2,179 results
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2. Menon-type identities again: A note on a paper by Li, Kim and Qiao
- Author
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László Tóth, Pentti Haukkanen, Informaatioteknologian ja viestinnän tiedekunta - Faculty of Information Technology and Communication Sciences, and Tampere University
- Subjects
Combinatorics ,Identity (mathematics) ,Character (mathematics) ,Mathematics - Number Theory ,Simple (abstract algebra) ,General Mathematics ,Matematiikka - Mathematics ,Arithmetic function ,Function (mathematics) ,11A07, 11A25 ,Type (model theory) ,Mathematics - Group Theory ,Mathematics - Abstract
We give common generalizations of the Menon-type identities by Sivaramakrishnan (1969) and Li, Kim, Qiao (2019). Our general identities involve arithmetic functions of several variables, and also contain, as special cases, identities for gcd-sum type functions. We point out a new Menon-type identity concerning the lcm function. We present a simple character free approach for the proof., Comment: 14 pages
- Published
- 2019
3. Flexible Polyhedral Surfaces with Two Flat Poses
- Author
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Hellmuth Stachel
- Subjects
Tessellation ,Physics and Astronomy (miscellaneous) ,Strophoid ,flexible polyhedral surface ,lcsh:Mathematics ,General Mathematics ,Kokotsakis tessellation ,Motion (geometry) ,Geometry ,Miura-ori ,paper folding ,Type (model theory) ,Dihedral angle ,lcsh:QA1-939 ,Topology ,strophoid ,Kokotsakis mesh ,Computer Science::Graphics ,Quadrangle ,Bricard octahedron of Type 3 ,Chemistry (miscellaneous) ,Face (geometry) ,Computer Science (miscellaneous) ,Mathematics - Abstract
We present three types of polyhedral surfaces, which are continuously flexible and have not only an initial pose, where all faces are coplanar, but pass during their self-motion through another pose with coplanar faces (“flat pose”). These surfaces are examples of so-called rigid origami, since we only admit exact flexions, i.e., each face remains rigid during the motion, only the dihedral angles vary. We analyze the geometry behind Miura-ori and address Kokotsakis’ example of a flexible tessellation with the particular case of a cyclic quadrangle. Finally, we recall Bricard’s octahedra of Type 3 and their relation to strophoids.
- Published
- 2015
4. Halfspace type Theorems for Self-Shrinkers
- Author
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Marcos P. Cavalcante and José M. Espinar
- Subjects
Mathematics - Differential Geometry ,0209 industrial biotechnology ,Minimal surface ,General Mathematics ,010102 general mathematics ,Short paper ,02 engineering and technology ,Radius ,Type (model theory) ,Lambda ,01 natural sciences ,Combinatorics ,020901 industrial engineering & automation ,Hypersurface ,Differential Geometry (math.DG) ,Hyperplane ,Catenoid ,FOS: Mathematics ,Mathematics::Differential Geometry ,0101 mathematics ,Mathematics - Abstract
In this short paper, we extend the classical Hoffman-Meeks Halfspace Theorem [Hoffman and Meeks, 'The strong halfspace theorem for minimal surfaces', Invent. Math. 101 (1990) 373-377] to self-shrinkers, that is: Let $P$ be a hyperplane passing through the origin. The only properly immersed self-shrinker $\Sigma $ contained in one of the closed half-space determined by $P$ is $\Sigma = P$. Our proof is geometric and uses a catenoid type hypersurface discovered by Kleene-Moller [Kleene and Moller, 'Self-shrinkers with a rotational symmetry', Trans. Amer. Math. Soc. 366 (2014) 3943-3963]. Also, using a similar geometric idea, we obtain that the only self-shrinker properly immersed in an closed cylinder $ \overline {B^{k+1} (R)} \times {\mathbb R}^{n-k}\subset {\mathbb R}^{n+1}$, for some $k\in \{1, \ldots, n\}$ and radius $R$, $R \leqslant \sqrt {2k}$, is the cylinder ${\mathbb S}^k (\sqrt {2k}) \times {\mathbb R}^{n-k}$. We also extend the above results for $\lambda $-hypersurfaces.
- Published
- 2014
5. Investigating a generalized Hilfer-type fractional differential equation with two-point and integral boundary conditions
- Author
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Mohammed S. Abdo, Kamaleldin Abodayeh, Tariq A. Aljaaidi, Saleh S. Redhwan, Mohammed A. Almalahi, Wasfi Shatanawi, Sadikali L. Shaikh, and Commerce, RozaBagh, Aurangabad , India
- Subjects
κ-hilfer fractional derivative ,General Mathematics ,boundary conditions ,Mathematical analysis ,QA1-939 ,fixed point theorem ,Point (geometry) ,Boundary value problem ,Type (model theory) ,Fractional differential ,Mathematics - Abstract
In this paper, we investigate a nonlinear generalized fractional differential equation with two-point and integral boundary conditions in the frame of $ \kappa $-Hilfer fractional derivative. The existence and uniqueness results are obtained using Krasnoselskii and Banach's fixed point theorems. We analyze different types of stability results of the proposed problem by using some mathematical methodologies. At the end of the paper, we present a numerical example to demonstrate and validate our findings.
- Published
- 2022
6. 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
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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
7. Error estimates of variational discretization for semilinear parabolic optimal control problems
- Author
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Zuliang Lu, Xuejiao Chen, Chunjuan Hou, and Fei Huang
- Subjects
Discretization ,General Mathematics ,lcsh:Mathematics ,Type (model theory) ,semilinear parabolic equations ,Residual ,Optimal control ,lcsh:QA1-939 ,Backward Euler method ,Omega ,Finite element method ,error estimates ,optimal control problems ,A priori and a posteriori ,Applied mathematics ,finite element methods ,Mathematics - Abstract
In this paper, variational discretization directed against the optimal control problem governed by nonlinear parabolic equations with control constraints is studied. It is known that the a priori error estimates is $|||u-u_h|||_{L^\infty(J; L^2(\Omega))} = O(h+k)$ using backward Euler method for standard finite element. In this paper, the better result $|||u-u_h|||_{L^\infty(J; L^2(\Omega))} = O(h^2+k)$ is gained. Beyond that, we get a posteriori error estimates of residual type.
- Published
- 2021
8. Unitary representations of type B rational Cherednik algebras and crystal combinatorics
- Author
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Emily Norton
- Subjects
Functor ,Unitarity ,General Mathematics ,Type (model theory) ,Unitary state ,Fock space ,Combinatorics ,Irreducible representation ,FOS: Mathematics ,Mathematics - Combinatorics ,Partition (number theory) ,Component (group theory) ,Combinatorics (math.CO) ,Representation Theory (math.RT) ,Mathematics::Representation Theory ,Mathematics - Representation Theory ,Mathematics - Abstract
We compare crystal combinatorics of the level 2 Fock space with the classification of unitary irreducible representations of type B rational Cherednik algebras to study how unitarity behaves under parabolic restriction. First, we show that any finite-dimensional unitary irreducible representation of such an algebra is labeled by a bipartition consisting of a rectangular partition in one component and the empty partition in the other component. This is a new proof of a result that can be deduced from theorems of Montarani and Etingof-Stoica. Second, we show that the crystal operators that remove boxes preserve the combinatorial conditions for unitarity, and that the parabolic restriction functors categorifying the crystals send irreducible unitary representations to unitary representations. Third, we find the supports of the unitary representations., This paper supersedes arXiv:1907.00919 and contains that paper as a subsection. 35 pages, some color figures
- Published
- 2021
9. Splines of the Fourth Order Approximation and the Volterra Integral Equations
- Author
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D.E. Zhilin, A.G. Doronina, and I. G. Burova
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Polynomial ,Series (mathematics) ,General Mathematics ,Type (model theory) ,Integral equation ,Volterra integral equation ,symbols.namesake ,Continuation ,Computer Science::Graphics ,symbols ,Applied mathematics ,Focus (optics) ,Mathematics ,Interpolation - Abstract
This paper is a continuation of a series of papers devoted to the numerical solution of integral equations using local interpolation splines. The main focus is given to the use of splines of the fourth order of approximation. The features of the application of the polynomial and non-polynomial splines of the fourth order of approximation to the solution of Volterra integral equation of the second kind are discussed. In addition to local splines of the Lagrangian type, integro-differential splines are also used to construct computational schemes. The comparison of the solutions obtained by different methods is carried out. The results of the numerical experiments are presented.
- Published
- 2021
10. Fragility of nonconvergence in preferential attachment graphs with three types
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Ben Andrews and Jonathan Jordan
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Random graph ,Vertex (graph theory) ,05C82 ,General Mathematics ,Probability (math.PR) ,Type (model theory) ,Preferential attachment ,Graph ,Combinatorics ,Fragility ,FOS: Mathematics ,Tournament ,Node (circuits) ,Mathematics - Probability ,Mathematics - Abstract
Preferential attachment networks are a type of random network where new nodes are connected to existing ones at random, and are more likely to connect to those that already have many connections. We investigate further a family of models introduced by Antunovi\'{c}, Mossel and R\'{a}cz where each vertex in a preferential attachment graph is assigned a type, based on the types of its neighbours. Instances of this type of process where the proportions of each type present do not converge over time seem to be rare. Previous work found that a "rock-paper-scissors" setup where each new node's type was determined by a rock-paper-scissors contest between its two neighbours does not converge. Here, two cases similar to that are considered, one which is like the above but with an arbitrarily small chance of picking a random type and one where there are four neighbours which perform a knockout tournament to determine the new type. These two new setups, despite seeming very similar to the rock-paper-scissors model, do in fact converge, perhaps surprisingly., Comment: 7 pages, 2 figures
- Published
- 2021
11. 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
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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
12. On some new quantum midpoint-type inequalities for twice quantum differentiable convex functions
- Author
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Zhiyue Zhang, Hüseyin Budak, Yu-Ming Chu, Necmettin Alp, Muhammad Ali, and [Belirlenecek]
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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
13. Noncommutative Counting Invariants and Curve Complexes
- Author
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Ludmil Katzarkov and George Dimitrov
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Intersection theory ,medicine.medical_specialty ,Functor ,Conjecture ,Group (mathematics) ,General Mathematics ,010102 general mathematics ,Quiver ,Type (model theory) ,01 natural sciences ,Combinatorics ,0103 physical sciences ,medicine ,010307 mathematical physics ,0101 mathematics ,Partially ordered set ,Commutative property ,Mathematics - Abstract
In our previous paper, viewing $D^b(K(l))$ as a noncommutative curve, where $K(l)$ is the Kronecker quiver with $l$-arrows, we introduced categorical invariants via counting of noncommutative curves. Roughly, these invariants are sets of subcategories in a given category and their quotients. The noncommutative curve-counting invariants are obtained by restricting the subcategories to be equivalent to $D^b(K(l))$. The general definition, however, defines a larger class of invariants and many of them behave properly with respect to fully faithful functors. Here, after recalling the definition, we focus on the examples and extend our studies beyond counting. We enrich our invariants with the following structures: the inclusion of subcategories makes them partially ordered sets and considering semi-orthogonal pairs of subcategories as edges amounts to directed graphs. It turns out that the problem for counting $D^b(A_k)$ in $D^b(A_n)$ has a geometric combinatorial parallel - counting of maps between polygons. Estimating the numbers counting noncommutative curves in $D^b({\mathbb P}^2)$ modulo the group of autoequivalences, we prove finiteness and that the exact determining of these numbers leads to a solution of Markov problem. Via homological mirror symmetry, this gives a new approach to this problem. Regarding the structure of a partially ordered set mentioned above, we initiate intersection theory of noncommutative curves focusing on the case of noncommutative genus zero. The above-mentioned structure of a directed graph (and related simplicial complex) is a categorical analogue of the classical curve complex, introduced by Harvey and Harrer. The paper contains pictures of the graphs in many examples and also presents an approach to Markov conjecture via counting of subgraphs in a graph associated with $D^b({{\mathbb{P}}}^2)$. Some of the results proved here were announced in a previous work.
- Published
- 2021
14. A new obstruction for normal spanning trees
- Author
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Max Pitz
- Subjects
Aleph ,Spanning tree ,General Mathematics ,010102 general mathematics ,Minor (linear algebra) ,Type (model theory) ,01 natural sciences ,Graph ,Combinatorics ,Mathematics::Logic ,Arbitrarily large ,Cardinality ,FOS: Mathematics ,Mathematics - Combinatorics ,Combinatorics (math.CO) ,0101 mathematics ,Connectivity ,05C83, 05C05, 05C63 ,Mathematics - Abstract
In a paper from 2001 (Journal of the LMS), Diestel and Leader offered a proof that a connected graph has a normal spanning tree if and only if it does not contain a minor from two specific forbidden classes of graphs, all of cardinality $\aleph_1$. Unfortunately, their proof contains a gap, and their result is incorrect. In this paper, we construct a third type of obstruction: an $\aleph_1$-sized graph without a normal spanning tree that contains neither of the two types described by Diestel and Leader as a minor. Further, we show that any list of forbidden minors characterising the graphs with normal spanning trees must contain graphs of arbitrarily large cardinality., Comment: 9 pages. arXiv admin note: text overlap with arXiv:2005.02833
- Published
- 2021
15. Volume preserving flow and Alexandrov–Fenchel type inequalities in hyperbolic space
- Author
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Ben Andrews, Xuzhong Chen, and Yong Wei
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Pure mathematics ,Geodesic dome ,Applied Mathematics ,General Mathematics ,Hyperbolic space ,010102 general mathematics ,Type (model theory) ,Curvature ,01 natural sciences ,law.invention ,Hypersurface ,Flow (mathematics) ,Principal curvature ,law ,Mathematics::Differential Geometry ,Sectional curvature ,0101 mathematics ,Mathematics - Abstract
In this paper, we study flows of hypersurfaces in hyperbolic space, and apply them to prove geometric inequalities. In the first part of the paper, we consider volume preserving flows by a family of curvature functions including positive powers of $k$-th mean curvatures with $k=1,\cdots,n$, and positive powers of $p$-th power sums $S_p$ with $p>0$. We prove that if the initial hypersurface $M_0$ is smooth and closed and has positive sectional curvatures, then the solution $M_t$ of the flow has positive sectional curvature for any time $t>0$, exists for all time and converges to a geodesic sphere exponentially in the smooth topology. The convergence result can be used to show that certain Alexandrov-Fenchel quermassintegral inequalities, known previously for horospherically convex hypersurfaces, also hold under the weaker condition of positive sectional curvature. In the second part of this paper, we study curvature flows for strictly horospherically convex hypersurfaces in hyperbolic space with speed given by a smooth, symmetric, increasing and homogeneous degree one function $f$ of the shifted principal curvatures $\lambda_i=\kappa_i-1$, plus a global term chosen to impose a constraint on the quermassintegrals of the enclosed domain, where $f$ is assumed to satisfy a certain condition on the second derivatives. We prove that if the initial hypersurface is smooth, closed and strictly horospherically convex, then the solution of the flow exists for all time and converges to a geodesic sphere exponentially in the smooth topology. As applications of the convergence result, we prove a new rigidity theorem on smooth closed Weingarten hypersurfaces in hyperbolic space, and a new class of Alexandrov-Fenchel type inequalities for smooth horospherically convex hypersurfaces in hyperbolic space.
- Published
- 2021
16. Hadamard and Fejér–Hadamard Inequalities for Further Generalized Fractional Integrals Involving Mittag-Leffler Functions
- Author
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Chahn Yong Jung, Khuram Ali Khan, Ghulam Farid, and Muhammad Yussouf
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Pure mathematics ,Article Subject ,General Mathematics ,010102 general mathematics ,Mathematics::Classical Analysis and ODEs ,Regular polygon ,Type (model theory) ,01 natural sciences ,010101 applied mathematics ,Hadamard transform ,QA1-939 ,0101 mathematics ,Convex function ,Mathematics - Abstract
In this paper, generalized versions of Hadamard and Fejér–Hadamard type fractional integral inequalities are obtained. By using generalized fractional integrals containing Mittag-Leffler functions, some well-known results for convex and harmonically convex functions are generalized. The results of this paper are connected with various published fractional integral inequalities.
- Published
- 2021
17. THE COHOMOLOGY OF UNRAMIFIED RAPOPORT–ZINK SPACES OF EL-TYPE AND HARRIS’S CONJECTURE
- Author
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Alexander Bertoloni Meli
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Conjecture ,Mathematics - Number Theory ,General Mathematics ,Prove it ,Type (model theory) ,Cohomology ,Combinatorics ,Mathematics - Algebraic Geometry ,Mathematics::Algebraic Geometry ,Morphism ,Square-integrable function ,FOS: Mathematics ,Number Theory (math.NT) ,Mathematics::Representation Theory ,Algebraic Geometry (math.AG) ,Mathematics - Abstract
We study the $l$-adic cohomology of unramified Rapoport-Zink spaces of EL-type. These spaces were used in Harris and Taylor's proof of the local Langlands correspondence for $\mathrm{GL_n}$ and to show local-global compatibilities of the Langlands correspondence. In this paper we consider certain morphisms, $\mathrm{Mant}_{b, \mu}$, of Grothendieck groups of representations constructed from the cohomology of the above spaces, as studied by Harris and Taylor, Mantovan, Fargues, Shin, and others. Due to earlier work of Fargues and Shin we have a description of $\mathrm{Mant}_{b, \mu}(\rho)$ for $\rho$ a supercuspidal representation. In this paper, we give a conjectural formula for $\mathrm{Mant}_{b, \mu}(\rho)$ for all $\rho$ and prove it when $\rho$ is essentially square integrable. Our proof works for general $\rho$ conditionally on a conjecture appearing in Shin's work. We show that our description agrees with a conjecture of Harris in the case of parabolic inductions of supercuspidal representations of a Levi subgroup., Comment: 50 pages, published version
- Published
- 2021
18. Khintchine-type theorems for values of subhomogeneous functions at integer points
- Author
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Mishel Skenderi and Dmitry Kleinbock
- Subjects
Mathematics - Number Theory ,010505 oceanography ,General Mathematics ,010102 general mathematics ,Second moment of area ,Function (mathematics) ,Type (model theory) ,01 natural sciences ,Minimax approximation algorithm ,Combinatorics ,Integer ,FOS: Mathematics ,11J25, 11J54, 11J83, 11H06, 11H60, 37A17 ,Number Theory (math.NT) ,0101 mathematics ,Element (category theory) ,Axiom ,0105 earth and related environmental sciences ,Mathematics - Abstract
This work has been motivated by recent papers that quantify the density of values of generic quadratic forms and other polynomials at integer points, in particular ones that use Rogers' second moment estimates. In this paper we establish such results in a very general framework. Given any subhomogeneous function (a notion to be defined) $f: \mathbb{R}^n \to \mathbb{R}$, we derive a necessary and sufficient condition on the approximating function $\psi$ for guaranteeing that a generic element $f\circ g$ in the $G$-orbit of $f$ is $\psi$-approximable; that is, $|f\circ g(\mathbf{v})| \le \psi(\|\mathbf{v}\|)$ for infinitely many $\mathbf{v} \in \mathbb{Z}^n$. We also deduce a sufficient condition in the case of uniform approximation. Here, $G$ can be any closed subgroup of $\rm{ASL}_n(\mathbb{R})$ satisfying certain axioms that allow for the use of Rogers-type estimates., Comment: 26 pages; misprints corrected, concluding remarks added
- Published
- 2021
19. Well defined extinction time of solutions for a class of weak-viscoelastic parabolic equation with positive initial energy
- Author
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Ahmed Himadan
- Subjects
Class (set theory) ,heat equation ,lcsh:Mathematics ,General Mathematics ,Mathematical analysis ,weak-memory ,Type (model theory) ,lcsh:QA1-939 ,variable exponents ,Term (time) ,Sobolev space ,blow up ,sobolev spaces ,Point (geometry) ,Heat equation ,Well-defined ,Energy (signal processing) ,Mathematics - Abstract
In the present paper, we consider an important problem from the point of view of application in sciences and mechanic, namely, a class of $ p(x) $-Laplacian type parabolic equation with weak-viscoelasticity. Here, we are concerned with global in time non-existence under suitable conditions on the exponents $ q(x) $ and $ p(x) $ with positive initial energy. We show that the weak-memory term is unable to stabilize problem (1.2) under conditions (1.5) and (1.7). Our main interest in this paper arose in the first place in consequence of a query to blow-up phenomenon.
- Published
- 2021
20. Erratum: A companion of Ostrowski type integral inequality using a 5-step Kernel with some applications
- Author
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Andrea Aglic-Aljinovic
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General Mathematics ,Kernel (statistics) ,Ostrowski inequality, Grüss inequality ,Applied mathematics ,Type (model theory) ,Mathematics - Abstract
The aim of this paper is to correct results from the published paper: A companion of Ostrowski Type Integral Inequality Using a 5-Step Kernel with Some Applications, Filomat 30:13 (2016), 3601-3614.
- Published
- 2021
21. A new approach to persistence and periodicity of logistic systems with jumps
- Author
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Kegang Zhao
- Subjects
Class (set theory) ,Computer science ,General Mathematics ,jumps ,persistence ,periodicity ,Type (model theory) ,Differential systems ,globally attractive ,logistic differential system ,Control theory ,QA1-939 ,Applied mathematics ,Persistence (discontinuity) ,Mathematics - Abstract
This paper considers a class of logistic type differential system with jumps. Based on discontinuous control theory, a new approach is developed to guarantee the persistence and existence of a unique globally attractive positive periodic solution. The development results of this paper emphasize the effects of jumps on system, which are different from the existing ones in the literature. Two examples and their simulations are given to illustrate the effectiveness of the proposed results.
- Published
- 2021
22. Some inequalities for multiplicative tempered fractional integrals involving the $ \lambda $-incomplete gamma functions
- Author
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Tingsong Du, Yu Peng, and Hao Fu
- Subjects
multiplicative tempered fractional integrals ,Pure mathematics ,Class (set theory) ,General Mathematics ,Multiplicative function ,fractional integrals ,Type (model theory) ,Lambda ,hermite–hadamard inequality ,multiplicatively convex mappings ,Convexity ,Identity (mathematics) ,Hermite–Hadamard inequality ,QA1-939 ,Gamma function ,Mathematics - Abstract
In this paper, we introduce a class of the multiplicative tempered fractional integral operators. Then, we investigate two Hermite–Hadamard type inequalities for this class. By using the established identity and the multiplicative convexity, we establish some integral inequalities for the multiplicative tempered fractional integrals involving the $ \lambda $-incomplete gamma functions. And our results obtained in the present paper generalize some results given by Budak and Tunc (2020) and Ali et al. (2019). Also, we provide three examples to demonstrate the simplicities of the calculations.
- Published
- 2021
23. Infinitely many solutions for a class of fractional Robin problems with variable exponents
- Author
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Ramzi Alsaedi
- Subjects
Class (set theory) ,Work (thermodynamics) ,General Mathematics ,variational methods ,robin ,Mathematics::Spectral Theory ,Type (model theory) ,variable exponents ,Euler equations ,symbols.namesake ,Continuation ,fracional sobolev spaces ,Operator (computer programming) ,QA1-939 ,symbols ,Applied mathematics ,Boundary value problem ,Mathematics ,Variable (mathematics) - Abstract
In this paper, we are concerned with a class of fractional Robin problems with variable exponents. Their main feature is that the associated Euler equation is driven by the fractional $ p(\cdot)- $Laplacian operator with variable coefficient while the boundary condition is of Robin type. This paper is a continuation of the recent work established by A. Bahrouni, V. Radulescu and P. Winkert [ 5 ].
- Published
- 2021
24. Asymptotic analysis of a tumor growth model with fractional operators
- Author
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Pierluigi Colli, Gianni Gilardi, and Jürgen Sprekels
- Subjects
35K90 ,Asymptotic analysis ,Generalization ,General Mathematics ,35Q92 ,Type (model theory) ,01 natural sciences ,Mathematics - Analysis of PDEs ,Operator (computer programming) ,Fractional operators ,well-posedness ,FOS: Mathematics ,Applied mathematics ,0101 mathematics ,Mathematics ,regularity of solutions ,35B40 ,010102 general mathematics ,Relaxation (iterative method) ,Function (mathematics) ,35B40, 35K55, 35K90, 35Q92, 92C17 ,92C17 ,010101 applied mathematics ,asymptotic analysis ,Monotone polygon ,Cahn--Hilliard systems ,35K55 ,Variational inequality ,tumor growth models ,Analysis of PDEs (math.AP) - Abstract
In this paper, we study a system of three evolutionary operator equations involving fractional powers of selfadjoint, monotone, unbounded, linear operators having compact resolvents. This system constitutes a generalized and relaxed version of a phase field system of Cahn-Hilliard type modelling tumor growth that has originally been proposed in Hawkins-Daarud et al. (Int. J. Numer. Math. Biomed. Eng. 28 (2012), 3-24). The original phase field system and certain relaxed versions thereof have been studied in recent papers co-authored by the present authors and E. Rocca. The model consists of a Cahn-Hilliard equation for the tumor cell fraction, coupled to a reaction-diffusion equation for a function S representing the nutrient-rich extracellular water volume fraction. Effects due to fluid motion are neglected. Motivated by the possibility that the diffusional regimes governing the evolution of the different constituents of the model may be of different (e.g., fractional) type, the present authors studied in a recent note a generalization of the systems investigated in the abovementioned works. Under rather general assumptions, well-posedness and regularity results have been shown. In particular, by writing the equation governing the evolution of the chemical potential in the form of a general variational inequality, also singular or nonsmooth contributions of logarithmic or of double obstacle type to the energy density could be admitted. In this note, we perform an asymptotic analysis of the governing system as two (small) relaxation parameters approach zero separately and simultaneously. Corresponding well-posedness and regularity results are established for the respective cases; in particular, we give a detailed discussion which assumptions on the admissible nonlinearities have to be postulated in each of the occurring cases., Comment: Key words: fractional operators, Cahn-Hilliard systems, well-posedness, regularity of solutions, tumor growth models, asymptotic analysis
- Published
- 2020
25. Ideal, non-extended formulations for disjunctive constraints admitting a network representation
- Author
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Markó Horváth and Tamás Kis
- Subjects
Combinatorics ,Cardinality ,Series (mathematics) ,Unit vector ,General Mathematics ,Embedding ,Polytope ,QA75 Electronic computers. Computer science / számítástechnika, számítógéptudomány ,Ideal (ring theory) ,Characterization (mathematics) ,Type (model theory) ,Software ,Mathematics - Abstract
In this paper we reconsider a known technique for constructing strong MIP formulations for disjunctive constraints of the form $$x \in \bigcup _{i=1}^m P_i$$ x ∈ ⋃ i = 1 m P i , where the $$P_i$$ P i are polytopes. The formulation is based on the Cayley Embedding of the union of polytopes, namely, $$Q := \mathrm {conv}(\bigcup _{i=1}^m P_i\times \{\epsilon ^i\})$$ Q : = conv ( ⋃ i = 1 m P i × { ϵ i } ) , where $$\epsilon ^i$$ ϵ i is the ith unit vector in $${\mathbb {R}}^m$$ R m . Our main contribution is a full characterization of the facets of Q, provided it has a certain network representation. In the second half of the paper, we work-out a number of applications from the literature, e.g., special ordered sets of type 2, logical constraints, the cardinality indicating polytope, union of simplicies, etc., along with a more complex recent example. Furthermore, we describe a new formulation for piecewise linear functions defined on a grid triangulation of a rectangular region $$D \subset {\mathbb {R}}^d$$ D ⊂ R d using a logarithmic number of auxilirary variables in the number of gridpoints in D for any fixed d. The series of applications demonstrates the richness of the class of disjunctive constraints for which our method can be applied.
- Published
- 2022
26. On Boundedness Property of Singular Integral Operators Associated to a Schrödinger Operator in a Generalized Morrey Space and Applications
- Author
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Thanh-Nhan Nguyen, Xuan Truong Le, and Ngoc Trong Nguyen
- Subjects
Mathematics::Functional Analysis ,Pure mathematics ,Property (philosophy) ,General Mathematics ,010102 general mathematics ,Mathematics::Classical Analysis and ODEs ,General Physics and Astronomy ,Function (mathematics) ,Type (model theory) ,Space (mathematics) ,01 natural sciences ,Schrödinger equation ,010101 applied mathematics ,symbols.namesake ,Riesz transform ,Operator (computer programming) ,symbols ,0101 mathematics ,Schrödinger's cat ,Mathematics - Abstract
In this paper, we provide the boundedness property of the Riesz transforms associated to the Schrodinger operator $${\cal L} = \Delta + {\bf{V}}$$ in a new weighted Morrey space which is the generalized version of many previous Morrey type spaces. The additional potential V considered in this paper is a non-negative function satisfying the suitable reverse Holder’s inequality. Our results are new and general in many cases of problems. As an application of the boundedness property of these singular integral operators, we obtain some regularity results of solutions to Schrodinger equations in the new Morrey space.
- Published
- 2020
27. Halanay Inequality on Time Scales with Unbounded Coefficients and Its Applications
- Author
-
Boqun Ou
- Subjects
Halanay inequality ,Inequality ,Applied Mathematics ,General Mathematics ,Numerical analysis ,media_common.quotation_subject ,010102 general mathematics ,Zero (complex analysis) ,Type (model theory) ,01 natural sciences ,010101 applied mathematics ,Dynamic problem ,Stability theory ,Applied mathematics ,0101 mathematics ,Mathematics ,media_common - Abstract
In the present paper, we obtain a Halanay inequality on time scales with unbounded coefficient for a dynamic problem, which extends a result of Wen et al. (J. Math. Anal. Appl., 347 (2008), 169–178.) to the inequality of integral type on time scales. Moreover, we list two dynamic problems to which the Halanay inequality obtained above can be applied and prove the zero solution of two delay dynamic problems are asymptotically stable. Moreover, it is worth mentioning that the Halanay inequality obtained in the present paper is more precise than the results in [3, 14, 17].
- Published
- 2020
28. Hyperbolicity and Uniformity of Varieties of Log General type
- Author
-
Amos Turchet, Kristin DeVleming, Kenneth Ascher, Ascher, Kenneth, Devleming, Kristin, and Turchet, Amos
- Subjects
Pure mathematics ,Conjecture ,Mathematics - Number Theory ,Generalization ,General Mathematics ,010102 general mathematics ,Type (model theory) ,01 natural sciences ,Mathematics - Algebraic Geometry ,Mathematics::Algebraic Geometry ,0103 physical sciences ,FOS: Mathematics ,Sheaf ,Trigonometric functions ,Uniform boundedness ,Cotangent bundle ,Number Theory (math.NT) ,010307 mathematical physics ,0101 mathematics ,Variety (universal algebra) ,Algebraic Geometry (math.AG) ,Mathematics::Symplectic Geometry ,Mathematics - Abstract
Projective varieties with ample cotangent bundle satisfy many notions of hyperbolicity, and one goal of this paper is to discuss generalizations to quasi-projective varieties. A major hurdle is that the naive generalization fails, i.e. the log cotangent bundle is never ample. Instead, we define a notion called almost ample which roughly asks that the log cotangent is as positive as possible. We show that all subvarieties of a quasi-projective variety with almost ample log cotangent bundle are of log general type. In addition, if one assumes globally generated then we obtain that such varieties contain finitely many integral points. In another direction, we show that the Lang-Vojta conjecture implies the number of stably integral points on curves of log general type, and surfaces of log general type with almost ample log cotangent sheaf are uniformly bounded., v5: exposition greatly improved. Previous section on function fields removed, to be expanded upon in a future paper. To appear in IMRN
- Published
- 2020
29. Low dimensional orders of finite representation type
- Author
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Daniel Chan and Colin Ingalls
- Subjects
Ring (mathematics) ,Plane curve ,Root of unity ,General Mathematics ,010102 general mathematics ,14E16 ,Local ring ,Order (ring theory) ,Mathematics - Rings and Algebras ,Type (model theory) ,01 natural sciences ,Noncommutative geometry ,Combinatorics ,Minimal model program ,Mathematics - Algebraic Geometry ,Rings and Algebras (math.RA) ,Mathematics - Quantum Algebra ,0103 physical sciences ,FOS: Mathematics ,Quantum Algebra (math.QA) ,010307 mathematical physics ,0101 mathematics ,Algebraic Geometry (math.AG) ,Mathematics - Abstract
In this paper, we study noncommutative surface singularities arising from orders. The singularities we study are mild in the sense that they have finite representation type or, equivalently, are log terminal in the sense of the Mori minimal model program for orders (Chan and Ingalls in Invent Math 161(2):427–452, 2005). These were classified independently by Artin (in terms of ramification data) and Reiten–Van den Bergh (in terms of their AR-quivers). The first main goal of this paper is to connect these two classifications, by going through the finite subgroups $$G \subset {{{\,\mathrm{GL}\,}}_2}$$ , explicitly computing $$H^2(G,k^*)$$ , and then matching these up with Artin’s list of ramification data and Reiten–Van den Bergh’s AR-quivers. This provides a semi-independent proof of their classifications and extends the study of canonical orders in Chan et al. (Proc Lond Math Soc (3) 98(1):83–115, 2009) to the case of log terminal orders. A secondary goal of this paper is to study noncommutative analogues of plane curves which arise as follows. Let $$B = k_{\zeta } \llbracket x,y \rrbracket $$ be the skew power series ring where $$\zeta $$ is a root of unity, or more generally a terminal order over a complete local ring. We consider rings of the form $$A = B/(f)$$ where $$f \in Z(B)$$ which we interpret to be the ring of functions on a noncommutative plane curve. We classify those noncommutative plane curves which are of finite representation type and compute their AR-quivers.
- Published
- 2020
30. Fixed point theorem for new type of auxiliary functions
- Author
-
Vishal Gupta, Arslan Hojat Ansari, and Naveen Mani
- Subjects
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.
- Published
- 2020
31. Fixed point results for multivalued mappings of Ćirić type via F-contractions on quasi metric spaces
- Author
-
Wasfi Shatanawi, Hacer Dağ, Ishak Altun, and KKÜ
- Subjects
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.
- Published
- 2020
32. Convergence of linking Baskakov-type operators
- Author
-
Ulrich Abel, Margareta Heilmann, and Vitaliy Kushnirevych
- Subjects
010101 applied mathematics ,Combinatorics ,Pointwise ,Polynomial (hyperelastic model) ,General Mathematics ,Uniform convergence ,010102 general mathematics ,Convergence (routing) ,0101 mathematics ,Type (model theory) ,01 natural sciences ,Complex plane ,Mathematics - Abstract
In this paper we consider a link $$B_{n,\rho }$$Bn,ρ between Baskakov type operators $$B_{n,\infty }$$Bn,∞ and genuine Baskakov–Durrmeyer type operators $$ B_{n,1}$$Bn,1 depending on a positive real parameter $$\rho $$ρ. The topic of the present paper is the pointwise limit relation $$\left( B_{n,\rho }f\right) \left( x\right) \rightarrow \left( B_{n,\infty }f\right) \left( x\right) $$Bn,ρfx→Bn,∞fx as $$\rho \rightarrow \infty $$ρ→∞ for $$x\ge 0.$$x≥0. As a main result we derive uniform convergence on each compact subinterval of the positive real axis for all continuous functions f of polynomial growth.
- Published
- 2020
33. Remarks on the geodesic-Einstein metrics of a relative ample line bundle
- Author
-
Xueyuan Wan and Xu Wang
- Subjects
Ample line bundle ,Pure mathematics ,Geodesic ,General Mathematics ,010102 general mathematics ,Holomorphic function ,Fibration ,Type (model theory) ,01 natural sciences ,Mathematics::Algebraic Geometry ,Flow (mathematics) ,Bounded function ,Bundle ,0103 physical sciences ,Mathematics::Differential Geometry ,010307 mathematical physics ,0101 mathematics ,Mathematics::Symplectic Geometry ,Mathematics - Abstract
In this paper, we introduce the associated geodesic-Einstein flow for a relative ample line bundle L over the total space $$\mathcal {X}$$ of a holomorphic fibration and obtain a few properties of that flow. In particular, we prove that the pair $$(\mathcal {X}, L)$$ is nonlinear semistable if the associated Donaldson type functional is bounded from below and the geodesic-Einstein flow has long-time existence property. We also define the associated S-classes and C-classes for $$(\mathcal {X}, L)$$ and obtain two inequalities between them when L admits a geodesic-Einstein metric. Finally, in the appendix of this paper, we prove that a relative ample line bundle is geodesic-Einstein if and only if an associated infinite rank bundle is Hermitian–Einstein.
- Published
- 2020
34. A simple characterization of H-convergence for a class of nonlocal problems
- Author
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Anton Evgrafov and José C. Bellido
- Subjects
G-convergence ,Sequence ,H-convergenc ,Laplace transform ,General Mathematics ,010102 general mathematics ,Characterization (mathematics) ,Type (model theory) ,Homogenization of nonlocal problems ,01 natural sciences ,010101 applied mathematics ,Quantum nonlocality ,Mathematics - Analysis of PDEs ,Simple (abstract algebra) ,Convergence (routing) ,FOS: Mathematics ,Applied mathematics ,0101 mathematics ,Laplace operator ,Analysis of PDEs (math.AP) ,Mathematics - Abstract
This is a follow-up of the paper J. Fernandez-Bonder, A. Ritorto and A. Salort, H-convergence result for nonlocal elliptic-type problems via Tartar’s method, SIAM J. Math. Anal., 49 (2017), pp. 2387–2408, where the classical concept of H-convergence was extended to fractional $$p$$ -Laplace type operators. In this short paper we provide an explicit characterization of this notion by demonstrating that the weak- $$*$$ convergence of the coefficients is an equivalent condition for H-convergence of the sequence of nonlocal operators. This result takes advantage of nonlocality and is in stark contrast to the local $$p$$ -Laplacian case.
- Published
- 2020
35. Difference gap functions and global error bounds for random mixed equilibrium problems
- Author
-
Jen-Chih Yao, Xiaolong Qin, Vo Minh Tam, and Nguyen Van Hung
- Subjects
Class (set theory) ,symbols.namesake ,General Mathematics ,Hilbert space ,symbols ,Applied mathematics ,Function (mathematics) ,Type (model theory) ,Global error ,Mathematics - Abstract
The aim of this paper is to study the difference gap (in short, D-gap) function and error bounds for a class of the random mixed equilibrium problems in real Hilbert spaces. Firstly, we consider regularized gap functions of the Fukushima type and Moreau-Yosida type. Then difference gap functions are established by using these terms of regularized gap functions. Finally, the global error bounds for random mixed equilibrium problems are also developed. The results obtained in this paper are new and extend some corresponding known results in literatures. Some examples are given for the illustration of our results.
- Published
- 2020
36. A new characterization of a proper type B semigroup
- Author
-
Zhi Pei, Chunhua Li, and Baogen Xu
- Subjects
type b semigroup ,Pure mathematics ,20m10 ,Mathematics::Operator Algebras ,Semigroup ,Computer Science::Information Retrieval ,General Mathematics ,010102 general mathematics ,e-unitary ,proper ,0102 computer and information sciences ,Characterization (mathematics) ,Type (model theory) ,01 natural sciences ,06f05 ,010201 computation theory & mathematics ,q-semigroup ,QA1-939 ,0101 mathematics ,Mathematics - Abstract
In this paper, we develop the elementary theory of inverse semigroups to the cases of type B semigroups. The main aim of this paper is to study proper type B semigroups. We introduce first the concept of a left admissible triple. After obtaining some basic properties of left admissible triple, we give the definition of a Q-semigroup and get a structure theorem of Q-semigroup. In particular, we introduce the notion of an admissible triple and give some characterization of proper type B semigroups. It is proved that an arbitrary Q-semigroup with an admissible triple is an E-unitary type B semigroup.
- Published
- 2020
37. Solvability for boundary value problems of nonlinear fractional differential equations with mixed perturbations of the second type
- Author
-
Yilin Wang, Yibing Sun, Yige Zhao, and Zhi Liu
- Subjects
General Mathematics ,lcsh:Mathematics ,existence ,Existence theorem ,Fixed-point theorem ,Type (model theory) ,Expression (computer science) ,Differential operator ,Lipschitz continuity ,lcsh:QA1-939 ,mixed perturbations ,Banach algebra ,boundary value problem ,fractional differential equation ,Applied mathematics ,Boundary value problem ,Mathematics - Abstract
In this paper, we consider the solvability for boundary value problems of nonlinear fractional differential equations with mixed perturbations of the second type. The expression of the solution for the boundary value problem of nonlinear fractional differential equations with mixed perturbations of the second type is discussed based on the definition and the property of the Caputo differential operators. By the fixed point theorem in Banach algebra due to Dhage, an existence theorem for the boundary value problem of nonlinear fractional differential equations with mixed perturbations of the second type is given under mixed Lipschitz and Caratheodory conditions. As an application, an example is presented to illustrate the main results. Our results in this paper extend and improve some well-known results. To some extent, our work fills the gap on some basic theory for the boundary value problems of fractional differential equations with mixed perturbations of the second type involving Caputo differential operator.
- Published
- 2020
38. EXISTENCE OF SOLUTIONS FOR DUAL SINGULAR INTEGRAL EQUATIONS WITH CONVOLUTION KERNELS IN CASE OF NON-NORMAL TYPE
- Author
-
Pingrun Li
- Subjects
General Mathematics ,010102 general mathematics ,Singular integral ,Type (model theory) ,01 natural sciences ,Integral equation ,Dual (category theory) ,Convolution ,010101 applied mathematics ,Riemann hypothesis ,symbols.namesake ,Fourier transform ,symbols ,Applied mathematics ,Boundary value problem ,0101 mathematics ,Mathematics - Abstract
This paper is devoted to the study of dual singular integral equations with convolution kernels in the case of non-normal type. Via using the Fourier transforms, we transform such equations into Riemann boundary value problems. To solve the equation, we establish the regularity theory of solvability. The general solutions and the solvable conditions of the equation are obtained. Especially, we investigate the asymptotic property of solutions at nodes. This paper will have a significant meaning for the study of improving and developing complex analysis, integral equations and Riemann boundary value problems.
- Published
- 2020
39. Relatively equi-statistical convergence via deferred Nörlund mean based on difference operator of fractional-order and related approximation theorems
- Author
-
S. A. Mohiuddine, Vishnu Narayan Mishra, Bidu Bhusan Jena, and Susanta Kumar Paikray
- Subjects
Operator (computer programming) ,Rate of convergence ,Generalization ,General Mathematics ,Convergence (routing) ,Zero (complex analysis) ,Applied mathematics ,Function (mathematics) ,Type (model theory) ,Modulus of continuity ,Mathematics - Abstract
In the proposed paper, we have introduced the notion of point-wise relatively statistical convergence, relatively equi-statistical convergence and relatively uniform statistical convergence of sequences of functions based on the difference operator of fractional order including (p, q)-gamma function via the deferred Norlund mean. As an application point of view, we have proved a Korovkin type approximation theorem by using the relatively deferred Norlund equi-statistical convergence of difference sequences of functions and intimated that our theorem is a generalization of some well-established approximation theorems of Korovkin type which was presented in earlier works. Moreover, we estimate the rate of the relatively deferred Norlund equi-statistical convergence involving a non-zero scale function. Furthermore, we use the modulus of continuity to estimate the rate of convergence of approximating positive linear operators. Finally, we set up various fascinating examples in connection with our results and definitions presented in this paper.
- Published
- 2020
40. Fractional convex type contraction with solution of fractional differential equation
- Author
-
Aftab Hussain
- Subjects
fractional convex α-η-contraction ,Pure mathematics ,Differential equation ,lcsh:Mathematics ,General Mathematics ,Regular polygon ,$\mathcal{f}$ -metric space ,Order (ring theory) ,Context (language use) ,Type (model theory) ,Fixed point ,lcsh:QA1-939 ,Metric space ,$\mathcal{f}$ -cauchy ,$\mathcal{f}$ -complete ,Boundary value problem ,Mathematics - Abstract
The focus of this paper is to present a new idea of fractional convex type contraction and establish some new results for such contraction under the improved approach of fractional convex type contractive condition in the context of $\mathcal{F}$ -complete $\mathcal{F}$ -metric space. The authors derive some results for Suzuki type contractions, orbitally T-complete and orbitally continuous mappings in $\mathcal{F}$ -metric spaces and obtain some consequences by using graphic contraction. The motivation of this paper is to observe the solution of fractional order differential equation with one of the boundary condition using fixed point technique in $\mathcal{F}$ -metric space.
- Published
- 2020
41. Common Fixed Points of Generalized Cyclic C Class Ψ-ɸ-Λ Weak Nonexpansive Mappings
- Author
-
Sahar Mohamed Ali Abou Bakr
- Subjects
Statistics and Probability ,Pure mathematics ,Class (set theory) ,General Mathematics ,Common fixed point ,Fixed-point theorem ,Fixed point ,Type (model theory) ,Mathematics - Abstract
This paper shows that if S and T are two joint generalized cyclic F-Ψ-ɸ-Λ weak nonexpansive type mappings, then they have only one common fixed point. In particular, every generalized cyclic C class Ψ-ɸ-Λ weak nonexpansive mapping has a unique fixed point. Hence it extends the results of the attached references of this paper.
- Published
- 2020
42. New extensions of Chebyshev-Pólya-Szegö type inequalities via conformable integrals
- Author
-
Ahmet Ocak Akdemir, Erhan Deniz, and Ebru Yüksel
- Subjects
Pure mathematics ,Operator (computer programming) ,Chebyshev's inequality ,General Mathematics ,Product (mathematics) ,Type (model theory) ,Conformable matrix ,Chebyshev filter ,Mathematics - Abstract
Recently, several papers related to integral inequalities involving various fractional integral operators have been presented. In this work, motivated essentially by the previous works, we prove some new Polya-Szego inequalities via conformable fractional integral operator and use them to prove some new fractional Chebyshev type inequalities concerning the integral of the product of two functions and the product of two integrals which are improvement of the results in the paper [Ntouyas, S.K., Agarwal, P. and Tariboon, J., On Polya-Szego and Chebyshev type inequalities involving the Riemann-Liouville fractional integral operators, J. Math. Inequal (see [ 9 ])].
- Published
- 2020
43. Ramanujan denesting formulae for cubic radicals
- Author
-
K. I. Pimenov and M. A. Antipov
- Subjects
Pure mathematics ,Polynomial ,Mathematics::Number Theory ,General Mathematics ,010102 general mathematics ,General Physics and Astronomy ,Inverse ,Extension (predicate logic) ,Type (model theory) ,01 natural sciences ,010305 fluids & plasmas ,Ramanujan's sum ,symbols.namesake ,0103 physical sciences ,symbols ,0101 mathematics ,Cubic function ,Mathematics - Abstract
This paper contains an explanation of Ramanujan-type formulas with cubic radicals of cubic irrationalities in the situation when these radicals are contained in a pure cubic extension. We give a complete description of formulas of such type, answering the Zippel’s question. It turns out that Ramanujan-type formulas are in some sense unique in this situation. In particular, there must be no more than three summands in the right-hand side and the norm of the irrationality in question must be a cube. In this situation we associate cubic irrationalities with a cyclic cubic polynomial, which is reducible if and only if one can simplify the corresponding cubic radical. This correspondence is inverse to the so-called Ramanujan correspondence defined in the preceding papers, where one associates a pure cubic extension to some cyclic polynomial.
- Published
- 2020
44. On Bloom type estimates for iterated commutators of fractional integrals
- Author
-
Israel P. Rivera-Ríos, Javier C. Martínez-Perales, and Natalia Accomazzo
- Subjects
Pure mathematics ,General Mathematics ,010102 general mathematics ,Type (model theory) ,Characterization (mathematics) ,Mathematical proof ,Space (mathematics) ,01 natural sciences ,Mathematics - Classical Analysis and ODEs ,Iterated function ,Classical Analysis and ODEs (math.CA) ,FOS: Mathematics ,0101 mathematics ,Mathematics - Abstract
In this paper we provide quantitative Bloom type estimates for iterated commutators of fractional integrals improving and extending results from a work of Holmes, Rahm and Spencer. We give new proofs for those inequalities relying upon a new sparse domination that we provide as well in this paper and also in techniques developed in a recent paper due to Lerner, Ombrosi and the third author. We extend as well the necessity established in the work of Holmes, Rahm and Spencer to iterated commutators providing a new proof. As a consequence of the preceding results we recover the one weight estimates in works of Cruz-Uribe and Moen and B\'enyi, Martell, Moen, Stachura, Torres and establish the sharpness in the iterated case. Our result provides as well a new characterization of the BMO space., Comment: 18 pages
- Published
- 2020
45. On the polar Orlicz-Minkowski problems and the p-capacitary Orlicz-Petty bodies
- Author
-
Xiaokang Luo, Deping Ye, and Baocheng Zhu
- Subjects
Mathematics::Functional Analysis ,Pure mathematics ,General Mathematics ,010102 general mathematics ,Mathematics::Classical Analysis and ODEs ,Metric Geometry (math.MG) ,Type (model theory) ,01 natural sciences ,Measure (mathematics) ,52A20, 52A38, 52A39, 52A40, 53A15 ,Mathematics - Metric Geometry ,0103 physical sciences ,Minkowski space ,FOS: Mathematics ,Mathematics::Metric Geometry ,Polar ,010307 mathematical physics ,Orthogonal matrix ,0101 mathematics ,Isoperimetric inequality ,Mathematics - Abstract
In this paper, we propose and study the polar Orlicz-Minkowski problems: under what conditions on a nonzero finite measure $\mu$ and a continuous function $\varphi:(0,\infty)\rightarrow(0,\infty)$, there exists a convex body $K\in\mathcal{K}_0$ such that $K$ is an optimizer of the following optimization problems: \begin{equation*} \inf/\sup \bigg\{\int_{S^{n-1}}\varphi\big( h_L \big) \,d \mu: L \in \mathcal{K}_{0} \ \text{and}\ |L^\circ|=\omega_{n}\bigg\}. \end{equation*} The solvability of the polar Orlicz-Minkowski problems is discussed under different conditions. In particular, under certain conditions on $\varphi,$ the existence of a solution is proved for a nonzero finite measure $\mu$ on $S^{n-1}$ which is not concentrated on any hemisphere of $S^{n-1}.$ Another part of this paper deals with the $p$-capacitary Orlicz-Petty bodies. In particular, the existence of the $p$-capacitary Orlicz-Petty bodies is established and the continuity of the $p$-capacitary Orlicz-Petty bodies is proved., Comment: This paper has been accepted by Indiana University Mathematics Journal
- Published
- 2020
46. Archimedean non-vanishing, cohomological test vectors, and standard L-functions of $${\mathrm {GL}}_{2n}$$: real case
- Author
-
Cheng Chen, Fangyang Tian, Dihua Jiang, and Bingchen Lin
- Subjects
Pure mathematics ,Mathematics - Number Theory ,General Mathematics ,media_common.quotation_subject ,010102 general mathematics ,Linear model ,Structure (category theory) ,22E45 (Primary), 11F67 (Secondary) ,Type (model theory) ,Lambda ,Infinity ,01 natural sciences ,Invariant theory ,Linear form ,0103 physical sciences ,FOS: Mathematics ,Number Theory (math.NT) ,010307 mathematical physics ,Representation Theory (math.RT) ,0101 mathematics ,Mathematics - Representation Theory ,Mathematics ,media_common - Abstract
The standard $L$-functions of $\mathrm{GL}_{2n}$ expressed in terms of the Friedberg-Jacquet global zeta integrals have better structure for arithmetic applications, due to the relation of the linear periods with the modular symbols. The most technical obstacles towards such arithmetic applications are (1) non-vanishing of modular symbols at infinity and (2) the existance or construction of uniform cohomological test vectors. Problem (1) is also called the non-vanishing hypothesis at infinity, which was proved by Binyong Sun, by establishing the existence of certain cohomological test vectors. In this paper, we explicitly construct an archimedean local integral that produces a new type of a twisted linear functional $\Lambda_{s,\chi}$, which, when evaluated with our explicitly constructed cohomological vector, is equal to the local twisted standard $L$-function $L(s,\pi\otimes\chi)$ as a meromorphic function of $s\in \mathbb{C}$. With the relations between linear models and Shalika models, we establish (1) with an explicitly constructed cohomological vector, and hence recovers a non-vanishing result of Binyong Sun via a completely different method. Our main result indicates a complete solution to (2), which will be presented in a paper of Dihua Jiang, Binyong Sun and Fangyang Tian with full details and with applications to the global period relations for the twisted standard $L$-functions at critical places., Comment: 39 pages. The current version of this paper is significantly shorter than the previous one, as the first author pointed out a conceptual intepretation of construction of cohomological test vector in the old version of this paper. Section 4 is completely rewritten. Also fix some inaccuracies
- Published
- 2019
47. A Polynomial Sieve and Sums of Deligne Type
- Author
-
Dante Bonolis
- Subjects
Polynomial (hyperelastic model) ,Mathematics - Number Theory ,Degree (graph theory) ,General Mathematics ,Sieve (category theory) ,010102 general mathematics ,Multiplicative function ,Type (model theory) ,01 natural sciences ,Combinatorics ,Hypersurface ,Homogeneous polynomial ,0103 physical sciences ,FOS: Mathematics ,Number Theory (math.NT) ,010307 mathematical physics ,0101 mathematics ,Mathematics - Abstract
Let $f\in\mathbb{Z}[T]$ be any polynomial of degree $d>1$ and $F\in\mathbb{Z}[X_{0},...,X_{n}]$ an irreducible homogeneous polynomial of degree $e>1$ such that the projective hypersurface $V(F)$ is smooth. In this paper we give a bound for \[ N(f,F,B):=|\{\textbf{x}\in\mathbb{Z}^{n+1}:\max_{0\leq i\leq n}|x_{i}|\leq B,\exists t\in\mathbb{Z}\text{ such that }f(t)=F(\textbf{x})\}|, \] To do this, we introduce a generalization of the Heath-Brown and Munshi's power sieve and we extend two results by Deligne and Katz on estimates for additive and multiplicative characters in many variables., Theorem 1 has been improved. The paper has been reorganized to improve the exposition
- Published
- 2019
48. On Some Features of the Numerical Solving of Coefficient Inverse Problems for an Equation of the Reaction-Diffusion-Advection-Type with Data on the Position of a Reaction Front
- Author
-
Alexandr Gorbachev, Raul Argun, Dmitry Lukyanenko, and Maxim A. Shishlenin
- Subjects
Asymptotic analysis ,Series (mathematics) ,Differential equation ,General Mathematics ,inverse problem with data on the position of a reaction front ,Type (model theory) ,Inverse problem ,coefficient inverse problem ,reaction–diffusion equation ,Nonlinear system ,Position (vector) ,Reaction–diffusion system ,Computer Science (miscellaneous) ,QA1-939 ,Applied mathematics ,singularly perturbed problem ,Engineering (miscellaneous) ,blow-up ,Mathematics ,reaction–diffusion–advection equation - Abstract
The work continues a series of articles devoted to the peculiarities of solving coefficient inverse problems for nonlinear singularly perturbed equations of the reaction-diffusion-advection-type with data on the position of the reaction front. In this paper, we place the emphasis on some problems of the numerical solving process. One of the approaches to solving inverse problems of the class under consideration is the use of methods of asymptotic analysis. These methods, under certain conditions, make it possible to construct the so-called reduced formulation of the inverse problem. Usually, a differential equation in this formulation has a lower dimension/order with respect to the differential equation, which is included in the full statement of the inverse problem. In this paper, we consider an example that leads to a reduced formulation of the problem, the solving of which is no less a time-consuming procedure in comparison with the numerical solving of the problem in the full statement. In particular, to obtain an approximate numerical solution, one has to use the methods of the numerical diagnostics of the solution’s blow-up. Thus, it is demonstrated that the possibility of constructing a reduced formulation of the inverse problem does not guarantee its more efficient solving. Moreover, the possibility of constructing a reduced formulation of the problem does not guarantee the existence of an approximate solution that is qualitatively comparable to the true one. In previous works of the authors, it was shown that an acceptable approximate solution can be obtained only for sufficiently small values of the singular parameter included in the full statement of the problem. However, the question of how to proceed if the singular parameter is not small enough remains open. The work also gives an answer to this question.
- Published
- 2021
49. Preventive Maintenance of the k-out-of-n System with Respect to Cost-Type Criterion
- Author
-
Olga Kochueva, Vladimir Rykov, and Yaroslav Rykov
- Subjects
Mathematical optimization ,Current (mathematics) ,Computer science ,General Mathematics ,Decision theory ,Type (model theory) ,Lifetime distribution ,Preventive maintenance ,lifetime distribution ,Order (business) ,k-out-of-n: F system ,Ordered statistics ,preventive maintenance ,reliability function ,Computer Science (miscellaneous) ,QA1-939 ,Sensitivity (control systems) ,Engineering (miscellaneous) ,cost-type optimization criterion ,Mathematics - Abstract
In a previous paper, the problem of how the preventive maintenance organization for the k-out-of-n: F system could be used, in order to maximize system availability, was considered. The current paper continues these investigations using a different optimization criterion. The proposed approach is based on decision making theory for regenerative processes. We propose a general procedure for comparing different preventive maintenance strategies based on the ordered statistics distributions, aiming to choose the best one with respect to cost-type criterion. The lifetime distributions of system units are usually unknown and only one or two of their moments are available. For this reason, we pay special attention to the sensitivity analysis of decision making about preventive maintenance, taking into account the shape of the system unit lifetime distributions. A numerical study of two examples based on a real-world system illustrates the results of the proposed approach.
- Published
- 2021
50. Lie-Group Modeling and Numerical Simulation of a Helicopter
- Author
-
Simone Fiori and Alessandro Tarsi
- Subjects
Computer simulation ,Series (mathematics) ,Computer science ,General Mathematics ,Numerical analysis ,Motion (geometry) ,Lie group ,Control engineering ,ComputerApplications_COMPUTERSINOTHERSYSTEMS ,Type (model theory) ,Space (mathematics) ,Object (computer science) ,helicopter model ,Computer Science::Robotics ,non-conservative dynamical system ,Computer Science (miscellaneous) ,QA1-939 ,Lagrange–d’Alembert principle ,Engineering (miscellaneous) ,Euler–Poincaré equation ,Mathematics - Abstract
Helicopters are extraordinarily complex mechanisms. Such complexity makes it difficult to model, simulate and pilot a helicopter. The present paper proposes a mathematical model of a fantail helicopter type based on Lie-group theory. The present paper first recalls the Lagrange–d’Alembert–Pontryagin principle to describe the dynamics of a multi-part object, and subsequently applies such principle to describe the motion of a helicopter in space. A good part of the paper is devoted to the numerical simulation of the motion of a helicopter, which was obtained through a dedicated numerical method. Numerical simulation was based on a series of values for the many parameters involved in the mathematical model carefully inferred from the available technical literature.
- Published
- 2021
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