71 results
Search Results
2. An Iterative Method for a Common Solution of a Combination of the Split Equilibrium Problem, a Finite Family of Nonexpansive Mapping and a Combination of Variational Inequality Problem
- Author
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Abdellah Bnouhachem, Themistocles M. Rassias, and Ihssane Hay
- Subjects
Iterative method ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,Hilbert space ,01 natural sciences ,symbols.namesake ,Fixed point problem ,Variational inequality ,Convergence (routing) ,Projection method ,symbols ,Applied mathematics ,Equilibrium problem ,0101 mathematics ,Mathematics - Abstract
The present paper aims to deal with an iterative algorithm for finding common solution of the combination of the split equilibrium problem and a finite family of non-expansive mappings and the combination of variational inequality problem in the setting of real Hilbert spaces. Further, we prove that the sequences generated by the proposed iterative method converge strongly to a common solution to these problems. A numerical example is presented to illustrate the proposed method and convergence result. The results and method presented in this paper generalize, extend and unify some known results in the literatures.
- Published
- 2021
3. Some results on uniqueness of entire functions concerning difference polynominals
- Author
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Pulak Sahoo and Gurudas Biswas
- Subjects
010101 applied mathematics ,Pure mathematics ,Applied Mathematics ,General Mathematics ,Entire function ,010102 general mathematics ,Function (mathematics) ,Uniqueness ,0101 mathematics ,01 natural sciences ,Mathematics - Abstract
In the paper we use the notion of weakly weighted sharing and relaxed weighted sharing to investigate the uniqueness problems when two difference products of entire functions share a small function. The results of the paper improve and extend some recent results due to the present first author [Commu. Math. Stat., 3 (2015), 227-238].
- Published
- 2018
4. Uniqueness of difference-differential polynomials of entire functions sharing one value
- Author
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Ashwini M. Hattikal and Renukadevi S. Dyavanal
- Subjects
010101 applied mathematics ,Discrete mathematics ,Applied Mathematics ,General Mathematics ,Entire function ,010102 general mathematics ,Zhàng ,Multiplicity (mathematics) ,Uniqueness ,0101 mathematics ,01 natural sciences ,Nevanlinna theory ,Mathematics - Abstract
In this paper, we study the uniqueness of difference-differential polynomials of entire functions $f$ and $g$ sharing one value with counting multiplicity. In this paper we extend and generalize the results of X. Y. Zhang, J. F. Chen and W. C. Lin [17] L. Kai, L. Xin-ling and C. Ting-bin [7] and many others [2, 16].
- Published
- 2016
5. Boundedness and Stability Properties of Solutions of Mathematical Model of Measles
- Author
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James Akingbade and B. S. Ogundare
- Subjects
Lyapunov function ,Work (thermodynamics) ,Open population ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,Stability (learning theory) ,medicine.disease ,01 natural sciences ,Measles ,symbols.namesake ,Exponential stability ,Jacobian matrix and determinant ,symbols ,medicine ,Quantitative Biology::Populations and Evolution ,Applied mathematics ,0101 mathematics ,Basic reproduction number ,Mathematics - Abstract
In this paper, asymptotic stability and global asymptotic stability of solutions to a deterministic and compartmental mathematical model of measles infection is considered using the ideas of the Jacobian determinant as well as the second method of Lyapunov, criteria/conditions that guaranteed asymptotic stability of disease free equilibrium and endemic equilibrium were established. Also the basic reproductive number $R_0$ was obtained. The results in this work compliments existing work and provided further information in controlling the disease in an open population.
- Published
- 2021
6. On $L_1$-biharmonic timelike hypersurfaces in pseudo-Euclidean space $E_1^4$
- Author
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Firooz Pashaie
- Subjects
Pure mathematics ,Mean curvature ,Applied Mathematics ,General Mathematics ,Pseudo-Euclidean space ,010102 general mathematics ,Type (model theory) ,Space (mathematics) ,01 natural sciences ,First variation ,Hypersurface ,Principal curvature ,Biharmonic equation ,Mathematics::Differential Geometry ,0101 mathematics ,Mathematics - Abstract
A well-known conjecture of Bang Yen-Chen says that the only biharmonic Euclidean submanifolds are minimal ones. In this paper, we consider an extended condition (namely, $L_1$-biharmonicity) on non-degenerate timelike hypersurfaces of the pseudo-Euclidean space $E_1^4$. A Lorentzian hypersurface $x: M_1^3\rightarrow\E_1^4$ is called $L_1$-biharmonic if it satisfies the condition $L_1^2x=0$, where $L_1$ is the linearized operator associated to the first variation of 2-th mean curvature vector field on $M_1^3$. According to the multiplicities of principal curvatures, the $L_1$-extension of Chen's conjecture is affirmed for Lorentzian hypersurfaces with constant ordinary mean curvature in pseudo-Euclidean space $E_1^4$. Additionally, we show that there is no proper $L_1$-biharmonic $L_1$-finite type connected orientable Lorentzian hypersurface in $E_1^4$.
- Published
- 2020
7. Generalized Wright Function and Its Properties Using Extended Beta Function
- Author
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Talha Usma, Nabiullah Khan, and Mohd Aman
- Subjects
Mellin transform ,Recurrence relation ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,Wright Omega function ,Function (mathematics) ,Derivative ,01 natural sciences ,Fox–Wright function ,Fractional calculus ,symbols.namesake ,symbols ,Applied mathematics ,0101 mathematics ,Beta function ,Mathematics - Abstract
Solving a linear partial differential equation witness a noteworthy role of Wright function. Due to its usefulness and various applications, a variety of its extentions (and generalizations) have been investigated and presented. The purpose and design of the paper is intended to study and come up with a new extention of the genralized Wright function by using generalized beta function and obtain some integral representation of the freshly defined function. Also we present the Mellin transform of this function in the form of Fox Wright function. Furthermore, we obtain the recurrence relation, derivative formula for the said function and also by using an extended Riemann-Liouville fractional derivative, we present a fractional derivative formula for the extended Wright function.
- Published
- 2020
8. Mathematical Modelling of Listeriosis Epidemics in Animal and Human Population with Optimal Control
- Author
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Oluwole Daniel Makinde, David Mwangi Theuri, and Shaibu Osman
- Subjects
education.field_of_study ,Transmission (medicine) ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,Population ,Disease ,Optimal control ,medicine.disease_cause ,01 natural sciences ,Pontryagin's minimum principle ,Listeria monocytogenes ,Environmental health ,medicine ,0101 mathematics ,education ,Basic reproduction number ,Contaminated food ,Mathematics - Abstract
Listeriosis is a serious disease caused by the germ Listeria monocytogenes. People usually become ill with listeriosis after eating contaminated food including meat. The disease primarily affects pregnant women, newborns, older adults, and people with weakened immune systems. In this paper, we propose and scrutinize a model problem describing the transmission dynamics of Listeriosis epidemic in animal and human population using the stability theory of differential equations. The model is qualitatively analysed for the basic reproduction number as well as possibility of forward and backward bifurcation with respect to the stability of disease free and endemic equilibria. The impact of the model parameters on the disease was evaluated via sensitivity analysis. An extension of the model to include time dependent control variables such as treatment, vaccination and education of susceptible (human) is carried out. Using Pontryagin’s Maximum Principle, we obtain the optimal control strategies needed for combating Listeriosis disease. Numerical simulation of the model is performed and pertinent results are displayed graphically and discussed quantitatively.
- Published
- 2020
9. Analytical Solution of the Effect of Awareness Program by Media on the Spread of an Infectious Disease by Homotopy Perturbation Method
- Author
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Kavitha Ts and Devipriya Ganeshan
- Subjects
Computer simulation ,business.industry ,Applied Mathematics ,General Mathematics ,Wireless computing ,ComputerSystemsOrganization_COMPUTER-COMMUNICATIONNETWORKS ,010102 general mathematics ,computer.software_genre ,01 natural sciences ,Homotopy perturbation ,Malware ,0101 mathematics ,Homotopy perturbation method ,business ,Approximate solution ,Wireless sensor network ,computer ,Mathematics ,Computer network - Abstract
Wireless sensor networks (WSNs) have received wide-ranging considerationdue to their boundless potential in civil and military applications. Maliciousself-replicating codes, known as malware, pose substantial threat to the wireless computing infrastructure. The attacks of the malicious signals in the WSNare epidemic in nature. Biological epidemic models will be helpful to understand the dynamical behavior of the malware attack in WSN. In this paper,A (SEIRS-V) Susceptible - Exposed - Infected - Recovered - Susceptible witha Vaccination compartment, describing the undercurrents of worm propagation with respect to time in wireless sensor network (WSN) is considered. Theanalytical solution of WSN is obtained by Homotopy Perturbation Method.Numerical results are obtained and are graphically interpreted using Maple.The results assures that the dynamics of worm propagation in WSN by theproposed model exhibits rich dynamics.
- Published
- 2020
10. On Three Dimensional Cosymplectic Manifolds Admitting Almost Ricci Solitons
- Author
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Chiranjib Dey and Uday Chand De
- Subjects
Applied Mathematics ,General Mathematics ,010102 general mathematics ,Function (mathematics) ,Lambda ,01 natural sciences ,Manifold ,Ricci soliton ,Killing vector field ,Nonlinear Sciences::Exactly Solvable and Integrable Systems ,Mathematics::Differential Geometry ,0101 mathematics ,Nonlinear Sciences::Pattern Formation and Solitons ,Mathematics ,Mathematical physics - Abstract
In the present paper we study three dimensional cosymplectic manifolds admitting almost Ricci solitons. Among others we prove that in a three dimensional compact orientable cosymplectic manifold M^3 withoutboundary an almost Ricci soliton reduces to Ricci soliton under certain restriction on the potential function lambda. As a consequence we obtain several corollaries. Moreover we study gradient almost Ricci solitons.
- Published
- 2020
11. Controllability and observability of linear impulsive adjoint dynamic system on time scale
- Author
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Asif Mansoor, Awais Younus, Nusrat Yasmin, and Safia Mirza
- Subjects
Controllability ,Scale (ratio) ,Control theory ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,Observability ,0101 mathematics ,01 natural sciences ,Stability (probability) ,Mathematics - Abstract
This paper deals with the controllability, observability of the solution of time-varying system on time scales. We obtain new results about controllability and observability and generalize to a time scale some known properties about stability from the continuous case.
- Published
- 2020
12. CONSONANCY OF DYNAMIC INEQUALITIES CORRELATED ON TIME SCALE CALCULUS
- Author
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Muhammad Jibril Shahab Sahir
- Subjects
Scale (ratio) ,Inequality ,Applied Mathematics ,General Mathematics ,media_common.quotation_subject ,010102 general mathematics ,Nesbitt's inequality ,Time-scale calculus ,0101 mathematics ,01 natural sciences ,Mathematical economics ,media_common ,Mathematics - Abstract
In this paper, discrete and continuous versions of some inequalitiessuch as Radon's Inequality, Bergstrom's Inequality, Nesbitt's Inequality,Rogers-Holder's Inequality and Schlomilch's Inequality are unified on dynamictime scale calculus in extended form.
- Published
- 2020
13. Property $(w)$ of upper triangular operator Matrices
- Author
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Mohammad M.H Rashid
- Subjects
Direct sum ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,Triangular matrix ,Hilbert space ,Type (model theory) ,01 natural sciences ,Combinatorics ,symbols.namesake ,Operator matrix ,symbols ,0101 mathematics ,Mathematics - Abstract
Let $M_C=\begin{pmatrix} A & C \\ 0 & B \\ \end{pmatrix}\in\LB(\x,\y)$ be be an upper triangulate Banach spaceoperator. The relationship between the spectra of $M_C$ and $M_0,$ and theirvarious distinguished parts, has been studied by a large number of authors inthe recent past. This paper brings forth the important role played by SVEP,the {\it single-valued extension property,} in the study of some of these relations. In this work, we prove necessary and sufficient conditions of implication of the type $M_0$ satisfies property $(w)$ $\Leftrightarrow$ $M_C$ satisfies property $(w)$ to hold. Moreover, we explore certain conditions on $T\in\LB(\hh)$ and $S\in\LB(\K)$ so that the direct sum $T\oplus S$ obeys property $(w)$, where $\hh$ and $\K$ are Hilbert spaces.
- Published
- 2020
14. Pointwise approximation of modified conjugate functions by matrix operators of their Fourier series with the use of some parameters
- Author
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Bogdan Szal and Wlodzimierz Lenski
- Subjects
Pointwise ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,Function (mathematics) ,01 natural sciences ,Measure (mathematics) ,Combinatorics ,Rate of approximation ,0101 mathematics ,Matrix operator ,Conjugate functions ,Fourier series ,Mathematics - Abstract
We extend and generalize the results of Xh. Z. Krasniqi [Acta Comment. Univ.Tartu. Math. 17 (2013), 89-101] and the authors [Acta Comment. Univ. Tartu.Math. 13 (2009), 11-24], [Proc. Estonian Acad. Sci. 2018, 67, 1, 50--60] aswell the jont paper with M. Kubiak [Journal of Inequalities and Applications(2018) 2018:92]. We consider the modified conjugate function $\widetilde{f}%_{r}$ for $2\pi /\rho $--periodic function $f$ . Moreover, the measure ofapproximations depends on \textbf{\ }$\mathbf{\rho }$\textbf{ - }differencesof the entries of matrices defined the method of summability.
- Published
- 2020
15. BBDF-Alpha for solving stiff ordinary differential equations with oscillating solutions
- Author
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Iskandar Shah Mohd Zawawi
- Subjects
Plane (geometry) ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,Zero (complex analysis) ,01 natural sciences ,Stability (probability) ,Stability conditions ,symbols.namesake ,Consistency (statistics) ,Ordinary differential equation ,Convergence (routing) ,symbols ,Applied mathematics ,0101 mathematics ,Newton's method ,Mathematics - Abstract
In this paper, the block backward differentiation α formulas (BBDF-α) is derived for solving first order stiff ordinary differential equations with oscillating solutions. The consistency and zero stability conditions are investigated to prove the convergence of the method. The stability region in the entire negative half plane shows that the derived method is A-stable for certain values of α. The implementation of the method using Newton iteration is also discussed. Several numerical experiments are conducted to demonstrate the performance of the method in terms of accuracy and computational time.
- Published
- 2020
16. Best approximation of conjugate of a function in generalized Zygmund
- Author
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H. K. Nigam
- Subjects
Pure mathematics ,Class (set theory) ,Degree (graph theory) ,Applied Mathematics ,General Mathematics ,Product (mathematics) ,010102 general mathematics ,Conjugate Fourier series ,Function (mathematics) ,0101 mathematics ,01 natural sciences ,Mathematics ,Conjugate - Abstract
In this paper, we, for the very first time, study the error estimates of conjugate of a function ~g of g(2-periodic) in generalized Zygmund class Y wz (z 1); by Matix-Euler (TEq) product operatorof conjugate Fourier series. In fact, we establish two theorems on degree of approximation of afunction ~g of g (2-periodic) in generalized Zygmund class Y wz (z 1); by Matix-Euler (TEq)product means of its conjugate Fourier series. Our main theorem generalizes three previouslyknown results. Thus the results of [7], [8] and [26] become the particular cases of our Theorem2.1. Some corollaries are also deduced from our main theorem.
- Published
- 2019
17. Doubly Warped Product Submanifolds of a Riemannian Manifold of Nearly Quasi-constant Curvature
- Author
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Mohamd Saleem Lone, Mehraj Ahmad Lone, and Mohammad Shahid
- Subjects
Pure mathematics ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,Riemannian manifold ,Curvature ,Submanifold ,01 natural sciences ,Constant curvature ,Product (mathematics) ,Mathematics::Differential Geometry ,0101 mathematics ,Mathematics::Symplectic Geometry ,Mathematics - Abstract
In the present paper, we form a sharp inequality for a doubly warped product submanifold of a Riemannian manifold of nearly quasi-constant curvature.
- Published
- 2021
18. Several Determinantal Expressions of Generalized Tribonacci Polynomials and Sequences
- Author
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Wei-Shih Du, Feng Qi, and Can Kızılateş
- Subjects
Narayana number ,Jacobsthal number ,Combinatorics ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,0101 mathematics ,01 natural sciences ,Mathematics - Abstract
In the paper, the authors present several explicit formulas for the $(p,q,r)$-Tribonacci polynomials and generalized Tribonacci sequences in terms of the Hessenberg determinants and, consequently, derive several explicit formulas for the Tribonacci numbers and polynomials, the Tribonacci--Lucas numbers, the Perrin numbers, the Padovan (Cordonnier) numbers, the Van der Laan numbers, the Narayana numbers, the third order Jacobsthal numbers, and the third order Jacobsthal--Lucas numbers in terms of special Hessenberg determinants.
- Published
- 2021
19. Quenching for Porous Medium Equations
- Author
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Burhan Selçuk
- Subjects
Combinatorics ,Quenching ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,Nonlinear diffusion equation ,Boundary (topology) ,0101 mathematics ,Finite time ,01 natural sciences ,Mathematics - Abstract
This paper studies the following two porous medium equations with singular boundary conditions. First, we obtain that finite time quenching on the boundary, as well as $k_{t}\ $blows up at the same finite time\ and lower bound estimates of the quenching time of the equation $k_{t}=(k^{n})_{xx}+(1-k)^{-\alpha }$,\ $(x,t)\in (0,L)\times (0,T)\ $with $(k^{n})_{x}\left( 0,t\right) =0$, $\ (k^{n})_{x}\left( L,t\right)=(1-k(L,t))^{-\beta }$,$\ t\in (0,T)\ $and initial function $k\left(x,0\right) =k_{0}\left( x\right) $,$\ x\in \lbrack 0,L]\ $where $n>1$, $\alpha \ $and $\beta \ $and positive constants. Second, we obtain that finite time quenching on the boundary, as well as $k_{t}\ $blows up at the same finite time\ and a local existence result by the help of steady state of the equation $k_{t}=(k^{n})_{xx}$,\ $(x,t)\in (0,L)\times (0,T)\ $with $(k^{n})_{x}\left( 0,t\right) =(1-k(0,t))^{-\alpha }$, $\ (k^{n})_{x}\left(L, t\right) =(1-k(L,t))^{-\beta }$,$\ t\in (0,T)\ $and initial function $k\left( x,0\right) =k_{0}\left( x\right) $,$\ x\in \lbrack 0,L]\ $where $n>1$, $\alpha \ $and $\beta \ $and positive constants.
- Published
- 2021
20. Green’s Relations on Regular Elements of Semigroup of Relational Hypersubstitutions for Algebraic Systems of Type ((m), (n))
- Author
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Jukkrit Daengsaen and Sorasak Leeratanavalee
- Subjects
Monoid ,Discrete mathematics ,Semigroup ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,Green's relations ,Type (model theory) ,Term (logic) ,01 natural sciences ,Set (abstract data type) ,Order (group theory) ,0101 mathematics ,Algebraic number ,Mathematics - Abstract
Any relational hypersubstitution for algebraic systems of type (τ,τ′) = ((mi)i∈I,(nj)j∈J) is a mapping which maps any mi-ary operation symbol to an mi-ary term and maps any nj - ary relational symbol to an nj-ary relational term preserving arities, where I,J are indexed sets. Some algebraic properties of the monoid of all relational hypersubstitutions for algebraic systems of a special type, especially the characterization of its order and the set of all regular elements, were first studied by Phusanga and Koppitz[13] in 2018. In this paper, we study the Green’srelationsontheregularpartofthismonoidofaparticulartype(τ,τ′) = ((m),(n)), where m, n ≥ 2.
- Published
- 2021
21. On The Ricci Symmetry of Almost Kenmotsu Manifolds
- Author
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Dibakar Dey
- Subjects
Applied Mathematics ,General Mathematics ,010102 general mathematics ,Einstein manifold ,01 natural sciences ,symbols.namesake ,symbols ,Mathematics::Differential Geometry ,Sectional curvature ,0101 mathematics ,Symmetry (geometry) ,Einstein ,Mathematics ,Mathematical physics - Abstract
In the present paper, we characterize Ricci symmetric almost Kenmotsu manifolds under several constraints and proved that they are Einstein manifolds. As a consequence, we obtain several corollaries. Finally, an illustrative example is presented to verify our results.
- Published
- 2021
22. Inverse nodal problem for nonlocal differential operators
- Author
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Chuan-Fu Yang and Xin-Jian Xu
- Subjects
Diffusion (acoustics) ,Class (set theory) ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,Mathematical analysis ,Inverse ,Function (mathematics) ,Eigenfunction ,Differential operator ,01 natural sciences ,Scattering theory ,0101 mathematics ,NODAL ,Mathematics - Abstract
Inverse nodal problem consists in constructing operators from the given zeros of their eigenfunctions. The problem of differential operators with nonlocal boundary condition appears, e.g., in scattering theory, diffusion processes and the other applicable fields. In this paper, we consider a class of differential operators with nonlocal boundary condition, and show that the potential function can be determined by nodal data.
- Published
- 2019
23. A note on Lamarle formula in Minkowski $3$-space
- Author
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Esra Betul Koc Ozturk, Emilija Nešović, Ufuk Öztürk, Kazım İlarslan, and Kırıkkale Üniversitesi
- Subjects
Pseudo-null curve ,Surface (mathematics) ,Minkowski 3-space ,Ruled surface ,Plane (geometry) ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,Null (mathematics) ,ruled surface ,01 natural sciences ,General Relativity and Quantum Cosmology ,symbols.namesake ,Distribution (mathematics) ,0103 physical sciences ,Minkowski space ,Gaussian curvature ,symbols ,Vector field ,010307 mathematical physics ,0101 mathematics ,Mathematics ,Mathematical physics - Abstract
Nesovic, Emilija/0000-0003-3600-0486; Ozturk, Ufuk/0000-0002-8800-7869 WOS: 000449022500003 The Lamarle formula is known as a simple relation between the Gaussian curvature and the distribution parameter of a non-developable ruled surface. In this paper, we obtain the Lamarle formula of a non-developable ruled surface with pseudo null base curve and null director vector field inMinkowski 3-space. We also obtain the corresponding striction line and distribution parameter of such surface. We prove that there is no Lamarle formula when the director vector field is spacelike and its derivative is null, because the ruled surface in that case is a lightlike plane. Finally, we give some examples. Serbian Ministry of Education, Science and Technological Development [174012] The last author was partially supported by the Serbian Ministry of Education, Science and Technological Development (grant number 174012).
- Published
- 2018
24. On compact Einstein doubly warped product manifolds
- Author
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Punam Gupta
- Subjects
Applied Mathematics ,General Mathematics ,010102 general mathematics ,Einstein manifold ,Base (topology) ,01 natural sciences ,Manifold ,010101 applied mathematics ,symbols.namesake ,Product (mathematics) ,symbols ,Mathematics::Differential Geometry ,0101 mathematics ,Einstein ,Scalar curvature ,Mathematical physics ,Mathematics - Abstract
In this paper, the non-existence of connected, compact Einstein doubly warped product semi-Riemannian manifold with non-positive scalar curvature is proved. It is also shown that there does not exist non-trivial connected Einstein doubly warped product semi-Riemannian manifold with compact base $B$ or fibre $F$.
- Published
- 2018
25. Fitted Numerical Scheme for Solving Singularly Perturbed Parabolic Delay Partial Differential Equations
- Author
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Mesfin Mekuria Woldaregay and Gemechis File Duressa
- Subjects
Partial differential equation ,Discretization ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,Finite difference method ,Delay differential equation ,01 natural sciences ,Parabolic partial differential equation ,Euler method ,symbols.namesake ,Rate of convergence ,symbols ,Applied mathematics ,0101 mathematics ,Temporal discretization ,Mathematics - Abstract
In this paper, exponentially fitted finite difference scheme is developed for solving singularly perturbed parabolic delay partial differential equations having small delay on the spatial variable. The term with the delay is approximated using Taylor series approximation. The resulting singularly perturbed parabolic partial differential equation is treated using im- plicit Euler method in the temporal discretization with exponentially fitted operator finite difference method in the spatial discretization. The parameter uniform convergence analysis has been carried out with the order of convergence one. Test examples and numerical results are considered to validate the theoretical analysis of the scheme.
- Published
- 2021
26. A Characterization of Orthonormal Multilevel Wavelet Families in Sobolev Space over Local Fields of Positive Characteristic
- Author
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Dileep Kumar and Ashish Pathak
- Subjects
Pure mathematics ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,Characterization (mathematics) ,01 natural sciences ,Sobolev space ,symbols.namesake ,Wavelet ,Fourier transform ,symbols ,Orthonormal basis ,0101 mathematics ,Local field ,Mathematics - Abstract
In this paper, a characterization of orthonormal multilevel wavelet families in Sobolev space over a local fields of positive characteristic (Hs(K)) is established. Finally an example is presented.
- Published
- 2021
27. Some Results on Quantile-based Dynamic Survival and Failure Tsallis Entropy
- Author
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Rekha Rani, Vikas Kumar, and Nirdesh Singh
- Subjects
Applied Mathematics ,General Mathematics ,Tsallis entropy ,010102 general mathematics ,Quantile function ,01 natural sciences ,Measure (mathematics) ,Weighted entropy ,Statistical physics ,0101 mathematics ,Entropy (energy dispersal) ,Reliability (statistics) ,Mathematics ,Quantile - Abstract
Non-additive entropy measures are important for many applications. In this paper, we introduce a quantile-based non-additive entropy measure, based on Tsallis entropy and study their properties. Some relationships of this measure with well-known reliability mea- sures and ageing classes are studied and some characterization results are presented. Also the concept of quantile-based shift independent entropy measures has been introduced and studied various properties.
- Published
- 2021
28. Existence and Stability Results for the Solution of Neutral Fractional Integro-Differential Equation with Nonlocal Conditions
- Author
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Tellab Brahim, Abdellouahab Naimi, and Khaled Zennir
- Subjects
Nonlinear system ,Integro-differential equation ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,Fixed-point theorem ,Applied mathematics ,Uniqueness ,0101 mathematics ,Stability result ,01 natural sciences ,Stability (probability) ,Mathematics - Abstract
This paper deals with the existence and uniqueness results for the solution of a Neutral fractional integro-differential problem with nonlocal conditions. Using the Nonlinear alternative for single valued maps, Krasnoselskii's and Banach fixed point theorems to proof our main results. An example is given to illustrate our main results.
- Published
- 2021
29. Symmetries of Sasakian Generalized Sasakian-Space-Form Admitting Generalized Tanaka–Webster Connection
- Author
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Chawngthu Lalmalsawma and Jay Prakash Singh
- Subjects
Pure mathematics ,Mathematics::Complex Variables ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,Space form ,Object (computer science) ,01 natural sciences ,Connection (mathematics) ,Homogeneous space ,Mathematics::Differential Geometry ,0101 mathematics ,Mathematics::Symplectic Geometry ,Mathematics - Abstract
The object of this paper is to study symmetric properties of Sasakian generalized Sasakian-space-form with respect to generalized Tanaka–Webster connection. We studied semisymmetry and Ricci semisymmetry of Sasakian generalized Sasakian-space-form with respect to generalized Tanaka–Webster connection. Further we obtain results for Ricci pseudosymmetric and Ricci-generalized pseudosymmetric Sasakian generalized Sasakian-space-form.
- Published
- 2021
30. A Common Solution of Equilibrium, Constrained Convex Minimization, and Fixed Point Problems
- Author
-
Maryam Yazdi
- Subjects
Iterative method ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,Fixed point ,01 natural sciences ,Fixed point problem ,Scheme (mathematics) ,Convex optimization ,Convergence (routing) ,Applied mathematics ,Equilibrium problem ,0101 mathematics ,Dykstra's projection algorithm ,Mathematics - Abstract
In this paper, we propose a new iterative scheme with the help of the gradient- projection algorithm (GPA) for finding a common solution of an equilibrium problem, a constrained convex minimization problem, and a fixed point problem. Then, we prove some strong convergence theorems which improve and extend some recent results. Moreover, we give a numerical result to show the validity of our main theorem.
- Published
- 2021
31. P53-Mdm2 Loop Stability and Oscillatory Dynamics with Mdm2-Induced Delay Effect in P53
- Author
-
Mohd Younus Baba, Abdur Raheem, and Mohammad Saleem
- Subjects
Applied Mathematics ,General Mathematics ,010102 general mathematics ,Dynamics (mechanics) ,01 natural sciences ,Stability (probability) ,Loop (topology) ,Minimal model ,Control theory ,Nyquist stability criterion ,Negative feedback ,0101 mathematics ,Boolean data type ,Mathematics ,Degradation (telecommunications) - Abstract
In this paper, we consider P53-Mdm2 negative feedback loop supposed to be the core circuit of genome. We study stability and the oscillatory dynamics of the loop. Many of the studies modeled this loop by delay-differential equations with P53-induced transcrip- tional delay in the production of Mdm2. We, however, highlight the importance of Mdm2- induced delay in the degradation of P53 protein. We consider two forms of P53 protein i.e., plain P53 and active P53 along with its principal antagonist protein Mdm2 to formulate a minimal model. Active P53 finds its inclusion in the loop in the presence of DNA damage represented by a Boolean variable ‘s’. The analysis of the model provides thresholds on delays using Nyquist criterion such that delays in the degradation of P53 lower than these thresholds guarantee stability of the loop in that all proteins plain P53, active P53 and Mdm2 approach to stable equilibrium state. The oscillatory dynamics in proteins, if any, would exist beyond these thresholds.
- Published
- 2021
32. On the Dimension of Non-Abelian Tensor Squares of $n$-Lie Algebras
- Author
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Nafiseh Akbarossadat and F. Saeedi
- Subjects
Applied Mathematics ,General Mathematics ,010102 general mathematics ,Dimension (graph theory) ,01 natural sciences ,Square (algebra) ,Combinatorics ,Tensor (intrinsic definition) ,Lie algebra ,Ideal (ring theory) ,0101 mathematics ,Algebra over a field ,Abelian group ,Group theory ,Mathematics - Abstract
Let $L$ be an $n$-Lie algebra over a field $\F$. In this paper, we introduce the notion of non-abelian tensor square $L\otimes L$ of $L$ and define the central ideal $L\square L$ of it. Using techniques from group theory and Lie algebras, we show that that $L\square L\cong L^{ab}\square L^{ab}$. Also, we establish the short exact sequence\[0\lra\M(L)\lra\frac{L\otimes L}{L\square L}\lra L^2\lra0\]and apply it to compute an upper bound for the dimension of non-abelian tensor square of $L$.
- Published
- 2021
33. *-Weyl Curvature Tensor within the Framework of Sasakian and $(\kappa,\mu)$-Contact Manifolds
- Author
-
H. Aruna Kumara and V. Venkatesha
- Subjects
Weyl tensor ,Riemann curvature tensor ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,Object (computer science) ,01 natural sciences ,symbols.namesake ,symbols ,Mathematics::Differential Geometry ,0101 mathematics ,Mathematics::Symplectic Geometry ,Ricci curvature ,Kappa ,Mathematics ,Mathematical physics - Abstract
The object of the present paper is to study $*$-Weyl curvature tensor within the framework of Sasakian and $(\kappa,\mu)$-contact manifolds.
- Published
- 2021
34. Approximation of Functions in Besov Space
- Author
-
H. K. Nigam and Supriya Rani
- Subjects
Pure mathematics ,Work (thermodynamics) ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,Besov space ,Function (mathematics) ,0101 mathematics ,01 natural sciences ,Fourier series ,Mathematics - Abstract
In the present paper, we establish a theorem on best approximation of a function g ∈ Bqλ(Lr) of its Fourier series. Our main theorem generalizes some known results of this direction of work. Thus, the results of [10], [26] and [27] become the particular case of our main Theorem 3.1.
- Published
- 2021
35. Applications of Krasnoselskii-Dhage Type Fixed-Point Theorems to Fractional Hybrid Differential Equations
- Author
-
Fahad Alsharari, Teh Yuan Ying, and Habibulla Akhadkulov
- Subjects
Differential equation ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,Applied mathematics ,Fixed-point theorem ,0101 mathematics ,Type (model theory) ,01 natural sciences ,Differential (mathematics) ,Mathematics - Abstract
In this paper, we prove the existence of a solution of a fractional hybrid differential equation involving the Riemann-Liouville differential and integral operators by utilizing a new version of Kransoselskii-Dhage type fixed-point theorem obtained in [13]. Moreover, we provide an example to support our result.
- Published
- 2021
36. $\tau$-Atomicity and Quotients of Size Four
- Author
-
Richard Erwin Hasenauer and Bethany Kubik
- Subjects
Ring (mathematics) ,Mathematics::Commutative Algebra ,Mathematics::Number Theory ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,Lambda ,01 natural sciences ,Combinatorics ,Factorization ,Ideal (ring theory) ,0101 mathematics ,Commutative algebra ,Unit (ring theory) ,Quotient ,Mathematics - Abstract
Given a ring $R$, an ideal $I$ of $R$, and an element $a\in I$, we say $a=\lambda b_1\cdots b_k$ is a $\tau_I$-factorization of $a$ if $\lambda$ is any unit and $b_1\equiv\cdots\equiv b_k\pmod{I}$. In this paper, we investigate the $\tau_I$-atomicity of PIDs with ideals where $R/I$ has size four.
- Published
- 2021
37. A Study of New Class of Almost Contact Metric Manifolds of Kenmotsu Type
- Author
-
Habeeb M. Abood and Mohammed Y. Abass
- Subjects
Pure mathematics ,Riemann curvature tensor ,Direct sum ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,Structure (category theory) ,Einstein manifold ,Type (model theory) ,Mathematics::Geometric Topology ,01 natural sciences ,Manifold ,symbols.namesake ,Metric (mathematics) ,symbols ,Mathematics::Differential Geometry ,0101 mathematics ,Mathematics::Symplectic Geometry ,Ricci curvature ,Mathematics - Abstract
In this paper, we characterized a new class of almost contact metric manifolds and established the equivalent conditions of the characterization identity in term of Kirichenko’s tensors. We demonstrated that the Kenmotsu manifold provides the mentioned class; i.e., the new class can be decomposed into a direct sum of the Kenmotsu and other classes. We proved that the manifold of dimension 3 coincided with the Kenmotsu manifold and provided an example of the new manifold of dimension 5, which is not the Kenmotsu manifold. Moreover, we established the Cartan’s structure equations, the components of Riemannian curvature tensor and the Ricci tensor of the class under consideration. Further,the conditions required for this to be an Einstein manifold have been determined.
- Published
- 2021
38. Upper bounds for Ricci curvatures for submanifolds in Bochner-Kaehler manifolds
- Author
-
Falleh R. Al-Solamy, Mehraj Ahmad Lone, Mohammad Shahid, Yoshio Matsuyama, and Mohammed Jamali
- Subjects
Pure mathematics ,Mean curvature ,Mathematics::Complex Variables ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,Einstein manifold ,Codimension ,01 natural sciences ,Riemannian space ,Complex space ,Norm (mathematics) ,Mathematics::Differential Geometry ,0101 mathematics ,Algebraic number ,Mathematics::Symplectic Geometry ,Ricci curvature ,Mathematics - Abstract
Chen established the relationship between the Ricci curvature and the squared norm of meancurvature vector for submanifolds of Riemannian space form with arbitrary codimension knownas Chen-Ricci inequality. Deng improved the inequality for Lagrangian submanifolds in complexspace form by using algebraic technique. In this paper, we establish the same inequalitiesfor different submanifolds of Bochner-Kaehler manifolds. Moreover, we obtain improvedChen-Ricci inequality for Kaehlerian slant submanifolds of Bochner-Kaehler manifolds.
- Published
- 2020
39. A new class of double integrals involving Generalized Hypergeometric Function 3F2
- Author
-
Insuk Kim
- Subjects
Combinatorics ,Applied Mathematics ,General Mathematics ,Multiple integral ,010102 general mathematics ,0101 mathematics ,Generalized hypergeometric function ,01 natural sciences ,Mathematics - Abstract
The aim of this research paper is to evaluate fifty double integrals invoving generalized hypergeometric function (25 each) in the form of\begin{align*}\int_{0}^{1}\int_{0}^{1} & x^{c-1}y^{c+\al-1} (1-x)^{\al- 1}(1-y)^{\be-1}\, (1-xy)^{c+\ell-\al-\be+1}\;\\ &\times \;{}_3F_2 \left[\begin{array}{c}a,\,\,\,\,\,b,\,\,\,\,\,2c+\ell+ 1 \\ \frac{1}{2}(a+b+i+1),\,\,2c+j \end{array}; xy\right]\,dxdy\end{align*}and\begin{align*}\int_{0}^{1}\int_{0}^{1} & x^{c+\ell}y^{c+\ell+\al} (1-x)^{\al-1}(1-y)^{\be-1}\, (1-xy)^{c- \al-\be}\;\\ &\times \;{}_3F_2 \left[\begin{array}{c}a,\,\,\,\,\,b,\,\,\,\,\,2c+\ell+ 1 \\ \frac{1}{2}(a+b+i+1),\,\,2c+j \end{array}; 1-xy\right]\,dxdy\end{align*}in the most general form for any $\ell \in \mathbb{Z}$ and $i, j = 0, \pm 1, \pm2$.The results are derived with the help of generalization of Edwards's well known double integral due to Kim, {\it et al.} and generalized classical Watson's summation theorem obtained earlier by Lavoie, {\it et al}.More than one hundred ineteresting special cases have also been obtained.
- Published
- 2020
40. RateofConvergenceofHermite-Fej´erPolynomialsfor Functions with Derivatives of Bounded Variation
- Author
-
Abedallah Rababah
- Subjects
Chebyshev polynomials ,Hermite polynomials ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,Mathematics::Classical Analysis and ODEs ,01 natural sciences ,Rate of convergence ,Bounded function ,Bounded variation ,Applied mathematics ,0101 mathematics ,Interpolation ,Mathematics - Abstract
In this paper, the behavior of the Hermite-Fej´er interpolation for functionswithderivativesofboundedvariationon[−1,1]isstudiedbytakingtheinterpolation over the zeros of Chebyshev polynomials of the second kind. An estimate for the rate of convergence using the zeros of the Chebyshev polynomials of the second kind is given.
- Published
- 2020
41. Factorized enhancement of Copson's inequality
- Author
-
Atanu Manna
- Subjects
010101 applied mathematics ,Algebra ,Inequality ,Factorization ,Applied Mathematics ,General Mathematics ,media_common.quotation_subject ,010102 general mathematics ,0101 mathematics ,01 natural sciences ,media_common ,Mathematics - Abstract
This paper dealt with the factorized enhancement of Copson's inequality and improves one of the results given by Leindler.
- Published
- 2018
42. Certain results on N(k)-contact metric manifolds
- Author
-
Uday Chand De
- Subjects
Pure mathematics ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,Dimension (graph theory) ,Field (mathematics) ,0102 computer and information sciences ,01 natural sciences ,Ricci soliton ,010201 computation theory & mathematics ,Metric (mathematics) ,Mathematics::Differential Geometry ,0101 mathematics ,Distribution (differential geometry) ,Eigenvalues and eigenvectors ,Mathematics - Abstract
In the present paper we study contact metric manifolds whose characteristic vector field $\xi$ belonging to the $k$-nullity distribution. First we consider concircularly pseudosymmetric $N(k)$-contact metric manifolds of dimension $(2n+1)$. Beside these, we consider Ricci solitons and gradient Ricci solitons on three dimensional $N(k)$-contact metric manifolds. As a consequence we obtain several results. Finally, an example is given.
- Published
- 2018
43. Optimal casorati inequalities on bi-slant submanifolds of generalized sasakian space forms
- Author
-
Aliya Naaz Siddiqui
- Subjects
Pure mathematics ,Mathematics::Complex Variables ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,Space (mathematics) ,01 natural sciences ,010101 applied mathematics ,Continuation ,Mathematics::Differential Geometry ,0101 mathematics ,Mathematics::Symplectic Geometry ,Scalar curvature ,Mathematics - Abstract
In this paper, we use T Oprea's optimization method to establish some optimal Casorati inequalities, which involve the normalized scalar curvature for bi-slant submanifolds of generalized Sasakian space forms. In the continuation, we show that in both cases, the equalities hold if and only if submanifolds are invariantly quasi-umbilical.
- Published
- 2018
44. The restrained rainbow bondage number of a graph
- Author
-
Jafar Amjadi, Nasrin Dehgardi, Seyed Mahmoud Sheikholeslami, Lutz Volkmann, and Rana Khoeilar
- Subjects
Vertex (graph theory) ,Domination analysis ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,Rainbow ,0102 computer and information sciences ,01 natural sciences ,Graph ,Combinatorics ,010201 computation theory & mathematics ,Bondage number ,0101 mathematics ,Mathematics - Abstract
A restrained $k$-rainbow dominating function (R$k$RDF) of a graph $G$ is a function $f$ from the vertex set $V(G)$ to the set of all subsets of the set $\{1,2,\ldots,k\}$ such that for any vertex $v \in V (G)$ with $f(v) = \emptyset$ the conditions $\bigcup_{u \in N(v)} f(u)=\{1,2,\ldots,k\}$ and $|N(v)\cap \{u\in V\mid f(u)=\emptyset\}|\ge 1$ are fulfilled, where $N(v)$ is the open neighborhood of $v$. The weight of a restrained $k$-rainbow dominating function is the value $w(f)=\sum_{v\in V}|f (v)|$. The minimum weight of a restrained $k$-rainbow dominating function of $G$ is called the restrained $k$-rainbow domination number of $G$, denoted by $\gamma_{rrk}(G)$. The restrained $k$-rainbow bondage number $b_{rrk}(G)$ of a graph $G$ with maximum degree at least two is the minimum cardinality of all sets $F \subseteq E(G)$ for which $\gamma_{rrk}(G-F) > \gamma_{rrk}(G)$. In this paper, we initiate the study of the restrained $k$-rainbow bondage number in graphs and we present some sharp bounds for $b_{rr2}(G)$. In addition, we determine the restrained 2-rainbow bondage number of some classes of graphs.
- Published
- 2018
45. Lower bounds of generalised normalised δ- Casorati curvature for real hypersurfaces in complex quadric endowed with semi-symmetric metric connection
- Author
-
Mohammad Shahid and Pooja Bansal
- Subjects
Pure mathematics ,Mean curvature ,Quadric ,Mathematics::Complex Variables ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,Curvature ,01 natural sciences ,010101 applied mathematics ,Mathematics::Differential Geometry ,0101 mathematics ,Metric connection ,Ricci curvature ,Mathematics - Abstract
The main intention of the present paper is to develop two extremal inequalities involving normalized δ-Casorati curvature and extrinsic generalised normalised δ-Casorati curvature for real hypersurfaces in complex quadric Qm admitting semi-symmetric metric connection. Further, we derive the necessary and sufficient condition for the equality in both cases
- Published
- 2018
46. Nevanlinna's five-value theorem for derivatives of algebroid functions on annuli
- Author
-
Ashok M Rathod
- Subjects
010101 applied mathematics ,Pure mathematics ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,0101 mathematics ,01 natural sciences ,Value (mathematics) ,Nevanlinna theory ,Mathematics - Abstract
In this paper, we first obtain the famous Xiong Inequality for algebroid functions on annuli and also generalise Nevanlinna's five-value theorem for derivatives of algebroid functions by considering weaker assumptions of sharing five values and small functions to partially sharing $k(\geq 5)$ values and small functions on annuli. As a particular cases of our results, we deduce several results.
- Published
- 2018
47. Generalized Wintgen inequality for submanifolds in Kenmotsu space forms
- Author
-
Mohd. Aquib and Mohammad Shahid
- Subjects
Pure mathematics ,Inequality ,Applied Mathematics ,General Mathematics ,media_common.quotation_subject ,010102 general mathematics ,Space (mathematics) ,Submanifold ,01 natural sciences ,Ambient space ,010101 applied mathematics ,Mathematics::Differential Geometry ,0101 mathematics ,Mathematics::Symplectic Geometry ,media_common ,Mathematics - Abstract
In this paper, we obtain the generalized Wintgen inequality for Legendrian submanifolds in Kenmotsu space forms and discuss the equality case of the inequality. Further, we discuss the inequality for bi-slant submanifold in the same ambient space and derive its application in various slant cases.
- Published
- 2018
48. Dual wavelets associated with nonuniform MRA
- Author
-
Mohd Younus Bhat
- Subjects
Pure mathematics ,Discrete group ,Generalization ,Applied Mathematics ,General Mathematics ,Multiresolution analysis ,010102 general mathematics ,02 engineering and technology ,01 natural sciences ,Dilation (operator theory) ,Wavelet ,Integer ,Biorthogonal system ,0202 electrical engineering, electronic engineering, information engineering ,020201 artificial intelligence & image processing ,0101 mathematics ,Scaling ,Mathematics - Abstract
A generalization of Mallats classical multiresolution analysis, based on thetheory of spectral pairs, was considered in two articles by Gabardo and Nashed. In thissetting, the associated translation set is no longer a discrete subgroup of R but a spectrumassociated with a certain one-dimensional spectral pair and the associated dilation is aneven positive integer related to the given spectral pair. In this paper, we construct dualwavelets which are associated with Nonuniform Multiresolution Analysis. We show thatif the translates of the scaling functions of two multiresolution analyses are biorthogonal,then the associated wavelet families are also biorthogonal. Under mild assumptions onthe scaling functions and the wavelets, we also show that the wavelets generate Rieszbases
- Published
- 2018
49. New f-divergnce and Jensen-Ostrowsk's type inequalities
- Author
-
Ajay Tak and Ram Naresh Saraswat
- Subjects
Inequality ,Applied Mathematics ,General Mathematics ,media_common.quotation_subject ,010102 general mathematics ,020206 networking & telecommunications ,02 engineering and technology ,Type (model theory) ,01 natural sciences ,0202 electrical engineering, electronic engineering, information engineering ,0101 mathematics ,Jensen's inequality ,Mathematical economics ,Mathematics ,media_common - Abstract
In this paper we derive new information inequalities of Jensen-Ostrowski type, by considering two Jensen-Ostrowski type inequalities, new $f$-divergence and\\ Chi-divergences. The special cases of these information inequalities are established as applications of new $f$-divergence and its particular instances.
- Published
- 2018
50. Uniqueness of certain type of differential-difference and difference polyniminals
- Author
-
Abhijit Banerjee and Sujoy Majumder
- Subjects
Pure mathematics ,Polynomial ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,010103 numerical & computational mathematics ,Uniqueness ,0101 mathematics ,Type (model theory) ,01 natural sciences ,Differential (mathematics) ,Mathematics ,Meromorphic function - Abstract
In this paper we consider certain difference and differential-difference polynomials sharing some polynomial and improve a number of results in \cite{8a}, \cite{8aa} and \cite{18}. In particular we point out a gap in the argument in the proof of the main results in \cite {8aa} and rectifying the same we improve and extend the result to a large extent.
- Published
- 2018
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