25,420 results
Search Results
302. Flow equivalence of G-SFTs
- Author
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Toke Meier Carlsen, Søren Eilers, and Mike Boyle
- Subjects
Pure mathematics ,Finite group ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,MathematicsofComputing_GENERAL ,Dynamical Systems (math.DS) ,01 natural sciences ,Matrix (mathematics) ,Group action ,Flow (mathematics) ,FOS: Mathematics ,Equivariant map ,Mathematics - Dynamical Systems ,0101 mathematics ,Connection (algebraic framework) ,Equivalence (measure theory) ,Group ring ,Mathematics - Abstract
In this paper, a G-shift of finite type (G-SFT) is a shift of finite type together with a free continuous shift-commuting action by a finite group G. We reduce the classification of G-SFTs up to equivariant flow equivalence to an algebraic classification of a class of poset-blocked matrices over the integral group ring of G. For a special case of two irreducible components with G$=\mathbb Z_2$, we compute explicit complete invariants. We relate our matrix structures to the Adler-Kitchens-Marcus group actions approach. We give examples of G-SFT applications, including a new connection to involutions of cellular automata., The paper has been augmented considerably and the second version is now 81 pages long. This version has been accepted for publication in Transactions of the American Mathematical Society
- Published
- 2020
303. Titchmarsh’s theorem and some remarks concerning the right-sided quaternion Fourier transform
- Author
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Azzedine Achak, Radouan Daher, Aziz Bouhlal, and N. Safouane
- Subjects
Pure mathematics ,Quaternion algebra ,General Mathematics ,010102 general mathematics ,Space (mathematics) ,Lipschitz continuity ,01 natural sciences ,Square (algebra) ,Function of several real variables ,010101 applied mathematics ,Translation operator ,symbols.namesake ,Fourier transform ,symbols ,0101 mathematics ,Quaternion ,Mathematics - Abstract
This paper is based mainly on Titchmarsh’s theorem (Introduction to the theory of Fourier integrals. Clarendon Press, Oxford, 1937, Theorem 84) in the one-dimensional case. Abilov et al. (Comput Math Math Phys 48:2146, 2008) proved two useful estimates for the Fourier transform in the space of square integral multivariable functions on certain classes of functions characterized by the generalized continuity modulus, and these estimates are proved by Abilovs for only two variables, using a translation operator. The purpose of this paper is to study these estimates for Quaternion Fourier transforms, also the functions satisfy Lipschitz conditions of certain orders. Thus we study the Quaternion Fourier transforms of Lipschitz function in the functions space $$L^r({\mathbb {R}}^{2},{\mathcal {H}})$$, where $${\mathcal {H}}$$ a quaternion algebra which will be specified in due course.
- Published
- 2020
304. Hyperelliptic integrals modulo p and Cartier-Manin matrices
- Author
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Alexander Varchenko
- Subjects
Polynomial ,Pure mathematics ,Mathematics - Number Theory ,Mathematics::Number Theory ,General Mathematics ,010102 general mathematics ,Holomorphic function ,FOS: Physical sciences ,Field (mathematics) ,Mathematical Physics (math-ph) ,Algebraic geometry ,01 natural sciences ,Mathematics - Algebraic Geometry ,Finite field ,FOS: Mathematics ,Elliptic integral ,Number Theory (math.NT) ,0101 mathematics ,Algebraic Geometry (math.AG) ,Hyperelliptic curve ,Mathematical Physics ,Mathematics ,Knizhnik–Zamolodchikov equations - Abstract
The hypergeometric solutions of the KZ equations were constructed almost 30 years ago. The polynomial solutions of the KZ equations over the finite field $F_p$ with a prime number $p$ of elements were constructed recently. In this paper we consider the example of the KZ equations whose hypergeometric solutions are given by hyperelliptic integrals of genus $g$. It is known that in this case the total $2g$-dimensional space of holomorphic solutions is given by the hyperelliptic integrals. We show that the recent construction of the polynomial solutions over the field $F_p$ in this case gives only a $g$-dimensional space of solutions, that is, a "half" of what the complex analytic construction gives. We also show that all the constructed polynomial solutions over the field $F_p$ can be obtained by reduction modulo $p$ of a single distinguished hypergeometric solution. The corresponding formulas involve the entries of the Cartier-Manin matrix of the hyperelliptic curve. That situation is analogous to the example of the elliptic integral considered in the classical Y.I. Manin's paper in 1961., Latex, 16 pages
- Published
- 2020
305. Linear operators preserving majorization of matrix tuples
- Author
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Alexander Guterman and Pavel Shteyner
- Subjects
Doubly stochastic matrix ,General Mathematics ,010102 general mathematics ,Stochastic matrix ,General Physics and Astronomy ,01 natural sciences ,Square matrix ,010305 fluids & plasmas ,Combinatorics ,Linear map ,Matrix (mathematics) ,0103 physical sciences ,Ordered pair ,0101 mathematics ,Tuple ,Majorization ,Mathematics - Abstract
In this paper, we consider weak, directional and strong matrix majorizations. Namely, for square matrices A and B of the same size we say that A is weakly majorized by B if there is a row stochastic matrix X such that A = XB. Further, A is strongly majorized by B if there is a doubly stochastic matrix X such that A = XB. Finally, A is directionally majorized by B if Ax is majorized by Bx for any vector x where the usual vector majorization is used. We introduce the notion of majorization of matrix tuples which is defined as a natural generalization of matrix majorizations: for a chosen type of majorization we say that one tuple of matrices is majorized by another tuple of the same size if every matrix of the “smaller” tuple is majorized by a matrix in the same position in the “bigger” tuple. We say that a linear operator preserves majorization if it maps ordered pairs to ordered pairs and the image of the smaller element does not exceed the image of the bigger one. This paper contains a full characterization of linear operators that preserve weak, strong or directional majorization of tuples of matrices and linear operators that map tuples that are ordered with respect to strong majorization to tuples that are ordered with respect to directional majorization. We have shown that every such operator preserves respective majorization of each component. For all types of majorization we provide counterexamples that demonstrate that the inverse statement does not hold, that is if majorization of each component is preserved, majorization of tuples may not.
- Published
- 2020
306. Bidimensionality and Kernels
- Author
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Saket Saurabh, Fedor V. Fomin, Dimitrios M. Thilikos, Daniel Lokshtanov, Department of Informatics [Bergen] (UiB), University of Bergen (UiB), Department of Computer Science [Santa Barbara] (CS-UCSB), University of California [Santa Barbara] (UCSB), University of California-University of California, Institute of Mathematical Sciences [Chennai] (IMSc), Algorithmes, Graphes et Combinatoire (ALGCO), Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier (LIRMM), and Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM)
- Subjects
FOS: Computer and information sciences ,General Computer Science ,General Mathematics ,[INFO.INFO-DS]Computer Science [cs]/Data Structures and Algorithms [cs.DS] ,G.2.1 ,Parameterized algorithms ,G.2.2 ,0102 computer and information sciences ,[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM] ,01 natural sciences ,Combinatorics ,Computer Science::Discrete Mathematics ,Computer Science - Data Structures and Algorithms ,FOS: Mathematics ,Mathematics - Combinatorics ,Data Structures and Algorithms (cs.DS) ,0101 mathematics ,Computer Science::Data Structures and Algorithms ,Mathematics ,010102 general mathematics ,Bidimensionality ,Treewidth ,010201 computation theory & mathematics ,Kernelization ,68R10, 05C83, 05C85 ,Combinatorics (math.CO) - Abstract
Bidimensionality Theory was introduced by [E.D. Demaine, F.V. Fomin, M.Hajiaghayi, and D.M. Thilikos. Subexponential parameterized algorithms on graphs of bounded genus and H-minor-free graphs, J. ACM, 52 (2005), pp.866--893] as a tool to obtain sub-exponential time parameterized algorithms on H-minor-free graphs. In [E.D. Demaine and M.Hajiaghayi, Bidimensionality: new connections between FPT algorithms and PTASs, in Proceedings of the 16th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), SIAM, 2005, pp.590--601] this theory was extended in order to obtain polynomial time approximation schemes (PTASs) for bidimensional problems. In this work, we establish a third meta-algorithmic direction for bidimensionality theory by relating it to the existence of linear kernels for parameterized problems. In particular, we prove that every minor (respectively contraction) bidimensional problem that satisfies a separation property and is expressible in Countable Monadic Second Order Logic (CMSO), admits a linear kernel for classes of graphs that exclude a fixed graph (respectively an apex graph) H as a minor. Our results imply that a multitude of bidimensional problems g graph classes. For most of these problems no polynomial kernels on H-minor-free graphs were known prior to our work., Comment: An an earlier version of this paper appeared in SODA 2010. That paper contained preliminary versions of some of the results of this paper
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- 2020
307. A new characterization of a proper type B semigroup
- Author
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Zhi Pei, Chunhua Li, and Baogen Xu
- Subjects
type b semigroup ,Pure mathematics ,20m10 ,Mathematics::Operator Algebras ,Semigroup ,Computer Science::Information Retrieval ,General Mathematics ,010102 general mathematics ,e-unitary ,proper ,0102 computer and information sciences ,Characterization (mathematics) ,Type (model theory) ,01 natural sciences ,06f05 ,010201 computation theory & mathematics ,q-semigroup ,QA1-939 ,0101 mathematics ,Mathematics - Abstract
In this paper, we develop the elementary theory of inverse semigroups to the cases of type B semigroups. The main aim of this paper is to study proper type B semigroups. We introduce first the concept of a left admissible triple. After obtaining some basic properties of left admissible triple, we give the definition of a Q-semigroup and get a structure theorem of Q-semigroup. In particular, we introduce the notion of an admissible triple and give some characterization of proper type B semigroups. It is proved that an arbitrary Q-semigroup with an admissible triple is an E-unitary type B semigroup.
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- 2020
308. EXISTENCE AND MULTIPLICITY OF WEAK SOLUTIONS FOR A CLASS OF FRACTIONAL STURM-LIOUVILLE BOUNDARY VALUE PROBLEMS WITH IMPULSIVE CONDITIONS
- Author
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Yan Qiao, Fangqi Chen, and Yukun An
- Subjects
Class (set theory) ,General Mathematics ,010102 general mathematics ,Mathematical analysis ,Sturm–Liouville theory ,Multiplicity (mathematics) ,Mathematics::Spectral Theory ,01 natural sciences ,Boundary values ,010101 applied mathematics ,Homogeneous ,Critical point (thermodynamics) ,Boundary value problem ,0101 mathematics ,Fractional differential ,Mathematics - Abstract
In this paper, we consider the existence and multiplicity of weak solutions for a class of fractional differential equations with non-homogeneous Sturm-Liouville conditions and impulsive conditions by using the critical point theory. In addition, at the end of this paper, we also give the existence results of infinite weak solutions of fractional differential equations under homogeneous Sturm-Liouville boundary value conditions. Finally, several examples are given to illustrate our main results.
- Published
- 2020
309. Orbital exponential sums for prehomogeneous vector spaces
- Author
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Takashi Taniguchi and Frank Thorne
- Subjects
Pure mathematics ,Prehomogeneous vector space ,Mathematics - Number Theory ,Characteristic function (probability theory) ,General Mathematics ,010102 general mathematics ,Structure (category theory) ,Space (mathematics) ,01 natural sciences ,symbols.namesake ,Fourier transform ,Distribution (mathematics) ,Linear algebra ,FOS: Mathematics ,symbols ,Number Theory (math.NT) ,0101 mathematics ,Vector space ,Mathematics - Abstract
Let (G, V) be a prehomogeneous vector space, let O be any G(F_q)-invariant subset of V(F_q), and let f be the characteristic function of O. In this paper we develop a method for explicitly and efficiently evaluating the Fourier transform of f, based on combinatorics and linear algebra. We then carry out these computations in full for each of five prehomogeneous vector spaces, including the 12-dimensional space of pairs of ternary quadratic forms. Our computations reveal that these Fourier transforms enjoy a great deal of structure, and sometimes exhibit more than square root cancellation on average. These Fourier transforms naturally arise in analytic number theory, where explicit formulas (or upper bounds) lead to sieve level of distribution results for related arithmetic sequences. We describe some examples, and in a companion paper we develop a new method to do so, designed to exploit the particular structure of these Fourier transforms., 28 pages; to appear in American Journal of Mathematics. Includes a table after the bibliography. Also includes relevant PARI/GP code, embedded as a comment in the LaTeX code
- Published
- 2020
310. Application of a Special Form of Differential Equations to Study Movements of a Loaded Stewart Platform
- Author
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S. A. Zegzhda, M. P. Yushkov, and V. I. Petrova
- Subjects
Holonomic ,Differential equation ,General Mathematics ,media_common.quotation_subject ,010102 general mathematics ,Mathematical analysis ,Equations of motion ,Stewart platform ,Inertia ,Rigid body ,01 natural sciences ,010305 fluids & plasmas ,Position (vector) ,0103 physical sciences ,Center of mass ,0101 mathematics ,media_common ,Mathematics - Abstract
We study movements of a loaded Stewart platform in this paper. A special form of differential equations is used (motion equations in excess coordinates are derived) to compose the motion equations. In this form, vectorial Lagrange equations of the first kind are compiled using differentiation with respect to the radius-vector of the center of mass of the system and the unit vectors (orts) of the main central axes of inertia of the moving body and with respect to their derivatives. These determine the position of a rigid body in space. The length invariance of the unit vectors and their orthogonality are taken into account as abstract holonomic relations imposed on vectors describing the motion of a rigid body. “Spurious oscillations” are some of the technical effects seen in the behavior of the Stewart platform in the equilibrium position. This reason for the system to leave the unstable equilibrium position is discussed in this paper. Such standard motion of the Stewart platform as vertical oscillations of the platform will be equally unstable. The simplest mechanism of the instability of such vertical movements of the platform is revealed in this work. We propose introducing classical feedbacks to obtain steady movement. The numerical solutions of the derived differential equations completely correspond to the numerical results obtained by solving the motion equations compiled using theorems on the motion of the center of mass and on the change in the kinetic moment when the system moves relative to the center of mass.
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- 2020
311. EXISTENCE OF SOLUTIONS FOR DUAL SINGULAR INTEGRAL EQUATIONS WITH CONVOLUTION KERNELS IN CASE OF NON-NORMAL TYPE
- Author
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Pingrun Li
- Subjects
General Mathematics ,010102 general mathematics ,Singular integral ,Type (model theory) ,01 natural sciences ,Integral equation ,Dual (category theory) ,Convolution ,010101 applied mathematics ,Riemann hypothesis ,symbols.namesake ,Fourier transform ,symbols ,Applied mathematics ,Boundary value problem ,0101 mathematics ,Mathematics - Abstract
This paper is devoted to the study of dual singular integral equations with convolution kernels in the case of non-normal type. Via using the Fourier transforms, we transform such equations into Riemann boundary value problems. To solve the equation, we establish the regularity theory of solvability. The general solutions and the solvable conditions of the equation are obtained. Especially, we investigate the asymptotic property of solutions at nodes. This paper will have a significant meaning for the study of improving and developing complex analysis, integral equations and Riemann boundary value problems.
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- 2020
312. Homological properties of quotient divisible Abelian groups and compact groups dual to them
- Author
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Nikolay I. Kryuchkov
- Subjects
Pure mathematics ,Fundamental group ,General Mathematics ,010102 general mathematics ,General Physics and Astronomy ,Topological space ,01 natural sciences ,Triviality ,Divisible group ,010305 fluids & plasmas ,Universality (dynamical systems) ,0103 physical sciences ,Homomorphism ,0101 mathematics ,Abelian group ,Quotient ,Mathematics - Abstract
Homological properties of quotient divisible Abelian groups are studied. These groups form an important class of groups, which has been extensively studied in recent years. The first part of the paper is devoted to conditions for the triviality of extension groups in which one of the arguments is a quotient divisible group. Under certain additional assumptions, groups of homomorphisms from quotient divisible groups to reduced Abelian groups are described. Universality properties of quotient divisible Abelian groups are investigated. The second part of the paper considers homological properties of compact Abelian groups dual to quotient divisible groups in the sense of L.S. Pontryagin. Such groups are said to be “quotient toroidal.” Conditions for the triviality of group extensions in which one of the arguments is a quotient toroidal group are studied. Certain groups of continuous homomorphisms in which the second argument is a quotient toroidal group are described. The last part of the paper is devoted to conditions for the triviality of the groups of extensions of quotient divisible groups by compact quotient toroidal ones. The fundamental group of the topological space of a quotient toroidal group is characterized.
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- 2020
313. On the Aizerman Problem: Coefficient Conditions for the Existence of a Four-Period Cycle in a Second-Order Discrete-Time System
- Author
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T. E. Zvyagintseva
- Subjects
Automatic control ,business.industry ,General Mathematics ,010102 general mathematics ,Order (ring theory) ,Robotics ,Kalman filter ,Type (model theory) ,Motion control ,01 natural sciences ,010305 fluids & plasmas ,Nonlinear system ,Stability theory ,0103 physical sciences ,Applied mathematics ,Artificial intelligence ,0101 mathematics ,business ,Mathematics - Abstract
We consider in this paper an automatic control second-order discrete-time system whose nonlinearity satisfies the generalized Routh–Hurwitz conditions. Systems of this type are widely used in solving modern application problems that arise in engineering, theory of motion control, mechanics, physics, and robotics. Two constructed examples of discrete-time systems with nonlinearities that lie in a Hurwitz angle were presented in recent papers by W. Heath, J. Carrasco, and M. de la Sen. These examples demonstrate that in the discrete case, the Aizerman and Kalman conjectures are untrue even for second-order systems. One such system in these examples has a three-period cycle and the other system, a four-period cycle. We assume in the present paper that the nonlinearity is two-periodic and lies in a Hurwitz angle; here, we study a system for all possible parameter values. We explicitly present the conditions (for the parameters) under which it is possible to construct a two-periodic nonlinearity in such a way that a system with it is not globally asymptotically stable. Such a nonlinearity can be constructed in more than one way. We propose a method for constructing the nonlinearity in such a way that a family of four-period cycles is found in the system. The cycles are nonisolated; any solution of the system with the initial data, which lies on a certain specified ray, is a periodic solution.
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- 2020
314. Ramanujan denesting formulae for cubic radicals
- Author
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K. I. Pimenov and M. A. Antipov
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Pure mathematics ,Polynomial ,Mathematics::Number Theory ,General Mathematics ,010102 general mathematics ,General Physics and Astronomy ,Inverse ,Extension (predicate logic) ,Type (model theory) ,01 natural sciences ,010305 fluids & plasmas ,Ramanujan's sum ,symbols.namesake ,0103 physical sciences ,symbols ,0101 mathematics ,Cubic function ,Mathematics - Abstract
This paper contains an explanation of Ramanujan-type formulas with cubic radicals of cubic irrationalities in the situation when these radicals are contained in a pure cubic extension. We give a complete description of formulas of such type, answering the Zippel’s question. It turns out that Ramanujan-type formulas are in some sense unique in this situation. In particular, there must be no more than three summands in the right-hand side and the norm of the irrationality in question must be a cube. In this situation we associate cubic irrationalities with a cyclic cubic polynomial, which is reducible if and only if one can simplify the corresponding cubic radical. This correspondence is inverse to the so-called Ramanujan correspondence defined in the preceding papers, where one associates a pure cubic extension to some cyclic polynomial.
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- 2020
315. Cosmological meaning of geometric curvatures
- Author
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Nenad O. Vesić
- Subjects
Mathematics - Differential Geometry ,General Mathematics ,010102 general mathematics ,Scalar (physics) ,I.1.0 ,01 natural sciences ,Riemannian space ,Functional Analysis (math.FA) ,Mathematics - Functional Analysis ,010101 applied mathematics ,Theoretical physics ,53B50, 47B15, 53A45, 53B05 ,Differential Geometry (math.DG) ,FOS: Mathematics ,Meaning (existential) ,Tensor ,0101 mathematics ,Mathematics - Abstract
In this paper, we analyzed the physical meaning of scalar curvatures for a generalized Riemannian space. It is developed the Madsen's formulae for pressures and energy-densities with respect to the corresponding energy-momentum tensors. After that, the energy-momentum tensors, pressures, energy-densities and state-parameters are analyzed with respect to different concepts of generalized Riemannian spaces. At the end of this paper, linearities of the energy-momentum tensor, pressure, energy-density and the state-parameter are examined., Comment: 17 pages, 0 figures, manuscript
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- 2020
316. On Bloom type estimates for iterated commutators of fractional integrals
- Author
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Israel P. Rivera-Ríos, Javier C. Martínez-Perales, and Natalia Accomazzo
- Subjects
Pure mathematics ,General Mathematics ,010102 general mathematics ,Type (model theory) ,Characterization (mathematics) ,Mathematical proof ,Space (mathematics) ,01 natural sciences ,Mathematics - Classical Analysis and ODEs ,Iterated function ,Classical Analysis and ODEs (math.CA) ,FOS: Mathematics ,0101 mathematics ,Mathematics - Abstract
In this paper we provide quantitative Bloom type estimates for iterated commutators of fractional integrals improving and extending results from a work of Holmes, Rahm and Spencer. We give new proofs for those inequalities relying upon a new sparse domination that we provide as well in this paper and also in techniques developed in a recent paper due to Lerner, Ombrosi and the third author. We extend as well the necessity established in the work of Holmes, Rahm and Spencer to iterated commutators providing a new proof. As a consequence of the preceding results we recover the one weight estimates in works of Cruz-Uribe and Moen and B\'enyi, Martell, Moen, Stachura, Torres and establish the sharpness in the iterated case. Our result provides as well a new characterization of the BMO space., Comment: 18 pages
- Published
- 2020
317. On the polar Orlicz-Minkowski problems and the p-capacitary Orlicz-Petty bodies
- Author
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Xiaokang Luo, Deping Ye, and Baocheng Zhu
- Subjects
Mathematics::Functional Analysis ,Pure mathematics ,General Mathematics ,010102 general mathematics ,Mathematics::Classical Analysis and ODEs ,Metric Geometry (math.MG) ,Type (model theory) ,01 natural sciences ,Measure (mathematics) ,52A20, 52A38, 52A39, 52A40, 53A15 ,Mathematics - Metric Geometry ,0103 physical sciences ,Minkowski space ,FOS: Mathematics ,Mathematics::Metric Geometry ,Polar ,010307 mathematical physics ,Orthogonal matrix ,0101 mathematics ,Isoperimetric inequality ,Mathematics - Abstract
In this paper, we propose and study the polar Orlicz-Minkowski problems: under what conditions on a nonzero finite measure $\mu$ and a continuous function $\varphi:(0,\infty)\rightarrow(0,\infty)$, there exists a convex body $K\in\mathcal{K}_0$ such that $K$ is an optimizer of the following optimization problems: \begin{equation*} \inf/\sup \bigg\{\int_{S^{n-1}}\varphi\big( h_L \big) \,d \mu: L \in \mathcal{K}_{0} \ \text{and}\ |L^\circ|=\omega_{n}\bigg\}. \end{equation*} The solvability of the polar Orlicz-Minkowski problems is discussed under different conditions. In particular, under certain conditions on $\varphi,$ the existence of a solution is proved for a nonzero finite measure $\mu$ on $S^{n-1}$ which is not concentrated on any hemisphere of $S^{n-1}.$ Another part of this paper deals with the $p$-capacitary Orlicz-Petty bodies. In particular, the existence of the $p$-capacitary Orlicz-Petty bodies is established and the continuity of the $p$-capacitary Orlicz-Petty bodies is proved., Comment: This paper has been accepted by Indiana University Mathematics Journal
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- 2020
318. 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
- Subjects
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.
- Published
- 2021
- Full Text
- View/download PDF
319. The universality of Hughes-free division rings
- Author
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Andrei Jaikin-Zapirain and UAM. Departamento de Matemáticas
- Subjects
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
- Published
- 2021
320. Quadruple Roman Domination in Trees
- Author
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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
321. 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
322. 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.
- Published
- 2021
323. 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
324. 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
325. A New Class of Plane Curves with Arc Length Parametrization and Its Application to Linear Analysis of Curved Beams
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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
326. 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]
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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
327. 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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328. Sheaves of maximal intersection and multiplicities of stable log maps
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Sheldon Katz, Michel van Garrel, Nobuyoshi Takahashi, and Jinwon Choi
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High Energy Physics - Theory ,Pure mathematics ,Logarithm ,010308 nuclear & particles physics ,General Mathematics ,010102 general mathematics ,Deformation theory ,FOS: Physical sciences ,General Physics and Astronomy ,Tangent ,Multiplicity (mathematics) ,01 natural sciences ,Moduli space ,Mathematics - Algebraic Geometry ,Mathematics::Algebraic Geometry ,High Energy Physics - Theory (hep-th) ,Intersection ,Genus (mathematics) ,0103 physical sciences ,FOS: Mathematics ,0101 mathematics ,Algebraic Geometry (math.AG) ,Mathematics::Symplectic Geometry ,General position ,Mathematics - Abstract
A great number of theoretical results are known about log Gromov-Witten invariants, but few calculations are worked out. In this paper we restrict to surfaces and to genus 0 stable log maps of maximal tangency. We ask how various natural components of the moduli space contribute to the log Gromov-Witten invariants. The first such calculation by Gross-Pandharipande-Siebert deals with multiple covers over rigid curves in the log Calabi-Yau setting. As a natural continuation, in this paper we compute the contributions of non-rigid irreducible curves in the log Calabi-Yau setting and that of the union of two rigid curves in general position. For the former, we construct and study a moduli space of "logarithmic" 1-dimensional sheaves and compare the resulting multiplicity with tropical multiplicity. For the latter, we explicitly describe the components of the moduli space and work out the logarithmic deformation theory in full, which we then compare with the deformation theory of the analogous relative stable maps., Comment: Added two example sections including a comparison with tropical multiplicity. 53 pages, 4 figures
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- 2021
329. 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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330. 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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331. 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
332. Some Fixed Point Theorems in Banach Spaces and Application to a Transport Equation with Delayed Neutrons
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Khalid Latrach, Ahmed Zeghal, and Mohamed Yassine Abdallah
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Pure mathematics ,General Mathematics ,010102 general mathematics ,Banach space ,Fixed-point theorem ,Type (model theory) ,Fixed point ,Mathematical proof ,01 natural sciences ,010101 applied mathematics ,Nonlinear system ,0101 mathematics ,Convection–diffusion equation ,Delayed neutron ,Mathematics - Abstract
In this paper, we present some fixed point theorems of Krasnosel’skii’s type in Banach spaces. The involved operators need not to be compact nor weakly continuous. The results are obtained and formulated with the use of the measures of weak noncompactness and a large classes of contractions (strict contractions, nonlinear contractions, as well as nonexpansive or pseudocontractive mappings). Throughout the paper, we use the hypothesis $$\mathsf {(H1)}$$ and $$\mathsf {(H2)}$$ , which are one of the main ingredients of the proofs. Finally, with the obtained fixed point results, we discuss the existence of solutions to a stationary transport equation with delayed neutrons.
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- 2021
333. 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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334. Existence and Regularity of Weak Solutions for $$\psi $$-Hilfer Fractional Boundary Value Problem
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J. Vanterler da C. Sousa, E. Capelas de Oliveira, and M. Aurora P. Pulido
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Pure mathematics ,General Mathematics ,010102 general mathematics ,Hilbert space ,01 natural sciences ,Fractional calculus ,010101 applied mathematics ,symbols.namesake ,symbols ,High Energy Physics::Experiment ,Integration by parts ,Boundary value problem ,0101 mathematics ,Mathematics - Abstract
In the present paper, we investigate the existence and regularity of weak solutions for $$\psi $$ -Hilfer fractional boundary value problem in $$\mathbb {C}^{\alpha ,\beta ;\psi }_{2}$$ and $$\mathcal {H}$$ (Hilbert space) spaces, using extension of the Lax–Milgram theorem. In this sense, to finalize the paper, we discuss the integration by parts for $$\psi $$ -Riemann–Liouville fractional integral and $$\psi $$ -Hilfer fractional derivative.
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- 2021
335. Explicit Solutions of Initial Value Problems for Fractional Generalized Proportional Differential Equations with and without Impulses
- Author
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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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336. Second-Order PDE Constrained Controlled Optimization Problems with Application in Mechanics
- Author
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Savin Treanţă
- Subjects
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
337. 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
338. 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
339. 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
340. Archimedean non-vanishing, cohomological test vectors, and standard L-functions of $${\mathrm {GL}}_{2n}$$: real case
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Cheng Chen, Fangyang Tian, Dihua Jiang, and Bingchen Lin
- Subjects
Pure mathematics ,Mathematics - Number Theory ,General Mathematics ,media_common.quotation_subject ,010102 general mathematics ,Linear model ,Structure (category theory) ,22E45 (Primary), 11F67 (Secondary) ,Type (model theory) ,Lambda ,Infinity ,01 natural sciences ,Invariant theory ,Linear form ,0103 physical sciences ,FOS: Mathematics ,Number Theory (math.NT) ,010307 mathematical physics ,Representation Theory (math.RT) ,0101 mathematics ,Mathematics - Representation Theory ,Mathematics ,media_common - Abstract
The standard $L$-functions of $\mathrm{GL}_{2n}$ expressed in terms of the Friedberg-Jacquet global zeta integrals have better structure for arithmetic applications, due to the relation of the linear periods with the modular symbols. The most technical obstacles towards such arithmetic applications are (1) non-vanishing of modular symbols at infinity and (2) the existance or construction of uniform cohomological test vectors. Problem (1) is also called the non-vanishing hypothesis at infinity, which was proved by Binyong Sun, by establishing the existence of certain cohomological test vectors. In this paper, we explicitly construct an archimedean local integral that produces a new type of a twisted linear functional $\Lambda_{s,\chi}$, which, when evaluated with our explicitly constructed cohomological vector, is equal to the local twisted standard $L$-function $L(s,\pi\otimes\chi)$ as a meromorphic function of $s\in \mathbb{C}$. With the relations between linear models and Shalika models, we establish (1) with an explicitly constructed cohomological vector, and hence recovers a non-vanishing result of Binyong Sun via a completely different method. Our main result indicates a complete solution to (2), which will be presented in a paper of Dihua Jiang, Binyong Sun and Fangyang Tian with full details and with applications to the global period relations for the twisted standard $L$-functions at critical places., Comment: 39 pages. The current version of this paper is significantly shorter than the previous one, as the first author pointed out a conceptual intepretation of construction of cohomological test vector in the old version of this paper. Section 4 is completely rewritten. Also fix some inaccuracies
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- 2019
341. A sparse approach to mixed weak type inequalities
- Author
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Marcela Caldarelli and Israel P. Rivera-Ríos
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Pure mathematics ,Inequality ,General Mathematics ,media_common.quotation_subject ,010102 general mathematics ,Novelty ,Singular integral ,Weak type ,01 natural sciences ,0103 physical sciences ,010307 mathematical physics ,0101 mathematics ,GEOM ,media_common ,Mathematics - Abstract
In this paper we provide some quantitative mixed weak-type estimates assuming conditions that imply that $$uv\in A_{\infty }$$ for Calderon–Zygmund operators, rough singular integrals and commutators. The main novelty of this paper lies in the fact that we rely upon sparse domination results, pushing an approach to endpoint estimates that was introduced in Domingo-Salazar et al. (Bull Lond Math Soc 48(1):63–73, 2016) and extended in Lerner et al. (Adv Math 319:153–181, 2017) and Li et al. (J Geom Anal, 2018).
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- 2019
342. Moving Frames and Differential Invariants on Fully Affine Planar Curves
- Author
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Yun Yang and Yanhua Yu
- Subjects
Pure mathematics ,Fundamental theorem ,General Mathematics ,010102 general mathematics ,Differential operator ,01 natural sciences ,010101 applied mathematics ,Moving frame ,Affine curvature ,Affine group ,Equivariant map ,Affine transformation ,0101 mathematics ,Invariant (mathematics) ,Mathematics - Abstract
In this paper, by the affine analogue of the fundamental theorem for Euclidean planar curves, we classify the affine curves with constant affine curvatures. Note that we use the fully affine group and not the equi-affine subgroup consisting of area-preserving affine transformations. (Caution: much of the literature omits the “equi-” in their treatment.) According to the equivariant method of moving frames, explicit formulas for the generating affine differential invariants and invariant differential operators are constructed. At the same time, by using the fact that the affine transformation group GA$$(2,\mathbb {R})$$ can factor as a product of two subgroup $$B\cdot \mathrm{SE}(2,\mathbb {R})$$ and the moving frame of the subgroup SE$$(2,\mathbb {R})$$, we build the moving frame of GA$$(2,\mathbb {R})$$ and obtain the relations among invariants of group GA$$(2,\mathbb {R})$$ and its subgroup SE$$(2,\mathbb {R})$$. Applying the affine curvature to recognize affine equivalent objects is considered in the last part of this paper.
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- 2019
343. Necessary optimality conditions for a semivectorial bilevel optimization problem using the kth-objective weighted-constraint approach
- Author
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Khadija Hamdaoui, Mohammed El Idrissi, and N. Gadhi
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021103 operations research ,General Mathematics ,010102 general mathematics ,0211 other engineering and technologies ,02 engineering and technology ,Operator theory ,First order ,Mathematical proof ,01 natural sciences ,Bilevel optimization ,Potential theory ,Theoretical Computer Science ,Constraint (information theory) ,symbols.namesake ,Fourier analysis ,symbols ,Applied mathematics ,0101 mathematics ,Variational analysis ,Analysis ,Mathematics - Abstract
In this paper, we have pointed out that the proof of Theorem 11 in the recent paper (Lafhim in Positivity, 2019. https://doi.org/10.1007/s11117-019-00685-1 ) is erroneous. Using techniques from variational analysis, we propose other proofs to detect necessary optimality conditions in terms of Karush–Kuhn–Tucker multipliers. Our main results are given in terms of the limiting subdifferentials and the limiting normal cones. Completely detailed first order necessary optimality conditions are then given in the smooth setting while using the generalized differentiation calculus of Mordukhovich.
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- 2019
344. Martingale decomposition of an L2 space with nonlinear stochastic integrals
- Author
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Clarence Simard
- Subjects
Statistics and Probability ,Optimization problem ,General Mathematics ,010102 general mathematics ,Stochastic calculus ,01 natural sciences ,010104 statistics & probability ,Nonlinear system ,Integrator ,Bounded function ,Applied mathematics ,0101 mathematics ,Statistics, Probability and Uncertainty ,Lp space ,Martingale (probability theory) ,Brownian motion ,Mathematics - Abstract
This paper generalizes the Kunita–Watanabe decomposition of an $L^2$ space. The generalization comes from using nonlinear stochastic integrals where the integrator is a family of continuous martingales bounded in $L^2$ . This result is also the solution of an optimization problem in $L^2$ . First, martingales are assumed to be stochastic integrals. Then, to get the general result, it is shown that the regularity of the family of martingales with respect to its spatial parameter is inherited by the integrands in the integral representation of the martingales. Finally, an example showing how the results of this paper, with the Clark–Ocone formula, can be applied to polynomial functions of Brownian integrals.
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- 2019
345. On Extensions of Semigroups and Their Applications to Toeplitz Algebras
- Author
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Suren A. Grigoryan, R. N. Gumerov, and Ekaterina Lipacheva
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Pure mathematics ,Toeplitz algebra ,Mathematics::Operator Algebras ,Semigroup ,General Mathematics ,010102 general mathematics ,Normal extension ,01 natural sciences ,Toeplitz matrix ,010305 fluids & plasmas ,Numerical semigroup ,0103 physical sciences ,Grothendieck group ,0101 mathematics ,Commutative property ,Mathematics ,Additive group - Abstract
The paper deals with the normal extensions of cancellative commutative semigroups and the Toeplitz algebras for those semigroups. By the Toeplitz algebra for a semigroup S one means the reduced semigroup C*-algebra C*(S). We study the normal extensions of cancellative commutative semigroups by the additive group ℤn of integers modulo n. Moreover, we assume that such an extension is generated by one element. We present a general method for constructing normal extensions of semigroups which contain no non-trivial subgroups. The Grothendieck group for a given semigroup and the group of all integers are involved in this construction. Examples of such extensions for the additive semigroup of non-negative integers are given. A criterion for a normal extension generated by an element to be isomorphic to a numerical semigroup is given in number-theoretic terms. The results concerning the Toeplitz algebras are the following. For a cancellative commutative semigroup S and its normal extension L generated by one element, there exists a natural embedding the semigroup C*-algebra C*(S) into C*(L). The semigroup C*-algebra C*(L) is topologically ℤn-graded. The results in the paper are announced without proofs.
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- 2019
346. Explicit order 3/2 Runge-Kutta method for numerical solutions of stochastic differential equations by using Itô-Taylor expansion
- Author
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Yazid Alhojilan
- Subjects
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
347. A note on the consistency of wavelet estimators in nonparametric regression model under widely orthant dependent random errors
- Author
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Ping Chen and Liwang Ding
- Subjects
010104 statistics & probability ,Wavelet ,Consistency (statistics) ,General Mathematics ,010102 general mathematics ,Random error ,Statistics ,Estimator ,0101 mathematics ,01 natural sciences ,Nonparametric regression ,Mathematics ,Orthant - Abstract
In this paper, we consider the wavelet estimators of a nonparametric regression model based on widely orthant dependent random errors. The moment consistency and the completely consistency for wavelet estimators under some more mild moment conditions are investigated. The results obtained in the paper improve and extend the corresponding ones for dependent random variables. Finally, we provide a numerical simulation to verify the validity of our results.
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- 2019
348. A Modified Analytic Function Space Feynman Integral of Functionals on Function Space
- Author
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Seung-Jun Chang and Hyun Soo Chung
- Subjects
Class (set theory) ,Pure mathematics ,Function space ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,Space (mathematics) ,Translation (geometry) ,01 natural sciences ,First variation ,010104 statistics & probability ,Banach algebra ,Fubini's theorem ,0101 mathematics ,Analytic function ,Mathematics - Abstract
In this paper, the authors introduce a class of functionals. This class forms a Banach algebra for the special cases. The main purpose of this paper is to investigate some properties of the modified analytic function space Feynman integral of functionals in the class. Those properties contain various results and formulas which were not obtained in previous papers. Also, the authors establish some relationships involving the first variation via the translation theorem on function space. In particular, the authors establish the Fubini theorem for the modified analytic function space Feynman integral which was not obtained in previous researches yet.
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- 2019
349. Virtual Retraction Properties in Groups
- Author
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Ashot Minasyan
- Subjects
Property (philosophy) ,Conjecture ,Group (mathematics) ,General Mathematics ,010102 general mathematics ,20E26, 20E25, 20E08 ,Group Theory (math.GR) ,01 natural sciences ,Commensurability (mathematics) ,Combinatorics ,Mathematics::Group Theory ,Simple (abstract algebra) ,Retract ,0103 physical sciences ,Free group ,FOS: Mathematics ,Graph (abstract data type) ,010307 mathematical physics ,0101 mathematics ,Mathematics - Group Theory ,Mathematics - Abstract
If $G$ is a group, a virtual retract of $G$ is a subgroup which is a retract of a finite index subgroup. Most of the paper focuses on two group properties: property (LR), that all finitely generated subgroups are virtual retracts, and property (VRC), that all cyclic subgroups are virtual retracts. We study the permanence of these properties under commensurability, amalgams over retracts, graph products and wreath products. In particular, we show that (VRC) is stable under passing to finite index overgroups, while (LR) is not. The question whether all finitely generated virtually free groups satisfy (LR) motivates the remaining part of the paper, studying virtual free factors of such groups. We give a simple criterion characterizing when a finitely generated subgroup of a virtually free group is a free factor of a finite index subgroup. We apply this criterion to settle a conjecture of Brunner and Burns., 30 pages, 1 figure. v3: added Lemma 5.8 and made minor corrections following referee's comments. This version of the paper has been accepted for publication
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- 2019
350. Solutions of fractional gas dynamics equation by a new technique
- Author
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Alicia Cordero Barbero, Juan Ramón Torregrosa Sánchez, and Ali Akgül
- Subjects
Fractional gas dynamics equation ,General Mathematics ,Operators ,010102 general mathematics ,Hilbert space ,General Engineering ,Gas dynamics ,01 natural sciences ,010101 applied mathematics ,symbols.namesake ,symbols ,0101 mathematics ,MATEMATICA APLICADA ,Mathematics ,Mathematical physics - Abstract
[EN] In this paper, a novel technique is formed to obtain the solution of a fractional gas dynamics equation. Some reproducing kernel Hilbert spaces are defined. Reproducing kernel functions of these spaces have been found. Some numerical examples are shown to confirm the efficiency of the reproducing kernel Hilbert space method. The accurate pulchritude of the paper is arisen in its strong implementation of Caputo fractional order time derivative on the classical equations with the success of the highly accurate solutions by the series solutions. Reproducing kernel Hilbert space method is actually capable of reducing the size of the numerical work. Numerical results for different particular cases of the equations are given in the numerical section., This research was partially supported by Spanish Ministerio de Ciencia, Innovacion y Universidades PGC2018-095896-B-C22 and Generalitat Valenciana PROMETEO/2016/089.
- Published
- 2019
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