6,639 results
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2. 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
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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.
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- 2018
3. Corrigendum to our paper : How Expressions can code for Automata
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Sylvain Lombardy, Jacques Sakarovitch, Laboratoire d'Informatique Gaspard-Monge (LIGM), Centre National de la Recherche Scientifique (CNRS)-Fédération de Recherche Bézout-ESIEE Paris-École des Ponts ParisTech (ENPC)-Université Paris-Est Marne-la-Vallée (UPEM), Laboratoire Traitement et Communication de l'Information (LTCI), Télécom ParisTech-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS), and Université Paris-Est Marne-la-Vallée (UPEM)-École des Ponts ParisTech (ENPC)-ESIEE Paris-Fédération de Recherche Bézout-Centre National de la Recherche Scientifique (CNRS)
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TheoryofComputation_COMPUTATIONBYABSTRACTDEVICES ,Powerset construction ,General Mathematics ,010102 general mathematics ,Continuous automaton ,Timed automaton ,Pushdown automaton ,Büchi automaton ,0102 computer and information sciences ,16. Peace & justice ,Nonlinear Sciences::Cellular Automata and Lattice Gases ,01 natural sciences ,Computer Science Applications ,Algebra ,TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES ,010201 computation theory & mathematics ,Deterministic automaton ,[INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering ,Probabilistic automaton ,Two-way deterministic finite automaton ,0101 mathematics ,Algorithm ,Software ,Computer Science::Formal Languages and Automata Theory ,Mathematics - Abstract
International audience; In a previous paper, we have described the construction of an automaton from a rational expression which has the property that the automaton built from an expression which is itself computed from a co-deterministic automaton by the state elimination method is co-deterministic. It turned out that the definition on which the construction is based was inappropriate, and thus the proof of the property was flawed. We give here the correct definition of the broken derived terms of an expression which allow to define the automaton and the detailed full proof of the property.
- Published
- 2010
4. Rebuttal of Donnelly's paper on the spectral gap
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Antoine Henrot, Mark S. Ashbaugh, Richard S. Laugesen, Department of Mathematics, University of Missouri Columbia, University of Missouri [Columbia] (Mizzou), University of Missouri System-University of Missouri System, Institut Élie Cartan de Nancy (IECN), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS), Robust control of infinite dimensional systems and applications (CORIDA), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire de Mathématiques et Applications de Metz (LMAM), Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria), Department of Mathematics [Urbana], University of Illinois at Urbana-Champaign [Urbana], University of Illinois System-University of Illinois System, CORIDA, and Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Inria Nancy - Grand Est
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Discrete mathematics ,Sequence ,Conjecture ,General Mathematics ,010102 general mathematics ,Mathematics::History and Overview ,Mathematics::Spectral Theory ,01 natural sciences ,Domain (mathematical analysis) ,Computer Science::Computers and Society ,010101 applied mathematics ,symbols.namesake ,Physics::Popular Physics ,Dirichlet boundary condition ,Euclidean geometry ,symbols ,Calculus ,Convex body ,Quantitative Biology::Populations and Evolution ,[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] ,Spectral gap ,0101 mathematics ,Mathematics ,Unit interval - Abstract
The spectral gap conjecture of M. van den Berg [2, formula (65)] asserts that λ2 − λ1 ≥ 3π for all convex euclidean domains of diameter 1, where λ1 and λ2 denote the first two eigenvalues of the Dirichlet Laplacian. Notice that equality holds for the 1-dimensional unit interval, which can be regarded also as a degenerate n-dimensional rectangular box. The gap estimate is conjectured to hold more generally for Schrodinger operators with convex potentials, under Dirichlet boundary conditions; see the work of S.-T. Yau and collaborators [9, 11]. This Schrodinger gap conjecture was proved some time ago in 1 dimension by R. Lavine [8], and more recently in all dimensions by B. Andrews and J. Clutterbuck [1]. The proof in this journal by H. Donnelly [3] of the original gap conjecture in 2 dimensions (for the Dirichlet Laplacian with zero potential) is not correct. The Editors of Mathematische Zeitschrift have asked us to describe the flaws in the proof, in order to clarify the state of the literature. Donnelly’s approach to the problem is a natural one: first perform a shape optimization to rule out a non-degenerate minimizing domain, and then analyze the spectral gap for a sequence of domains degenerating to an interval, with the help of results by D. Jerison [5]. (For some history on this approach, and on the gap conjecture more generally, see the report on the AIM meeting “Low Eigenvalues of Laplace and Schrodinger Operators” [10], especially page 12 of the open problems list.) The error lies in the proof of the shape optimization step, as we now explain. Donnelly wishes to prove that no minimizing domain can exist for
- Published
- 2011
5. Addendum to the paper 'A note on weighted Bergman spaces and the Cesàro operator'
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Stevo Stević and Der-Chen Chang
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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. (CMMSE2018 paper) Solving the random Pielou logistic equation with the random variable transformation technique: Theory and applications
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Ana Navarro-Quiles, M.-D. Roselló, José Vicente Romero, and Juan Carlos Cortés
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education.field_of_study ,Differential equation ,Stochastic process ,General Mathematics ,Computation ,010102 general mathematics ,Population ,General Engineering ,Probability density function ,01 natural sciences ,010101 applied mathematics ,Transformation (function) ,Applied mathematics ,0101 mathematics ,Logistic function ,education ,Random variable ,Mathematics - Abstract
The study of the dynamics of the size of a population via mathematical modelling is a problem of interest and widely studied. Traditionally, continuous deterministic methods based on differential equations have been used to deal with this problem. However discrete versions of some models are also available and sometimes more adequate. In this paper, we randomize the Pielou logistic equation in order to include the inherent uncertainty in modelling. Taking advantage of the method of transformation of random variables, we provide a full probabilistic description to the randomized Pielou logistic model via the computation of the probability density functions of the solution stochastic process, the steady state and the time until a certain level of population is reached. The theoretical results are illustrated by means of two examples, the first one consists of a numerical experiment and the second one shows an application to study the diffusion of a technology using real data.
- Full Text
- View/download PDF
7. Improving the performance of deep learning models using statistical features: The case study of COVID‐19 forecasting
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Hossein Abbasimehr, Reza Paki, and Aram Bahrini
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2019-20 coronavirus outbreak ,Coronavirus disease 2019 (COVID-19) ,62‐07 ,General Mathematics ,Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) ,Context (language use) ,97r40 ,Machine learning ,computer.software_genre ,01 natural sciences ,Convolutional neural network ,Special Issue Paper ,0101 mathematics ,Combined method ,Mathematics ,Special Issue Papers ,business.industry ,Deep learning ,010102 general mathematics ,General Engineering ,deep learning ,COVID‐19 pandemic ,010101 applied mathematics ,hybrid methods ,Memory model ,Artificial intelligence ,business ,computer ,statistical features - Abstract
COVID-19 pandemic has affected all aspects of people's lives and disrupted the economy. Forecasting the number of cases infected with this virus can help authorities make accurate decisions on the interventions that must be implemented to control the pandemic. Investigation of the studies on COVID-19 forecasting indicates that various techniques such as statistical, mathematical, and machine and deep learning have been utilized. Although deep learning models have shown promising results in this context, their performance can be improved using auxiliary features. Therefore, in this study, we propose two hybrid deep learning methods that utilize the statistical features as auxiliary inputs and associate them with their main input. Specifically, we design a hybrid method of the multihead attention mechanism and the statistical features (ATT_FE) and a combined method of convolutional neural network and the statistical features (CNN_FE) and apply them to COVID-19 data of 10 countries with the highest number of confirmed cases. The results of experiments indicate that the hybrid models outperform their conventional counterparts in terms of performance measures. The experiments also demonstrate the superiority of the hybrid ATT_FE method over the long short-term memory model.
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- 2021
8. Bounds on entanglement dimensions and quantum graph parameters via noncommutative polynomial optimization
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Sander Gribling, Monique Laurent, David de Laat, Econometrics and Operations Research, and Research Group: Operations Research
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Optimization problem ,General Mathematics ,Quantum correlation ,Dimension (graph theory) ,quantum graph parameters ,FOS: Physical sciences ,Quantum entanglement ,90C22 ,Squashed entanglement ,01 natural sciences ,90C26 ,81P40 ,81P45 ,0103 physical sciences ,polynomial optimization ,FOS: Mathematics ,0101 mathematics ,010306 general physics ,Mathematics - Optimization and Control ,Mathematics ,Discrete mathematics ,Semidefinite programming ,Quantum Physics ,Quantum discord ,Full Length Paper ,quantum correlations ,010102 general mathematics ,90C30 ,TheoryofComputation_GENERAL ,16. Peace & justice ,entanglement dimension ,05C15 ,Optimization and Control (math.OC) ,Quantum graph ,Quantum Physics (quant-ph) ,Software - Abstract
In this paper we study bipartite quantum correlations using techniques from tracial noncommutative polynomial optimization. We construct a hierarchy of semidefinite programming lower bounds on the minimal entanglement dimension of a bipartite correlation. This hierarchy converges to a new parameter: the minimal average entanglement dimension, which measures the amount of entanglement needed to reproduce a quantum correlation when access to shared randomness is free. For synchronous correlations, we show a correspondence between the minimal entanglement dimension and the completely positive semidefinite rank of an associated matrix. We then study optimization over the set of synchronous correlations by investigating quantum graph parameters. We unify existing bounds on the quantum chromatic number and the quantum stability number by placing them in the framework of tracial optimization. In particular, we show that the projective packing number, the projective rank, and the tracial rank arise naturally when considering tracial analogues of the Lasserre hierarchy for the stability and chromatic number of a graph. We also introduce semidefinite programming hierarchies converging to the commuting quantum chromatic number and commuting quantum stability number., Comment: 26 pages
- Published
- 2018
9. Improved bounds for solutions of ϕ-Laplacians
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Jorge Huentutripay and Waldo Arriagada
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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.
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- 2018
10. Derived Non-archimedean analytic Hilbert space
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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)
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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
11. Tikhonov regularization of a second order dynamical system with Hessian driven damping
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Szilárd László, Radu Ioan Boţ, and Ernö Robert Csetnek
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Hessian matrix ,General Mathematics ,0211 other engineering and technologies ,Dynamical Systems (math.DS) ,02 engineering and technology ,Dynamical system ,01 natural sciences ,Hessian-driven damping ,90C26 ,Tikhonov regularization ,symbols.namesake ,34G25, 47J25, 47H05, 90C26, 90C30, 65K10 ,Convergence (routing) ,FOS: Mathematics ,Applied mathematics ,0101 mathematics ,Mathematics - Dynamical Systems ,Mathematics - Optimization and Control ,Mathematics ,65K10 ,021103 operations research ,Full Length Paper ,47J25 ,47H05 ,010102 general mathematics ,Hilbert space ,90C30 ,Function (mathematics) ,Convex optimization ,Optimization and Control (math.OC) ,Second order dynamical system ,34G25 ,symbols ,Fast convergence methods ,Convex function ,Software - Abstract
We investigate the asymptotic properties of the trajectories generated by a second-order dynamical system with Hessian driven damping and a Tikhonov regularization term in connection with the minimization of a smooth convex function in Hilbert spaces. We obtain fast convergence results for the function values along the trajectories. The Tikhonov regularization term enables the derivation of strong convergence results of the trajectory to the minimizer of the objective function of minimum norm.
- Published
- 2020
12. The r-Hunter-Saxton equation, smooth and singular solutions and their approximation
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Colin J. Cotter, Tristan Pryer, Jacob Deasy, Cotter, Colin J [0000-0001-7962-8324], Apollo - University of Cambridge Repository, and Engineering & Physical Science Research Council (EPSRC)
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Paper ,singular solutions ,GEODESIC-FLOW ,Work (thermodynamics) ,General Mathematics ,Mathematics, Applied ,HYPERBOLIC VARIATIONAL EQUATION ,Mathematics::Analysis of PDEs ,General Physics and Astronomy ,FOS: Physical sciences ,01 natural sciences ,Piecewise linear function ,37K06 ,Mathematics - Analysis of PDEs ,0102 Applied Mathematics ,37K05 ,FOS: Mathematics ,Hunter–Saxton equation ,Applied mathematics ,Initial value problem ,Lie symmetries ,0101 mathematics ,nlin.SI ,math.AP ,Mathematical Physics ,Mathematics ,Science & Technology ,Nonlinear Sciences - Exactly Solvable and Integrable Systems ,Physics ,Applied Mathematics ,010102 general mathematics ,4901 Applied Mathematics ,4904 Pure Mathematics ,Statistical and Nonlinear Physics ,Action (physics) ,Symmetry (physics) ,Physics, Mathematical ,010101 applied mathematics ,35Q53 ,Nonlinear Sciences::Exactly Solvable and Integrable Systems ,nonlinear PDEs ,Physical Sciences ,49 Mathematical Sciences ,37K58 ,Exactly Solvable and Integrable Systems (nlin.SI) ,Analysis of PDEs (math.AP) - Abstract
In this work we introduce the r-Hunter-Saxton equation, a generalisation of the Hunter-Saxton equation arising as extremals of an action principle posed in L_r. We characterise solutions to the Cauchy problem, quantifying the blow-up time and studying various symmetry reductions. We construct piecewise linear functions and show that they are weak solutions to the r-Hunter-Saxton equation., Revised after referee comments
- Published
- 2019
13. A note on gonality of curves on general hypersurfaces
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Flaminio Flamini, Paola Supino, Ciro Ciliberto, Francesco Bastianelli, Bastianelli, Francesco, Ciliberto, Ciro, Flamini, Flaminio, and Supino, Paola
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Series (mathematics) ,Degree (graph theory) ,family of curves ,General Mathematics ,010102 general mathematics ,Short paper ,Birational geometry ,gonality of curves, projective hypersurfaces ,01 natural sciences ,Hypersurfaces ,Combinatorics ,Mathematics::Algebraic Geometry ,Hypersurface ,Product (mathematics) ,0103 physical sciences ,Hypersurfaces, family of curves, gonality ,010307 mathematical physics ,gonality ,Settore MAT/03 - Geometria ,0101 mathematics ,Mathematics - Abstract
This short paper concerns the existence of curves with low gonality on smooth hypersurfaces $$X\subset \mathbb {P}^{n+1}$$ . After reviewing a series of results on this topic, we report on a recent progress we achieved as a product of the Workshop Birational geometry of surfaces, held at University of Rome “Tor Vergata” on January 11th–15th, 2016. In particular, we obtained that if $$X\subset \mathbb {P}^{n+1}$$ is a very general hypersurface of degree $$d\geqslant 2n+2$$ , the least gonality of a curve $$C\subset X$$ passing through a general point of X is $$\mathrm {gon}(C)=d-\left\lfloor \frac{\sqrt{16n+1}-1}{2}\right\rfloor $$ , apart from some exceptions we list.
- Published
- 2018
14. 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)
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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
15. Halfspace type Theorems for Self-Shrinkers
- Author
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Marcos P. Cavalcante and José M. Espinar
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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
16. 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
17. AN ALMOST SCHUR THEOREM ON 4-DIMENSIONAL MANIFOLDS
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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)
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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
18. 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
19. Analyzing the Weyl Construction for Dynamical Cartan Subalgebras
- Author
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Elizabeth Gillaspy, Anna Duwenig, and Rachael Norton
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General Mathematics ,01 natural sciences ,Section (fiber bundle) ,Combinatorics ,Mathematics::K-Theory and Homology ,Mathematics::Category Theory ,Mathematics::Quantum Algebra ,46L05, 22D25, 22A22 ,0103 physical sciences ,FOS: Mathematics ,0101 mathematics ,Twist ,Operator Algebras (math.OA) ,Mathematics::Representation Theory ,Quotient ,Mathematics ,Science & Technology ,Mathematics::Operator Algebras ,010102 general mathematics ,Spectrum (functional analysis) ,Mathematics - Operator Algebras ,Cartan subalgebra ,C-ASTERISK-ALGEBRAS ,Physical Sciences ,010307 mathematical physics ,EQUIVALENCE - Abstract
When the reduced twisted $C^*$-algebra $C^*_r(\mathcal{G}, c)$ of a non-principal groupoid $\mathcal{G}$ admits a Cartan subalgebra, Renault's work on Cartan subalgebras implies the existence of another groupoid description of $C^*_r(\mathcal{G}, c)$. In an earlier paper, joint with Reznikoff and Wright, we identified situations where such a Cartan subalgebra arises from a subgroupoid $\mathcal{S}$ of $\mathcal{G}$. In this paper, we study the relationship between the original groupoids $\mathcal{S}, \mathcal{G}$ and the Weyl groupoid and twist associated to the Cartan pair. We first identify the spectrum $\mathfrak{B}$ of the Cartan subalgebra $C^*_r(\mathcal{S}, c)$. We then show that the quotient groupoid $\mathcal{G}/\mathcal{S}$ acts on $\mathfrak{B}$, and that the corresponding action groupoid is exactly the Weyl groupoid of the Cartan pair. Lastly we show that, if the quotient map $\mathcal{G}\to\mathcal{G}/\mathcal{S}$ admits a continuous section, then the Weyl twist is also given by an explicit continuous $2$-cocycle on $\mathcal{G}/\mathcal{S} \ltimes \mathfrak{B}$., 32 pages
- Published
- 2022
20. 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
21. Generalization of uniqueness and value sharing of meromorphic functions concerning differential polynomials
- Author
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Ramya Maligi and Harina P. Waghamore
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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
22. (p,Q) systems with critical singular exponential nonlinearities in the Heisenberg group
- Author
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Patrizia Pucci and Letizia Temperini
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General Mathematics ,variational methods ,35b08 ,nonlinear system ,01 natural sciences ,(p ,Heisenberg group ,0101 mathematics ,Q system ,Geometry and topology ,Mathematics ,Mathematical physics ,Q) Laplacian ,35b33 ,lcsh:Mathematics ,010102 general mathematics ,heisenberg group ,(p,q) laplacian ,35j50 ,lcsh:QA1-939 ,Exponential function ,010101 applied mathematics ,Nonlinear system ,35j47 ,(p,Q) Laplacian, Nonlinear system, Critical exponential nonlinearities, Variational methods, Heisenberg group ,35b09 ,critical exponential nonlinearities ,35r03 - Abstract
The paper deals with the existence of solutions for(p,Q)(p,Q)coupled elliptic systems in the Heisenberg group, with critical exponential growth at infinity and singular behavior at the origin. We derive existence of nonnegative solutions with both components nontrivial and different, that is solving an actual system, which does not reduce into an equation. The main features and novelties of the paper are the presence of a general coupled critical exponential term of the Trudinger-Moser type and the fact that the system is set inℍn{{\mathbb{H}}}^{n}.
- Published
- 2020
23. Some asymptotic properties of kernel regression estimators of the mode for stationary and ergodic continuous time processes
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Salim Bouzebda, Sultana Didi, Laboratoire de Mathématiques Appliquées de Compiègne (LMAC), Université de Technologie de Compiègne (UTC), and Qassim University [Kingdom of Saudi Arabia]
- Subjects
60A10 ,Measurable function ,General Mathematics ,Context (language use) ,[MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA] ,Conditional mode ,01 natural sciences ,Article ,Combinatorics ,Mixing (mathematics) ,Martingale difference arrays ,62G08 ,60F05 ,62G07 ,Ergodic theory ,Conditional density ,62G05 ,60E05 ,0101 mathematics ,ComputingMilieux_MISCELLANEOUS ,Strong consistency ,Mathematics ,62E20 ,Smoothness (probability theory) ,Kernel (set theory) ,010102 general mathematics ,Ergodicity ,Confidence regions ,[STAT.TH]Statistics [stat]/Statistics Theory [stat.TH] ,Rate of convergence ,010101 applied mathematics ,[MATH.MATH-PR]Mathematics [math]/Probability [math.PR] ,Nadaraya–Watson estimators ,Continuous time processes ,Ergodic processes ,Kernel regression ,Kernel estimate ,Prediction - Abstract
In the present paper, we consider the nonparametric regression model with random design based on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\mathbf{X}_\mathrm{t},\mathbf{Y}_\mathrm{t})_{\mathrm{t}\ge 0}$$\end{document}(Xt,Yt)t≥0 a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {R}^{d}\times \mathbb {R}^{q}$$\end{document}Rd×Rq-valued strictly stationary and ergodic continuous time process, where the regression function is given by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m(\mathbf{x},\psi ) = \mathbb {E}(\psi (\mathbf{Y}) \mid \mathbf{X} = \mathbf{x}))$$\end{document}m(x,ψ)=E(ψ(Y)∣X=x)), for a measurable function \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\psi : \mathbb {R}^{q} \rightarrow \mathbb {R}$$\end{document}ψ:Rq→R. We focus on the estimation of the location \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varvec{\Theta }}$$\end{document}Θ (mode) of a unique maximum of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m(\cdot , \psi )$$\end{document}m(·,ψ) by the location \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \widehat{{\varvec{\Theta }}}_\mathrm{T}$$\end{document}Θ^T of a maximum of the Nadaraya–Watson kernel estimator \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\widehat{m}_\mathrm{T}(\cdot , \psi )$$\end{document}m^T(·,ψ) for the curve \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m(\cdot , \psi )$$\end{document}m(·,ψ). Within this context, we obtain the consistency with rate and the asymptotic normality results for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \widehat{{\varvec{\Theta }}}_\mathrm{T}$$\end{document}Θ^T under mild local smoothness assumptions on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m(\cdot , \psi )$$\end{document}m(·,ψ) and the design density \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f(\cdot )$$\end{document}f(·) of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf{X}$$\end{document}X. Beyond ergodicity, any other assumption is imposed on the data. This paper extends the scope of some previous results established under the mixing condition. The usefulness of our results will be illustrated in the construction of confidence regions.
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- 2020
24. Fixed point results for multivalued mappings of Ćirić type via F-contractions on quasi metric spaces
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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
25. Explicit order 3/2 Runge-Kutta method for numerical solutions of stochastic differential equations by using Itô-Taylor expansion
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Yazid Alhojilan
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itô-taylor expansion ,General Mathematics ,lcsh:Mathematics ,010102 general mathematics ,lcsh:QA1-939 ,01 natural sciences ,stochastic differential equations ,secondary 65c30 ,010104 statistics & probability ,Stochastic differential equation ,Runge–Kutta methods ,symbols.namesake ,pathwise approximation ,Taylor series ,symbols ,runge-kutta method ,Applied mathematics ,Order (group theory) ,primary 60h35 ,0101 mathematics ,Mathematics - Abstract
This paper aims to present a new pathwise approximation method, which gives approximate solutions of order $\begin{array}{} \displaystyle \frac{3}{2} \end{array}$ for stochastic differential equations (SDEs) driven by multidimensional Brownian motions. The new method, which assumes the diffusion matrix non-degeneracy, employs the Runge-Kutta method and uses the Itô-Taylor expansion, but the generating of the approximation of the expansion is carried out as a whole rather than individual terms. The new idea we applied in this paper is to replace the iterated stochastic integrals Iα by random variables, so implementing this scheme does not require the computation of the iterated stochastic integrals Iα. Then, using a coupling which can be found by a technique from optimal transport theory would give a good approximation in a mean square. The results of implementing this new scheme by MATLAB confirms the validity of the method.
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- 2019
26. Linear representation of a graph
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Eduardo Peña Cabrera, José A. González Campos, Eduardo Montenegro, and Ronald A. Manríquez Peñafiel
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Abstract algebra ,Linear representation ,Group (mathematics) ,General Mathematics ,lcsh:Mathematics ,010102 general mathematics ,Order (ring theory) ,lcsh:QA1-939 ,01 natural sciences ,Graph ,law.invention ,010101 applied mathematics ,Combinatorics ,Invertible matrix ,Simple (abstract algebra) ,law ,0101 mathematics ,Graphs ,Mathematics ,MathematicsofComputing_DISCRETEMATHEMATICS - Abstract
In this paper the linear representation of a graph is defined. A linear representation of a graph is a subgroup of $GL(p,\mathbb{R})$, the group of invertible matrices of order $ p $ and real coefficients. It will be demonstrated that every graph admits a linear representation. In this paper, simple and finite graphs will be used, framed in the graphs theory's area
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- 2019
27. The moduli space of matroids
- Author
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Oliver Lorscheid, Matthew Baker, and Dynamical Systems, Geometry & Mathematical Physics
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Mathematics::Combinatorics ,Functor ,F-geometry ,Group (mathematics) ,General Mathematics ,010102 general mathematics ,0102 computer and information sciences ,Tracts ,01 natural sciences ,Matroid ,Moduli space ,Combinatorics ,Matroids ,Mathematics - Algebraic Geometry ,Morphism ,010201 computation theory & mathematics ,Scheme (mathematics) ,Blueprints ,FOS: Mathematics ,Isomorphism ,0101 mathematics ,Algebraic Geometry (math.AG) ,Mathematics ,Initial and terminal objects - Abstract
In the first part of the paper, we clarify the connections between several algebraic objects appearing in matroid theory: both partial fields and hyperfields are fuzzy rings, fuzzy rings are tracts, and these relations are compatible with the respective matroid theories. Moreover, fuzzy rings are ordered blueprints and lie in the intersection of tracts with ordered blueprints; we call the objects of this intersection pastures. In the second part, we construct moduli spaces for matroids over pastures. We show that, for any non-empty finite set $E$, the functor taking a pasture $F$ to the set of isomorphism classes of rank-$r$ $F$-matroids on $E$ is representable by an ordered blue scheme $Mat(r,E)$, the moduli space of rank-$r$ matroids on $E$. In the third part, we draw conclusions on matroid theory. A classical rank-$r$ matroid $M$ on $E$ corresponds to a $\mathbb{K}$-valued point of $Mat(r,E)$ where $\mathbb{K}$ is the Krasner hyperfield. Such a point defines a residue pasture $k_M$, which we call the universal pasture of $M$. We show that for every pasture $F$, morphisms $k_M\to F$ are canonically in bijection with $F$-matroid structures on $M$. An analogous weak universal pasture $k_M^w$ classifies weak $F$-matroid structures on $M$. The unit group of $k_M^w$ can be canonically identified with the Tutte group of $M$. We call the sub-pasture $k_M^f$ of $k_M^w$ generated by ``cross-ratios' the foundation of $M$,. It parametrizes rescaling classes of weak $F$-matroid structures on $M$, and its unit group is coincides with the inner Tutte group of $M$. We show that a matroid $M$ is regular if and only if its foundation is the regular partial field, and a non-regular matroid $M$ is binary if and only if its foundation is the field with two elements. This yields a new proof of the fact that a matroid is regular if and only if it is both binary and orientable., 85 pages; some additional material, e.g. a new section 5.6; the terminology has been adapted to the usage in follow-up papers
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- 2021
28. A free boundary problem arising from branching Brownian motion with selection
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Sarah Penington, James Nolen, Éric Brunet, and Julien Berestycki
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Mathematics(all) ,Interacting particle system ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,Mathematical analysis ,Probability (math.PR) ,35R35, 35K55, 82C22 ,Boundary (topology) ,01 natural sciences ,Parabolic partial differential equation ,Constraint (information theory) ,Mathematics - Analysis of PDEs ,Free boundary problem ,FOS: Mathematics ,Uniqueness ,Limit (mathematics) ,0101 mathematics ,Mathematics - Probability ,Brownian motion ,Mathematics ,Analysis of PDEs (math.AP) - Abstract
We study a free boundary problem for a parabolic partial differential equation in which the solution is coupled to the moving boundary through an integral constraint. The problem arises as the hydrodynamic limit of an interacting particle system involving branching Brownian motion with selection, the so-called Brownian bees model which is studied in a companion paper. In this paper we prove existence and uniqueness of the solution to the free boundary problem, and we characterise the behaviour of the solution in the large time limit., Comment: 53 pages
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- 2021
29. McKay Quivers and Lusztig Algebras of Some Finite Groups
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Ragnar-Olaf Buchweitz, Matthew Lewis, Colin Ingalls, and Eleonore Faber
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General Mathematics ,Field (mathematics) ,Group Theory (math.GR) ,01 natural sciences ,Combinatorics ,Elementary algebra ,Symmetric group ,FOS: Mathematics ,Mathematics - Combinatorics ,0101 mathematics ,Representation Theory (math.RT) ,Mathematics::Representation Theory ,Mathematics ,Finite group ,05E10 16G20 16S35 16S37 20F55 20C30 ,010102 general mathematics ,Quiver ,Mathematics - Rings and Algebras ,010101 applied mathematics ,Clifford theory ,Rings and Algebras (math.RA) ,Combinatorics (math.CO) ,Mathematics - Group Theory ,Mathematics - Representation Theory ,Vector space ,Group ring - Abstract
We are interested in the McKay quiver $\Gamma(G)$ and skew group rings $A*G$, where $G$ is a finite subgroup of $\mathrm{GL}(V)$, where $V$ is a finite dimensional vector space over a field $K$, and $A$ is a $K-G$-algebra. These skew group rings appear in Auslander's version of the McKay correspondence. In the first part of this paper we consider complex reflection groups $G \subseteq \mathrm{GL}(V)$ and find a combinatorial method, making use of Young diagrams, to construct the McKay quivers for the groups $G(r,p,n)$. We first look at the case $G(1,1,n)$, which is isomorphic to the symmetric group $S_n$, followed by $G(r,1,n)$ for $r >1$. Then, using Clifford theory, we can determine the McKay quiver for any $G(r,p,n)$ and thus for all finite irreducible complex reflection groups up to finitely many exceptions. In the second part of the paper we consider a more conceptual approach to McKay quivers of arbitrary finite groups: we define the Lusztig algebra $\widetilde A(G)$ of a finite group $G \subseteq \mathrm{GL}(V)$, which is Morita equivalent to the skew group ring $A*G$. This description gives us an embedding of the basic algebra Morita equivalent to $A*G$ into a matrix algebra over $A$., Comment: v2: minor revision, final version to appear in Algebr. Represent. Theory
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- 2021
30. Stability Analysis and Existence of Solutions for a Modified SIRD Model of COVID-19 with Fractional Derivatives
- Author
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Farid Nouioua, Nacereddine Hammami, Bilal Basti, Noureddine Benhamidouche, Rabah Djemiat, and Imadeddine Berrabah
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Physics and Astronomy (miscellaneous) ,Coronavirus disease 2019 (COVID-19) ,General Mathematics ,Population ,Fixed-point theorem ,0102 computer and information sciences ,Stability result ,system ,01 natural sciences ,Stability (probability) ,Hadamard transform ,QA1-939 ,Computer Science (miscellaneous) ,Applied mathematics ,Quantitative Biology::Populations and Evolution ,Uniqueness ,0101 mathematics ,education ,Mathematics ,education.field_of_study ,pandemic ,010102 general mathematics ,existence ,COVID-19 ,fractional derivative ,uniqueness ,Fractional calculus ,010201 computation theory & mathematics ,Chemistry (miscellaneous) ,SIRD model - Abstract
This paper discusses and provides some analytical studies for a modified fractional-order SIRD mathematical model of the COVID-19 epidemic in the sense of the Caputo–Katugampola fractional derivative that allows treating of the biological models of infectious diseases and unifies the Hadamard and Caputo fractional derivatives into a single form. By considering the vaccine parameter of the suspected population, we compute and derive several stability results based on some symmetrical parameters that satisfy some conditions that prevent the pandemic. The paper also investigates the problem of the existence and uniqueness of solutions for the modified SIRD model. It does so by applying the properties of Schauder’s and Banach’s fixed point theorems.
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- 2021
- Full Text
- View/download PDF
31. The universality of Hughes-free division rings
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Andrei Jaikin-Zapirain and UAM. Departamento de Matemáticas
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Group (mathematics) ,Matemáticas ,General Mathematics ,Existential quantification ,010102 general mathematics ,Universality (philosophy) ,General Physics and Astronomy ,Universal division ring of fractions ,Division (mathematics) ,01 natural sciences ,Combinatorics ,Crossed product ,0103 physical sciences ,Hughes-free division ring ,Division ring ,010307 mathematical physics ,0101 mathematics ,Locally indicable groups ,Mathematics - Abstract
Let E∗ G be a crossed product of a division ring E and a locally indicable group G. Hughes showed that up to E∗ G-isomorphism, there exists at most one Hughes-free division E∗G-ring. However, the existence of a Hughes-free division E∗ G-ring DE∗G for an arbitrary locally indicable group G is still an open question. Nevertheless, DE∗G exists, for example, if G is amenable or G is bi-orderable. In this paper we study, whether DE∗G is the universal division ring of fractions in some of these cases. In particular, we show that if G is a residually-(locally indicable and amenable) group, then there exists DE[G] and it is universal. In Appendix we give a description of DE[G] when G is a RFRS group, This paper is partially supported by the Spanish Ministry of Science and Innovation through the grant MTM2017-82690-P and the “Severo Ochoa Programme for Centres of Excellence in R&D” (CEX2019-000904-S4). I would like to thank Dawid Kielak and an anonymous referee for useful suggestions and comments
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- 2021
32. Quadruple Roman Domination in Trees
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Saeed Kosari, Jafar Amjadi, Nesa Khalili, Zheng Kou, and Guoliang Hao
- Subjects
Vertex (graph theory) ,Physics and Astronomy (miscellaneous) ,Domination analysis ,General Mathematics ,Roman domination ,MathematicsofComputing_GENERAL ,Value (computer science) ,Minimum weight ,quadruple Roman domination ,0102 computer and information sciences ,01 natural sciences ,Upper and lower bounds ,Combinatorics ,Integer ,Computer Science (miscellaneous) ,QA1-939 ,0101 mathematics ,Mathematics ,010102 general mathematics ,Function (mathematics) ,trees ,TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES ,010201 computation theory & mathematics ,Chemistry (miscellaneous) ,Symmetry (geometry) - Abstract
This paper is devoted to the study of the quadruple Roman domination in trees, and it is a contribution to the Special Issue “Theoretical computer science and discrete mathematics” of Symmetry. For any positive integer k, a [k]-Roman dominating function ([k]-RDF) of a simple graph G is a function from the vertex set V of G to the set {0,1,2,…,k+1} if for any vertex u∈V with f(u)<, k, ∑x∈N(u)∪{u}f(x)≥|{x∈N(u):f(x)≥1}|+k, where N(u) is the open neighborhood of u. The weight of a [k]-RDF is the value Σv∈Vf(v). The minimum weight of a [k]-RDF is called the [k]-Roman domination number γ[kR](G) of G. In this paper, we establish sharp upper and lower bounds on γ[4R](T) for nontrivial trees T and characterize extremal trees.
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- 2021
- Full Text
- View/download PDF
33. Approximation of Endpoints for α—Reich–Suzuki Nonexpansive Mappings in Hyperbolic Metric Spaces
- Author
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Afrah An Abdou, Izhar Uddin, and Sajan Aggarwal
- Subjects
Pure mathematics ,General Mathematics ,010102 general mathematics ,endpoint ,MathematicsofComputing_GENERAL ,Fixed-point theorem ,Fixed point ,01 natural sciences ,fixed point theorems ,010101 applied mathematics ,Metric space ,TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES ,α—Riech–Suzuki nonexpansive mapping ,Convergence (routing) ,Computer Science (miscellaneous) ,QA1-939 ,Computer Science::Programming Languages ,hyperbolic metric space ,0101 mathematics ,Engineering (miscellaneous) ,Mathematics - Abstract
The concept of an endpoint is a relatively new concept compared to the concept of a fixed point. The aim of this paper is to perform a convergence analysis of M—iteration involving α—Reich–Suzuki nonexpansive mappings. In this paper, we prove strong and Δ—convergence theorems in a hyperbolic metric space. Thus, our results generalize and improve many existing results.
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- 2021
34. Existence and U-H-R Stability of Solutions to the Implicit Nonlinear FBVP in the Variable Order Settings
- Author
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Mohammed Said Souid, Mohammed K. A. Kaabar, Zailan Siri, Shahram Rezapour, Francisco Martínez, Sina Etemad, and Ahmed Refice
- Subjects
Ulam–Hyers–Rassias stability ,Mathematics::Functional Analysis ,General Mathematics ,010102 general mathematics ,Fixed-point theorem ,variable-order operators ,implicit problem ,01 natural sciences ,Stability (probability) ,fixed point theorems ,010101 applied mathematics ,Nonlinear fractional differential equations ,piecewise constant functions ,Nonlinear system ,Computer Science (miscellaneous) ,QA1-939 ,Applied mathematics ,Order (group theory) ,Boundary value problem ,0101 mathematics ,Engineering (miscellaneous) ,Mathematics ,Variable (mathematics) - Abstract
In this paper, the existence of the solution and its stability to the fractional boundary value problem (FBVP) were investigated for an implicit nonlinear fractional differential equation (VOFDE) of variable order. All existence criteria of the solutions in our establishments were derived via Krasnoselskii’s fixed point theorem and in the sequel, and its Ulam–Hyers–Rassias (U-H-R) stability is checked. An illustrative example is presented at the end of this paper to validate our findings.
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- 2021
35. Viscosity approximation method for solving variational inequality problem in real Banach spaces
- Author
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Godwin Chidi Ugwunnadi
- Subjects
Sequence ,021103 operations research ,General Mathematics ,010102 general mathematics ,0211 other engineering and technologies ,Banach space ,Lipschitzian Mapping ,02 engineering and technology ,Nonexpansive Mapping ,Fixed point ,01 natural sciences ,Viscosity (programming) ,Fixed Point ,Variational inequality ,Strongly Accretive Mapping ,QA1-939 ,Applied mathematics ,Hierarchical Fixed Point Problems ,0101 mathematics ,Mathematics - Abstract
In this paper, we study the implicit and inertial-type viscosity approximation method for approximating a solution to the hierarchical variational inequality problem. Under some mild conditions on the parameters, we prove that the sequence generated by the proposed methods converges strongly to a solution of the above-mentioned problem in $q$-uniformly smooth Banach spaces. The results obtained in this paper generalize and improve many recent results in this direction.
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- 2021
36. Metaplectic representations of Hecke algebras, Weyl group actions, and associated polynomials
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Vidya Venkateswaran, Jasper V. Stokman, Siddhartha Sahi, Algebra, Geometry & Mathematical Physics (KDV, FNWI), Quantum Matter and Quantum Information, KdV Other Research (FNWI), Faculty of Science, and KDV (FNWI)
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Weyl group ,Polynomial ,Pure mathematics ,Algebraic combinatorics ,Series (mathematics) ,General Mathematics ,010102 general mathematics ,General Physics and Astronomy ,20C08 (Primary), 11F68, 22E50 (Secondary) ,Rational function ,01 natural sciences ,symbols.namesake ,Macdonald polynomials ,Gauss sum ,0103 physical sciences ,symbols ,FOS: Mathematics ,010307 mathematical physics ,0101 mathematics ,Representation Theory (math.RT) ,Mathematics::Representation Theory ,Dirichlet series ,Mathematics - Representation Theory ,Mathematics - Abstract
Chinta and Gunnells introduced a rather intricate multi-parameter Weyl group action on rational functions on a torus, which, when the parameters are specialized to certain Gauss sums, describes the functional equations of Weyl group multiple Dirichlet series associated to metaplectic (n-fold) covers of algebraic groups. In subsequent joint work with Puskas, they extended this action to a "metaplectic" representation of the equal parameter affine Hecke algebra, which allowed them to obtain explicit formulas for the p-parts of these Dirichlet series. They have also verified by a computer check the remarkable fact that their formulas continue to define a group action for general (unspecialized) parameters. In the first part of paper we give a conceptual explanation of this fact, by giving a uniform and elementary construction of the "metaplectic" representation for generic Hecke algebras as a suitable quotient of a parabolically induced affine Hecke algebra module, from which the associated Chinta-Gunnells Weyl group action follows through localization. In the second part of the paper we extend the metaplectic representation to the double affine Hecke algebra, which provides a generalization of Cherednik's basic representation. This allows us to introduce a new family of "metaplectic" polynomials, which generalize nonsymmetric Macdonald polynomials. In this paper, we provide the details of the construction of metaplectic polynomials in type A; the general case will be handled in the sequel to this paper., 39 pages. Version 2 is a significant revision. Added second part introducing a new family of "metaplectic" polynomials, which generalize nonsymmetric Macdonald polynomials and metaplectic Iwahori-Whittaker functions. Title has been changed and the introduction has been expanded
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- 2021
37. A New Class of Plane Curves with Arc Length Parametrization and Its Application to Linear Analysis of Curved Beams
- Author
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Snježana Maksimović and Aleksandar Borković
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Basis (linear algebra) ,Plane curve ,General Mathematics ,010102 general mathematics ,Mathematical analysis ,Static analysis ,Space (mathematics) ,01 natural sciences ,Computer Science::Digital Libraries ,010101 applied mathematics ,analytical solution ,Bernoulli–Euler beam ,special functions ,Special functions ,Computer Science (miscellaneous) ,QA1-939 ,arc-length parametrization ,Development (differential geometry) ,0101 mathematics ,Sturm–Liouville differential equation ,Engineering (miscellaneous) ,Arc length ,Parametrization ,Mathematics - Abstract
The objective of this paper is to define one class of plane curves with arc-length parametrization. To accomplish this, we constructed a novel class of special polynomials and special functions. These functions form a basis of L2(R) space and some of their interesting properties are discussed. The developed curves are used for the linear static analysis of curved Bernoulli–Euler beam. Due to the parametrization with arc length, the exact analytical solution can be obtained. These closed-form solutions serve as the benchmark results for the development of numerical procedures. One such example is provided in this paper.
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- 2021
38. Hermite–Hadamard Inclusions for Co-Ordinated Interval-Valued Functions via Post-Quantum Calculus
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Jessada Tariboon, Sotiris K. Ntouyas, Hüseyin Budak, Muhammad Ali, and [Belirlenecek]
- Subjects
Pure mathematics ,Physics and Astronomy (miscellaneous) ,General Mathematics ,Quantum calculus ,co-ordinated convexity ,quantum calculus ,01 natural sciences ,Interval valued ,Hadamard transform ,(p ,Hermite–Hadamard inequality ,Hermite–Hadamard inclusion ,Computer Science (miscellaneous) ,QA1-939 ,0101 mathematics ,interval-valued functions ,Mathematics ,Hermite polynomials ,010102 general mathematics ,Regular polygon ,(p, q)-integral ,Convex ,010101 applied mathematics ,Hermite-Hadamard inequality ,Chemistry (miscellaneous) ,Hermite-Hadamard inclusion ,q)-integral ,Midpoint Type Inequalities ,Symmetry (geometry) - Abstract
In this paper, the notions of post-quantum integrals for two-variable interval-valued functions are presented. The newly described integrals are then used to prove some new Hermite-Hadamard inclusions for co-ordinated convex interval-valued functions. Many of the findings in this paper are important extensions of previous findings in the literature. Finally, we present a few examples of our new findings. Analytic inequalities of this nature and especially the techniques involved have applications in various areas in which symmetry plays a prominent role. WOS:000677046700001 2-s2.0-85110868353
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- 2021
39. Entropy in the cusp and phase transitions for geodesic flows
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Godofredo Iommi, Felipe Riquelme, Anibal Velozo, Facultad de Matemáticas [Santiago de Chile], Pontificia Universidad Católica de Chile (UC), Institut de Recherche Mathématique de Rennes (IRMAR), AGROCAMPUS OUEST, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Université de Rennes 2 (UR2), Université de Rennes (UNIV-RENNES)-École normale supérieure - Rennes (ENS Rennes)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA), Department of Mathematics - Princeton University, Princeton University, Facultad de Matematicas, Pontificia Universidad Catolica de Chile, Institut de Recherche Mathématique de Rennes ( IRMAR ), Université de Rennes 1 ( UR1 ), Université de Rennes ( UNIV-RENNES ) -Université de Rennes ( UNIV-RENNES ) -AGROCAMPUS OUEST-École normale supérieure - Rennes ( ENS Rennes ) -Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National des Sciences Appliquées ( INSA ) -Université de Rennes 2 ( UR2 ), Université de Rennes ( UNIV-RENNES ) -Centre National de la Recherche Scientifique ( CNRS ), Guillemer, Marie-Annick, Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-INSTITUT AGRO Agrocampus Ouest, and Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)
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Phase transition ,Markov chain ,Geodesic ,General Mathematics ,010102 general mathematics ,Mathematical analysis ,[ MATH.MATH-DS ] Mathematics [math]/Dynamical Systems [math.DS] ,[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS] ,[MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS] ,Dynamical Systems (math.DS) ,15A15, 26E60, 37A30, 60B20, 60F15 ,01 natural sciences ,010101 applied mathematics ,Geodesic flow ,FOS: Mathematics ,Sectional curvature ,0101 mathematics ,Mathematics - Dynamical Systems ,Mathematics - Abstract
In this paper we study the geodesic flow for a particular class of Riemannian non-compact manifolds with variable pinched negative sectional curvature. For a sequence of invariant measures we are able to prove results relating the loss of mass and bounds on the measure entropies. We compute the entropy contribution of the cusps. We develop and study the corresponding thermodynamic formalism. We obtain certain regularity results for the pressure of a class of potentials. We prove that the pressure is real analytic until it undergoes a phase transition, after which it becomes constant. Our techniques are based on the one side on symbolic methods and Markov partitions and on the other on geometric techniques and approximation properties at level of groups., 34 pages, 4 figures. In this new version we have improved the organization of the paper and the clarity of some statements
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- 2015
40. On Coefficient Problems for Functions Connected with the Sine Function
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Katarzyna Tra̧bka-Wiȩcław
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Pure mathematics ,Class (set theory) ,functions starlike with respect to symmetric points ,Physics and Astronomy (miscellaneous) ,Logarithm ,Mathematics::Complex Variables ,General Mathematics ,010102 general mathematics ,01 natural sciences ,010101 applied mathematics ,generalized Zalcman coefficient functional ,Hankel determinant ,Chemistry (miscellaneous) ,coefficients of analytic functions ,Computer Science (miscellaneous) ,QA1-939 ,Sine ,0101 mathematics ,Mathematics ,Analytic function - Abstract
In this paper, some coefficient problems for starlike analytic functions with respect to symmetric points are considered. Bounds of several coefficient functionals for functions belonging to this class are provided. The main aim of this paper is to find estimates for the following: coefficients, logarithmic coefficients, some cases of the generalized Zalcman coefficient functional, and some cases of the Hankel determinant.
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- 2021
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41. Special Functions as Solutions to the Euler–Poisson–Darboux Equation with a Fractional Power of the Bessel Operator
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Yuri Luchko, Azamat Dzarakhohov, and Elina Shishkina
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General Mathematics ,Fox–Wright function ,02 engineering and technology ,01 natural sciences ,symbols.namesake ,fractional powers of the Bessel operator ,fractional Euler–Poisson–Darboux equation ,QA1-939 ,0202 electrical engineering, electronic engineering, information engineering ,Computer Science (miscellaneous) ,Applied mathematics ,0101 mathematics ,Euler–Poisson–Darboux equation ,fractional ODE ,Engineering (miscellaneous) ,Mathematics ,Operator (physics) ,010102 general mathematics ,Integral transform ,Differential operator ,Fractional calculus ,Special functions ,Meijer integral transform ,Ordinary differential equation ,symbols ,020201 artificial intelligence & image processing ,H-function ,Bessel function - Abstract
In this paper, we consider fractional ordinary differential equations and the fractional Euler–Poisson–Darboux equation with fractional derivatives in the form of a power of the Bessel differential operator. Using the technique of the Meijer integral transform and its modification, fundamental solutions to these equations are derived in terms of the Fox–Wright function, the Fox H-function, and their particular cases. We also provide some explicit formulas for the solutions to the corresponding initial-value problems in terms of the generalized convolutions introduced in this paper.
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- 2021
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42. General Summation Formulas Contiguous to the q-Kummer Summation Theorems and Their Applications
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Hari M. Srivastava, Kalpana Fatawat, Yashoverdhan Vyas, and Shivani Pathak
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Pure mathematics ,Physics and Astronomy (miscellaneous) ,General Mathematics ,Quantum calculus ,symmetric quantum calculus ,Mathematical proof ,01 natural sciences ,q-Kummer second and third summation theorems ,symbols.namesake ,Heine’s transformation ,QA1-939 ,Computer Science (miscellaneous) ,0101 mathematics ,Invariant (mathematics) ,Hypergeometric function ,Mathematics ,Series (mathematics) ,q-Kummer summation theorem ,010102 general mathematics ,Gauss ,Thomae’s q-integral representation ,010101 applied mathematics ,Number theory ,Chemistry (miscellaneous) ,symbols ,quantum or basic (or q-) hypergeometric series ,Jacobi polynomials ,q-Binomial theorem - Abstract
This paper provides three classes of q-summation formulas in the form of general contiguous extensions of the first q-Kummer summation theorem. Their derivations are presented by using three methods, which are along the lines of the three types of well-known proofs of the q-Kummer summation theorem with a key role of the q-binomial theorem. In addition to the q-binomial theorem, the first proof makes use of Thomae’s q-integral representation and the second proof needs Heine’s transformation. Whereas the third proof utilizes only the q-binomial theorem. Subsequently, the applications of these summation formulas in obtaining the general contiguous extensions of the second and the third q-Kummer summation theorems are also presented. Furthermore, the investigated results are specialized to give many of the known as well as presumably new q-summation theorems, which are contiguous to the three q-Kummer summation theorems. This work is motivated by the observation that the basic (or q-) series and basic (or q-) polynomials, especially the basic (or q-) gamma and q-hypergeometric functions and basic (or q-) hypergeometric polynomials, are applicable particularly in several diverse areas including Number Theory, Theory of Partitions and Combinatorial Analysis as well as in the study of Combinatorial Generating Functions. Just as it is known in the theory of the Gauss, Kummer (or confluent), Clausen and the generalized hypergeometric functions, the parameters in the corresponding basic or quantum (or q-) hypergeometric functions are symmetric in the sense that they remain invariant when the order of the p numerator parameters or when the order of the q denominator parameters is arbitrarily changed. A case has therefore been made for the symmetry possessed not only by hypergeometric functions and basic or quantum (or q-) hypergeometric functions, which are studied in this paper, but also by the symmetric quantum calculus itself.
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- 2021
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43. Multidimensional linear and nonlinear partial integro-differential equation in Bessel potential spaces with applications in option pricing
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Daniel Sevcovic and Cyril Izuchukwu Udeani
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General Mathematics ,Bessel potential ,Black–Scholes model ,Space (mathematics) ,bessel potential spaces ,01 natural sciences ,FOS: Economics and business ,strong kernel ,Mathematics - Analysis of PDEs ,partial integro-differential equation ,Integro-differential equation ,0502 economics and business ,45K05, 35K58, 34G20, 91G20 ,QA1-939 ,FOS: Mathematics ,Computer Science (miscellaneous) ,hölder continuity ,Applied mathematics ,Uniqueness ,0101 mathematics ,option pricing ,Engineering (miscellaneous) ,Mathematics ,050208 finance ,Probability (math.PR) ,010102 general mathematics ,05 social sciences ,Mathematical Finance (q-fin.MF) ,Parabolic partial differential equation ,Nonlinear system ,Valuation of options ,Quantitative Finance - Mathematical Finance ,lévy measure ,Mathematics - Probability ,Analysis of PDEs (math.AP) - Abstract
The purpose of this paper is to analyze solutions of a non-local nonlinear partial integro-differential equation (PIDE) in multidimensional spaces. Such class of PIDE often arises in financial modeling. We employ the theory of abstract semilinear parabolic equations in order to prove existence and uniqueness of solutions in the scale of Bessel potential spaces. We consider a wide class of Lévy measures satisfying suitable growth conditions near the origin and infinity. The novelty of the paper is the generalization of already known results in the one space dimension to the multidimensional case. We consider Black–Scholes models for option pricing on underlying assets following a Lévy stochastic process with jumps. As an application to option pricing in the one-dimensional space, we consider a general shift function arising from a nonlinear option pricing model taking into account a large trader stock-trading strategy. We prove existence and uniqueness of a solution to the nonlinear PIDE in which the shift function may depend on a prescribed large investor stock-trading strategy function.
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- 2021
44. Generalized Variational Principle for the Fractal (2 + 1)-Dimensional Zakharov–Kuznetsov Equation in Quantum Magneto-Plasmas
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Yan-Hong Liang and Kang-Jia Wang
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Physics ,two-scale fractal theory ,Physics and Astronomy (miscellaneous) ,General Mathematics ,010102 general mathematics ,One-dimensional space ,Structure (category theory) ,Space (mathematics) ,01 natural sciences ,Symmetry (physics) ,010305 fluids & plasmas ,semi-inverse method ,Fractal ,Chemistry (miscellaneous) ,Variational principle ,Fractal derivative ,0103 physical sciences ,Computer Science (miscellaneous) ,QA1-939 ,fractal variational principle ,0101 mathematics ,Quantum ,Mathematics ,Mathematical physics ,symmetry - Abstract
In this paper, we propose the fractal (2 + 1)-dimensional Zakharov–Kuznetsov equation based on He’s fractal derivative for the first time. The fractal generalized variational formulation is established by using the semi-inverse method and two-scale fractal theory. The obtained fractal variational principle is important since it not only reveals the structure of the traveling wave solutions but also helps us study the symmetric theory. The finding of this paper will contribute to the study of symmetry in the fractal space.
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- 2021
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45. Some Remarks on the Location of Non-Asymptotic Zeros of Whittaker and Kummer Hypergeometric Functions
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Islam Boussaada, Guilherme Mazanti, Silviu-Iulian Niculescu, Dynamical Interconnected Systems in COmplex Environments (DISCO), Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire des signaux et systèmes (L2S), CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Laboratoire des signaux et systèmes (L2S), CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), and Institut Polytechnique des Sciences Avancées (IPSA)
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Confluent hypergeometric functions ,General Mathematics ,zeros location ,010102 general mathematics ,30A10 ,010103 numerical & computational mathematics ,[MATH.MATH-CA]Mathematics [math]/Classical Analysis and ODEs [math.CA] ,16. Peace & justice ,01 natural sciences ,Whittaker function ,34M03 ,Mathematics - Classical Analysis and ODEs ,Kummer function ,Classical Analysis and ODEs (math.CA) ,FOS: Mathematics ,zeros location 2020 MSC: 33C15 ,0101 mathematics ,zeros location Mathematics Subject Classification (2020) 33C15 ,MSC 2020: 33C15, 34M03, 30A10 - Abstract
International audience; This paper focuses on the location of the non-asymptotic zeros of Whittaker and Kummer confluent hypergeometric functions. Based on a technique by E. Hille for the analysis of solutions of some second-order ordinary differential equations, we characterize the sign of the real part of zeros of Whittaker and Kummer functions and provide estimates on the regions of the complex plane where those zeros can be located. Our main result is a correction of a previous statement by G. E. Tsvetkov whose propagation has induced mistakes in the literature. In particular, we review some results of E. B. Saff and R. S. Varga on the error of Padé's rational approximation of the exponential function, which are based on the latter.
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- 2021
46. Explicit Solutions of Initial Value Problems for Fractional Generalized Proportional Differential Equations with and without Impulses
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Mohamed I. Abbas and Snezhana Hristova
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Physics and Astronomy (miscellaneous) ,Differential equation ,General Mathematics ,010102 general mathematics ,Scalar (physics) ,Function (mathematics) ,Type (model theory) ,01 natural sciences ,Symmetry (physics) ,010101 applied mathematics ,symbols.namesake ,Transformation (function) ,generalized proportional fractional derivatives ,Chemistry (miscellaneous) ,Mittag-Leffler function ,QA1-939 ,Computer Science (miscellaneous) ,symbols ,Initial value problem ,Applied mathematics ,Mittag–Leffler function ,0101 mathematics ,Mathematics - Abstract
The object of investigation in this paper is a scalar linear fractional differential equation with generalized proportional derivative of Riemann–Liouville type (LFDEGD). The main goal is the obtaining an explicit solution of the initial value problem of the studied equation. Note that the locally solvability, being the same as the existence of solutions to the initial value problem, is connected with the symmetry of a transformation of a system of differential equations. At the same time, several criteria for existence of the initial value problem for nonlinear fractional differential equations with generalized proportional derivative are connected with the linear ones. It leads to the necessity of obtaining an explicit solution of LFDEGD. In this paper two cases are studied: the case of no impulses in the differential equation are presented and the case when instantaneous impulses at initially given points are involved. All obtained formulas are based on the application of Mittag–Leffler function with two parameters. In the case of impulses, initially the appropriate impulsive conditions are set up and later the explicit solutions are obtained.
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- 2021
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47. Second-Order PDE Constrained Controlled Optimization Problems with Application in Mechanics
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Savin Treanţă
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0209 industrial biotechnology ,Class (computer programming) ,Mathematical optimization ,Optimization problem ,multi-time controlled second-order Lagrangian ,multiple integral functional ,Computer science ,General Mathematics ,Multiple integral ,010102 general mathematics ,02 engineering and technology ,Euler–Lagrange equations ,01 natural sciences ,020901 industrial engineering & automation ,second-order PDE constraints ,Computer Science (miscellaneous) ,QA1-939 ,Order (group theory) ,Partial derivative ,0101 mathematics ,Engineering (miscellaneous) ,Mathematics - Abstract
The present paper deals with a class of second-order PDE constrained controlled optimization problems with application in Lagrange–Hamilton dynamics. Concretely, we formulate and prove necessary conditions of optimality for the considered class of control problems driven by multiple integral cost functionals involving second-order partial derivatives. Moreover, an illustrative example is provided to highlight the effectiveness of the results derived in the paper. In the final part of the paper, we present an algorithm to summarize the steps for solving a control problem such as the one investigated here.
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- 2021
48. Gottlieb Polynomials and Their q-Extensions
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Esra ErkuŞ-Duman and Junesang Choi
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Power series ,General Mathematics ,q-Jacobi polynomials ,q-Meixner polynomials ,q-exponential functions ,q-binomial theorem ,02 engineering and technology ,q-Gottlieb polynomials in several variables ,01 natural sciences ,generating functions ,0202 electrical engineering, electronic engineering, information engineering ,Computer Science (miscellaneous) ,QA1-939 ,q-calculus ,0101 mathematics ,Engineering (miscellaneous) ,Mathematics ,generalized and generalized basic (or -q) hypergeometric function ,Discrete orthogonal polynomials ,Multivariable calculus ,010102 general mathematics ,Representation (systemics) ,020206 networking & telecommunications ,Function of several real variables ,Lauricella’s multiple hypergeometric series in several variables ,Algebra ,Gottlieb polynomials in several variables - Abstract
Since Gottlieb introduced and investigated the so-called Gottlieb polynomials in 1938, which are discrete orthogonal polynomials, many researchers have investigated these polynomials from diverse angles. In this paper, we aimed to investigate the q-extensions of these polynomials to provide certain q-generating functions for three sequences associated with a finite power series whose coefficients are products of the known q-extended multivariable and multiparameter Gottlieb polynomials and another non-vanishing multivariable function. Furthermore, numerous possible particular cases of our main identities are considered. Finally, we return to Khan and Asif’s q-Gottlieb polynomials to highlight certain connections with several other known q-polynomials, and provide its q-integral representation. Furthermore, we conclude this paper by disclosing our future investigation plan.
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- 2021
49. Hardy inequalities on metric measure spaces, II: the case p > q
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Daulti Verma and Michael Ruzhansky
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metric measure spaces ,Pure mathematics ,General Mathematics ,General Physics and Astronomy ,Characterization (mathematics) ,01 natural sciences ,Measure (mathematics) ,010305 fluids & plasmas ,Mathematics - Spectral Theory ,Mathematics - Analysis of PDEs ,homogeneous group ,0103 physical sciences ,Riemannian manifolds with negative curvature ,0101 mathematics ,Mathematical Physics ,Research Articles ,Mathematics ,Sinc function ,26D10, 22E30 ,Hyperbolic space ,010102 general mathematics ,Hardy inequalities ,General Engineering ,Mathematics - Functional Analysis ,Mathematics and Statistics ,hyperbolic space ,Metric (mathematics) ,Homogeneous group - Abstract
In this note we continue giving the characterisation of weights for two-weight Hardy inequalities to hold on general metric measure spaces possessing polar decompositions. Since there may be no differentiable structure on such spaces, the inequalities are given in the integral form in the spirit of Hardy's original inequality. This is a continuation of our paper [M. Ruzhansky and D. Verma. Hardy inequalities on metric measure spaces, Proc. R. Soc. A., 475(2223):20180310, 2018] where we treated the case $p\leq q$. Here the remaining range $p>q$ is considered, namely, $0, Comment: 18 pages; this is the second part to the paper arXiv:1806.03728. Final version, to appear in Proc. Royal Soc. A
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- 2021
50. Modeling Interactions among Migration, Growth and Pressure in Tumor Dynamics
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Juan Campos, Juan José Soler, Juan Melchor, Beatriz Blanco, [Blanco, Beatriz] Univ Granada, Dept Struct Mech, Granada 18071, Spain, [Blanco, Beatriz] Ibs GRANADA, Inst Invest Biosanitaria, Granada 18012, Spain, [Melchor, Juan] Ibs GRANADA, Inst Invest Biosanitaria, Granada 18012, Spain, [Campos, Juan] Univ Granada, Fac Ciencias, Dept Matemat Aplicada, Granada 18071, Spain, [Soler, Juan] Univ Granada, Fac Ciencias, Dept Matemat Aplicada, Granada 18071, Spain, [Campos, Juan] Univ Granada, Res Unit Modelling Nat MNat, Granada 18071, Spain, [Melchor, Juan] Univ Granada, Res Unit Modelling Nat MNat, Granada 18071, Spain, [Soler, Juan] Univ Granada, Res Unit Modelling Nat MNat, Granada 18071, Spain, [Melchor, Juan] Univ Granada, Dept Stat & Operat Res, Granada 18071, Spain, MINECO-Feder (Spain), Junta de Andalucia (Spain), Instituto de Salud Carlos III, Ministry of Science, Innovation and Universities of Spain, Consejeria de Economia, Conocimiento, Empresas y Universidad, European Regional Development Fund (ERDF), [Blanco,B] Department of Structural Mechanics, University of Granada, Granada, Spain. [Blanco,B, Melchor,J] Instituto de Investigación Biosanitaria, ibs.GRANADA, Granada, Spain. [Campos,J, Soler,J] Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Granada, Granada, Spain. [Campos,J, Melchor,J, Soler,J] Research Unit 'Modelling Nature' (MNat), Universidad de Granada, Granada, Spain., and This paper has been partially supported by the MINECO-Feder (Spain) research grant num bers RTI2018-098850-B-I00 (J.C., J.S.) & EQC2018-004508-P (B.B., J.M.), the Junta de Andalucía (Spain) Projects PY18-RT-2422 (J.C., J.S.), A-FQM-311-UGR18 (J.C., J.S.) & IE2017-5537 (B.B., J.M.), and by the Instituto de Salud Carlos III, project number DTS17/00087 (J.M., J.S.). This study was also funded by Ministry of Science, Innovation and Universities of Spain, project numbers DPI2017-85359-R (B.B., J.M.) & PID2019-106947RA-C22 (B.B., J.M.) and by Consejería de Economía, Conocimiento, Empresas y Universidad and European Regional Development Fund (ERDF), ref. SOMM17/6109/UGR (J.C., J.M., J.S.). Lastly, B.B. research was granted by Ministry of Science, Innovation and Universities of Spain, FPU2017/01415.
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Computer science ,01 natural sciences ,Forces ,Phenomena and Processes::Cell Physiological Phenomena::Cell Physiological Processes::Cell Movement [Medical Subject Headings] ,Diffusion ,porous media ,Qualitative behavior ,Computer Science (miscellaneous) ,Numerical simulations ,Homeostasis ,Statistical physics ,Diffusion (business) ,Solid tumor ,Analytical, Diagnostic and Therapeutic Techniques and Equipment::Investigative Techniques::Epidemiologic Methods::Data Collection::Vital Statistics::Mortality::Cause of Death [Medical Subject Headings] ,Cancer ,0303 health sciences ,Partial differential equation ,Mathematical modelling ,Dynamics (mechanics) ,Traveling-waves ,mathematical modeling ,tumor dynamics ,Phenomena and Processes::Chemical Phenomena::Biochemical Phenomena::Biochemical Processes::Signal Transduction [Medical Subject Headings] ,Diseases::Neoplasms [Medical Subject Headings] ,flux-saturated ,Modelos teóricos ,General Mathematics ,Phenomena and Processes::Physical Phenomena::Mechanical Phenomena::Porosity [Medical Subject Headings] ,Context (language use) ,Information Science::Information Science::Communication::Cybernetics::Feedback [Medical Subject Headings] ,cell motility ,Stress ,Mechanics ,03 medical and health sciences ,QA1-939 ,Hele-Shaw model ,Movimiento celular ,Phenomena and Processes::Physical Phenomena::Mechanical Phenomena::Elasticity [Medical Subject Headings] ,0101 mathematics ,Engineering (miscellaneous) ,030304 developmental biology ,Computer simulation ,010102 general mathematics ,Porous-media equations ,Mass ,numerical simulation ,Floculadores ,Phenomena and Processes::Cell Physiological Phenomena::Cell Physiological Processes::Cell Transdifferentiation::Epithelial-Mesenchymal Transition [Medical Subject Headings] ,mechanical feedback ,Phenomena and Processes::Physiological Phenomena::Physiological Processes::Homeostasis [Medical Subject Headings] ,Mathematics - Abstract
What are the biomechanical implications in the dynamics and evolution of a growing solid tumor? Although the analysis of some of the biochemical aspects related to the signaling pathways involved in the spread of tumors has advanced notably in recent times, their feedback with the mechanical aspects is a crucial challenge for a global understanding of the problem. The aim of this paper is to try to illustrate the role and the interaction between some evolutionary processes (growth, pressure, homeostasis, elasticity, or dispersion by flux-saturated and porous media) that lead to collective cell dynamics and defines a propagation front that is in agreement with the experimental data. The treatment of these topics is approached mainly from the point of view of the modeling and the numerical approach of the resulting system of partial differential equations, which can be placed in the context of the Hele-Shaw-type models. This study proves that local growth terms related to homeostatic pressure give rise to retrograde diffusion phenomena, which compete against migration through flux-saturated dispersion terms., MINECO-Feder (Spain) research grant numbers RTI2018-098850-B-I00 (J.C., J.S.) & EQC2018-004508-P (B.B., J.M.), Junta de Andalucía (Spain) Projects PY18-RT-2422 (J.C., J.S.), A-FQM-311-UGR18 (J.C., J.S.) & IE2017-5537 (B.B., J.M.), Instituto de Salud Carlos III, project number DTS17/00087 (J.M., J.S.), Ministry of Science, Innovation and Universities of Spain, project numbers DPI2017-85359-R (B.B., J.M.) & PID2019-106947RA-C22 (B.B., J.M.), Consejería de Economía, Conocimiento, Empresas y Universidad and European Regional Development Fund (ERDF), ref. SOMM17/6109/UGR (J.C., J.M., J.S.), Ministry of Science, Innovation and Universities of Spain, FPU2017/01415
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- 2021
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