250 results
Search Results
2. Non-uniqueness of energy-conservative solutions to the isentropic compressible two-dimensional Euler equations
- Author
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Simon Markfelder and Christian Klingenberg
- Subjects
Isentropic process ,General Mathematics ,010102 general mathematics ,Non uniqueness ,Mathematical analysis ,Mathematics::Analysis of PDEs ,Gas dynamics ,01 natural sciences ,Euler equations ,010101 applied mathematics ,symbols.namesake ,Compressibility ,symbols ,0101 mathematics ,Analysis ,Energy (signal processing) ,Mathematics - Abstract
We consider the 2-d isentropic compressible Euler equations. It was shown in [E. Chiodaroli, C. De Lellis and O. Kreml, Global ill-posedness of the isentropic system of gas dynamics, Comm. Pure Appl. Math. 68(7) (2015) 1157–1190] that there exist Riemann initial data as well as Lipschitz initial data for which there exist infinitely many weak solutions that fulfill an energy inequality. In this paper, we will prove that there is Riemann initial data for which there exist infinitely many weak solutions that conserve energy, i.e. they fulfill an energy equality. As in the aforementioned paper, we will also show that there even exist Lipschitz initial data with the same property.
- Published
- 2018
3. Some inequalities of Hermite–Hadamard, Ostrowski and Simpson type for (ξ,m,MT)-preinvex functions
- Author
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Mahmood Shakoori and Leila Nasiri
- Subjects
010101 applied mathematics ,Pure mathematics ,Hermite polynomials ,Hadamard transform ,General Mathematics ,010102 general mathematics ,Mathematics::Classical Analysis and ODEs ,0101 mathematics ,Type (model theory) ,01 natural sciences ,Mathematics - Abstract
In this paper, we first introduce a new class of [Formula: see text]-preinvex functions, which are called [Formula: see text]-preinvex functions, then we give some new estimates of Hermite–Hadamard, Ostrowski and Simpson type inequalities using Riemann–Liouville fractional integral. The obtained results in this paper generalize the well-known results in recent years.
- Published
- 2019
4. Rank, trace, eigenvalues and norms of a structured matrix
- Author
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Ahmet İpek
- Subjects
Sequence ,Trace (linear algebra) ,Rank (linear algebra) ,General Mathematics ,010102 general mathematics ,Astrophysics::Instrumentation and Methods for Astrophysics ,Matrix norm ,Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing) ,01 natural sciences ,010101 applied mathematics ,Euclidean distance ,Combinatorics ,Matrix (mathematics) ,Computer Science::General Literature ,Symmetric matrix ,0101 mathematics ,ComputingMilieux_MISCELLANEOUS ,Eigenvalues and eigenvectors ,Mathematics - Abstract
The paper deals with rank, trace, eigenvalues and norms of the matrix [Formula: see text], where [Formula: see text] are ith components of any real sequence [Formula: see text]. A result in this paper is that the Euclidean and spectral norms of the matrix [Formula: see text] is [Formula: see text]. This is a generalization of the main result by Solak [Appl. Math. Comput. 232 (2014) 919–921], with the proof based on a simple property of norms of real matrices.
- Published
- 2019
5. Orthogonal sets; orthogonal contractions
- Author
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Hasti Habibi, Madjid Eshaghi Gordji, and Mohammad Bagher Sahabi
- Subjects
010101 applied mathematics ,Discrete mathematics ,Metric space ,General Mathematics ,Completeness (order theory) ,010102 general mathematics ,Fixed-point theorem ,0101 mathematics ,Fixed point ,01 natural sciences ,Mathematics - Abstract
In this paper, we are interested in obtaining fixed point theorems by keeping the orthogonal completeness of the orthogonal metric space and replacing the [Formula: see text]-contraction condition in theorems by another slightly modified conditions. The paper contains an example illustrating our results.
- Published
- 2019
6. Explicit logarithmic formulas of special values of hypergeometric functions 3F2
- Author
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Toshifumi Yabu and Masanori Asakura
- Subjects
Pure mathematics ,Logarithm ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,Complex multiplication ,Special values ,14D07, 19F27, 33C20, 11G15, 14K22 ,01 natural sciences ,010101 applied mathematics ,Mathematics - Algebraic Geometry ,FOS: Mathematics ,0101 mathematics ,Hypergeometric function ,Algebraic Geometry (math.AG) ,Mathematics - Abstract
In a joint paper [4] by Otsubo, Terasoma and the first author, we proved that the special value 3F2(a,b,q;a+b,q;1) of the generalized hypergeometric function is a linear combination of log of algebraic numbers if the triplet (a,b,q) of rational numbers satisfies a certain numerical condition. However there remains a question how to obtain explicit descriptions of the values. In this paper, we give a method to do this, which is a further development of the technique in [4]., Comment: 22pages, To appear in Communications in Contemporary Mathematics
- Published
- 2019
7. Semi-linear optimal control problem on a smooth oscillating domain
- Author
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A. K. Nandakumaran, S. Aiyappan, and Ravi Prakash
- Subjects
010101 applied mathematics ,Asymptotic analysis ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,Mathematical analysis ,Boundary (topology) ,0101 mathematics ,Optimal control ,01 natural sciences ,Homogenization (chemistry) ,Domain (mathematical analysis) ,Mathematics - Abstract
We demonstrate the asymptotic analysis of a semi-linear optimal control problem posed on a smooth oscillating boundary domain in the present paper. We have considered a more general oscillating domain than the usual “pillar-type” domains. Consideration of such general domains will be useful in more realistic applications like circular domain with rugose boundary. We study the asymptotic behavior of the problem under consideration using a new generalized periodic unfolding operator. Further, we are studying the homogenization of a non-linear optimal control problem and such non-linear problems are limited in the literature despite the fact that they have enormous real-life applications. Among several other technical difficulties, the absence of a sufficient criteria for the optimal control is one of the most attention-grabbing issues in the current setting. We also obtain corrector results in this paper.
- Published
- 2019
8. The Fekete–Szegö coefficient functional problems for q-starlike and q-convex functions related with lemniscate of Bernoulli
- Author
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P. Gurusamy and S. Sivasubramanian
- Subjects
010101 applied mathematics ,Subordination (linguistics) ,Pure mathematics ,TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES ,General Mathematics ,010102 general mathematics ,Lemniscate of Bernoulli ,0101 mathematics ,Convex function ,01 natural sciences ,ComputingMilieux_MISCELLANEOUS ,Mathematics ,Analytic function - Abstract
The area of [Formula: see text]-calculus has attracted the serious attention of researchers. This great interest is due its application in various branches of mathematics and physics. The application of [Formula: see text]-calculus was initiated by Jackson [Jackson, On [Formula: see text]-definite integrals, Quart. J. Pure Appl. Math. 41 (1910) 193–203; On [Formula: see text]-functions and a certain difference operator, Trans. Roy. Soc. Edinburgh 46 (1908) 253–281.], who was the first to develop [Formula: see text]-integral and [Formula: see text]-derivative in a systematic way. In this paper, we make use of the concept of [Formula: see text]-calculus in the theory of univalent functions, to obtain the bounds for certain coefficient functional problems of [Formula: see text]-starlike and [Formula: see text]-convex functions. Further, we also obtain similar type of inequalities related to lemniscate of Bernoulli. The authors sincerely hope that this paper will revive this concept and encourage other researchers to work in this [Formula: see text]-calculus in the near-future in the area of complex function theory. Also, we present a direct and shortened proof for the estimates of [Formula: see text] found in [Mishra and Gochhayat, Fekete–Szego problem for [Formula: see text]-uniformly convex functions and for a class defined by Owa–Srivastava operator, J. Math. Anal. Appl. 347(2) (2008) 563–572] for [Formula: see text], [Formula: see text].
- Published
- 2019
9. Duality relations for second-order programming problem under (G,αf)-bonvexity assumptions
- Author
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Ramu Dubey, Puneet Tomar, and Vishnu Narayan Mishra
- Subjects
010101 applied mathematics ,Algebra ,General Mathematics ,010102 general mathematics ,Order (group theory) ,Duality (optimization) ,0101 mathematics ,Construct (philosophy) ,01 natural sciences ,Mathematics - Abstract
In this paper, we introduce the definition of [Formula: see text]-bonvex/[Formula: see text]-pseudobonvex functions and to show the existence of such functions, we construct nontrivial numerical examples. In the next section, we formulate a pair of second-order symmetric dual model in optimization problem and proved the duality results under [Formula: see text]-bonvexity/[Formula: see text]-pseudobonvexity assumptions. Further, we also construct nontrivial concrete examples which justifying definitions as well as the weak duality theorem presented in the paper.
- Published
- 2018
10. The 3-point quadrature rules with constant weight function
- Author
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Ch. Mahesh
- Subjects
010101 applied mathematics ,symbols.namesake ,Weight function ,General Mathematics ,010102 general mathematics ,Mathematical analysis ,symbols ,Gaussian quadrature ,0101 mathematics ,01 natural sciences ,Mathematics ,Polynomial interpolation ,Quadrature (mathematics) - Abstract
In this paper, we present all types of 3-point quadrature rules on continuous function on interval [Formula: see text] with constant weight function and compare there with the composite type also. All 3-point (open and closed) rules are taken from available papers and some new results like non-polynomial fitting and derivative type are introduced. Also, differences, comparisons, and errors between method procedures have been shown.
- Published
- 2018
11. Properties of ϕ-δ-primary and 2-absorbing δ-primary ideals of commutative rings
- Author
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Ameer Jaber
- Subjects
Pure mathematics ,Ideal (set theory) ,Mathematics::Commutative Algebra ,Computer Science::Information Retrieval ,General Mathematics ,Prime ideal ,010102 general mathematics ,Astrophysics::Instrumentation and Methods for Astrophysics ,Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing) ,Commutative ring ,01 natural sciences ,010101 applied mathematics ,TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES ,Primary ideal ,Primary (astronomy) ,ComputingMethodologies_DOCUMENTANDTEXTPROCESSING ,Computer Science::General Literature ,0101 mathematics ,ComputingMilieux_MISCELLANEOUS ,Mathematics - Abstract
Let [Formula: see text] be a commutative ring with unity [Formula: see text] and let [Formula: see text] be an ideal expansion. In the first part of this paper, we extend the concept of [Formula: see text]-primary ideals to [Formula: see text]-[Formula: see text]-primary ideals, where [Formula: see text] is an ideal reduction and [Formula: see text] is an ideal expansion. We introduce some of the ideal expansion [Formula: see text] and define [Formula: see text]-[Formula: see text]-primary ideals, where [Formula: see text] is an ideal reduction. Also, we investigate ideal expansions satisfying some additional conditions and prove more properties of the generalized [Formula: see text]-[Formula: see text]-primary ideals with respect to such an ideal expansion [Formula: see text]. In the second part of this paper we investigate 2-absorbing [Formula: see text]-primary ideals which unify 2-absorbing ideals and 2-absorbing primary ideals, where [Formula: see text] is an ideal expansion. A number of results in the two parts are given.
- Published
- 2018
12. Adams inequality with exact growth in the hyperbolic space ℍ4 and Lions lemma
- Author
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Debabrata Karmakar
- Subjects
010101 applied mathematics ,Pure mathematics ,Lemma (mathematics) ,Inequality ,Applied Mathematics ,General Mathematics ,Hyperbolic space ,media_common.quotation_subject ,010102 general mathematics ,0101 mathematics ,01 natural sciences ,Mathematics ,media_common - Abstract
In this paper, we prove Adams inequality with exact growth condition in the four-dimensional hyperbolic space ℍ4, ∫ℍ4 e32π2u2 − 1 (1 + |u|)2 dvg ≤ C∥u∥L2(ℍ4)2, (0.1) for all u ∈ Cc∞(ℍ4) with ∫ ℍ4(P2u)udvg ≤ 1. We will also establish an Adachi–Tanaka-type inequality in this setting. Another aspect of this paper is the Lions lemma in the hyperbolic space. We prove Lions lemma for the Moser functional and for a few cases of the Adams functional on the whole hyperbolic space.
- Published
- 2018
13. Diophantine quadruples and near-Diophantine quintuples from P3,K sequences
- Author
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A. M. S. Ramasamy
- Subjects
Discrete mathematics ,Sequence ,Polynomial ,Fibonacci number ,Diophantine set ,General Mathematics ,Diophantine equation ,010102 general mathematics ,Natural number ,01 natural sciences ,Square (algebra) ,010101 applied mathematics ,TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES ,ComputingMethodologies_DOCUMENTANDTEXTPROCESSING ,Pell's equation ,0101 mathematics ,ComputingMilieux_MISCELLANEOUS ,Mathematics - Abstract
The question of a non-[Formula: see text]-type [Formula: see text] sequence wherein the fourth term shares the property [Formula: see text] with the first term has not been investigated so far. The present paper seeks to fill up the gap in this unexplored area. Let [Formula: see text] denote the set of all natural numbers and [Formula: see text] the sequence of Fibonacci numbers. Choose two integers [Formula: see text] and [Formula: see text] with [Formula: see text] such that their product increased by [Formula: see text] is a square [Formula: see text]. Certain properties of the sequence [Formula: see text] defined by the relation [Formula: see text] are established in this paper and polynomial expressions for Diophantine quadruples from the [Formula: see text] sequence [Formula: see text] are derived. The concept of a near-Diophantine quintuple is introduced and it is proved that there exist an infinite number of near-Diophantine quintuples.
- Published
- 2017
14. Hilbert–Samuel functions of well bifiltered modules
- Author
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D. Sangare and H. Dichi
- Subjects
Noetherian ,Noetherian ring ,Ring (mathematics) ,Pure mathematics ,Mathematics::Commutative Algebra ,Computer Science::Information Retrieval ,General Mathematics ,010102 general mathematics ,Astrophysics::Instrumentation and Methods for Astrophysics ,Local ring ,Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing) ,Function (mathematics) ,Hilbert's basis theorem ,Base (topology) ,01 natural sciences ,010101 applied mathematics ,Algebra ,symbols.namesake ,symbols ,Computer Science::General Literature ,Krull dimension ,0101 mathematics ,Mathematics - Abstract
In an earlier paper, we studied the Hilbert quasi-polynomial functions of finitely generated bigraded modules in the general framework when the base ring is bigraded and generated by finitely many homogeneous elements of arbitrary degrees. In this paper, we introduce the concept of [Formula: see text]-good bifiltration [Formula: see text] on a finitely generated [Formula: see text]-module [Formula: see text], where [Formula: see text] and [Formula: see text] are specified noetherian filtrations on the noetherian ring [Formula: see text]. The bigraded modules associated with such bifiltrations are shown to be finitely generated under reasonable hypotheses. Their Hilbert functions are studied. The Hilbert–Samuel function of [Formula: see text] with respect to the [Formula: see text]-good bifiltration [Formula: see text] of [Formula: see text] is one of them. It is proved, among others, that this function is a quasi-polynomial function in two variables and that if [Formula: see text] is a noetherian local ring and if the filtrations [Formula: see text] and [Formula: see text] are primary filtrations, then its degree equals the Krull dimension of [Formula: see text].
- Published
- 2016
15. Generalized distance and new fixed point results
- Author
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Hamidreza Rahimi, Poom Kumam, and Ghasem Soleimani Rad
- Subjects
Unit sphere ,General Mathematics ,010102 general mathematics ,Mathematical analysis ,Minkowski distance ,Fixed point ,Fixed-point property ,01 natural sciences ,Chebyshev distance ,Intrinsic metric ,010101 applied mathematics ,Metric space ,Metric (mathematics) ,0101 mathematics ,Mathematics - Abstract
In this paper, we prove some common fixed point theorems by using the generalized distance in a cone metric space. The results of this paper extend well-known results in the literature.
- Published
- 2016
16. Cross-connection structure of concordant semigroups
- Author
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P. G. Romeo, K. S. S. Nambooripad, and P. A. Azeef Muhammed
- Subjects
Pure mathematics ,Ideal (set theory) ,CONSISTENT CATEGORY ,20M10, 20M50, 18A32 ,Semigroup ,General Mathematics ,CONCORDANT SEMIGROUP ,INDUCTIVE CANCELLATIVE CATEGORY ,010102 general mathematics ,Cross connection ,Structure (category theory) ,Mathematics - Category Theory ,Group Theory (math.GR) ,CONSISTENT FACTORIZATION ,01 natural sciences ,Dual (category theory) ,CROSS-CONNECTIONS ,010101 applied mathematics ,Mathematics::Category Theory ,DUAL ,FOS: Mathematics ,Category Theory (math.CT) ,0101 mathematics ,Mathematics - Group Theory ,Mathematics - Abstract
Cross-connection theory provides the construction of a semigroup from its ideal structure using small categories. A concordant semigroup is an idempotent-connected abundant semigroup whose idempotents generate a regular subsemigroup. We characterize the categories arising from the generalized Green relations in the concordant semigroup as consistent categories and describe their interrelationship using cross-connections. Conversely, given a pair of cross-connected consistent categories, we build a concordant semigroup. We use this correspondence to prove a category equivalence between the category of concordant semigroups and the category of cross-connected consistent categories. In the process, we illustrate how our construction is a generalization of the cross-connection analysis of regular semigroups. We also identify the inductive cancellative category associated with a pair of cross-connected consistent categories. © 2020 World Scientific Publishing Company. The first author acknowledges the financial support of the Competitiveness Enhancement Program of Ural Federal University, Russia during the preparation of this paper.
- Published
- 2019
17. Sharp lifespan estimates of blowup solutions to semi-linear wave equations with time-dependent effective damping
- Author
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Motohiro Sobajima, Yuta Wakasugi, and Masahiro Ikeda
- Subjects
General Mathematics ,010102 general mathematics ,Mathematical analysis ,Mathematics::Analysis of PDEs ,Wave equation ,35L71 ,01 natural sciences ,Term (time) ,010101 applied mathematics ,Mathematics - Analysis of PDEs ,FOS: Mathematics ,Initial value problem ,0101 mathematics ,Analysis ,Analysis of PDEs (math.AP) ,Mathematics - Abstract
We consider the initial value problem for the semilinear wave equation with time-dependent effective damping. The interest is the behavior of lifespan of solutions in view of the asymptotic profile of the damping as $t\to \infty$. The result of this paper is the sharp lifespan estimates of blowup solutions for general time-dependent damping including threshold cases between effective and overdamping., 20 pages, typos are corrected, references are updated, to appear in J. Hyperbolic Differ. Equ
- Published
- 2019
18. The two-dimensional unsteady supersonic flow around a convex corner
- Author
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Shouke You and Wancheng Sheng
- Subjects
Physics::Fluid Dynamics ,010101 applied mathematics ,Flow (mathematics) ,General Mathematics ,010102 general mathematics ,Regular polygon ,Geometry ,0101 mathematics ,01 natural sciences ,Choked flow ,Analysis ,Geology - Abstract
The flow around a convex corner is one of the most important elementary flows. In this paper, we are concerned with the two-dimensional (2D) unsteady supersonic flow turning a convex corner. We firstly give the properties of general centered simple for the two-dimensional isentropic irrotational pesudo-steady Euler equations. Then, by using the properties of general centered simple waves, we construct the self-similar solution for the two-dimensional isentropic irrotational supersonic flow around a convex corner and prove that the supersonic flow turns the convex corner by a centered expansion wave or a centered compression wave under appropriate conditions on the downstream state.
- Published
- 2018
19. Definitions of solutions to the IBVP for multi-dimensional scalar balance laws
- Author
-
Elena Rossi and Rossi, E
- Subjects
General Mathematics ,010102 general mathematics ,Scalar (mathematics) ,Boundary condition ,01 natural sciences ,Initial-boundary value problem ,010101 applied mathematics ,Entropy-entropy flux pair ,Law ,Multi dimensional ,Balance law ,Boundary value problem ,0101 mathematics ,Analysis ,Mathematics - Abstract
We consider four definitions of solution to the initial-boundary value problem (IBVP) for a scalar balance laws in several space dimensions. These definitions are extended to the same most general framework and then compared. The first aim of this paper is to detail differences and analogies among them. We focus then on the ways the boundary conditions are fulfilled according to each definition, providing also connections among these various modes. The main result is the proof of the equivalence among the presented definitions of solution.
- Published
- 2018
20. Convergence of the Godunov scheme for a scalar conservation law with time and space discontinuities
- Author
-
John D. Towers
- Subjects
010101 applied mathematics ,Physics ,Conservation law ,Spacetime ,General Mathematics ,010102 general mathematics ,Mathematical analysis ,Scalar (mathematics) ,Godunov's scheme ,0101 mathematics ,Classification of discontinuities ,01 natural sciences ,Analysis - Abstract
We consider the Godunov scheme as applied to a scalar conservation law whose flux has discontinuities in both space and time. The time-and space-dependence of the flux occurs through a positive multiplicative coefficient. That coefficient has a spatial discontinuity along a fixed interface at [Formula: see text]. Time discontinuities occur in the coefficient independently on either side of the interface. This setup applies to the Lighthill–Witham–Richards (LWR) traffic model in the case where different time-varying speed limits are imposed on different segments of a road. We prove that the approximate solutions produced by the Godunov scheme converge to the unique entropy solution, as defined by Coclite and Risebro in 2005. Convergence of the Godunov scheme in the presence of spatial flux discontinuities alone is a well-established fact. The novel aspect of this paper is convergence in the presence of additional temporal flux discontinuities.
- Published
- 2018
21. Homogenization of nonlinear hyperbolic stochastic equation via Tartar’s method
- Author
-
Mogtaba Mohammed
- Subjects
Constant coefficients ,General Mathematics ,010102 general mathematics ,Mathematical analysis ,Probabilistic logic ,Stochastic calculus ,01 natural sciences ,Homogenization (chemistry) ,010101 applied mathematics ,Nonlinear system ,Compact space ,0101 mathematics ,Hyperbolic partial differential equation ,Analysis ,Mathematics - Abstract
In this paper, We establish new homogenization results for stochastic nonlinear hyperbolic equations with periodically oscillating coefficients. We use a delicate blending of Tartar’s method of oscillating test functions and deep probabilistic compactness results due to Prokhorov and Skorokhod. We prove that the sequence of solutions of the original problem converges in suitable topologies to the solution of a homogenized stochastic hyperbolic problem with constant coefficients. We also prove the convergence of the associated energies.
- Published
- 2017
22. Global existence theory for general hyperbolic-parabolic balance laws with application
- Author
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Yanni Zeng
- Subjects
Conservation law ,Rank (linear algebra) ,Thermodynamic equilibrium ,General Mathematics ,010102 general mathematics ,Mathematical analysis ,Space (mathematics) ,01 natural sciences ,010101 applied mathematics ,symbols.namesake ,Flow (mathematics) ,Law ,Jacobian matrix and determinant ,symbols ,Initial value problem ,0101 mathematics ,Constant (mathematics) ,Analysis ,Mathematics - Abstract
We study a general system of hyperbolic-parabolic balance laws in [Formula: see text] space dimensions ([Formula: see text]). The system has rank deficient viscosity matrices and a lower order term whose Jacobian matrix is rank deficient as well. We consider the Cauchy problem when initial data are small perturbations of a constant equilibrium state. Under a set of reasonable assumptions including Kawashima–Shizuta condition, we establish the existence of solution global in time via energy method. The proposed assumptions are sufficiently general for applications to physical models such as electro-magneto flows and physical gas flows. In particular, we study the gas flow with an internal non-equilibrium mode besides the translational non-equilibrium. The general result in this paper recovers the existing results in literature on hyperbolic-parabolic conservation laws and hyperbolic balance laws, respectively, as two special cases.
- Published
- 2017
23. Vanishing of the first-order cohomology on Olshanski spherical pairs
- Author
-
Marouane Rabaoui
- Subjects
Pure mathematics ,General Mathematics ,010102 general mathematics ,Spherical representation ,Direct limit ,Space (mathematics) ,First order ,01 natural sciences ,Unitary state ,Cohomology ,010101 applied mathematics ,Countable set ,0101 mathematics ,Mathematics::Representation Theory ,Mathematics - Abstract
In this paper, we study the first-order cohomology space of countable direct limit groups related to Olshanski spherical pairs, relatively to unitary representations which do not have almost invariant vectors. In particular, we prove a variant of Delorme’s vanishing result of the first-order cohomology space for spherical representations of Olshanski spherical pairs.
- Published
- 2021
24. Some weighted Hardy and Rellich inequalities on the Heisenberg group
- Author
-
Jingbo Dou and Lin Xi
- Subjects
Pure mathematics ,Class (set theory) ,Inequality ,General Mathematics ,media_common.quotation_subject ,010102 general mathematics ,Mathematics::Analysis of PDEs ,Mathematics::Spectral Theory ,01 natural sciences ,010101 applied mathematics ,Heisenberg group ,0101 mathematics ,Mathematics ,media_common - Abstract
In this paper, we establish some weighted Hardy and Rellich inequalities and discuss its best constants on the Heisenberg group. Moreover, we also present a class of higher-order weighted Hardy–Rellich inequalities with the remainder term.
- Published
- 2021
25. Modified iteration method for numerical solution of nonlinear differential equations arising in science and engineering
- Author
-
Maheshwar Pathak and Pratibha Joshi
- Subjects
Iterative method ,General Mathematics ,Science and engineering ,010102 general mathematics ,Ode ,01 natural sciences ,Nonlinear differential equations ,010101 applied mathematics ,Nonlinear system ,Convergence (routing) ,Applied mathematics ,Initial value problem ,0101 mathematics ,Mathematics - Abstract
In this paper, a modified iteration method (MIM) has been proposed to solve nonlinear second-order ODEs. Convergence analysis and error estimate of the proposed method are also discussed. Computational efficiency of this method is illustrated through numerical examples.
- Published
- 2021
26. Time periodic traveling waves in a three-component non-autonomous and reaction-diffusion epidemic model
- Author
-
Jiangbo Zhou, Zaili Zhen, Lixin Tian, and Jingdong Wei
- Subjects
Time periodic ,Component (thermodynamics) ,General Mathematics ,010102 general mathematics ,Mathematical analysis ,Astrophysics::Instrumentation and Methods for Astrophysics ,Fixed-point theorem ,Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing) ,01 natural sciences ,Infection rate ,010101 applied mathematics ,Reaction–diffusion system ,Traveling wave ,Computer Science::General Literature ,0101 mathematics ,Epidemic model ,Mathematics - Abstract
In this paper, we propose a non-autonomous and diffusive SIR epidemic model based on the fact that the infection rate, the removal rate and the death rate often vary in time. The explicit formulas of the basic reproduction number [Formula: see text] and the minimum wave speed [Formula: see text] are derived. Applying upper-lower solution method and Schauder’s fixed point theorem, we show that when [Formula: see text], [Formula: see text] and the diffusion rates satisfy a certain condition, a time periodic traveling wave solution exists in the model. By the method of contradiction analysis and the comparison arguments together with the properties of the spreading speed of an associated subsystem, we prove that when [Formula: see text] and [Formula: see text] or [Formula: see text] and [Formula: see text], the model possesses no time periodic traveling wave solutions.
- Published
- 2021
27. The complex green operator with Sobolev estimates up to a finite order
- Author
-
Bingyuan Liu and Andrew Raich
- Subjects
Pure mathematics ,Computer Science::Information Retrieval ,General Mathematics ,Operator (physics) ,010102 general mathematics ,Astrophysics::Instrumentation and Methods for Astrophysics ,Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing) ,Type (model theory) ,01 natural sciences ,010101 applied mathematics ,Sobolev space ,Hypersurface ,Computer Science::General Literature ,Order (group theory) ,CR manifold ,0101 mathematics ,Mathematics - Abstract
The purpose of this paper is to explore the geometry of a smooth CR manifold of hypersurface type and its relationship to the higher regularity properties of the complex Green operator on [Formula: see text]-forms in the [Formula: see text]-Sobolev space [Formula: see text] for a fixed [Formula: see text] and [Formula: see text].
- Published
- 2020
28. On a Newton-type method under weak conditions with dynamics
- Author
-
Arvind Singh and Manoj Kumar Singh
- Subjects
Iterative method ,General Mathematics ,010102 general mathematics ,Dynamics (mechanics) ,Iteration function ,Type (model theory) ,01 natural sciences ,010101 applied mathematics ,symbols.namesake ,Algebraic equation ,Nonlinear system ,Rate of convergence ,symbols ,Applied mathematics ,0101 mathematics ,Newton's method ,Mathematics - Abstract
In this paper, we present new cubically convergent Newton-type iterative methods with dynamics for solving nonlinear algebraic equations under weak conditions. The proposed methods are free from second-order derivative and work well when [Formula: see text]. Numerical results show that the proposed method performs better when Newton’s method fails or diverges and competes well with same order existing method. Fractal patterns of different methods also support the numerical results and explain the compactness regarding the convergence, divergence, and stability of the methods to different roots.
- Published
- 2020
29. A non-local expanding flow of convex closed curves in the plane
- Author
-
Ke Shi
- Subjects
Plane (geometry) ,General Mathematics ,010102 general mathematics ,Convex curve ,Mathematical analysis ,Regular polygon ,Non local ,01 natural sciences ,010101 applied mathematics ,Perimeter ,Flow (mathematics) ,Euclidean geometry ,0101 mathematics ,Mathematics - Abstract
This paper presents a new non-local expanding flow for convex closed curves in the Euclidean plane which increases both the perimeter of the evolving curves and the enclosed area. But the flow expands the evolving curves to a finite circle smoothly if they do not develop singularity during the evolving process. In addition, it is shown that an additional assumption about the initial curve will ensure that the flow exists on the time interval [Formula: see text]. Meanwhile, a numerical experiment reveals that this flow may blow up for some initial convex curves.
- Published
- 2020
30. Regularity properties of nonlinear abstract Schrödinger equations and applications
- Author
-
Veli B. Shakhmurov
- Subjects
Function space ,General Mathematics ,010102 general mathematics ,Mathematical analysis ,Banach space ,Type (model theory) ,01 natural sciences ,Schrödinger equation ,010101 applied mathematics ,Harmonic analysis ,Nonlinear system ,symbols.namesake ,symbols ,0101 mathematics ,Mathematics - Abstract
In this paper, regularity properties, Strichartz type estimates for solution of integral problem for linear and nonlinear abstract Schrödinger equations in vector-valued function spaces are obtained. The equation includes a linear operator [Formula: see text] defined in a Banach space [Formula: see text], in which by choosing [Formula: see text] and [Formula: see text] we can obtain numerous classis of initial value problems for Schrödinger equations which occur in a wide variety of physical systems.
- Published
- 2020
31. Two-dimensional centered wave flow patches to the Guderley Mach reflection configurations for steady flows in gas dynamics
- Author
-
Geng Lai and Wancheng Sheng
- Subjects
Prandtl–Meyer expansion fan ,Shock (fluid dynamics) ,Mach reflection ,General Mathematics ,010102 general mathematics ,Mathematical analysis ,Geometry ,Mach wave ,01 natural sciences ,Euler equations ,010101 applied mathematics ,symbols.namesake ,Flow (mathematics) ,symbols ,Reflection (physics) ,Supersonic speed ,0101 mathematics ,Analysis ,Mathematics - Abstract
In an attempt to resolve the von Neumann triple point paradox in shock reflection phenomenon, a new type of reflection configuration, called Guderley Mach reflection, was observed both in numerical simulations and physical experiments recently. In this type of reflection configuration, there exists a sequence of triple points, with a centered expansion fan and a supersonic patch at each triple point. In this paper, we present a mathematical analysis of the centered wave flow patches of Guderley Mach reflection. In order to construct such a flow patch, a centered wave problem is introduced. The existence of a global classical solution to the centered wave problem for the two-dimensional isentropic irrotational steady Euler equations is established.
- Published
- 2016
32. Conformal vector fields on Finsler manifolds
- Author
-
Qiaoling Xia
- Subjects
Pure mathematics ,Conformal vector field ,General Mathematics ,010102 general mathematics ,Conformal map ,Characterization (mathematics) ,01 natural sciences ,010101 applied mathematics ,Metric (mathematics) ,Vector field ,Mathematics::Differential Geometry ,Finsler manifold ,0101 mathematics ,Mathematics::Symplectic Geometry ,Mathematics - Abstract
In this paper, we give an equivalent characterization of conformal vector fields on a Finsler manifold [Formula: see text], whose metric [Formula: see text] is defined by a Riemannian metric [Formula: see text] and a 1-form [Formula: see text]. This characterization contains all related results in [Z. Shen and Q. Xia, On conformal vector fields on Randers manifolds, Sci. China Math. 55(9) (2012) 1869–1882; Z. Shen and M. Yuan, Conformal vector fields on some Finsler manifolds, Sci. China Math. 59(1) (2016) 107–114; X. Cheng, Y. Li and T. Li, The conformal vector fields on Kropina manifolds, Diff. Geom. Appl. 56 (2018) 344–354] as special cases. Further, we determine conformal fields on some Finsler manifolds [Formula: see text] when [Formula: see text] is of constant sectional curvature and [Formula: see text] is a conformal 1-form with respect to [Formula: see text].
- Published
- 2020
33. On the rim tori refinement of relative Gromov–Witten invariants
- Author
-
Mohammad Farajzadeh Tehrani and Aleksey Zinger
- Subjects
010101 applied mathematics ,Pure mathematics ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,Torus ,Divisor (algebraic geometry) ,0101 mathematics ,Abelian group ,Mathematics::Symplectic Geometry ,01 natural sciences ,Mathematics ,Symplectic geometry - Abstract
We construct Ionel–Parker’s proposed refinement of the standard relative Gromov–Witten invariants in terms of abelian covers of the symplectic divisor and discuss in what sense it gives rise to invariants. We use it to obtain some vanishing results for the standard relative Gromov–Witten invariants. In a separate paper, we describe to what extent this refinement sharpens the usual symplectic sum formula and give further qualitative applications.
- Published
- 2020
34. Chain level proof for the isomorphism between Lie and Hochschild homologies
- Author
-
Zuhier Altawallbeh
- Subjects
Pure mathematics ,General Mathematics ,010102 general mathematics ,Mathematics::Algebraic Topology ,01 natural sciences ,Homology (biology) ,Square (algebra) ,010101 applied mathematics ,Chain (algebraic topology) ,Mathematics::K-Theory and Homology ,Mathematics::Category Theory ,Isomorphism ,0101 mathematics ,Commutative property ,Mathematics - Abstract
In this paper, we prove the commutativity of the square in the chain level of both Chevalley Eilenberg complex of Lie homology and Hochschild complex, where the antisymmetrization map is used between the complexes. Originally, Loday proved this isomorphism by constructing a certain map satisfying relations of a presimplicial homotopy to prove the commutativity of the square mentioned above. Here, we present a different approach for the proof of the commutativity without constructing that certain map satisfying the relations of the presimplicial homotopy.
- Published
- 2020
35. On a subclass of close-to-convex harmonic mappings
- Author
-
J. K. Prajapat and Rajbala
- Subjects
010101 applied mathematics ,Pure mathematics ,Class (set theory) ,General Mathematics ,010102 general mathematics ,Regular polygon ,Harmonic (mathematics) ,0101 mathematics ,Hypergeometric function ,01 natural sciences ,Unit disk ,Subclass ,Mathematics - Abstract
In this paper, we introduce a new class of sense preserving harmonic mappings [Formula: see text] in the open unit disk and prove that functions in this class are close-to-convex. We give some basic properties such as coefficient bounds, growth estimates, convolution and determine the radius of convexity for the sections of functions belonging to this family. In addition, we construct certain harmonic univalent polynomials belonging to this family.
- Published
- 2020
36. Note on topological ternary semigroup
- Author
-
S. Jana, S. Samanta, and Sukhendu Kar
- Subjects
Mathematics::Operator Algebras ,Group (mathematics) ,Semigroup ,General Mathematics ,010102 general mathematics ,Hausdorff space ,Cartesian product ,Topology ,01 natural sciences ,010101 applied mathematics ,symbols.namesake ,symbols ,0101 mathematics ,Ternary operation ,Mathematics - Abstract
In this paper, we have discussed various topological properties of (Hausdörff) topological ternary semigroup and topological ternary group. We have proved that the Cartesian product of an arbitrary family of topological ternary semigroups is again a topological ternary semigroup. We have investigated the existence of identity and idempotent in a topological ternary semigroup and discussed a method to topologize a ternary semigroup (group) with a compatible topology using some family of pseudometrics. Finally, we have proved that a compact topological ternary semigroup contains a ternary subgroup.
- Published
- 2020
37. Closed knight’s tour problem on some (m,n,k,1)-rectangular tubes
- Author
-
Sirirat Singhun, Nathaphat Loykaew, Ratinan Boonklurb, and Wasupol Srichote
- Subjects
010101 applied mathematics ,Combinatorics ,symbols.namesake ,General Mathematics ,Knight's tour ,010102 general mathematics ,symbols ,Knight ,0101 mathematics ,01 natural sciences ,Hamiltonian path ,Mathematics - Abstract
A closed knight’s tour of a normal two-dimensional chessboard by using legal moves of the knight has been generalized in several ways. One way is to consider a closed knight’s tour on a ringboard of width [Formula: see text], which is the [Formula: see text] chessboard with the middle part missing and the rim contains [Formula: see text] rows and [Formula: see text] columns. Another way is to stack [Formula: see text] copies of the [Formula: see text] chessboard to construct an [Formula: see text] rectangular chessboard and the closed knight’s tour can be on the surface or within the [Formula: see text] rectangular chessboard. This paper combines these two ideas by stacking [Formula: see text] copies of [Formula: see text] ringboard of width [Formula: see text], which we call the [Formula: see text]-rectangular tube. We explore the existence and the nonexistence of closed knight’s tours for [Formula: see text]-tube and [Formula: see text]-tube.
- Published
- 2020
38. On the initial value problems for the Caputo–Fabrizio impulsive fractional differential equations
- Author
-
Mohamed I. Abbas
- Subjects
010101 applied mathematics ,General Mathematics ,010102 general mathematics ,Initial value problem ,Fixed-point theorem ,Applied mathematics ,0101 mathematics ,Type (model theory) ,Fractional differential ,01 natural sciences ,Fractional calculus ,Mathematics - Abstract
This paper is devoted to initial value problems for impulsive fractional differential equations of Caputo–Fabrizio type fractional derivative. By means of Banach’s fixed point theorem and Schaefer’s fixed point theorem, the existence and uniqueness results are obtained. Finally, an example is given to illustrate one of the main results.
- Published
- 2020
39. Nonlocal Riemann–Liouville fractional evolution inclusions in Banach space
- Author
-
Nikolay Kitanov, Shamas Bilal, Nasir Javaid, and T. Donchev
- Subjects
010101 applied mathematics ,General Mathematics ,0103 physical sciences ,Banach space ,Fixed-point theorem ,Derivative ,0101 mathematics ,Riemann liouville ,010301 acoustics ,01 natural sciences ,Mathematical physics ,Mathematics - Abstract
In this paper, we study the existence of solutions for nonlocal semilinear fractional evolution inclusions involving Riemann–Liouville derivative in a general Banach space. The fixed point theorem for contractive valued multifunction is used. Illustrative example is provided.
- Published
- 2020
40. On the construction of supergrassmannians as homogeneous superspaces
- Author
-
Saad Varsaie and Mohammad Mohammadi
- Subjects
010101 applied mathematics ,Pure mathematics ,Functor ,Homogeneous ,General Mathematics ,010102 general mathematics ,Lie group ,Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing) ,0101 mathematics ,01 natural sciences ,Action (physics) ,Mathematics - Abstract
In this paper, we give an explicit description of the action of the super Lie group [Formula: see text] on supergrassmannian [Formula: see text] in the functor of points language. In particular, we give a concrete proof of the transitively of this action, and the gluing of the local charts of the supergrassmannian.
- Published
- 2020
41. A viscosity-type proximal point algorithm for monotone equilibrium problem and fixed point problem in an Hadamard space
- Author
-
Chinedu Izuchukwu, A. A. Mebawondu, Oluwatosin Temitope Mewomo, and Kazeem Olalekan Aremu
- Subjects
General Mathematics ,010102 general mathematics ,Type (model theory) ,Composition (combinatorics) ,01 natural sciences ,Hadamard space ,010101 applied mathematics ,Proximal point ,Monotone polygon ,Fixed point problem ,Viscosity (programming) ,Equilibrium problem ,0101 mathematics ,Algorithm ,Mathematics - Abstract
In this paper, we introduce a viscosity-type proximal point algorithm comprising of a finite composition of resolvents of monotone bifunctions and a generalized asymptotically nonspreading mapping recently introduced by Phuengrattana [Appl. Gen. Topol. 18 (2017) 117–129]. We establish a strong convergence result of the proposed algorithm to a common solution of a finite family of equilibrium problems and fixed point problem for a generalized asymptotically nonspreading and nonexpansive mappings, which is also a unique solution of some variational inequality problems in an Hadamard space. We apply our result to solve convex feasibility problem and to approximate a common solution of a finite family of minimization problems in an Hadamard space.
- Published
- 2020
42. Quasi-compactness of linear operators on Banach spaces: New properties and application to Markov chains
- Author
-
Mohammed Benharrat, Leila Mebarki, and Bekkai Messirdi
- Subjects
010101 applied mathematics ,Pure mathematics ,Compact space ,Markov chain ,General Mathematics ,010102 general mathematics ,Linear operators ,Banach space ,0101 mathematics ,01 natural sciences ,Mathematics - Abstract
The purpose of this paper is to study the notion of quasi-compact linear operators acting in a Banach space. This class of operators contains the set of compact, polynomially compact, quasi-nilpotent and that of all Riesz operators. We show the equivalence between different definitions of quasi-compactness known in the mathematical literature and we present several general theorems about quasi-compact endomorphisms: stability under algebraic operations, extension of Schauder theorem and the Fredholm alternative. We also study the question of existence of invariant subspaces and we examine the class of semigroups for quasi-compact operators. The obtained results are used to describe Markov chains.
- Published
- 2020
43. Convergence theorems for mixed type iterative process of single-valued and multi-valued nonexpansive mappings and applications
- Author
-
Yongquan Liu
- Subjects
Mathematics::Functional Analysis ,Iterative and incremental development ,General Mathematics ,010102 general mathematics ,Banach space ,Mixed type ,Fixed point ,01 natural sciences ,Multi valued ,010101 applied mathematics ,Convergence (routing) ,Common fixed point ,Applied mathematics ,0101 mathematics ,Mathematics - Abstract
In this paper, we introduce a new mixed type iterative process, which approximates the common fixed points of single-valued nonexpansive mappings and two multi-valued nonexpansive mappings in a uniformly convex Banach space. We establish strong and weak convergence theorems for the new iterative process in Banach space and give their corresponding applications.
- Published
- 2020
44. A modified Lorenz system: Definition and solution
- Author
-
Biljana Zlatanovska and Donco Dimovski
- Subjects
Differential equation ,Approximations of π ,General Mathematics ,Lorentz transformation ,010102 general mathematics ,Lorenz system ,01 natural sciences ,010101 applied mathematics ,symbols.namesake ,System of differential equations ,symbols ,Applied mathematics ,0101 mathematics ,Mathematics - Abstract
Based on the approximations of the Lorenz system of differential equations from the papers [B. Zlatanovska and D. Dimovski, Systems of difference equations approximating the Lorentz system of differential equations, Contributions Sec. Math. Tech. Sci. Manu. XXXIII 1–2 (2012) 75–96, B. Zlatanovska and D. Dimovski, Systems of difference equations as a model for the Lorentz system, in Proc. 5th Int. Scientific Conf. FMNS, Vol. I (Blagoevgrad, Bulgaria, 2013), pp. 102–107, B. Zlatanovska, Approximation for the solutions of Lorenz system with systems of differential equations, Bull. Math. 41(1) (2017) 51–61], we define a Modified Lorenz system, that is a local approximation of the Lorenz system. It is a system of three differential equations, the first two are the same as the first two of the Lorenz system, and the third one is a homogeneous linear differential equation of fifth order with constant coefficients. The solution of this system is based on the results from [D. Dimitrovski and M. Mijatovic, A New Approach to the Theory of Ordinary Differential Equations (Numerus, Skopje, 1995), pp. 23–33].
- Published
- 2020
45. Some results on Srivastava’s triple hypergeometric matrix functions
- Author
-
Ashish Verma
- Subjects
010101 applied mathematics ,Pure mathematics ,General Mathematics ,Matrix function ,010102 general mathematics ,Mathematics::Classical Analysis and ODEs ,Recursion (computer science) ,0101 mathematics ,01 natural sciences ,Hypergeometric distribution ,Mathematics - Abstract
Inspired by the recent work by Abd-Elmageed et al., who established recursion formulas satisfied by the first Appell matrix function, namely [Formula: see text], Sahai et al. presented various recursion formulas for the Gauss hypergeometric matrix function and all four Appell matrix functions. In this paper, we obtain recursion formulas and infinte summation formulas for Srivastava’s triple hypergeometric matrix functions [Formula: see text], [Formula: see text] and [Formula: see text].
- Published
- 2020
46. Finite groups which are c-absolute central factor group and the union of Ac-centralizers
- Author
-
Esmat Alamshahi, Mohammad Reza R. Moghaddam, and F. Saeedi
- Subjects
Class (set theory) ,Group (mathematics) ,Computer Science::Information Retrieval ,General Mathematics ,010102 general mathematics ,Astrophysics::Instrumentation and Methods for Astrophysics ,Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing) ,Center (group theory) ,Automorphism ,01 natural sciences ,010101 applied mathematics ,Factor (chord) ,Combinatorics ,Computer Science::General Literature ,0101 mathematics ,Mathematics - Abstract
Let [Formula: see text] be a group and [Formula: see text] be the [Formula: see text]-absolute center of [Formula: see text], that is, the set of all elements of [Formula: see text] fixed by all class preserving automorphisms of [Formula: see text]. In this paper, we classify all finite groups [Formula: see text], whose [Formula: see text]-absolute central factors are isomorphic to the direct product of cyclic groups, [Formula: see text] and [Formula: see text]. Moreover, we consider finite groups which can be written as the union of centralizers of class preserving automorphisms and study the structure of [Formula: see text] for groups, in which the number of distinct centralizers of class preserving automorphisms is equal to 4 or 5.
- Published
- 2020
47. Some generalizations of linear finite difference inequalities of Pachpatte type
- Author
-
S. D. Kendre and Nagesh Kale
- Subjects
010101 applied mathematics ,Pure mathematics ,Inequality ,General Mathematics ,media_common.quotation_subject ,010102 general mathematics ,Finite difference ,Function (mathematics) ,0101 mathematics ,Type (model theory) ,01 natural sciences ,Mathematics ,media_common - Abstract
In this paper, we establish some linear finite difference inequalities and obtain an explicit bound on the unknown function. These inequalities can be used as handy tools to study the qualitative as well as the quantitative properties of solutions of some finite difference equations and its variants.
- Published
- 2020
48. On the Ricci–Bourguignon flow
- Author
-
Pak Tung Ho
- Subjects
010101 applied mathematics ,Flow (mathematics) ,General Mathematics ,010102 general mathematics ,Mathematical analysis ,Geometric flow ,Mathematics::Differential Geometry ,Soliton ,0101 mathematics ,Constant (mathematics) ,01 natural sciences ,Mathematics - Abstract
In this paper, we study the Ricci–Bourguignon flow of all locally homogenous geometries on closed three-dimensional manifolds. We also consider the evolution of the Yamabe constant under the Ricci–Bourguignon flow. Finally, we prove some results for the Bach-flat shrinking gradient soliton to the Ricci–Bourguignon flow.
- Published
- 2020
49. q-Differences theorems for meromorphic maps of several complex variables intersecting hypersurfaces
- Author
-
Noulorvang Vangty, Pham Duc Thoan, and Nguyen Hai Nam
- Subjects
Pure mathematics ,Mathematics::Complex Variables ,Computer Science::Information Retrieval ,General Mathematics ,010102 general mathematics ,Astrophysics::Instrumentation and Methods for Astrophysics ,Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing) ,Field (mathematics) ,01 natural sciences ,010101 applied mathematics ,Several complex variables ,Computer Science::General Literature ,0101 mathematics ,Meromorphic function ,Mathematics - Abstract
In this paper, we show some [Formula: see text]-difference analogues of the second main theorems for algebraically nondegenerate meromorphic mappings over the field [Formula: see text] of zero-order meromorphic functions in [Formula: see text] satisfying [Formula: see text] intersecting hypersurfaces, located in subgeneral position in [Formula: see text], where [Formula: see text] and [Formula: see text] may be different. As an application, we give some unicity theorems for meromorphic mappings of [Formula: see text] into [Formula: see text] under the growth condition “order [Formula: see text]”, which are analogous to Picard’s theorems.
- Published
- 2020
50. Group analysis to the time fractional nonlinear wave equation
- Author
-
Xiao-Jun Yang, Muhammad Iqbal, Jian-Gen Liu, and Yi-Ying Feng
- Subjects
010101 applied mathematics ,Waves and shallow water ,Conservation law ,Nonlinear phenomena ,Group analysis ,Nonlinear wave equation ,General Mathematics ,0103 physical sciences ,Mathematical analysis ,0101 mathematics ,01 natural sciences ,010305 fluids & plasmas ,Mathematics - Abstract
In this paper, we mainly investigate the time fractional nonlinear wave equation which can be usually used to express nonlinear phenomena appearing in shallow water waves by using group analysis scheme. First, the symmetry can be obtained make uses of the group analysis to the time fractional nonlinear wave equation. Based on the above-found symmetry, this equation was able to reduce into an ordinary differential equation of fractional order. As a result, some new invariant solutions were also constructed for this considered equation. Second, the scaling transformation was also obtained by introducing new independent and dependent variables. Finally, the conservation laws were also found to satisfy the time fractional nonlinear wave equation with the help of the Ibragimov theorem. These novel results show unique nonlinear phenomena.
- Published
- 2020
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