314 results
Search Results
2. Small function sharing results on uniqueness of meromorphic functions concerning differential polynomials
- Author
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Imrul Kaish and Majibur Rahaman
- Subjects
Pure mathematics ,General Mathematics ,010102 general mathematics ,010103 numerical & computational mathematics ,Uniqueness ,Function (mathematics) ,0101 mathematics ,01 natural sciences ,Differential (mathematics) ,Meromorphic function ,Mathematics - Abstract
In this paper, we investigate the uniqueness problems of meromorphic functions concerning differential polynomials sharing a small function. In particular, the resuts of the paper improve the results due to Waghamore and Anand [11].
- Published
- 2020
3. k-prime and k-semiprime ideals of semirings
- Author
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S. Purkait, T. K. Dutta, and Sukhendu Kar
- Subjects
Pure mathematics ,General Mathematics ,010102 general mathematics ,Semiprime ring ,02 engineering and technology ,01 natural sciences ,Prime (order theory) ,Semiring ,TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES ,ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION ,ComputingMethodologies_DOCUMENTANDTEXTPROCESSING ,0202 electrical engineering, electronic engineering, information engineering ,020201 artificial intelligence & image processing ,0101 mathematics ,ComputingMilieux_MISCELLANEOUS ,Mathematics - Abstract
In this paper, we study the notions of [Formula: see text]-prime and [Formula: see text]-semiprime ideals of semirings, [Formula: see text]-[Formula: see text]-system and [Formula: see text]-[Formula: see text]-system. We produce some properties and characterizations for [Formula: see text]-prime and [Formula: see text]-semiprime ideals of semirings in terms of [Formula: see text]-[Formula: see text]-system and [Formula: see text]-[Formula: see text]-system, respectively. We initiate the notion of prime semiring and semiprime semiring to set up characterizations for these two ideals of a semiring. The concept of power semiring associated to a semigroup is also studied in this paper.
- Published
- 2020
4. 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
5. 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
6. 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
7. 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
8. 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
9. The generalized solutions of a certain nth order Cauchy–Euler equation
- Author
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Somsak Orankitjaroen, Amornrat Sangsuwan, and Kamsing Nonlaopon
- Subjects
Pure mathematics ,Laplace transform ,Computer Science::Information Retrieval ,General Mathematics ,Weak solution ,010102 general mathematics ,Astrophysics::Instrumentation and Methods for Astrophysics ,Dirac delta function ,Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing) ,01 natural sciences ,010101 applied mathematics ,symbols.namesake ,TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES ,Cauchy–Euler equation ,symbols ,Computer Science::General Literature ,Order (group theory) ,0101 mathematics ,ComputingMilieux_MISCELLANEOUS ,Mathematics - Abstract
In this paper, we propose the generalized solutions of a certain [Formula: see text]th order Cauchy–Euler equation of the form [Formula: see text], where [Formula: see text] and [Formula: see text] are any integers with [Formula: see text], and [Formula: see text] using Laplace transform technique. We find that the types of solutions either distributional solutions or weak solutions, depend on the values of [Formula: see text]. At the end of the paper, we give some examples showing the types of solutions.
- 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. Solution of certain Pell equations
- Author
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Hafsa Masood Malik and Zahid Raza
- Subjects
Fibonacci number ,Mathematics - Number Theory ,Lucas sequence ,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) ,0102 computer and information sciences ,Square-free integer ,Automorphism ,01 natural sciences ,Combinatorics ,Integer ,010201 computation theory & mathematics ,FOS: Mathematics ,Pell's equation ,Mathematics - Combinatorics ,Computer Science::General Literature ,Binary quadratic form ,Fraction (mathematics) ,Number Theory (math.NT) ,Combinatorics (math.CO) ,0101 mathematics ,Mathematics - Abstract
Let $a,b,c $ be any positive integers such that $c\mid ab$ and $d_i^\pm$ is a square free positive integer of the form $d_i^\pm=a^{2k} b^{2l}\pm i c^m$ where $k,l \geq m$ and $i=1,2.$ The main focus of this paper to find the fundamental solution of the equation $ x^2-d_i^\pm y^2=1$ with the help of the continued fraction of $\sqrt{d_i^\pm}.$ We also obtain all the positive solutions of the equations $ x^2-d_i^\pm y^2=\pm 1$ and $ x^2-d_i^\pm y^2=\pm 4$ by means of the Fibonacci and Lucas sequences. Furthermore, in this work, we derive some algebraic relations on the Pell form $ F_{d_i^\pm}(x, y) = x^2-d_i^\pm y^2 $ including cycle, proper cycle, reduction and proper automorphism of it. We also determine the integer solutions of the Pell equation $ F_{\Delta_{d_i^\pm}} (x, y) = 1 $ in terms of $d_i^\pm. We generalized all the results of the papers [2], [9], [26], and [37]., Comment: 16 pages
- 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. On irrational Brun-type constants
- Author
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Dipl. Math. Klaus Lange
- Subjects
General Mathematics ,Irrational number ,010102 general mathematics ,0103 physical sciences ,Calculus ,010307 mathematical physics ,Quadratic irrational ,0101 mathematics ,Type (model theory) ,01 natural sciences ,Mathematics - Abstract
This paper is removed because it was found to be a plagiarism from another published journal paper.
- Published
- 2017
15. Finite presentability of generalized Bruck–Reilly ∗-extension of groups
- Author
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Eylem Güzel Karpuz, Seda Oğuz, and [Oguz, Seda] Cumhuriyet Univ, Fac Educ, Dept Sch Sci & Math Educ 2, TR-58140 Sivas, Turkey -- [Karpuz, Eylem G.] Karamanoglu Mehmetbey Univ, Kamil Ozdag Sci Fac, Dept Math, Yunus Emre Campus, TR-70100 Karaman, Turkey
- Subjects
General Mathematics ,0102 computer and information sciences ,01 natural sciences ,Combinatorics ,Morphism ,Computer Science::General Literature ,Finitely-generated abelian group ,0101 mathematics ,Algebra over a field ,Identity element ,Finite set ,ComputingMilieux_MISCELLANEOUS ,Mathematics ,Discrete mathematics ,Group (mathematics) ,Computer Science::Information Retrieval ,010102 general mathematics ,Astrophysics::Instrumentation and Methods for Astrophysics ,Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing) ,Extension (predicate logic) ,Generalized Bruck-Reilly extension ,finite presentability ,TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES ,010201 computation theory & mathematics ,finite generation ,ComputingMethodologies_DOCUMENTANDTEXTPROCESSING - Abstract
WOS: 000389311800021, In [Finite presentability of Bruck-Reilly extensions of groups, J. Algebra 242 (2001) 2030], Araujo and RuAtic studied finite generation and finite presentability of Bruck Reilly extension of a group. In this paper, we aim to generalize some results given in that paper to generalized Bruck Reilly s -extension of a group. In this way, we determine necessary and sufficent conditions for generalized Bruck Reilly s-extension of a group, G R. (G; beta, gamma; u), to be finitely generated and finitely presented. Let G be a group, (3,-y: be morphisms and u is an element of H-1 (H-1(*) and H-1 are the ?-G- and ?-t-classes, respectively, contains the identity element kr of T). We prove that GE R* (G; 3, 7; u) is finitely generated if and only if there exists a finite subset Xo C G such that G is generated by ((boolean OR(i >= 0) X-0,beta(i))U(Uj >= 0X0 gamma(j)). We also prove that C superset of R.* (C; beta, gamma; u) is finitely presented if and only if G is presented by (X; R), where X is a finite set and R = (U i >= 0 R-0 beta(i)) boolean OR (U-j >= 0 R0 gamma(j)) = {w(1)beta(i) = upsilon(1)beta(i) : i >= 0, w(1) = v(1) is an element of H-1* for some finite set of relations R0 subset of X* x X*.
- Published
- 2016
16. 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
17. Generalized distance and new fixed point results
- Author
-
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
18. On the Zagreb matrix and Zagreb energy
- Author
-
Akbar Jahanbani, Hajar Shooshtari, and Rana Khoeilar
- Subjects
Vertex (graph theory) ,Degree (graph theory) ,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) ,01 natural sciences ,Square matrix ,010101 applied mathematics ,Combinatorics ,Matrix (mathematics) ,Computer Science::General Literature ,Order (group theory) ,Graph (abstract data type) ,0101 mathematics ,Mathematics - Abstract
Let [Formula: see text] be a graph of order [Formula: see text], and [Formula: see text] be the degree of vertex [Formula: see text] in a graph [Formula: see text]. The Zagreb matrix of [Formula: see text] is the square matrix of order [Formula: see text] whose [Formula: see text]-entry is equal to [Formula: see text] if the vertex [Formula: see text] and the vertex [Formula: see text] of [Formula: see text] are adjacent, and [Formula: see text] otherwise. This matrix, related closely to the Zagreb (abbreviated as [Formula: see text]) index. The Zagreb eigenvalues of [Formula: see text] are the eigenvalues of its [Formula: see text] matrix and the Zagreb energy of [Formula: see text] is the sum of the absolute values of its Zagreb eigenvalues. In this paper, we obtain some new results for the eigenvalues of the Zagreb matrix, the spread of the Zagreb matrix. Moreover, we obtain some new bounds for the Zagreb energy of a graph.
- Published
- 2021
19. On existence and approximation of common fixed points in b-metric spaces
- Author
-
Stojan Radenović, M. Prabavathy, and D. Ramesh Kumar
- Subjects
010101 applied mathematics ,Pure mathematics ,Metric space ,General Mathematics ,010102 general mathematics ,Common fixed point ,Uniqueness ,0101 mathematics ,Fixed point ,Approx ,01 natural sciences ,Mathematics - Abstract
The purpose of this paper is to establish the uniqueness and existence of the common fixed point under generalized contractive conditions in [Formula: see text]-metric spaces with supportive examples. We also approximate the common fixed point by Jungck–Picard and Picard iteration procedures along with the [Formula: see text] property of the mappings. Further, [Formula: see text]-stability of Jungck–Picard iterative and [Formula: see text]-stability of Picard iterative schemes are proved.
- Published
- 2021
20. Generalized bounds for sine and cosine functions
- Author
-
Christophe Chesnea and Yogesh J. Bagul
- Subjects
Pure mathematics ,General Mathematics ,010102 general mathematics ,Trigonometric functions ,010103 numerical & computational mathematics ,Sine ,0101 mathematics ,01 natural sciences ,Bernoulli number ,Mathematics - Abstract
In this paper, we propose several new lower and upper bounds for the functions [Formula: see text] and [Formula: see text] In particular, we refine by generalizing some known inequalities involving these functions. To attain this aim, monotonicity rules and ratio of consecutive even indexed Bernoulli numbers play an important role. Graphic evidence of the results is provided.
- Published
- 2021
21. 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
22. 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
23. On Nagata rings with amalgamation properties
- Author
-
Kar Ping Shum and Ali Molkhasi
- Subjects
Pure mathematics ,Mathematics::Commutative Algebra ,Ring homomorphism ,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) ,010103 numerical & computational mathematics ,Commutative ring ,Characterization (mathematics) ,01 natural sciences ,Nagata ring ,Computer Science::General Literature ,Ideal (ring theory) ,0101 mathematics ,Algebra over a field ,Mathematics - Abstract
Let [Formula: see text] and [Formula: see text] be two commutative rings with unity, let [Formula: see text] be an ideal of [Formula: see text] and [Formula: see text] be a ring homomorphism. In this paper, we give a characterization for the amalgamated algebra [Formula: see text] to be a Nagata ring, a strong S-domain, and a catenarian. Also, we investigate the conditions that the ring of Hurwitz series over [Formula: see text] has a complete comaximal factorization.
- Published
- 2020
24. Characterizations of graphs with prescribed connected detour numbers
- Author
-
Ali A. Ali and Ahmed Ali
- Subjects
Combinatorics ,TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES ,General Mathematics ,010102 general mathematics ,ComputingMethodologies_DOCUMENTANDTEXTPROCESSING ,0202 electrical engineering, electronic engineering, information engineering ,020201 artificial intelligence & image processing ,02 engineering and technology ,0101 mathematics ,01 natural sciences ,ComputingMilieux_MISCELLANEOUS ,Graph ,Mathematics - Abstract
Let [Formula: see text] be a [Formula: see text], [Formula: see text]- graph, [Formula: see text] the detour diameter of [Formula: see text], and cdn[Formula: see text] is the connected detour number of [Formula: see text]. Santhakumaran and Athisayanathan are characterized by the graphs of [Formula: see text] 4 and cdn[Formula: see text], [Formula: see text] and [Formula: see text]. In this paper, we obtain a necessary and sufficient condition for a graph [Formula: see text], [Formula: see text] 2, of [Formula: see text] 8 to have cdn[Formula: see text]. Moreover, graphs G of [Formula: see text] 6, and [Formula: see text] = 5 and 6, such that cdn[Formula: see text], are characterized in this research.
- Published
- 2020
25. Connectivity, indecomposable, and weakly reversible in S-posets
- Author
-
Bana Al Subaiei
- Subjects
Pure mathematics ,General Mathematics ,010102 general mathematics ,Astrophysics::Instrumentation and Methods for Astrophysics ,Computer Science::General Literature ,Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing) ,010103 numerical & computational mathematics ,0101 mathematics ,Indecomposable module ,01 natural sciences ,Mathematics - Abstract
Over the past four decades an extensive literature covered the properties of [Formula: see text]-acts. However, only few studies had generalized some known properties of [Formula: see text]-acts to the [Formula: see text]-posets. The reversible, and indecomposable properties in [Formula: see text]-posets have been addressed previously but connectivity has not been defined in [Formula: see text]-posets yet. Connectivity property was found to be related to those of reversibility and flatness in the category of [Formula: see text]-acts. The primary objective of this paper is to define connectivity in the category of [Formula: see text]-posets for both versions: ordered “poconnected” and unordered “connected”. Examples are presented to show the difference between the two versions. The relationship between connectivity with other properties such as reversibility, and indecomposability had also been investigated. We show that the poconnected in [Formula: see text]-posets is always indecomposable, but the inverse is not true. We also find that the weakly reversible is always connected and indecomposable. These relations among these properties in [Formula: see text]-posets are different from their corresponding relations in [Formula: see text]-acts.
- Published
- 2020
26. Finite groups with given nearly SΦ-embedded subgroups
- Author
-
Yuemei Mao, Chenchen Cao, and Venus Amjid
- Subjects
Finite group ,Computer Science::Information Retrieval ,General Mathematics ,010102 general mathematics ,Sylow theorems ,Astrophysics::Instrumentation and Methods for Astrophysics ,Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing) ,01 natural sciences ,Combinatorics ,Mathematics::Group Theory ,010104 statistics & probability ,TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES ,ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION ,ComputingMethodologies_DOCUMENTANDTEXTPROCESSING ,Computer Science::General Literature ,0101 mathematics ,ComputingMilieux_MISCELLANEOUS ,Mathematics - Abstract
Let [Formula: see text] be a finite group and [Formula: see text] a subgroup of [Formula: see text]. Then [Formula: see text] is said to be [Formula: see text]-permutably embedded in [Formula: see text] if a Sylow [Formula: see text]-subgroup of [Formula: see text] is also a Sylow [Formula: see text]-subgroup of some [Formula: see text]-permutable subgroup of [Formula: see text] for every prime dividing the order of [Formula: see text]. We say that [Formula: see text] is nearly[Formula: see text]-embedded in [Formula: see text] if [Formula: see text] has a normal subgroup [Formula: see text] such that [Formula: see text] is [Formula: see text]-permutable in [Formula: see text] and [Formula: see text], where [Formula: see text] is the subgroup of [Formula: see text] generated by all those subgroups of [Formula: see text] which are [Formula: see text]-permutably embedded in [Formula: see text]. In this paper, we study the properties of the nearly [Formula: see text]-embedded subgroups and use them to determine the structure of finite groups. Some known results are generalized.
- Published
- 2020
27. On the compressed essential graph of a module over a commutative ring
- Author
-
Sh. Payrovi, S. Babaei, and E. Sengelen Sevim
- Subjects
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) ,0102 computer and information sciences ,Commutative ring ,01 natural sciences ,Graph ,Combinatorics ,TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES ,010201 computation theory & mathematics ,ComputingMethodologies_DOCUMENTANDTEXTPROCESSING ,Computer Science::General Literature ,0101 mathematics ,Undirected graph ,ComputingMilieux_MISCELLANEOUS ,Mathematics - Abstract
Let [Formula: see text] be a commutative ring and [Formula: see text] be an [Formula: see text]-module. The compressed essential graph of [Formula: see text], denoted by [Formula: see text] is a simple undirected graph associated to [Formula: see text] whose vertices are classes of torsion elements of [Formula: see text] and two distinct classes [Formula: see text] and [Formula: see text] are adjacent if and only if [Formula: see text] is an essential ideal of [Formula: see text]. In this paper, we study diameter and girth of [Formula: see text] and we characterize all modules for which the compressed essential graph is connected. Moreover, it is proved that [Formula: see text], whenever [Formula: see text] is Noetherian and [Formula: see text] is a finitely generated multiplication module with [Formula: see text].
- Published
- 2020
28. Fixed point theorems for generalized weak contraction mapping in generating space of b-dislocated metric spaces
- Author
-
Reena Jain
- Subjects
Pure mathematics ,Metric space ,General Mathematics ,010102 general mathematics ,Order (group theory) ,Fixed-point theorem ,Contraction mapping ,010103 numerical & computational mathematics ,0101 mathematics ,Space (mathematics) ,01 natural sciences ,Mathematics - Abstract
In this paper, the concept of generalized weak contraction mapping in the setting of generating space of [Formula: see text]-dislocated metric space endowed with partial order is introduced and some fixed-point theorems for the mappings in space satisfying the generalized weak contraction are proved. Example is also given in order to justify our main result.
- Published
- 2020
29. Factor rank preservers of matrices over additively-idempotent multiplicatively-cancellative semirings
- Author
-
Sushobhan Maity and A. K. Bhuniya
- Subjects
Pure mathematics ,Rank (linear algebra) ,General Mathematics ,010102 general mathematics ,Linear operators ,010103 numerical & computational mathematics ,01 natural sciences ,Semiring ,Linear map ,Factor (programming language) ,Idempotence ,Semimodule ,0101 mathematics ,computer ,Mathematics ,computer.programming_language - Abstract
Here, we characterize the linear operators that preserve factor rank of matrices over additively-idempotent multiplicatively-cancellative semirings. The main results in this paper generalize the corresponding results on the two element Boolean algebra [L. B. Beasley and N. J. Pullman, Boolean-rank-preserving opeartors and Boolean-rank-1 spaces, Linear Algebra Appl. 59 (1984) 55–77] and on the max algebra [R. B. Bapat, S. Pati and S.-Z. Song, Rank preservers of matrices over max algebra, Linear Multilinear Algebra 48(2) (2000) 149–164]; and hold on max-plus algebra and some other tropical semirings.
- Published
- 2020
30. Strongly continuous quasi semigroups in optimal control problems for non-autonomous systems
- Author
-
Christiana Rini Indrati, Lina Aryati, and Sutrima Sutrima
- Subjects
0209 industrial biotechnology ,General Mathematics ,010102 general mathematics ,Linear control systems ,02 engineering and technology ,Linear quadratic ,Optimal control ,01 natural sciences ,Parabolic system ,020901 industrial engineering & automation ,ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION ,Riccati equation ,Applied mathematics ,0101 mathematics ,Control (linguistics) ,Mathematics - Abstract
This paper addresses linear quadratic control optimal problems for non-autonomous linear control systems using strongly continuous quasi semigroups. Riccati equations are implemented to investigate the control optimal problems of cost functional with finite and infinite horizons. The unique optimal pair for the cost functional is determined by the mild solution of the associated closed-loop problem and the feedback control of the solution of the corresponding Riccati equation. In addition for the infinite horizon, the stabilizability of the system is a sufficiency for the solvability to the Riccati equation. An application in a parabolic system is proposed.
- Published
- 2020
31. 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
32. A graph associated to centralizer of elements of a group
- Author
-
Farangis Johari and Kazem Khashyarmanesh
- Subjects
Vertex (graph theory) ,Finite group ,Commutator ,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) ,010103 numerical & computational mathematics ,Center (group theory) ,01 natural sciences ,Centralizer and normalizer ,Combinatorics ,TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES ,ComputingMethodologies_DOCUMENTANDTEXTPROCESSING ,Computer Science::General Literature ,Graph (abstract data type) ,0101 mathematics ,ComputingMilieux_MISCELLANEOUS ,Mathematics - Abstract
For a given nonabelian finite group [Formula: see text] and [Formula: see text] where [Formula: see text] denotes the center of [Formula: see text] we introduce a new graph [Formula: see text] associated to the group [Formula: see text] as follows: Take [Formula: see text] as its vertex set and two distinct vertices [Formula: see text] and [Formula: see text] being adjacent if and only if there exists an element [Formula: see text] such that [Formula: see text] This paper is devoted to investigate the properties of graphs [Formula: see text] and establish some graph theoretical properties. Moreover, we describe the planarity of these graphs when [Formula: see text] Also, we provide some examples of finite nonabelian groups [Formula: see text] with the property that if [Formula: see text] and [Formula: see text] for some group [Formula: see text] and [Formula: see text] then [Formula: see text]
- Published
- 2020
33. General reduced second Zagreb index of graph operations
- Author
-
Akbar Jahanbani and Rana Khoeilar
- Subjects
Vertex (graph theory) ,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) ,0102 computer and information sciences ,Cartesian product ,01 natural sciences ,Combinatorics ,symbols.namesake ,TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES ,010201 computation theory & mathematics ,ComputingMethodologies_DOCUMENTANDTEXTPROCESSING ,symbols ,Computer Science::General Literature ,Graph (abstract data type) ,0101 mathematics ,Graph operations ,ComputingMilieux_MISCELLANEOUS ,Mathematics ,Real number - Abstract
Let [Formula: see text] be a graph with vertex set [Formula: see text] and edge set [Formula: see text]. The general reduced second Zagreb index of [Formula: see text] is defined as [Formula: see text], where [Formula: see text] is any real number and [Formula: see text] is the degree of the vertex [Formula: see text] of [Formula: see text]. In this paper, the general reduced second Zagreb index of the Cartesian product, corona product, join of graphs and two new operations of graphs are computed.
- Published
- 2020
34. On mutually m-permutable product of GS-groups
- Author
-
M. H. Abd-Ellatif and A. M. Elkholy
- Subjects
Combinatorics ,Finite group ,General Mathematics ,Product (mathematics) ,010102 general mathematics ,Structure (category theory) ,010103 numerical & computational mathematics ,Permutable prime ,0101 mathematics ,01 natural sciences ,Mathematics - Abstract
In this paper, we investigate the structure of a finite group [Formula: see text] which is totally, mutually or mutually [Formula: see text]-permutable product of proper subgroups [Formula: see text] and [Formula: see text] under theassumption that all maximal subgroups of [Formula: see text] are [Formula: see text]-groups.
- 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. On 3-total edge product cordial labeling of grid
- Author
-
Muhammad Kamran Siddiqui, Maria Naseem, Muhammad Irfan, Roslan Hasni, and Ali Ahmad
- Subjects
Vertex (graph theory) ,General Mathematics ,010102 general mathematics ,0102 computer and information sciences ,Edge (geometry) ,01 natural sciences ,Combinatorics ,TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES ,Integer ,010201 computation theory & mathematics ,Product (mathematics) ,ComputingMethodologies_DOCUMENTANDTEXTPROCESSING ,0101 mathematics ,Lattice graph ,ComputingMilieux_MISCELLANEOUS ,Mathematics - Abstract
Let us consider a mapping [Formula: see text] of a graph [Formula: see text], where [Formula: see text] is an integer, [Formula: see text]. The mapping [Formula: see text] induces for every vertex [Formula: see text] of [Formula: see text] the label [Formula: see text]. Let [Formula: see text] ([Formula: see text]) denote the number of edges (vertices) in [Formula: see text] that are labeled with the number [Formula: see text] under the labeling [Formula: see text], [Formula: see text]. The function [Formula: see text] is called a [Formula: see text]-total edge product cordial labeling of [Formula: see text] if [Formula: see text] for [Formula: see text]. A graph [Formula: see text] with a [Formula: see text]-total edge product cordial labeling is called a [Formula: see text]-total edge product cordial graph. In this paper, we prove that the grid graph [Formula: see text] for [Formula: see text] admits a [Formula: see text]-total edge product cordial labeling.
- Published
- 2020
37. Lie super-bialgebra structures on the N = 2 super-BMS3 algebra
- Author
-
Lili Chi, Jiancai Sun, and Hengyun Yang
- Subjects
Algebra ,Tensor product ,Yang–Baxter equation ,General Mathematics ,010102 general mathematics ,0103 physical sciences ,010307 mathematical physics ,0101 mathematics ,Algebra over a field ,01 natural sciences ,Mathematics ,Bialgebra - Abstract
In this paper, Lie super-bialgebra structures on the [Formula: see text] super-BMS3 algebra are investigated. By computing derivations from the super-BMS3 to the tensor product of its adjoint module, we obtain that all Lie bialgebra structures on the [Formula: see text] super-BMS3 Algebra are triangular coboundary.
- Published
- 2020
38. 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
39. On generalized gamma-Bazilevic functions
- Author
-
Shujaat Ali Shah, Afis Saliu, and Khalida Inayat Noor
- Subjects
Algebra ,Class (set theory) ,General Mathematics ,010102 general mathematics ,0202 electrical engineering, electronic engineering, information engineering ,020201 artificial intelligence & image processing ,02 engineering and technology ,0101 mathematics ,01 natural sciences ,Inclusion (education) ,Focus (linguistics) ,Mathematics - Abstract
In this paper, we define and study the class [Formula: see text] of generalized gamma-Bazilevic functions. Our main focus is to discuss certain problems such as inclusion results, covering theorem and radius problem.
- Published
- 2020
40. Theta series and weight enumerator over an imaginary quadratic field
- Author
-
K. P. Shum and Ankur
- Subjects
Pure mathematics ,Series (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) ,Field (mathematics) ,0102 computer and information sciences ,01 natural sciences ,Ring of integers ,TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES ,010201 computation theory & mathematics ,ComputingMethodologies_DOCUMENTANDTEXTPROCESSING ,Computer Science::General Literature ,Quadratic field ,0101 mathematics ,ComputingMilieux_MISCELLANEOUS ,The Imaginary ,Mathematics - Abstract
In this paper, we consider an imaginary quadratic field [Formula: see text] with [Formula: see text] (mod [Formula: see text]). In particular, we study the ring of integers corresponding to the field [Formula: see text] and visualize the form of [Formula: see text]. We also consider lattices over the ring of integers [Formula: see text] and discuss the theta series to see its relation with the weight enumerator. As a consequence, we will see how the theta series differs for different [Formula: see text] and [Formula: see text].
- Published
- 2020
41. On spectra and spectral radius of Signless Laplacian of power graphs of some finite groups
- Author
-
Subarsha Banerjee and Avishek Adhikari
- Subjects
Finite group ,Spectral radius ,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) ,Cyclic group ,010103 numerical & computational mathematics ,Signless laplacian ,Dihedral group ,01 natural sciences ,Graph ,Spectral line ,Power (physics) ,Combinatorics ,TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES ,ComputingMethodologies_DOCUMENTANDTEXTPROCESSING ,Computer Science::General Literature ,0101 mathematics ,ComputingMilieux_MISCELLANEOUS ,Mathematics - Abstract
Let [Formula: see text] denote the power graph of a finite group [Formula: see text]. Let [Formula: see text] denote the Signless Laplacian spectral radius of [Formula: see text]. In this paper, we give lower and upper bounds on [Formula: see text] for any [Formula: see text] and find those graphs for which the extremal values are attained. We give a comparison between the bounds obtained and exact value of [Formula: see text] for any [Formula: see text]. We then find the eigenvalues of [Formula: see text] and give lower and upper bounds on the spectral radius of [Formula: see text]. When [Formula: see text] and [Formula: see text] where [Formula: see text] are primes and [Formula: see text] is a positive integer, we obtain sharper bounds on [Formula: see text]. Finally, we make a conjecture on [Formula: see text] for any [Formula: see text].
- Published
- 2020
42. On difference sequence spaces of fractional-order involving Padovan numbers
- Author
-
Syed Abdul Mohiuddine, Bipan Hazarika, and Taja Yaying
- Subjects
010101 applied mathematics ,Combinatorics ,Sequence ,Matrix (mathematics) ,General Mathematics ,Operator (physics) ,010102 general mathematics ,Order (group theory) ,0101 mathematics ,Composition (combinatorics) ,01 natural sciences ,Mathematics - Abstract
In this paper, we introduce Padovan difference sequence spaces of fractional-order [Formula: see text] [Formula: see text] [Formula: see text] by the composition of the fractional-order difference operator [Formula: see text] and the Padovan matrix [Formula: see text] defined by [Formula: see text] and [Formula: see text]respectively, where the sequence [Formula: see text] is the Padovan sequence. We give some topological properties, Schauder basis and [Formula: see text]-, [Formula: see text]- and [Formula: see text]-duals of the newly defined spaces. We characterize certain matrix classes related to the [Formula: see text] space. Finally, we characterize certain classes of compact operators on [Formula: see text] using Hausdorff measure of noncompactness.
- Published
- 2020
43. 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
44. On the q-capability of groups
- Author
-
Saeed Kayvanfar, Forough Gharibi Monfared, and Farangis Johari
- Subjects
Discrete mathematics ,TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES ,010201 computation theory & mathematics ,General Mathematics ,010102 general mathematics ,ComputingMethodologies_DOCUMENTANDTEXTPROCESSING ,0102 computer and information sciences ,0101 mathematics ,01 natural sciences ,ComputingMilieux_MISCELLANEOUS ,Integer (computer science) ,Mathematics - Abstract
Given a positive integer [Formula: see text], in this paper, we investigate some more properties of the [Formula: see text]-capability of groups. For instance, the relationship between [Formula: see text]-capability and the varietal capability is determined. Moreover, we introduce the notion of [Formula: see text]-epicenter for a group and then we obtain some criteria for the [Formula: see text]-capability of groups. Finally, as an application, we characterize all [Formula: see text]-capable extra-special [Formula: see text]-groups when [Formula: see text] is a power of [Formula: see text]
- Published
- 2020
45. Gaussian third-order Jacobsthal and Gaussian third-order Jacobsthal–Lucas polynomials and their properties
- Author
-
Gamaliel Cerda-Morales
- Subjects
symbols.namesake ,Pure mathematics ,Third order ,Computer Science::Graphics ,General Mathematics ,Gaussian ,010102 general mathematics ,0103 physical sciences ,symbols ,010307 mathematical physics ,0101 mathematics ,01 natural sciences ,Mathematics - Abstract
In this paper, the Gaussian third-order Jacobsthal and Gaussian third-order Jacobsthal–Lucas polynomials are defined. Then Binet formula and generating functions of these numbers are given. Also, some summation identities for Gaussian third-order Jacobsthal and Gaussian third-order Jacobsthal–Lucas polynomials are obtained by using the recurrence relation satisfied by them. Then, some linear and quadratic relations are given between Gaussian third-order Jacobsthal and Gaussian third-order Jacobsthal–Lucas polynomials.
- Published
- 2020
46. On commuting additive mappings on semiprime rings
- Author
-
Utsanee Leerawat and Siriporn Lapuangkham
- Subjects
Pure mathematics ,Ring (mathematics) ,Mathematics::Commutative Algebra ,General Mathematics ,Mathematics::Rings and Algebras ,010102 general mathematics ,Semiprime ring ,Structure (category theory) ,010103 numerical & computational mathematics ,0101 mathematics ,01 natural sciences ,Mathematics - Abstract
The main purpose of this paper is to describe the structure of a pair of additive mappings that are commuting on a semiprime ring. Furthermore, we prove that the existence of different commuting epimorphisms on a prime ring forces the ring to be commutative. Finally, we characterize additive mappings, which act as homomorphisms or antihomomorphisms on a semiprime ring.
- Published
- 2020
47. 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
48. On a special case of Wilf’s conjecture
- Author
-
Donco Dimovski and Violeta Angjelkoska
- Subjects
Conjecture ,Computer Science::Information Retrieval ,General Mathematics ,010102 general mathematics ,Dimension (graph theory) ,Astrophysics::Instrumentation and Methods for Astrophysics ,Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing) ,0102 computer and information sciences ,01 natural sciences ,Combinatorics ,Set (abstract data type) ,TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES ,010201 computation theory & mathematics ,Numerical semigroup ,ComputingMethodologies_DOCUMENTANDTEXTPROCESSING ,Computer Science::General Literature ,Embedding ,0101 mathematics ,Special case ,ComputingMilieux_MISCELLANEOUS ,Mathematics - Abstract
Let [Formula: see text] be a numerical semigroup with embedding dimension [Formula: see text], minimal set of generators [Formula: see text], Frobenius number [Formula: see text], multiplicity [Formula: see text] and genus [Formula: see text]. In this paper, we prove that Wilfs conjecture i.e. the inequality [Formula: see text] holds for [Formula: see text] when [Formula: see text] is a basis for [Formula: see text]
- Published
- 2020
49. On uniqueness of meromorphic mappings from complete Kähler manifold into ℙn(ℂ)
- Author
-
Ha Huong Giang and Nguyen Thi Nhung
- Subjects
Pure mathematics ,021103 operations research ,General Mathematics ,010102 general mathematics ,Astrophysics::Instrumentation and Methods for Astrophysics ,0211 other engineering and technologies ,Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing) ,02 engineering and technology ,Kähler manifold ,01 natural sciences ,Uniqueness theorem for Poisson's equation ,Hyperplane ,Computer Science::General Literature ,Uniqueness ,0101 mathematics ,General position ,Meromorphic function ,Mathematics - Abstract
In this paper, we prove a uniqueness theorem for meromorphic mappings of a complete Kähler manifold [Formula: see text] into [Formula: see text] sharing hyperplanes in general position under a general condition that the codimension of the intersection of inverse images of any [Formula: see text] hyperplanes is at least two.
- Published
- 2020
50. 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
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