19 results
Search Results
2. gr-n-ideals in graded commutative rings
- Author
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Farah Al-Turman, Ece Yetkin Celikel, and Khaldoun Al-Zoubi
- Subjects
Pure mathematics ,13a02 ,General Mathematics ,010102 general mathematics ,020206 networking & telecommunications ,02 engineering and technology ,Commutative ring ,gr-prime ideals ,01 natural sciences ,graded rings ,0202 electrical engineering, electronic engineering, information engineering ,QA1-939 ,0101 mathematics ,gr-n-ideals ,16w50 ,Mathematics - Abstract
Let G be a group with identity e and let R be a G-graded ring. In this paper, we introduce and study the concept of gr-n-ideals of R. We obtain many results concerning gr-n-ideals. Some characterizations of gr-n-ideals and their homogeneous components are given.
- Published
- 2019
3. Fractional natural decomposition method for solving a certain class of nonlinear time-fractional wave-like equations with variable coefficients
- Author
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Ali Khalouta and Abdelouahab Kadem
- Subjects
35a22 ,Class (set theory) ,General Mathematics ,caputo fractional derivative ,010102 general mathematics ,nonlinear time-fractional wave-like equations ,01 natural sciences ,010101 applied mathematics ,Nonlinear system ,35r11 ,34k28 ,fractional natural decomposition method ,QA1-939 ,Applied mathematics ,Decomposition method (queueing theory) ,adomian polynomials ,0101 mathematics ,26a33 ,Mathematics ,Variable (mathematics) - Abstract
In this paper, we propose a new approximate method, namely fractional natural decomposition method (FNDM) in order to solve a certain class of nonlinear time-fractional wave-like equations with variable coefficients. The fractional natural decomposition method is a combined form of the natural transform method and the Adomian decomposition method. The nonlinear term can easily be handled with the help of Adomian polynomials which is considered to be a clear advantage of this technique over the decomposition method. Some examples are given to illustrate the applicability and the easiness of this approach.
- Published
- 2019
4. Computing metric dimension of compressed zero divisor graphs associated to rings
- Author
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M. Imran Bhat and Shariefuddin Pirzada
- Subjects
Discrete mathematics ,zero-divisor graph ,General Mathematics ,010102 general mathematics ,equivalence classes ,0102 computer and information sciences ,compressed zero-divisor graph ,01 natural sciences ,metric dimension ,Metric dimension ,13a99 ,010201 computation theory & mathematics ,QA1-939 ,05c78 ,05c12 ,0101 mathematics ,Zero divisor ,Mathematics - Abstract
For a commutative ring R with 1 ≠ 0, a compressed zero-divisor graph of a ring R is the undirected graph ΓE(R) with vertex set Z(RE) \ {[0]} = RE \ {[0], [1]} defined by RE = {[x] : x ∈ R}, where [x] = {y ∈ R : ann(x) = ann(y)} and the two distinct vertices [x] and [y] of Z(RE) are adjacent if and only if [x][y] = [xy] = [0], that is, if and only if xy = 0. In this paper, we study the metric dimension of the compressed zero divisor graph ΓE(R), the relationship of metric dimension between ΓE(R) and Γ(R), classify the rings with same or different metric dimension and obtain the bounds for the metric dimension of ΓE(R). We provide a formula for the number of vertices of the family of graphs given by ΓE(R×𝔽). Further, we discuss the relationship between metric dimension, girth and diameter of ΓE(R).
- Published
- 2018
5. On extensions of Baer and quasi-Baer modules
- Author
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Ebrahim Hashemi, Abdollah Alhevaz, and Marzieh Yazdanfar
- Subjects
Pure mathematics ,General Mathematics ,010102 general mathematics ,0102 computer and information sciences ,01 natural sciences ,16s36 ,010201 computation theory & mathematics ,16d80 ,reduced module ,quasi-baer module ,QA1-939 ,baer module ,skew monoid ring ,0101 mathematics ,16s34 ,Mathematics ,s-compatible module - Abstract
Let R be a ring, MR a module, S a monoid, ω : S → End(R) a monoid homomorphism and R * S a skew monoid ring. Then M[S] = {m1g1 + · · · + mngn | n ≥ 1, mi ∈ M and gi ∈ S for each 1 ≤ i ≤ n} is a module over R ∗ S. A module MR is Baer (resp. quasi-Baer) if the annihilator of every subset (resp. submodule) of M is generated by an idempotent of R. In this paper we impose S-compatibility assumption on the module MR and prove: (1) MR is quasi-Baer if and only if M[s]R∗S is quasi-Baer, (2) MR is Baer (resp. p.p) if and only if M[S]R∗S is Baer (resp. p.p), where MR is S-skew Armendariz, (3) MR satisfies the ascending chain condition on annihilator of submodules if and only if so does M[S]R∗S, where MR is S-skew quasi-Armendariz.
- Published
- 2018
6. Integrals of polylogarithmic functions with negative argument
- Author
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Anthony Sofo
- Subjects
polylogarithm function ,General Mathematics ,010102 general mathematics ,TheoryofComputation_GENERAL ,33b15 ,010103 numerical & computational mathematics ,01 natural sciences ,11m06 ,Argument ,TheoryofComputation_ANALYSISOFALGORITHMSANDPROBLEMCOMPLEXITY ,zeta functions ,ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION ,dirichlet functions ,QA1-939 ,Computer Science::Symbolic Computation ,euler sums ,0101 mathematics ,11m32 ,Computer Science::Data Structures and Algorithms ,Mathematical economics ,Mathematics ,MathematicsofComputing_DISCRETEMATHEMATICS - Abstract
The connection between polylogarithmic functions and Euler sums is well known. In this paper we explore the representation and many connections between integrals of products of polylogarithmic functions and Euler sums. We shall consider mainly, polylogarithmic functions with negative arguments, thereby producing new results and extending the work of Freitas. Many examples of integrals of products of polylogarithmic functions in terms of Riemann zeta values and Dirichlet values will be given.
- Published
- 2018
7. Some properties of analytic functions related with Booth lemniscate
- Author
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Ali Ebadian, Sh. Najafzadeh, and Parvaneh Najmadi
- Subjects
logarithmic coefficients ,Mathematics - Complex Variables ,General Mathematics ,010102 general mathematics ,convex ,strongly starlike ,subordination ,30c45 ,Object (computer science) ,01 natural sciences ,010101 applied mathematics ,Combinatorics ,Alpha (programming language) ,FOS: Mathematics ,QA1-939 ,starlike ,Lemniscate ,Complex Variables (math.CV) ,0101 mathematics ,univalent ,Mathematics ,Analytic function - Abstract
The object of the present paper is to study of two certain subclass of analytic functions related with Booth lemniscate which we denote by $\mathcal{BS}(\alpha)$ and $\mathcal{BK}(\alpha)$. Some properties of these subclasses are considered., Comment: 9 pages
- Published
- 2018
8. Certain classes of analytic functions defined by fractional q-calculus operator
- Author
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N. Ravikumar
- Subjects
General Mathematics ,010102 general mathematics ,30c45 ,medicine.disease ,30c50 ,01 natural sciences ,fractional q-calculus operator ,010101 applied mathematics ,Operator (computer programming) ,univalent functions ,Calculus ,medicine ,QA1-939 ,0101 mathematics ,Calculus (medicine) ,Mathematics ,Analytic function - Abstract
In this paper, the concept of fractional q-calculus and generalized Al-Oboudi differential operator defining certain classes of analytic functions in the open disc are used. The results investigated for these classes of functions include the coefficient estimates, inclusion relations, extreme points and some more properties.
- Published
- 2018
9. On the sum of the Lah numbers and zeros of the Kummer confluent hypergeometric function
- Author
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Feng Qi and Bai-Ni Guo
- Subjects
lah number ,Pure mathematics ,Confluent hypergeometric function ,General Mathematics ,010102 general mathematics ,sum ,secondary 05a10, 05a19, 11b65, 11b99, 30c15, 33c15, 65b10 ,kummer confluent hypergeometric function ,01 natural sciences ,Lah number ,010101 applied mathematics ,QA1-939 ,zero ,0101 mathematics ,primary 11b83 ,Mathematics - Abstract
In the paper, the authors find the sum of the Lah numbers and make sure that the Kummer confluent hypergeometric function 1F1(n+ 1; 2; z) has only n− 1real and negative zeros.
- Published
- 2018
10. On generalized Laguerre matrix polynomials
- Author
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A. A. Bathanya and Raed S. Batahan
- Subjects
Pure mathematics ,Recurrence relation ,15a15 ,42c05 ,General Mathematics ,010102 general mathematics ,010103 numerical & computational mathematics ,Expression (computer science) ,01 natural sciences ,Hypergeometric distribution ,33c45 ,Matrix (mathematics) ,Matrix function ,Laguerre polynomials ,QA1-939 ,three terms recurrence relation ,laguerre matrix polynomials ,0101 mathematics ,Representation (mathematics) ,generalized hypergeometric matrix function and gamma matrix function ,Mathematics - Abstract
The main object of the present paper is to introduce and study the generalized Laguerre matrix polynomials for a matrix that satisfies an appropriate spectral property. We prove that these matrix polynomials are characterized by the generalized hypergeometric matrix function. An explicit representation, integral expression and some recurrence relations in particular the three terms recurrence relation are obtained here. Moreover, these matrix polynomials appear as solution of a differential equation.
- Published
- 2018
11. Totally geodesic property of the unit tangent sphere bundle with g-natural metrics
- Author
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Farshad Firuzi and Esmaeil Peyghan
- Subjects
Pure mathematics ,Property (philosophy) ,General Mathematics ,010102 general mathematics ,sphere bundle ,58a10 ,totally geodesic submanifold ,53c40 ,53a45 ,01 natural sciences ,53d15 ,Tangent sphere ,Bundle ,0103 physical sciences ,QA1-939 ,Totally geodesic ,010307 mathematical physics ,Mathematics::Differential Geometry ,natural metrics ,0101 mathematics ,Unit (ring theory) ,Mathematics::Symplectic Geometry ,Mathematics - Abstract
In this paper, we consider the tangent bundle of a Riemannian manifold (M, g) with g-natural metrics and among all of these metrics, we specify those with respect to which the unit tangent sphere bundle with induced g-natural metric is totally geodesic. Also, we equip the unit tangent sphere bundle T1M with g-natural contact (paracontact) metric structures, and we show that such structures are totally geodesic K-contact (K-paracontact) submanifolds of TM, if and only if the base manifold (M, g) has positive (negative) constant sectional curvature. Moreover, we establish a condition for g-natural almost contact B-metric structures on T1Msuch that these structures be totally geodesic submanifolds of TM.
- Published
- 2018
12. Uniqueness of polynomial and differential monomial
- Author
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V. Husna and Harina P. Waghamore
- Subjects
Polynomial ,Pure mathematics ,Monomial ,differential monomial ,polynomial ,General Mathematics ,010102 general mathematics ,01 natural sciences ,sharing values ,010101 applied mathematics ,30d35 ,QA1-939 ,meromorphic function ,Uniqueness ,0101 mathematics ,Differential (mathematics) ,Mathematics - Abstract
In this paper, we discuss the problem of meromorphic functions sharing small function and present one theorem which extend a result of K. S. Charak and Banarasi Lal [16].
- Published
- 2017
13. A result regarding monotonicity of the Gamma function
- Author
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Pál A. Kupán, Róbert Szász, and Gyöngyvér Márton
- Subjects
Pure mathematics ,General Mathematics ,010102 general mathematics ,33b15 ,Monotonic function ,01 natural sciences ,010101 applied mathematics ,gamma function ,monotonic function ,QA1-939 ,0101 mathematics ,Gamma function ,Mathematics - Abstract
In this paper we analyze the monotony of the function ln Γ ( x ) ln ( x 2 + τ ) - ln ( x + τ ) ${{{\rm{ln}}\,\Gamma ({\rm{x}})} \over {{\rm{ln}}\,({\rm{x}}^2 + \tau) - {\rm{ln}}\,({\rm{x}} + \tau)}}$ , for τ > 0. Such functions have been used from different authors to obtain inequalities concerning the gamma function.
- Published
- 2017
14. Some fixed point results for rational type and subrational type contractive mappings
- Author
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Diana Dolićanin-Đekić, Huaping Huang, Arslan Hojat Ansari, and Stojan Radenović
- Subjects
Pure mathematics ,α-admissible mapping ,General Mathematics ,010102 general mathematics ,Type (model theory) ,Fixed point ,Topology ,01 natural sciences ,010101 applied mathematics ,μ-subadmissible mapping ,54h25 ,fixed point ,μ-subregular ,QA1-939 ,0101 mathematics ,generalized metric space ,47h10 ,Mathematics ,α-regular - Abstract
In this paper, we introduce the concepts of rational type and subrational type contractive mappings. We expand and improve some fixed point theorems obtained by Alsulami et al. (Fixed Point Theory Appl., 2015, 2015: 97). Moreover, we give an example to support our results.
- Published
- 2017
15. New characterization of symmetric groups of prime degree
- Author
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Alireza Khalili Asboei and Reza Mohammadyari
- Subjects
Pure mathematics ,20d08 ,General Mathematics ,010102 general mathematics ,Prime degree ,0211 other engineering and technologies ,021107 urban & regional planning ,02 engineering and technology ,Characterization (mathematics) ,01 natural sciences ,symmetric group ,conjugacy class length ,20d60 ,Symmetric group ,finite group ,QA1-939 ,0101 mathematics ,Mathematics - Abstract
In this paper, will show that a symmetric group of prime degree p ≥ 5 is recognizable by its order and a special conjugacy class size of (p − 1)!.
- Published
- 2017
16. Unbounded solutions of an iterative-difference equation
- Author
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Pingping Zhang and Lin Li
- Subjects
Semi-infinite ,Differential equation ,General Mathematics ,010102 general mathematics ,existence ,37e05 ,39b12 ,01 natural sciences ,unbounded solution ,convex solution ,010101 applied mathematics ,QA1-939 ,Applied mathematics ,iterative-difference equation ,concave solution ,0101 mathematics ,Mathematics - Abstract
Unbounded solutions for the iterative-difference equation f 2 ( x ) = λ f ( x + a ) + μ x , x ∈ ℝ , \font\msbm=MSBM10$${\rm{f}}^2 ({\rm{x}}) = \lambda {\rm{f}}({\rm{x}} + {\rm{a}}) + \mu {\rm{x}},\;\;\;{\rm{x}} \in {\msbm R},$$ have been considered in [Continuous solutions of an iterative-difference equation and Brillouët problem, Publ. Math. Debrecen, 78 (2011), 613–624], where λ, μ, a are real constants. In this paper, we continue to study the solutions not being included there, and further give the convex and concave ones. Finally, continuous solutions of this equation with an extra item were also given, which continuously depend on the parameter a.
- Published
- 2017
17. Common fixed point theorems for contractive mappings satisfying Φ-maps in S-metric spaces
- Author
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Mohammad Rezaee, Stojan Radenovic, Shaban Sedghi, and Tatjana Došenović
- Subjects
Discrete mathematics ,General Mathematics ,010102 general mathematics ,common fixed point ,01 natural sciences ,010101 applied mathematics ,Metric space ,54h25 ,Common fixed point ,QA1-939 ,0101 mathematics ,s-metric space ,Coincidence point ,contractive maps ,47h10 ,Mathematics - Abstract
In this paper we prove the existence of the unique fixed point for the pair of weakly compatible self-mappings satisfying some Ф-type contractive conditions in the framework of S-metric spaces. Our results generalize, extend, unify, complement and enrich recently fixed point results in existing literature.
- Published
- 2016
18. Ricci solitons on QR-hypersurfaces of a quaternionic space form ℚn
- Author
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Z. Nazari and E. Abedi
- Subjects
Pure mathematics ,quaternionic space form ,General Mathematics ,010102 general mathematics ,Space form ,53c40 ,Mathematics::Spectral Theory ,01 natural sciences ,53c25 ,53c15 ,0103 physical sciences ,QA1-939 ,010307 mathematical physics ,Mathematics::Differential Geometry ,0101 mathematics ,Nonlinear Sciences::Pattern Formation and Solitons ,ricci soliton ,qr-hypersurfaces ,Mathematics - Abstract
The purpose of this paper is to study Ricci solitons on QR-hypersurfaces M of a quaternionic space form ℚn such that the shape operator A with respect to N has one eigenvalue. We prove that Ricci soliton on QR-hypersurfaces M with eigenvalue zero is steady and for eigenvalue nonzero is shrinking.
- Published
- 2016
19. Some vector inequalities for two operators in Hilbert spaces with applications
- Author
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Silvestru Sever Dragomir
- Subjects
Pure mathematics ,General Mathematics ,projection ,010103 numerical & computational mathematics ,01 natural sciences ,Combinatorics ,Inner product space ,symbols.namesake ,selfadjoint operators ,26d15 ,QA1-939 ,46c05 ,0101 mathematics ,Cauchy–Schwarz inequality ,Mathematics ,buzano’s inequality ,inner product spaces ,Triangle inequality ,schwarz’s inequality ,Nuclear operator ,010102 general mathematics ,Hilbert space ,Operator theory ,operator norm ,26d1 ,Bounded function ,unitary operators ,symbols ,Operator norm ,numerical radius - Abstract
In this paper we establish some vector inequalities for two operators related to Schwarz and Buzano results. We show amongst others that in a Hilbert space H we have the inequality 1 2 [ 〈 | A | 2 + | B | 2 2 x , x 〉 1 / 2 〈 | A | 2 + | B | 2 2 y , y 〉 1 / 2 + | 〈 | A | 2 + | B | 2 2 x , y 〉 | ] ≥ | 〈 Re ( B * A ) x , y 〉 | $${1 \over 2}\left[ {\left\langle {{{\left| {\rm{A}} \right|^2 + \left| {\rm{B}} \right|^2 } \over 2}{\rm{x}},{\rm{x}}} \right\rangle ^{1/2} \left\langle {{{\left| {\rm{A}} \right|^2 + \left| {\rm{B}} \right|^2 } \over 2}{\rm{y}},{\rm{y}}} \right\rangle ^{1/2} + \left| {\left\langle {{{\left| {\rm{A}} \right|^2 + \left| {\rm{B}} \right|^2 } \over {\rm{2}}}} {\rm{x}},{\rm{y}}\right\rangle } \right|} \right] \ge \left| {\left\langle {{\mathop{\rm Re}\nolimits} ({\rm{B}}*{\rm{A}})\,{\rm{x}},{\rm{y}}} \right\rangle } \right|$$ for A, B two bounded linear operators on H such that Re (B*A) is a nonnegative operator and any vectors x, y ∈ H. Applications for norm and numerical radius inequalities are given as well.
- Published
- 2016
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