Followers: 0

Hybrid journal (It can contain Open Access articles)
ISSN (Print) 1420-9012 - ISSN (Online) 1422-6383
Published by Springer-Verlag

[2469 journals]

Some Non-Compactness Results for Locally Homogeneous Contact Metric
Manifolds
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  Abstract: Abstract We exhibit some sufficient conditions ensuring the non-compactness of a locally homogeneous, regular, contact metric manifold, under suitable assumptions on the Jacobi operator of the Reeb vector field.
  PubDate: 2022-06-20
Ricci-like Solitons with Arbitrary Potential and Gradient Almost
Ricci-like Solitons on Sasaki-like Almost Contact B-metric Manifolds
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  Abstract: Abstract Ricci-like solitons with arbitrary potential are introduced and studied on Sasaki-like almost contact B-metric manifolds. A manifold of this type can be considered as an almost contact complex Riemannian manifold which complex cone is a holomorphic complex Riemannian manifold. The soliton under study is characterized and proved that its Ricci tensor is equal to the vertical component of both B-metrics multiplied by a constant. Thus, the scalar curvatures with respect to both B-metrics are equal and constant. In the 3-dimensional case, it is found that the special sectional curvatures with respect to the structure are constant. Gradient almost Ricci-like solitons on Sasaki-like almost contact B-metric manifolds have been proved to have constant soliton coefficients. Explicit examples are provided of Lie groups as manifolds of dimensions 3 and 5 equipped with the structures under study.
  PubDate: 2022-06-18
On Another Characterization of Askey-Wilson Polynomials
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  Abstract: Abstract In this paper we show that the only sequences of orthogonal polynomials $(P_n)_{n\ge 0}$ satisfying $$\begin{aligned} \phi (x){\mathcal {D}}_q P_{n}(x)=a_n{\mathcal {S}}_q P_{n+1}(x) +b_n{\mathcal {S}}_q P_n(x) +c_n{\mathcal {S}}_q P_{n-1}(x), \end{aligned}$$ ( $c_n\ne 0$ ) where $\phi $ is a well chosen polynomial of degree at most two, ${\mathcal {D}}_q$ is the Askey-Wilson operator and ${\mathcal {S}}_q$ the averaging operator, are the multiple of Askey-Wilson polynomials, or specific or limiting cases of them.
  PubDate: 2022-06-18
Ruled Real Hypersurfaces in the Indefinite Complex Projective Space
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  Abstract: Abstract The main two families of real hypersurfaces in complex space forms are Hopf and ruled. However, very little is known about real hypersurfaces in the indefinite complex projective space ${\mathbb {C}}P^n_p$ . In a previous work, Kimura and the second author introduced Hopf real hypersurfaces in ${\mathbb {C}}P^n_p$ . In this paper, ruled real hypersurfaces in the indefinite complex projective space are introduced, as those whose maximal holomorphic distribution is integrable, and such that the leaves are totally geodesic holomorphic hyperplanes. A detailed description of the shape operator is computed, obtaining two main different families. A method of construction is exhibited, by gluing in a suitable way totally geodesic holomorphic hyperplanes along a non-null curve. Next, the classification of all minimal ruled real hypersurfaces is obtained, in terms of three main families of curves, namely geodesics, totally real circles and a third case which is not a Frenet curve, but can be explicitly computed. Four examples of minimal ruled real hypersurfaces are described.
  PubDate: 2022-06-08
Asymptotics for Some q-Hypergeometric Polynomials
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  Abstract: Abstract We tackle the study of a type of local asymptotics, known as Mehler–Heine asymptotics, for some q–hypergeometric polynomials. Some consequences about the asymptotic behavior of the zeros of these polynomials are discussed. We illustrate the results with numerical examples.
  PubDate: 2022-06-07
Seminormed approximation by deferred matrix means of integrable functions
in $$H_{P}^{(\omega )}$$ H P ( ω ) space
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  Abstract: Abstract In this paper we consider some deferred matrix means of Fourier series. We give the degree of seminormed approximation of functions from the spaces $ H_{P}^{(w)}$ space by such matrix means. As a measure of the approximation is used an almost nondecreasing function of the form $\frac{w}{v}$ with moduli of continuity type w and v.The obtained results generalize and improve the results from Deǧer and Küçükaslan (J. Inequal. Appl., 2015:14 ,16 pp 2015) and Das et al. (J. Math. Anal. Appl. 420(1), 563–575 2014).
  PubDate: 2022-06-06
On Classifying Spaces of Spin Groups
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  Abstract: Abstract For a split maximal torus T of a split spin group $G={{\mathrm {Spin}}}(n)$ over an arbitrary field, we consider the restriction homomorphism of the Chow rings of their classifying spaces with W the Weyl group of G. For $n\le 6$ , f is known to be surjective. For $n\ge 7$ , an obstruction for an element of to be in the image of f is given by the Steenrod operations on . Using it, we show that several standard generators of , including the defined for even n Euler class , are outside the image of f. This result differs from the analogues topological result.
  PubDate: 2022-06-06
Convergence of Two Simple Methods for Solving Monotone Inclusion Problems
in Reflexive Banach Spaces
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  Abstract: Abstract We propose two very simple methods, the first one with constant step sizes and the second one with self-adaptive step sizes, for finding a zero of the sum of two monotone operators in real reflexive Banach spaces. Our methods require only one evaluation of the single-valued operator at each iteration. Weak convergence results are obtained when the set-valued operator is maximal monotone and the single-valued operator is Lipschitz continuous, and strong convergence results are obtained when either one of these two operators is required, in addition, to be strongly monotone. We also obtain the rate of convergence of our proposed methods in real reflexive Banach spaces. Finally, we apply our results to solving generalized Nash equilibrium problems for gas markets.
  PubDate: 2022-06-04
$$\mathcal {PR}$$ PR -Semi Slant Warped Product Submanifold of
ParaKenmotsu Manifolds
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  Abstract: Abstract The main purpose of this paper is to study the properties of $\mathcal {PR}$ -semi-slant warped product submanifold of paraKenmotsu manifold. We obtain some necessary and sufficient conditions for the $\mathcal {PR}$ -semi-slant submanifold of paraKenmotsu manifold to be a $\mathcal {PR}$ -semi-slant warped product submanifold. Some examples of $\mathcal {PR}$ -semi-slant warped product submanifold of paraKenmotsu manifold also given in this paper.
  PubDate: 2022-06-03
A Note On the Nonexistence of a Complex Threefold as a Conjugate Orbit of
$$G_2$$ G 2
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  Abstract: Abstract The existence or nonexistence of a complex structure on $\mathrm{S}^6$ was a long standing unsolved problem. There is a well-known orbit $O(\varLambda )$ in $G_2$ which is diffeomorphic to $\mathrm{S}^6$ and used by Gábor Etesi in an effort to find a complex structure. Etesi suggested to give a complex structure in $\mathrm{S}^6$ through this orbit. In Daniel Guan’s earlier paper, he proved that the orbit can not be a complex submanifold. Since there was not a clear description of the map from $O(\varLambda )$ to $\mathrm{S}^6$ in that paper, we give another clearer, simpler and explicit proof of that result in this paper.
  PubDate: 2022-05-13
The Corner Element of Generalized Numerical Semigroups
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  Abstract: Abstract In this paper we introduce the concept of corner element of a generalized numerical semigroup, which extends in a sense the idea of conductor of a numerical semigroup to generalized numerical semigroups in higher dimensions. We present properties of this new notion and its relations with existing invariants in the literature, and provide an algorithm to compute all the generalized numerical semigroups with fixed corner. Besides that, we provide lower and upper bounds on the number of generalized numerical semigroups having a fixed corner element.
  PubDate: 2022-05-13
Intertwining Property for Compressions of Multiplication Operators
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  Abstract: Abstract Following Beurling’s theorem the natural compressions of the multiplication operator in the classical $L^2$ space are compressions to model spaces and to their orthogonal complements. Here, two possibly different model spaces are considered, hence asymmetric truncated Toeplitz and asymmetric dual truncated Toeplitz operators are investigated. The main purpose of the paper is to characterize operators which intertwine compressions of the unilateral shift.
  PubDate: 2022-05-13
Hyers–Ulam Stability for Differential Systems with $$2\times 2$$ 2 × 2
Constant Coefficient Matrix
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  Abstract: Abstract We explore the Hyers–Ulam stability of perturbations for a homogeneous linear differential system with $2\times 2$ constant coefficient matrix. New necessary and sufficient conditions for the linear system to be Hyers–Ulam stable are proven, and for the first time, the best (minimal) Hyers–Ulam constant for systems is found in some cases. Several examples are provided. Obtaining the best Hyers–Ulam constant for second-order constant coefficient differential equations illustrates the applicability of the strong results.
  PubDate: 2022-05-07
Note on the Fekete–Szegö Problem for Spirallike Mappings in
Banach Spaces
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  Abstract: Abstract In this note we present a remark on the paper “On the coefficient inequalities for a class of holomorphic mappings associated with spirallike mappings in several complex variables” by Y. Lai and Q. Xu [10] published recently in the journal Results in Mathematics. We show that one of the theorems in [10] concerning the finite-dimensional space ${{\mathbb {C}}}^n$ is a direct consequence of another one, so it does not need an independent proof. Moreover, we prove that a sharp norm estimate on the Fekete–Szegö functional over spirallike mappings in a general Banach space can be deduced from a result in [10].
  PubDate: 2022-05-07
A Note on Gauged Baby Skyrmions
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  Abstract: Abstract In this paper we study a gauged version of the two dimensional Skyrme model of nuclear physics; the field configurations are couples (u, A), where $u:{\mathbb {R}}^2\rightarrow S^2$ is a map constant at infinity, which can be classified by its topological degree, and $A:{\mathbb {R}}^2\rightarrow {\mathbb {R}}^2$ is the gauge field. We prove the existence of rotationally symmetric field configurations which minimize the gauged Skyrme energy on every topological sector (gauged baby skyrmions). Moreover we study the behavior of these skyrmions in the case of weak or strong coupling with the gauge field. In particular, we show that, as observed by many authors by means of numerical simulations, in the strong coupling regime the magnetic flux associated with the gauge field becomes quantized.
  PubDate: 2022-05-07
On Two Trigonometric Inequalities of Carslaw and Gasper
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  Abstract: Abstract The inequalities $$\begin{aligned} A_n(x)=\sum _{k=1}^n \frac{\sin ((2k-1)x)}{2k-1} >0 \quad (n\ge 1; 0<x<\pi ) \end{aligned}$$ and $$\begin{aligned} B_n(x)=\sum _{k=1}^n\frac{\cos ((2k-1)x)}{2k-1}>0 \quad (n\ge 1; 0\le x<\pi /2) \end{aligned}$$ are due to Carslaw (1917) and Gasper (1977), respectively. We prove the following counterparts: $$\begin{aligned} A_n(x)+B_n(x)>0 \quad (n\ge 1; 0\le x<3\pi /4) \end{aligned}$$ and $$\begin{aligned} B_n(x)\ge \frac{64}{75}\cos ^3(x) \quad (n\ge 2; -\pi /2<x<\pi /2). \end{aligned}$$ The constants $3\pi /4$ and 64/75 are best possible.
  PubDate: 2022-05-05
On Modified Mellin–Gauss–Weierstrass Convolution Operators
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  Abstract: Abstract Mellin transform has various applications to real-life problems in function approximation, signal processing, and image recognition, thus, it has been the main ingredient of many studies in diverse fields. This study is devoted to Mellin operators and their variants to improve approximation accuracy and approximate ratio. Two Mellin type operators are reconstructed by using two sequences of functions to enable lower pointwise approximation error as well as higher pointwise convergence rate. Keeping the idea of Mellin convolution, these classes aim to be associated with functions defined on the semi-real axis, and the affine and quadratic functions pairs are fixed points. It has been shown, both theoretically and numerically, that operators can be used to approximate functions pointwise. Indeed the approximation accuracy can be adjusted by tuning the parameters. Moreover, weighted approximation, as well as Voronovskaya type results, are studied throughout the paper. The advantages of each operator over the other in terms of both approximation errors and convergence rates are presented.
  PubDate: 2022-05-05
Generalized q-Bernoulli Polynomials Generated by Jackson q-Bessel
Functions
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  Abstract: Abstract In this paper, we introduce the polynomials $B^{(k)}_{n,\alpha }(x;q)$ generated by a function including Jackson q-Bessel functions $J^{(k)}_{\alpha }(x;q)$ $ (k=1,2,3),\,\alpha >-1$ . The cases $\alpha =\pm \frac{1}{2}$ are the q-analogs of Bernoulli and Euler $^{,}$ s polynomials introduced by Ismail and Mansour for $(k=1,2)$ , Mansour and Al-Towalib for $(k=3)$ . We study the main properties of these polynomials, their large n degree asymptotics and give their connection coefficients with the q-Laguerre polynomials and little q-Legendre polynomials.
  PubDate: 2022-05-05
Variational Inequality Problem Involving Multivalued Nonexpansive Mapping
in CAT(0) Spaces
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  Abstract: Abstract In this paper, we introduce a new type of variational inequality problem (VIP) involving nonself multivalued mappings in CAT(0) spaces. We show that this VIP problem admit a solution under suitable conditions. We also perform the convergence analysis of introduced VIP via proximal multivalued Picard-S iteration. We finish our paper with some convergence theorems for new iteration scheme and system of variational inequalities associated with finite family of nonself multivalued nonexpansive mappings.
  PubDate: 2022-05-05
Almost Complex Surfaces in the Nearly Kähler Flag Manifold
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  Abstract: Abstract We study and classify almost complex totally geodesic submanifolds of the nearly Kähler flag manifold $F_{1,2}(\mathbb C^3)$ , and of its semi-Riemannian counterpart. We also develop a structural approach to the nearly Kähler flag manifold $F_{1,2}(\mathbb C^3)$ , expressing for example the curvature tensor in terms of the nearly Kähler structure J and the three canonical orthogonal complex structures.
  PubDate: 2022-05-05