6,190 results
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2. Corrigendum to the paper 'On the ideal theorem for number fields' [Funct. Approximatio, Comment. Math. 53, No. 1, 31--45 (2015)]
- Author
-
Olivier Bordellès
- Subjects
11N37, 11R42 ,Pure mathematics ,Ideal (set theory) ,Mathematics - Number Theory ,General Mathematics ,FOS: Mathematics ,Number Theory (math.NT) ,Algebraic number field ,Dedekind zeta function ,Mathematics ,Term (time) - Abstract
This paper is a corrigendum to the article ``On the ideal theorem for number fields''. The main result of this paper proves to be untrue and is replaced by an estimate of a weighted sum with an improved error term.
- Published
- 2020
3. On a paper of Berestycki-Hamel-Rossi and its relations to the weak maximum principle at infinity, with applications
- Author
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Luciano Mari, Marco Rigoli, and Marco Magliaro
- Subjects
Pure mathematics ,Work (thermodynamics) ,Trace (linear algebra) ,General Mathematics ,media_common.quotation_subject ,010102 general mathematics ,Differential operator ,Infinity ,01 natural sciences ,010101 applied mathematics ,Type condition ,Maximum principle ,Bounded function ,Uniqueness ,0101 mathematics ,Mathematics ,media_common - Abstract
The aim of this paper is to study a new equivalent form of the weak maximum principle for a large class of differential operators on Riemannian manifolds. This new form has been inspired by the work of Berestycki, Hamel and Rossi for trace operators, and allows us to shed new light on it and to introduce a new sufficient bounded Khas’minskii type condition for its validity. We show its effectiveness by applying it to obtain some uniqueness results in a geometric setting.
- Published
- 2018
4. Remarks on the paper 'M. Kolibiar, On a construction of semigroups'
- Author
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Attila Nagy
- Subjects
20M10 ,Pure mathematics ,Semigroup ,Mathematics::Operator Algebras ,General Mathematics ,FOS: Mathematics ,Congruence (manifolds) ,Group Theory (math.GR) ,Mathematics - Group Theory ,Mathematics - Abstract
In his paper "On a construction of semigroups", M. Kolibiar gives a construction for a semigroup $T$ (beginning from a semigroup $S$) which is said to be derived from the semigroup $S$ by a $\theta$-construction. He asserted that every semigroup $T$ can be derived from the factor semigroup $T/\theta (T)$ by a $\theta$-construction, where $\theta (T)$ is the congruence on $T$ defined by: $(a, b)\in \theta (T)$ if and only if $xa=xb$ for all $x\in T$. Unfortunately, the paper contains some incorrect part. In our present paper we give a revision of the paper., Comment: Version v5 differs from the published and the earlier versions in the following: some part of the proof of Theorem 2 are clarified, and some typing errors are corrected
- Published
- 2015
5. Addendum to the paper 'A note on weighted Bergman spaces and the Cesàro operator'
- Author
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Stevo Stević and Der-Chen Chang
- Subjects
Pure mathematics ,010308 nuclear & particles physics ,General Mathematics ,Operator (physics) ,010102 general mathematics ,Mathematical analysis ,Weighted Bergman space ,Addendum ,01 natural sciences ,Bergman space ,0103 physical sciences ,ComputingMethodologies_DOCUMENTANDTEXTPROCESSING ,46E15 ,0101 mathematics ,polydisk ,Cesàro operator ,Mathematics ,Bergman kernel ,47B38 - Abstract
Let H(Dn) be the space of holomorphic functions on the unit polydisk Dn, and let , where p, q> 0, α = (α1,…,αn) with αj > -1, j =1,..., n, be the class of all measurable functions f defined on Dn such thatwhere Mp(f,r) denote the p-integral means of the function f. Denote the weighted Bergman space on . We provide a characterization for a function f being in . Using the characterization we prove the following result: Let p> 1, then the Cesàro operator is bounded on the space .
- Published
- 2005
6. A note on Rosay's paper
- Author
-
Armen Edigarian
- Subjects
Pure mathematics ,Closed manifold ,Stein manifold ,Plurisubharmonic function ,General Mathematics ,Mathematical analysis ,Liouville manifold ,Complex manifold ,Mathematics ,plurisubharmonic function - Published
- 2003
7. Derived Non-archimedean analytic Hilbert space
- Author
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Mauro Porta, Jorge António, Institut de Recherche Mathématique Avancée (IRMA), and Université de Strasbourg (UNISTRA)-Centre National de la Recherche Scientifique (CNRS)
- Subjects
Pure mathematics ,Fiber (mathematics) ,General Mathematics ,010102 general mathematics ,Short paper ,Formal scheme ,Hilbert space ,Space (mathematics) ,01 natural sciences ,symbols.namesake ,Mathematics - Algebraic Geometry ,Mathematics::Category Theory ,0103 physical sciences ,Localization theorem ,FOS: Mathematics ,symbols ,010307 mathematical physics ,[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG] ,0101 mathematics ,Algebraic Geometry (math.AG) ,Quotient ,Mathematics - Abstract
In this short paper we combine the representability theorem introduced in [17, 18] with the theory of derived formal models introduced in [2] to prove the existence representability of the derived Hilbert space RHilb(X) for a separated k-analytic space X. Such representability results relies on a localization theorem stating that if X is a quasi-compact and quasi-separated formal scheme, then the \infty-category Coh^+(X^rig) of almost perfect complexes over the generic fiber can be realized as a Verdier quotient of the \infty-category Coh^+(X). Along the way, we prove several results concerning the the \infty-categories of formal models for almost perfect modules on derived k-analytic spaces., 28 pages
- Published
- 2019
8. Improved bounds for solutions of ϕ-Laplacians
- Author
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Jorge Huentutripay and Waldo Arriagada
- Subjects
Pure mathematics ,Harnack inequality ,General Mathematics ,lcsh:T57-57.97 ,010102 general mathematics ,Short paper ,Sense (electronics) ,01 natural sciences ,\(\phi\)-Laplacian ,Orlicz-Sobolev space ,lcsh:Applied mathematics. Quantitative methods ,0101 mathematics ,Parametric statistics ,Mathematics ,Harnack's inequality - Abstract
In this short paper we prove a parametric version of the Harnack inequality for \(\phi\)-Laplacian equations. In this sense, the estimates are optimal and represent an improvement of previous bounds for this kind of operators.
- Published
- 2018
9. A supplement to my paper 'On zeta-theta functions'
- Author
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Koji Katayama
- Subjects
Pure mathematics ,General Mathematics ,10D15 ,10H10 ,Theta function ,Mathematics - Published
- 1973
10. Note on a paper of F. Treves concerning Mizohata type operators
- Author
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J. Sjöstrand
- Subjects
Pure mathematics ,58G07 ,General Mathematics ,35F05 ,Type (model theory) ,47F05 ,Mathematics - Published
- 1980
11. Appendix to O. Bratteli’s paper on 'Crossed products of UHF algebras'
- Author
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Jonathan Rosenberg
- Subjects
Algebra ,Pure mathematics ,46L05 ,Ultra high frequency ,General Mathematics ,Mathematics - Published
- 1979
12. Addendum to my paper 'On coloring manifolds'
- Author
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K. S. Sarkaria
- Subjects
Pure mathematics ,05C15 ,General Mathematics ,57M15 ,Addendum ,Mathematics - Published
- 1983
13. Addendum to my paper 'On Veronese manifolds'
- Author
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Takehiro Itoh
- Subjects
Pure mathematics ,General Mathematics ,Addendum ,53C40 ,Mathematics - Published
- 1978
14. Differential geometry of conics in the projective space of three dimensions.—IV. Remarks and corrections on the previous papers
- Author
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Akitsugu Kawaguchi
- Subjects
Pure mathematics ,Collineation ,General Mathematics ,Complex projective space ,Five points determine a conic ,Projective space ,Erlangen program ,Projective differential geometry ,Quaternionic projective space ,Topology ,Projective geometry ,Mathematics ,53.0X - Published
- 1928
15. Correction to my paper, 'on $\langle 8 \rangle$-cobordism'
- Author
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V. Giambalvo
- Subjects
Pure mathematics ,57D90 ,General Mathematics ,Cobordism ,Mathematics - Published
- 1972
16. A remark on my former paper 'Theory of Fuchsian groups'
- Author
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Masatsugu Tsuji
- Subjects
Pure mathematics ,30.0X ,General Mathematics ,Mathematics - Published
- 1955
17. Correction to my paper, 'On the Minkowski-Hlawka theorem'
- Author
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Wolfgang M. Schmidt
- Subjects
Pure mathematics ,Factor theorem ,Minkowski–Hlawka theorem ,General Mathematics ,Fixed-point theorem ,Shift theorem ,10.25 ,Mathematics - Published
- 1963
18. On Beilinson’s equivalence for p-adic cohomology
- Author
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Daniel Caro, Tomoyuki Abe, Institute for the Physics and Mathematics of the Universe (IPMU), The University of Tokyo (UTokyo), Laboratoire de Mathématiques Nicolas Oresme (LMNO), Centre National de la Recherche Scientifique (CNRS)-Université de Caen Normandie (UNICAEN), and Normandie Université (NU)-Normandie Université (NU)
- Subjects
Pure mathematics ,Derived category ,Functor ,Holonomic ,General Mathematics ,010102 general mathematics ,Short paper ,General Physics and Astronomy ,Unipotent ,01 natural sciences ,Cohomology ,Mathematics::K-Theory and Homology ,Mathematics::Category Theory ,0103 physical sciences ,010307 mathematical physics ,[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG] ,0101 mathematics ,Equivalence (formal languages) ,Mathematics::Representation Theory ,ComputingMilieux_MISCELLANEOUS ,Mathematics - Abstract
In this short paper, we construct a unipotent nearby cycle functor and show a p-adic analogue of Beilinson’s equivalence comparing two derived categories: the derived category of holonomic arithmetic $${\mathcal {D}}$$ -modules and the derived category of arithmetic $${\mathcal {D}}$$ -modules whose cohomologies are holonomic.
- Published
- 2018
19. Iterates of Generic Polynomials and Generic Rational Functions
- Author
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Jamie Juul
- Subjects
Pure mathematics ,Degree (graph theory) ,Mathematics - Number Theory ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,MathematicsofComputing_GENERAL ,Galois group ,37P05, 11G50, 14G25 ,Rational function ,01 natural sciences ,Unpublished paper ,Generic polynomial ,Number theory ,Symmetric group ,Iterated function ,0103 physical sciences ,FOS: Mathematics ,Number Theory (math.NT) ,010307 mathematical physics ,0101 mathematics ,Mathematics - Abstract
In 1985, Odoni showed that in characteristic 0 0 the Galois group of the n n -th iterate of the generic polynomial with degree d d is as large as possible. That is, he showed that this Galois group is the n n -th wreath power of the symmetric group S d S_d . We generalize this result to positive characteristic, as well as to the generic rational function. These results can be applied to prove certain density results in number theory, two of which are presented here. This work was partially completed by the late R.W.K. Odoni in an unpublished paper.
- Published
- 2014
20. On the hypersurface of Lüroth quartics
- Author
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Giorgio Ottaviani and Edoardo Sernesi
- Subjects
Pure mathematics ,Quartic plane curve ,Degree (graph theory) ,14H45 ,General Mathematics ,Short paper ,quartics ,invariant ,Morley ,Luroth ,Open set ,14A72 ,law.invention ,14D20 ,Mathematics - Algebraic Geometry ,Mathematics::Algebraic Geometry ,Hypersurface ,Invertible matrix ,15A72 ,14J26 ,law ,FOS: Mathematics ,Algebraic Geometry (math.AG) ,Mathematics - Abstract
The hypersurface of Luroth quartic curves inside the projective space of plane quartics has degree 54. We give a proof of this fact along the lines outlined in a paper by Morley, published in 1919. Another proof has been given by Le Potier and Tikhomirov in 2001, in the setting of moduli spaces of vector bundles on the projective plane. Morley's proof uses the description of plane quartics as branch curves of Geiser involutions and gives new geometrical interpretations of the 36 planes associated to the Cremona hexahedral representations of a nonsingular cubic surface., Comment: Final version to appear in Michigan Math. Journal. The last section of v1 has been removed and expanded in the paper "On singular Luroth quartics", arXiv:0911.2101v1
- Published
- 2010
21. AN ALMOST SCHUR THEOREM ON 4-DIMENSIONAL MANIFOLDS
- Author
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Guofang Wang, Yuxin Ge, Laboratoire d'Analyse et de Mathématiques Appliquées (LAMA), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Fédération de Recherche Bézout-Université Paris-Est Marne-la-Vallée (UPEM), and Université Paris-Est Marne-la-Vallée (UPEM)-Fédération de Recherche Bézout-Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Centre National de la Recherche Scientifique (CNRS)
- Subjects
Pure mathematics ,010308 nuclear & particles physics ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,Mathematical analysis ,Short paper ,01 natural sciences ,Schur's theorem ,Computer Science::Computers and Society ,[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph] ,Ricci-flat manifold ,0103 physical sciences ,Sectional curvature ,Mathematics::Differential Geometry ,0101 mathematics ,Mathematics::Symplectic Geometry ,Schur product theorem ,Mathematics ,Scalar curvature - Abstract
International audience; In this short paper we prove that the almost Schur theorem, introduced by De Lellis and Topping, is true on 4-dimensional Riemannian manifolds of nonnegative scalar curvature and discuss some related problems on other dimensional manifolds.
- Published
- 2012
22. A NOTE ON LOCALISED WEIGHTED INEQUALITIES FOR THE EXTENSION OPERATOR
- Author
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Anthony Carbery, Jonathan Bennett, and Juan Antonio Barceló
- Subjects
Unit sphere ,Pure mathematics ,weighted inequalities ,Mathematics(all) ,Inequality ,General Mathematics ,media_common.quotation_subject ,Mathematical analysis ,Short paper ,Fourier extension operators ,symbols.namesake ,Fourier transform ,Norm (mathematics) ,symbols ,EQUATION ,media_common ,Mathematics - Abstract
We prove optimal radially weighted L-2-norm inequalities for the Fourier extension operator associated to the unit sphere in R-n. Such inequalities valid at all scales are well understood. The purpose of this short paper is to establish certain more delicate single-scale versions of these.
- Published
- 2008
23. Some significant remarks on multivalued Perov type contractions on cone metric spaces with a directed graph
- Author
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Aleksandra Sretenovic, Nicola Fabiano, Ana Savić, Stojan Radenović, and Nikola Mirkov
- Subjects
Pure mathematics ,General Mathematics ,cone metric space ,010102 general mathematics ,multivalued mapping ,graphic contraction ,Directed graph ,common fixed point ,Fixed point ,Type (model theory) ,Mathematical proof ,directed graph ,01 natural sciences ,Cone (formal languages) ,c-sequence ,010101 applied mathematics ,Metric space ,QA1-939 ,0101 mathematics ,Contraction principle ,perov's type results ,Mathematics ,Complement (set theory) - Abstract
Using the approach of so-called c-sequences introduced by the fifth author in his recent work, we give much simpler and shorter proofs of multivalued Perov's type results with respect to the ones presented in the recently published paper by M. Abbas et al. Our proofs improve, complement, unify and enrich the ones from the recent papers. Further, in the last section of this paper, we correct and generalize the well-known Perov's fixed point result. We show that this result is in fact equivalent to Banach's contraction principle.
- Published
- 2022
24. Rough sets theory via new topological notions based on ideals and applications
- Author
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Mona Hosny
- Subjects
Pure mathematics ,$ \mathcal{i} $-$ {\bigwedge_{\beta}}_{j} $-sets ,ideals ,General Mathematics ,QA1-939 ,rough sets ,Rough set ,$ \mathcal{i} $-$ {\delta_{\beta}}_{j} $-open sets ,Mathematics - Abstract
There is a close analogy and similarity between topology and rough set theory. As, the leading idea of this theory is depended on two approximations, namely lower and upper approximations, which correspond to the interior and closure operators in topology, respectively. So, the joined study of this theory and topology becomes fundamental. This theory mainly propose to enlarge the lower approximations by adding new elements to it, which is an equivalent goal for canceling elements from the upper approximations. For this intention, one of the primary motivation of this paper is the desire of improving the accuracy measure and reducing the boundary region. This aim can be achieved easily by utilizing ideal in the construction of the approximations as it plays an important role in removing the vagueness of concept. The emergence of ideal in this theory leads to increase the lower approximations and decrease the upper approximations. Consequently, it minimizes the boundary and makes the accuracy higher than the previous. Therefore, this work expresses the set of approximations by using new topological notions relies on ideals namely $ \mathcal{I} $-$ {\delta_{\beta}}_{J} $-open sets and $ \mathcal{I} $-$ {\bigwedge_{\beta}}_{J} $-sets. Moreover, these notions are also utilized to extend the definitions of the rough membership relations and functions. The essential properties of the suggested approximations, relations and functions are studied. Comparisons between the current and previous studies are presented and turned out to be more precise and general. The brilliant idea of these results is increased in importance by applying it in the chemical field as it is shown in the end of this paper. Additionally, a practical example induced from an information system is introduced to elucidate that the current rough membership functions is better than the former ones in the other studies.
- Published
- 2022
25. Additive and Fréchet functional equations on restricted domains with some characterizations of inner product spaces
- Author
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Choonkil Park, Abbas Najati, M. B. Moghimi, and Batool Noori
- Subjects
Pure mathematics ,Inner product space ,Mathematics::Functional Analysis ,fréchet functional equation ,Mathematics::Operator Algebras ,General Mathematics ,hyers-ulam stability ,QA1-939 ,asymptotic behavior ,quadratic functional equation ,Mathematics - Abstract
In this paper, we investigate the Hyers-Ulam stability of additive and Fréchet functional equations on restricted domains. We improve the bounds and thus the results obtained by S. M. Jung and J. M. Rassias. As a consequence, we obtain asymptotic behaviors of functional equations of different types. One of the objectives of this paper is to bring out the involvement of functional equations in various characterizations of inner product spaces.
- Published
- 2022
26. Generalized split null point of sum of monotone operators in Hilbert spaces
- Author
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H. A. Abass, Olalwale K. Oyewole, Ojen Kumar Narain, Akindele Adebayo Mebawondu, and Kazeem Olalekan Aremu
- Subjects
47h09 ,Pure mathematics ,fixed point problem ,47j25 ,General Mathematics ,47j05 ,Hilbert space ,47h06 ,inertial iterative scheme ,symbols.namesake ,Monotone polygon ,firmly nonexpansive ,symbols ,generalized split monotone variational inclusion ,QA1-939 ,Null point ,Mathematics - Abstract
In this paper, we introduce a new type of a generalized split monotone variational inclusion (GSMVI) problem in the framework of real Hilbert spaces. By incorporating an inertial extrapolation method and an Halpern iterative technique, we establish a strong convergence result for approximating a solution of GSMVI and fixed point problems of certain nonlinear mappings in the framework of real Hilbert spaces. Many existing results are derived as corollaries to our main result. Furthermore, we present a numerical example to support our main result and propose an open problem for interested researchers in this area. The result obtained in this paper improves and generalizes many existing results in the literature.
- Published
- 2021
27. so-metrizable spaces and images of metric spaces
- Author
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Songlin Yang and Xun Ge
- Subjects
Pure mathematics ,General Mathematics ,MathematicsofComputing_GENERAL ,Mathematics::General Topology ,54e50 ,so-metrizable space ,54e40 ,54e45 ,54e35 ,Metric space ,Metrization theorem ,ComputingMethodologies_DOCUMENTANDTEXTPROCESSING ,QA1-939 ,σ-mapping ,so-open mapping ,GeneralLiterature_REFERENCE(e.g.,dictionaries,encyclopedias,glossaries) ,so-network ,compact-covering mapping ,Mathematics - Abstract
so-metrizable spaces are a class of important generalized metric spaces between metric spaces and s n sn -metrizable spaces where a space is called an so-metrizable space if it has a σ \sigma -locally finite so-network. As the further work that attaches to the celebrated Alexandrov conjecture, it is interesting to characterize so-metrizable spaces by images of metric spaces. This paper gives such characterizations for so-metrizable spaces. More precisely, this paper introduces so-open mappings and uses the “Pomomarev’s method” to prove that a space X X is an so-metrizable space if and only if it is an so-open, compact-covering, σ \sigma -image of a metric space, if and only if it is an so-open, σ \sigma -image of a metric space. In addition, it is shown that so-open mapping is a simplified form of s n sn -open mapping (resp. 2-sequence-covering mapping if the domain is metrizable). Results of this paper give some new characterizations of so-metrizable spaces and establish some equivalent relations among so-open mapping, s n sn -open mapping and 2-sequence-covering mapping, which further enrich and deepen generalized metric space theory.
- Published
- 2021
28. On 2-variable q-Hermite polynomials
- Author
-
Mohammed Fadel, Kottakkaran Sooppy Nisar, M. Zakarya, and Nusrat Raza
- Subjects
Pure mathematics ,Recurrence relation ,Hermite polynomials ,shift operator ,Series (mathematics) ,General Mathematics ,Generating function ,Quantum calculus ,quantum calculus ,Special functions ,QA1-939 ,Hypergeometric function ,post quantum calculus ,Mathematics ,Variable (mathematics) ,q-hermite polynomials - Abstract
The quantum calculus has emerged as a connection between mathematics and physics. It has wide applications, particularly in quantum mechanics, analytic number theory, combinatorial analysis, operation theory etc. The $ q $-calculus, which serves as a powerful tool to model quantum computing, has drawn attention of many researchers in the field of special functions and as a result the $ q $-analogues of certain special functions, especially hypergeometric function, 1-variable Hermite polynomials, Appell polynomials etc., are introduced and studied. In this paper, we introduce the 2-variable $ q $-Hermite polynomials by means of generating function. Also, its certain properties like series definition, recurrence relations, $ q $-differential equation and summation formulas are established. The operational definition and some integral representations of these polynomials are obtained. Some examples are also considerd to show the efficacy of the proposed method. Some concluding remarks are given. At the end of this paper, the graphical representations of these polynomials of certain degrees with specified values of $ q $ are given.
- Published
- 2021
29. Dynamical significance of generalized fractional integral inequalities via convexity
- Author
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M. Zakarya, Kottakkaran Sooppy Nisar, Ahmed Morsy, Gauhar Rahman, Sabila Ali, Rana Safdar Ali, Sunil Dutt Purohit, and Shahid Mubeen
- Subjects
Pure mathematics ,Inequality ,Kernel (set theory) ,General Mathematics ,media_common.quotation_subject ,Mathematics::Classical Analysis and ODEs ,η2)-convex function ,generalized fractional inequalities ,Function (mathematics) ,Type inequality ,Type (model theory) ,hadamard inequality ,Convexity ,symbols.namesake ,fractional inequalities ,symbols ,QA1-939 ,wright generalized bessel function ,Convex function ,(η1 ,Bessel function ,Mathematics ,media_common - Abstract
The main goal of this paper is to develop the significance of generalized fractional integral inequalities via convex functions. We obtain the new version of fractional integral inequalities with the extended Wright generalized Bessel function acting as a kernel for the convex function, which deals with the Hermite-Hadamard type and trapezoid type inequalities. Moreover, we establish new mid-point type and trapezoid type integral inequalities for $ (\eta_{1}, \eta_{2}) $-convex function related to Hermite-Hadamard type inequality. We establish new version of integral inequality for $ (\eta_{1}, \eta_{2}) $-convex function related to Fejer type. The results discussed in this paper are a generalized version of many inequalities in literature.
- Published
- 2021
30. On some new quantum midpoint-type inequalities for twice quantum differentiable convex functions
- Author
-
Zhiyue Zhang, Hüseyin Budak, Yu-Ming Chu, Necmettin Alp, Muhammad Ali, and [Belirlenecek]
- Subjects
Pure mathematics ,Inequality ,General Mathematics ,media_common.quotation_subject ,Type (model theory) ,Quantum calculus ,quantum calculus ,01 natural sciences ,Midpoint ,26d15 ,Hermite–Hadamard inequality ,QA1-939 ,26a51 ,Differentiable function ,0101 mathematics ,Quantum ,26d10 ,Mathematics ,media_common ,convex function ,hermite-hadamard inequality ,010102 general mathematics ,010101 applied mathematics ,Computer Science::Graphics ,q-integral ,Convex function - Abstract
The present paper aims to find some new midpoint-type inequalities for twice quantum differentiable convex functions. The consequences derived in this paper are unification and generalization of the comparable consequences in the literature on midpoint inequalities. © 2021 Muhammad Aamir Ali et al., published by De Gruyter. National Natural Science Foundation of China, NSFC: 11301127, 11601485, 11626101, 11701176, 11971241, 61673169 Funding information : The work was supported by the Natural Science Foundation of China (Grant Nos. 61673169, 11301127, 11701176, 11626101, 11601485, 11971241). 2-s2.0-85105011594
- Published
- 2021
31. Strongly essential set of vector Ky Fan's points problem and its applications
- Author
-
Dejin Zhang, Yan-Long Yang, Shu-Wen Xiang, and Xicai Deng
- Subjects
Pure mathematics ,Current (mathematics) ,General Mathematics ,lcsh:Mathematics ,Solution set ,hausdorff upper semimetric ,lcsh:QA1-939 ,vector ky fan's points ,Set (abstract data type) ,Section (fiber bundle) ,multiobjective games ,Component (UML) ,strong essential component ,ky fan's section problems ,weakly pareto-nash equilibrium ,Point (geometry) ,strong essential set ,Mathematics - Abstract
In this paper, several existence results of strongly essential set of the solution set for Ky Fan's section problems and vector Ky Fan's point problems are obtained. Firstly, two kinds of strongly essential sets of Ky Fan's section problems are defined, and some further results on existence of the strongly essential component of solutions set of Ky Fan's section problems are proved, which generalize the conclusion in [ 22 ], and further generalize the conclusions in [ 21 , 28 ]. Secondly, based on the above results, two classes of stronger perturbations of vector-valued inequality functions are proposed respectively, and several existence results of the strongly essential component of set of vector Ky Fan's points are obtained. By comparing several metrics, we give some strong and weak relationships among the various metrics involved in the text. The main results of this paper actually generalize the relevant conclusions in the current literature. Finally, as an application, we obtain an existence result of the strongly essential component of weakly Pareto-Nash equilibrium for multiobjective games.
- Published
- 2021
32. Generalization of uniqueness and value sharing of meromorphic functions concerning differential polynomials
- Author
-
Ramya Maligi and Harina P. Waghamore
- Subjects
Pure mathematics ,Generalization ,primary 30d35 ,General Mathematics ,010102 general mathematics ,uniqueness ,01 natural sciences ,differential polynomials ,010101 applied mathematics ,QA1-939 ,meromorphic functions ,Uniqueness ,sharing value ,0101 mathematics ,[MATH]Mathematics [math] ,Value (mathematics) ,Differential (mathematics) ,Mathematics ,Meromorphic function - Abstract
The motivation of this paper is to study the uniqueness problems of meromorphic functions concerning differential polynomials that share a small function. The results of the paper improve and generalize the recent results due to Fengrong Zhang and Linlin Wu [13]. We also solve an open problem as posed in the last section of [13].
- Published
- 2020
33. Vector fields on canonically polarized surfaces
- Author
-
Nikolaos Tziolas
- Subjects
Surface (mathematics) ,Pure mathematics ,Fundamental group ,General Mathematics ,Field (mathematics) ,Moduli ,Mathematics - Algebraic Geometry ,Mathematics::Algebraic Geometry ,FOS: Mathematics ,Vector field ,Gravitational singularity ,Algebraically closed field ,14J50, 14DJ29, 14J10 ,Algebraic Geometry (math.AG) ,Stack (mathematics) ,Mathematics - Abstract
This paper investigates the geometry of canonically polarized surfaces defined over a field of positive characteristic which have a nontrivial global vector field, and the implications that the existence of such surfaces has in the moduli problem of canonically polarized surfaces. In particular, an explicit integer valued function f(x) is obtained with the following properties. If X is a canonically polarized surface with canonical singularities defined over an algebraically closed field of characteristic p>0 such that p>f(K_X^2) and X has a nontrivial global vector field, then X is unirational and the algebraic fundamental group is trivial. As a consequence of this result, large classes of canonically polarized surfaces are identified whose moduli stack is Deligne-Mumford, a property that does not hold in general in positive characteristic. This paper is mathematically identical to the previous version. The reason that the paper is replaced is in order to point out that this paper is a generalization to the case of singular surfaces with canonical singularities of the paper "Vector fields and moduli of canonically polarized surfaces in positive characteristic" with reference arXiv:1710.03076 which treated only the case of smooth surfaces. The results of this paper supercede the results of the aforementioned paper making it obsolete., This paper is a generalization to the case of singular surfaces with canonical singularities of the paper "Vector fields and moduli of canonically polarized surfaces in positive characteristic" with reference arXiv:1710.03076 which treated only the case of smooth surfaces. The results of this paper supercede the results of the aforementioned paper making it obsolete. 46 pages
- Published
- 2022
34. Hardy–Littlewood–Sobolev inequalities for a class of non-symmetric and non-doubling hypoelliptic semigroups
- Author
-
Giulio Tralli and Nicola Garofalo
- Subjects
Pure mathematics ,Matrix (mathematics) ,Class (set theory) ,Trace (linear algebra) ,Semigroup ,General Mathematics ,Hypoelliptic operator ,Degenerate energy levels ,Special case ,Sobolev inequality ,Mathematics - Abstract
In his seminal 1934 paper on Brownian motion and the theory of gases Kolmogorov introduced a second order evolution equation which displays some challenging features. In the opening of his 1967 hypoellipticity paper Hörmander discussed a general class of degenerate Ornstein–Uhlenbeck operators that includes Kolmogorov’s as a special case. In this note we combine semigroup theory with a nonlocal calculus for these hypoelliptic operators to establish new inequalities of Hardy–Littlewood–Sobolev type in the situation when the drift matrix has nonnegative trace. Our work has been influenced by ideas of E. Stein and Varopoulos in the framework of symmetric semigroups. One of our objectives is to show that such ideas can be pushed to successfully handle the present degenerate non-symmetric setting.
- Published
- 2022
35. Locally finiteness and convolution products in groupoids
- Author
-
Joseph Neggers, Hee Sik Kim, and In Ho Hwang
- Subjects
Pure mathematics ,moebius function ,General Mathematics ,interval value function ,lcsh:Mathematics ,above ,locally finite ,below ,groupoid ,lcsh:QA1-939 ,convolution product ,Riemann zeta function ,zeta function ,symbols.namesake ,Number theory ,Special functions ,Lattice (order) ,symbols ,transitive interval property ,Mathematics - Abstract
In this paper, we introduce a version of the Moebius function and other special functions on a particular class of intervals for groupoids, and study them to obtain results analogous to those obtained in the usual lattice, combinatorics and number theory setting, but of course much more general due to the viewpoint taken in this paper.
- Published
- 2020
36. Role of shape operator in warped product submanifolds of nearly cosymplectic manifolds
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Rifaqat Ali, Nadia Alluhaibi, Fatemah Mofarreh, Khaled Mohamed Khedher, and Wan Ainun Mior Othman
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Pure mathematics ,General Mathematics ,lcsh:Mathematics ,Mathematics::History and Overview ,Physics::Optics ,Submanifold ,characterizations ,lcsh:QA1-939 ,Computer Science::Computers and Society ,Computer Science::Computer Vision and Pattern Recognition ,Shape operator ,integrability conditions ,Mathematics::Differential Geometry ,Invariant (mathematics) ,shape operators ,warped product ,Mathematics - Abstract
In this paper, first, we find the integrability theorems for the invariant and slant distributions which appeared in the concept of semi-slant submanifolds. Utilizing these theorems, we prove that a semi-slant submanifold reduces to be a warped product semi-slant submanifold, provided some necessary and sufficient conditions concerning the shape operators. Also, it is shown that a few earlier results are exceptional cases of this paper results.
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- 2020
37. Fixed point theorem for new type of auxiliary functions
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Vishal Gupta, Arslan Hojat Ansari, and Naveen Mani
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Pure mathematics ,021103 operations research ,metric spaces ,General Mathematics ,0211 other engineering and technologies ,Fixed-point theorem ,02 engineering and technology ,Auxiliary function ,Type (model theory) ,01 natural sciences ,010101 applied mathematics ,54h25 ,fixed point ,auxiliary function ,QA1-939 ,0101 mathematics ,47h10 ,Mathematics - Abstract
In this paper, we present some fixed point results satisfying generalized contractive condition with new auxiliary function in complete metric spaces. More precisely, the structure of the paper is the following. In the first section, we present some useful notions and results. The main aim of second section is to establish some new fixed point results in complete metric spaces. Finally, in the third section, we show the validity and superiority of our main results by suitable example. Also, as an application of our main result, some interesting corollaries have been included, which make our concepts and results effective. Our main result generalizes some well known existing results in the literature.
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- 2020
38. On a Generalized Convolution Operator
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Janusz Sokół, Poonam Sharma, and Ravinder Krishna Raina
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Pure mathematics ,convex functions ,Physics and Astronomy (miscellaneous) ,General Mathematics ,subordination ,Function (mathematics) ,Fractional calculus ,Convolution ,Riemann zeta function ,symbols.namesake ,Operator (computer programming) ,analytic functions ,Chemistry (miscellaneous) ,QA1-939 ,Computer Science (miscellaneous) ,symbols ,convolution ,Symmetry (geometry) ,Convex function ,Mathematics ,Analytic function - Abstract
Recently in the paper [Mediterr. J. Math. , 2016, 13, 1535–1553], the authors introduced and studied a new operator which was defined as a convolution of the three popular linear operators, namely the Sǎlǎgean operator, the Ruscheweyh operator and a fractional derivative operator. In the present paper, we consider an operator which is a convolution operator of only two linear operators (with lesser restricted parameters) that yield various well-known operators, defined by a symmetric way, including the one studied in the above-mentioned paper. Several results on the subordination of analytic functions to this operator (defined below) are investigated. Some of the results presented are shown to involve the familiar Appell function and Hurwitz–Lerch Zeta function. Special cases and interesting consequences being in symmetry of our main results are also mentioned.
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- 2021
- Full Text
- View/download PDF
39. Partial Covering of a Circle by 6 and 7 Congruent Circles
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Tibor Tarnai, Zsolt Gáspár, and Krisztián Hincz
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Pure mathematics ,Physics and Astronomy (miscellaneous) ,General Mathematics ,Structure (category theory) ,Radius ,partial covering ,Unit circle ,Cover (topology) ,Chemistry (miscellaneous) ,Simple (abstract algebra) ,Tensegrity ,equilibrium paths ,QA1-939 ,Computer Science (miscellaneous) ,tensegrity ,Symmetry (geometry) ,maximum ,covering by equal circles ,optimization ,Mathematics ,packing of equal circles ,symmetry - Abstract
Background: Some medical and technological tasks lead to the geometrical problem of how to cover the unit circle as much as possible by n congruent circles of given radius r, while r varies from the radius in the maximum packing to the radius in the minimum covering. Proven or conjectural solutions to this partial covering problem are known only for n = 2 to 5. In the present paper, numerical solutions are given to this problem for n = 6 and 7. Method: The method used transforms the geometrical problem to a mechanical one, where the solution to the geometrical problem is obtained by finding the self-stress positions of a generalised tensegrity structure. This method was developed by the authors and was published in an earlier publication. Results: The method applied results in locally optimal circle arrangements. The numerical data for the special circle arrangements are presented in a tabular form, and in drawings of the arrangements. Conclusion: It was found that the case of n = 6 is very complicated, whilst the case n = 7 is very simple. It is shown in this paper that locally optimal arrangements may exhibit different types of symmetry, and equilibrium paths may bifurcate.
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- 2021
- Full Text
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40. Structural properties of faces of the cone of copositive matrices
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Tatiana Tchemisova and Olga Kostyukova
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Pure mathematics ,General Mathematics ,Completely positive matrices ,completely positive matrices ,copositive cone ,Zero (complex analysis) ,Structure (category theory) ,Mathematics::Optimization and Control ,Copositive matrices ,Minimal exposed cone ,Mathematics::Spectral Theory ,Cone (formal languages) ,Copositive cone ,Face (geometry) ,minimal exposed cone ,QA1-939 ,Computer Science (miscellaneous) ,copositive matrices ,Engineering (miscellaneous) ,Mathematics ,Subspace topology - Abstract
In this paper, we study the properties of faces and exposed faces of the cone of copositive matrices (copositive cone), paying special attention to issues related to their geometric structure. Based on the concepts of zero and minimal zero vectors, we obtain several explicit representations of faces of the copositive cone and compare them. Given a face of the cone of copositive matrices, we describe the subspace generated by that face and the minimal exposed face containing it. Summarizing the results obtained in the paper, we systematically show what information can be extracted about the given copositive face in the case of incomplete data. Several examples for illustrating the main findings of the paper and also for justifying the usefulness of the developed approach to the study of the facial structure of the copositive cone are discussed.
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- 2021
41. Fuzzy Differential Subordinations Obtained Using a Hypergeometric Integral Operator
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Georgia Irina Oros
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Pure mathematics ,Confluent hypergeometric function ,Geometric function theory ,General Mathematics ,Fuzzy set ,fuzzy differential subordination ,integral operator ,univalent function ,Fuzzy logic ,confluent hypergeometric function ,Hypergeometric distribution ,analytic function ,Operator (computer programming) ,fuzzy best dominant ,Computer Science (miscellaneous) ,QA1-939 ,Hypergeometric function ,Engineering (miscellaneous) ,Mathematics ,Univalent function - Abstract
This paper is related to notions adapted from fuzzy set theory to the field of complex analysis, namely fuzzy differential subordinations. Using the ideas specific to geometric function theory from the field of complex analysis, fuzzy differential subordination results are obtained using a new integral operator introduced in this paper using the well-known confluent hypergeometric function, also known as the Kummer hypergeometric function. The new hypergeometric integral operator is defined by choosing particular parameters, having as inspiration the operator studied by Miller, Mocanu and Reade in 1978. Theorems are stated and proved, which give corollary conditions such that the newly-defined integral operator is starlike, convex and close-to-convex, respectively. The example given at the end of the paper proves the applicability of the obtained results.
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- 2021
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42. On Some New Inequalities of Hermite–Hadamard Midpoint and Trapezoid Type for Preinvex Functions in p,q-Calculus
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Jarunee Soontharanon, Muhammad Ali, Sotiris K. Ntouyas, Ghulam Murtaza, Ifra Bashir Sial, and Thanin Sitthiwirattham
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convex function ,Pure mathematics ,Hermite polynomials ,Physics and Astronomy (miscellaneous) ,General Mathematics ,(p,q)-integral ,Context (language use) ,Type (model theory) ,Midpoint ,Computer Science::Digital Libraries ,Hermite–Hadamard inequality ,Chemistry (miscellaneous) ,Hadamard transform ,Computer Science (miscellaneous) ,QA1-939 ,Computer Science::Programming Languages ,Symmetry (geometry) ,Convex function ,post quantum calculus ,Mathematics - Abstract
In this paper, we establish some new Hermite–Hadamard type inequalities for preinvex functions and left-right estimates of newly established inequalities for p,q-differentiable preinvex functions in the context of p,q-calculus. We also show that the results established in this paper are generalizations of comparable results in the literature of integral inequalities. Analytic inequalities of this nature and especially the techniques involved have applications in various areas in which symmetry plays a prominent role.
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- 2021
- Full Text
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43. Relative Gorenstein Dimensions over Triangular Matrix Rings
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Luis Oyonarte, Rachid El Maaouy, Driss Bennis, and Juan Ramón García Rozas
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Class (set theory) ,Pure mathematics ,Ring (mathematics) ,relative Gorenstein dimensions ,General Mathematics ,Structure (category theory) ,Triangular matrix ,weaklyWakamatsu tilting modules ,MathematicsofComputing_GENERAL ,Mathematics - Rings and Algebras ,Global dimension ,Morphism ,triangular matrix ring ,weakly Wakamatsu tilting modules ,Dimension (vector space) ,Rings and Algebras (math.RA) ,FOS: Mathematics ,Computer Science (miscellaneous) ,QA1-939 ,Engineering (miscellaneous) ,Mathematics ,Counterexample - Abstract
Let $A$ and $B$ be rings, $U$ a $(B,A)$-bimodule and $T=\begin{pmatrix} A&0\\U&B \end{pmatrix}$ the triangular matrix ring. In this paper, several notions in relative Gorenstein algebra over a triangular matrix ring are investigated. We first study how to construct w-tilting (tilting, semidualizing) over $T$ using the corresponding ones over $A$ and $B$. We show that when $U$ is relative (weakly) compatible we are able to describe the structure of $G_C$-projective modules over $T$. As an application, we study when a morphism in $T$-Mod has a special $G_CP(T)$-precover and when the class $G_CP(T)$ is a special precovering class. In addition, we study the relative global dimension of $T$. In some cases, we show that it can be computed from the relative global dimensions of $A$ and $B$. We end the paper with a counterexample to a result that characterizes when a $T$-module has a finite projective dimension., 39 pages
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- 2021
44. Several Integral Inequalities of Hermite–Hadamard Type Related to k-Fractional Conformable Integral Operators
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Thanin Sitthiwirattham, Jarunee Soontharanon, Hijaz Ahmad, Soubhagya Kumar Sahoo, and Muhammad Tariq
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Pure mathematics ,Convex geometry ,Hermite polynomials ,conformable integral ,Physics and Astronomy (miscellaneous) ,convexity ,General Mathematics ,Regular polygon ,Function (mathematics) ,k-fractional conformable integral ,Convexity ,Symmetric function ,Operator (computer programming) ,Chemistry (miscellaneous) ,Computer Science (miscellaneous) ,QA1-939 ,E-beta functions ,Convex function ,k-gamma function ,E-gamma functions ,Mathematics ,Riemann–Liouville fractional integral - Abstract
In this paper, we present some ideas and concepts related to the k-fractional conformable integral operator for convex functions. First, we present a new integral identity correlated with the k-fractional conformable operator for the first-order derivative of a given function. Employing this new identity, the authors have proved some generalized inequalities of Hermite–Hadamard type via Hölder’s inequality and the power mean inequality. Inequalities have a strong correlation with convex and symmetric convex functions. There exist expansive properties and strong correlations between the symmetric function and various areas of convexity, including convex functions, probability theory, and convex geometry on convex sets because of their fascinating properties in the mathematical sciences. The results of this paper show that the methodology can be directly applied and is computationally easy to use and exact.
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- 2021
45. Applications of the Fractional Calculus in Fuzzy Differential Subordinations and Superordinations
- Author
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Alina Alb Lupaş
- Subjects
Subordination (linguistics) ,fuzzy differential subordination ,fuzzy differential superordination ,fuzzy best dominant ,fuzzy best subordinant ,fractional integral ,confluent hypergeometric function ,Pure mathematics ,Confluent hypergeometric function ,Mathematics::General Mathematics ,General Mathematics ,Fuzzy logic ,Fractional calculus ,Mathematics::Probability ,Computer Science (miscellaneous) ,QA1-939 ,Engineering (miscellaneous) ,Differential (mathematics) ,Mathematics - Abstract
The fractional integral of confluent hypergeometric function is used in this paper for obtaining new applications using concepts from the theory of fuzzy differential subordination and superordination. The aim of the paper is to present new fuzzy differential subordinations and superordinations for which the fuzzy best dominant and fuzzy best subordinant are given, respectively. The original theorems proved in the paper generate interesting corollaries for particular choices of functions acting as fuzzy best dominant and fuzzy best subordinant. Another contribution contained in this paper is the nice sandwich-type theorem combining the results given in two theorems proved here using the two theories of fuzzy differential subordination and fuzzy differential superordination.
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- 2021
46. A Note on the Connection between Ordered Semihyperrings
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Saber Omidi, Mohammadsadegh Monemrad, Saeed Kosari, Maryam Akhoundi, and Zheng Kou
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Pure mathematics ,homomorphism ,Physics and Astronomy (miscellaneous) ,Relation (database) ,Generalization ,Mathematics::General Mathematics ,General Mathematics ,derivation ,Galois connection ,Connection (mathematics) ,ordered semihyperring ,Chemistry (miscellaneous) ,Computer Science (miscellaneous) ,QA1-939 ,Homomorphism ,ddc:510 ,Mathematik [510] ,Mathematics - Abstract
The notion of ordered semihyperrings is a generalization of ordered semirings and a generalization of semihyperrings. In this paper, the Galois connection between ordered semihyperrings are studied in detail and various interesting results are obtained. A construction of an ordered semihyperring via a regular relation is given. Furthermore, we present the Galois connection between homomorphisms and derivations on an ordered semihyperring. The notion of ordered semihyperrings is a generalization of ordered semirings and a generalization of semihyperrings. In this paper, the Galois connection between ordered semihyperrings are studied in detail and various interesting results are obtained. A construction of an ordered semihyperring via a regular relation is given. Furthermore, we present the Galois connection between homomorphisms and derivations on an ordered semihyperring.
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- 2021
47. Special Functions of Fractional Calculus in the Form of Convolution Series and Their Applications
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Yuri Luchko
- Subjects
Pure mathematics ,Integrable system ,Series (mathematics) ,Sonine kernel ,General Mathematics ,Zero (complex analysis) ,Mathematics::Classical Analysis and ODEs ,Sonine condition ,fractional differential equations ,fundamental theorems of fractional calculus ,general fractional integral ,Fractional calculus ,Convolution ,Singularity ,Kernel (image processing) ,Special functions ,Computer Science (miscellaneous) ,QA1-939 ,general fractional derivative ,Engineering (miscellaneous) ,convolution series ,Mathematics - Abstract
In this paper, we first discuss the convolution series that are generated by Sonine kernels from a class of functions continuous on a real positive semi-axis that have an integrable singularity of power function type at point zero. These convolution series are closely related to the general fractional integrals and derivatives with Sonine kernels and represent a new class of special functions of fractional calculus. The Mittag-Leffler functions as solutions to the fractional differential equations with the fractional derivatives of both Riemann-Liouville and Caputo types are particular cases of the convolution series generated by the Sonine kernel κ(t)=tα−1/Γ(α),0<, α<, 1. The main result of the paper is the derivation of analytic solutions to the single- and multi-term fractional differential equations with the general fractional derivatives of the Riemann-Liouville type that have not yet been studied in the fractional calculus literature.
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- 2021
48. Fixed point results for multivalued mappings of Ćirić type via F-contractions on quasi metric spaces
- Author
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Wasfi Shatanawi, Hacer Dağ, Ishak Altun, and KKÜ
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Pure mathematics ,General Mathematics ,010102 general mathematics ,primary 47h10 ,Fixed point ,Type (model theory) ,multivalued mappings ,01 natural sciences ,010101 applied mathematics ,Metric space ,fixed point ,QA1-939 ,secondary 54h25 ,0101 mathematics ,quasi metric space ,Mathematics - Abstract
Altun, Ishak/0000-0002-7967-0554 WOS:000537813000001 In this paper, we present some fixed point results for multivalued mappings with both closed values and proximinal values on left K-complete quasi metric spaces. We also provide a nontrivial example to illustrate our results. Prince Sultan University [RG-DES-2017-01-17] The authors are thankful to the referees for making valuable suggestions leading to the better presentations of the paper. This work was supported by the Prince Sultan University through the Research Group NAMAM under Grant RG-DES-2017-01-17.
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- 2020
49. Faber polynomial coefficients for meromorphic bi-subordinate functions of complex order
- Author
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Hatice Tuǧba Yolcu and Erhan Deniz
- Subjects
Subordination (linguistics) ,Pure mathematics ,Polynomial ,starlike functions ,Mathematics::Complex Variables ,General Mathematics ,lcsh:Mathematics ,subordination ,faber polynomial ,lcsh:QA1-939 ,bi-univalent functions ,Complex order ,analytic functions ,meromorphic functions ,Polynomial coefficients ,Analytic function ,Mathematics ,Meromorphic function - Abstract
In this paper, we obtain the upper bounds for the n-th (n ≥ 1) coefficients for meromorphic bi-subordinate functions of complex order by using Faber polynomial expansions. The results, which are presented in this paper, would generalize those in related works of several earlier authors.
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- 2020
50. Canonical stretched rings
- Author
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Nguyen Thi Anh Hang, Do Van Kien, and Hoang Le Truong
- Subjects
Pure mathematics ,Quantitative Biology::Biomolecules ,Mathematics::Commutative Algebra ,General Mathematics ,FOS: Mathematics ,Characterization (mathematics) ,Commutative Algebra (math.AC) ,Mathematics - Commutative Algebra ,Mathematics - Abstract
In this paper, we introduce the concept of canonical stretched rings, sparse stretched rings and maximum sparse ideals. Then we give characterizations of canonical stretched rings and sparse stretched rings; and a characterization of Gorenstein rings in terms of their maximum sparse ideals. Several explicit examples are provided along the paper to illustrate such rings., Accepted Acta Mathematica Vietnamica
- Published
- 2021
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