417 results
Search Results
52. Fractal fractional derivative on chemistry kinetics hires problem
- Author
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Sameh S. Askar, Aqeel Ahmad, Muhammad Farman, Muhammad Aslam, Hijaz Ahmad, and Tuan Nguyen Gia
- Subjects
Chemical kinetics ,fractal fractional derivative ,Materials science ,Fractal ,General Mathematics ,QA1-939 ,Thermodynamics ,uniqueness ,chemistry kinetics ,stability ,mittag-leffler kernel ,Mathematics ,Fractional calculus - Abstract
In this work, we construct the fractional order model for chemical kinetics issues utilizing novel fractal operators such as fractal fractional by using generalized Mittag-Leffler Kernel. To overcome the constraints of the traditional Riemann-Liouville and Caputo fractional derivatives, a novel notion of fractional differentiation with non-local and non-singular kernels was recently presented. Many scientific conclusions are presented in the study, and these results are supported by effective numerical results. These findings are critical for solving the nonlinear models in chemical kinetics. These concepts are very important to use for real life problems like brine tank cascade, recycled brine tank cascade, pond pollution, home heating and biomass transfer problem. Many scientific results are presented in the paper also prove these results by effective numerical results. These results are very important for solving the nonlinear model in chemistry kinetics which will be helpful to understand the chemical reactions and its actual behavior; also the observation can be developed for future kinematic chemical reactions with the help of these results.
- Published
- 2022
53. The generalization of Hermite-Hadamard type Inequality with exp-convexity involving non-singular fractional operator
- Author
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Muhammad Imran Asjad, Waqas Ali Faridi, Mohammed M. Al-Shomrani, Abdullahi Yusuf, and Mühendislik ve Doğa Bilimleri Fakültesi
- Subjects
hermite-hadamard inequality ,General Mathematics ,QA1-939 ,exp-convexity ,Exp-Convexity Caputo-Fabrizio Fractional Integral ,caputo-fabrizio fractional integral ,Mathematics - Abstract
The theory of convex function has a lot of applications in the field of applied mathematics and engineering. The Caputo-Fabrizio non-singular operator is the most significant operator of fractional theory which permits to generalize the classical theory of differentiation. This study consider the well known Hermite-Hadamard type and associated inequalities to generalize further. To full fill this mileage, we use the exponential convexity and fractional-order differential operator and also apply some existing inequalities like Holder, power mean, and Holder-Iscan type inequalities for further extension. The generalized exponential type fractional integral Hermite-Hadamard type inequalities establish involving the global integral. The applications of the developed results are displayed to verify the applicability. The establish results of this paper can be considered an extension and generalization of the existing results of convex function and inequality in literature and we hope that will be more helpful for the researcher in future work.
- Published
- 2022
54. A posteriori error estimates of hp spectral element method for parabolic optimal control problems
- Author
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Zuliang Lu, Fei Cai, Ruixiang Xu, Chunjuan Hou, Xiankui Wu, and Yin Yang
- Subjects
a posteriori error estimates ,General Mathematics ,QA1-939 ,parabolic optimal control problems ,hp spectral element method ,Mathematics - Abstract
In this paper, we investigate the spectral element approximation for the optimal control problem of parabolic equation, and present a hp spectral element approximation scheme for the parabolic optimal control problem. For improve the accuracy of the algorithm and construct an adaptive finite element approximation. Under the Scott-Zhang type quasi-interpolation operator, a $ L^2(H^1)-L^2(L^2) $ posteriori error estimates of the hp spectral element approximated solutions for both the state variables and the control variable are obtained. Adopting two auxiliary equations and stability results, a $ L^2(L^2)-L^2(L^2) $ posteriori error estimates are derived for the hp spectral element approximation of optimal parabolic control problem.
- Published
- 2022
55. Some families of differential equations associated with the Gould-Hopper-Frobenius-Genocchi polynomials
- Author
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Rabab Alyusof and Mdi Begum Jeelani
- Subjects
differential equation ,shift operators ,integro-differential equation ,General Mathematics ,partial differential equation ,recurrence relation ,QA1-939 ,Mathematics - Abstract
The basic objective of this paper is to utilize the factorization technique method to derive several properties such as, shift operators, recurrence relation, differential, integro-differential, partial differential expressions for Gould-Hopper-Frobenius-Genocchi polynomials, which can be utilized to tackle some new issues in different areas of science and innovation.
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- 2022
56. Hahn-Banach type theorems and the separation of convex sets for fuzzy quasi-normed spaces
- Author
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Ruini Li and Jianrong Wu
- Subjects
Pure mathematics ,General Mathematics ,Separation (statistics) ,Regular polygon ,Hahn–Banach theorem ,Type (model theory) ,Fuzzy logic ,separation theorem ,fuzzy quasi-normed space ,hahn-banach extension theorem ,QA1-939 ,continuous linear functional ,Mathematics - Abstract
In this paper, we first study continuous linear functionals on a fuzzy quasi-normed space, obtain a characterization of continuous linear functionals, and point out that the set of all continuous linear functionals forms a convex cone and can be equipped with a weak fuzzy quasi-norm. Next, we prove a theorem of Hahn-Banach type and two separation theorems for convex subsets of fuzzy quasinormed spaces.
- Published
- 2022
57. On ψ-Hilfer generalized proportional fractional operators
- Author
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Subhash Alha, Ali Akgül, Idris Ahmed, Fahd Jarad, and Ishfaq Ahmad Mallah
- Subjects
General Mathematics ,weighed space ,QA1-939 ,Applied mathematics ,generalized proportional fractional derivative ,hilfer fractional derivative ,fixed point theorems ,Mathematics ,existence and uniqueness - Abstract
In this paper, we introduce a generalized fractional operator in the setting of Hilfer fractional derivatives, the $ \psi $-Hilfer generalized proportional fractional derivative of a function with respect to another function. The proposed operator can be viewed as an interpolator between the Riemann-Liouville and Caputo generalized proportional fractional operators. The properties of the proposed operator are established under some classical and standard assumptions. As an application, we formulate a nonlinear fractional differential equation with a nonlocal initial condition and investigate its equivalence with Volterra integral equations, existence, and uniqueness of solutions. Finally, illustrative examples are given to demonstrate the theoretical results.
- Published
- 2022
58. Existence of positive periodic solutions for a class of in-host MERS-CoV infection model with periodic coefficients
- Author
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Tuersunjiang Keyoumu, Ke Guo, and Wanbiao Ma
- Subjects
Pure mathematics ,Class (set theory) ,General Mathematics ,mers-cov ,dipeptidyl peptidase 4 (dpp4) ,periodic model ,QA1-939 ,periodic solutions ,Host (network) ,Mathematics ,coincidence degree - Abstract
In this paper, a dynamic model of Middle East Respiratory Syndrome Coronavirus (MERS-CoV) with periodic coefficients is proposed and studied. By using the continuation theorem of the coincidence degree theory, we obtain some sufficient conditions for the existence of positive periodic solutions of the model. The periodic model degenerates to an autonomous case, and our conditions can be degenerated to the basic reproductive number $ R_0 > 1 $. Finally, we give some numerical simulations to illustrate our main theoretical results.
- Published
- 2022
59. Threshold dynamics of a general delayed HIV model with double transmission modes and latent viral infection
- Author
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Xin Jiang
- Subjects
General Mathematics ,Dynamics (mechanics) ,Human immunodeficiency virus (HIV) ,Biology ,medicine.disease_cause ,time delay ,Virology ,Viral infection ,law.invention ,double transmission modes ,Transmission (mechanics) ,threshold dynamics ,law ,latent viral infection ,medicine ,QA1-939 ,Quantitative Biology::Populations and Evolution ,Mathematics - Abstract
In this paper, a general HIV model incorporating intracellular time delay is investigated. Taking the latent virus infection, both virus-to-cell and cell-to-cell transmissions into consideration, the model exhibits threshold dynamics with respect to the basic reproduction number $ \mathfrak{R}_0 $. If $ \mathfrak{R}_0 < 1 $, then there exists a unique infection-free equilibrium $ E_0 $, which is globally asymptotically stable. If $ \mathfrak{R}_0 > 1 $, then there exists $ E_0 $ and a globally asymptotically stable infected equilibrium $ E^* $. When $ \mathfrak{R}_0 = 1 $, $ E_0 $ is linearly neutrally stable and a forward bifurcation takes place without time delay around $ \mathfrak{R}_0 = 1 $. The theoretical results and corresponding numerical simulations show that the existence of latently infected cells and the intracellular time delay have vital effect on the global dynamics of the general virus model.
- Published
- 2022
60. New Lyapunov-type inequalities for fractional multi-point boundary value problems involving Hilfer-Katugampola fractional derivative
- Author
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Wei Zhang, Jifeng Zhang, and Jinbo Ni
- Subjects
Lyapunov function ,General Mathematics ,hilfer-katugampola fractional derivative ,Type (model theory) ,Fractional calculus ,symbols.namesake ,multi-point boundary condition ,symbols ,QA1-939 ,Applied mathematics ,Boundary value problem ,lyapunov-type inequality ,Multi point ,Mathematics - Abstract
In this paper, we present new Lyapunov-type inequalities for Hilfer-Katugampola fractional differential equations. We first give some unique properties of the Hilfer-Katugampola fractional derivative, and then by using these new properties we convert the multi-point boundary value problems of Hilfer-Katugampola fractional differential equations into the equivalent integral equations with corresponding Green's functions, respectively. Finally, we make use of the Banach's contraction principle to derive the desired results, and give a series of corollaries to show that the current results extend and enrich the previous results in the literature.
- Published
- 2022
61. Stochastic pricing formulation for hybrid equity warrants
- Author
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Ali F. Jameel, Siti Zulaiha Ibrahim, Sharmila Karim, Teh Raihana Nazirah Roslan, and Zainor Ridzuan Yahya
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Warrant ,Stochastic volatility ,General Mathematics ,media_common.quotation_subject ,Equity (finance) ,hybrid model ,Black–Scholes model ,heston-cir model ,Interest rate ,stochastic interest rate ,Econometrics ,Economics ,QA1-939 ,equity warrants ,Call option ,stochastic volatility ,Moneyness ,Mathematics ,media_common ,Valuation (finance) - Abstract
A warrant is a financial agreement that gives the right but not the responsibility, to buy or sell a security at a specific price prior to expiration. Many researchers inadvertently utilize call option pricing models to price equity warrants, such as the Black Scholes model which had been found to hold many shortcomings. This paper investigates the pricing of equity warrants under a hybrid model of Heston stochastic volatility together with stochastic interest rates from Cox-Ingersoll-Ross model. This work contributes to exploration of the combined effects of stochastic volatility and stochastic interest rates on pricing equity warrants which fills the gap in the current literature. Analytical pricing formulas for hybrid equity warrants are firstly derived using partial differential equation approaches. Further, to implement the pricing formula to realistic contexts, a calibration procedure is performed using local optimization method to estimate all parameters involved. We then conducted an empirical application of our pricing formula, the Black Scholes model, and the Noreen Wolfson model against the real market data. The comparison between these models is presented along with the investigation of the models' accuracy using statistical error measurements. The outcomes revealed that our proposed model gives the best performance which highlights the crucial elements of both stochastic volatility and stochastic interest rates in valuation of equity warrants. We also examine the warrants' moneyness and found that 96.875% of the warrants are in-the-money which gives positive returns to investors. Thus, it is beneficial for warrant holders concerned in purchasing warrants to elect the best warrant with the most profitable and more benefits at a future date.
- Published
- 2022
62. Some new generalized κ–fractional Hermite–Hadamard–Mercer type integral inequalities and their applications
- Author
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Artion Kashuri, Muhammad Uzair Awan, Miguel Vivas-Cortez, Muhammad Zakria Javed, Muhammad Aslam Noor, and Khalida Inayat Noor
- Subjects
Pure mathematics ,Hermite polynomials ,General Mathematics ,Type (model theory) ,hermite–hadamard inequality ,jensen–mercer inequality ,Hadamard transform ,error estimation ,QA1-939 ,power mean inequality ,special means ,Kappa ,Mathematics ,hölder's inequality - Abstract
In this paper, we have established some new Hermite–Hadamard–Mercer type of inequalities by using $ {\kappa} $–Riemann–Liouville fractional integrals. Moreover, we have derived two new integral identities as auxiliary results. From the applied identities as auxiliary results, we have obtained some new variants of Hermite–Hadamard–Mercer type via $ {\kappa} $–Riemann–Liouville fractional integrals. Several special cases are deduced in detail and some know results are recaptured as well. In order to illustrate the efficiency of our main results, some applications regarding special means of positive real numbers and error estimations for the trapezoidal quadrature formula are provided as well.
- Published
- 2022
63. Varieties of a class of elementary subalgebras
- Author
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Yang Pan and Yanyong Hong
- Subjects
Physics ,General Mathematics ,Dimension (graph theory) ,Subalgebra ,elementary subalgebras ,commuting roots ,Type (model theory) ,Combinatorics ,Restricted Lie algebra ,Algebraic group ,Lie algebra ,QA1-939 ,Variety (universal algebra) ,Algebraically closed field ,Mathematics::Representation Theory ,irreducible components ,Mathematics - Abstract
Let $ G $ be a connected standard simple algebraic group of type $ C $ or $ D $ over an algebraically closed field $ \Bbbk $ of positive characteristic $ p > 0 $, and $ \mathfrak{g}: = \mathrm{Lie}(G) $ be the Lie algebra of $ G $. Motivated by the variety of $ \mathbb{E}(r, \mathfrak{g}) $ of $ r $-dimensional elementary subalgebras of a restricted Lie algebra $ \mathfrak{g} $, in this paper we characterize the irreducible components of $ \mathbb{E}(\mathrm{rk}_{p}(\mathfrak{g})-1, \mathfrak{g}) $ where the $ p $-rank $ \mathrm{rk}_{p}(\mathfrak{g}) $ is defined to be the maximal dimension of an elementary subalgebra of $ \mathfrak{g} $.
- Published
- 2022
64. Mathematical modelling of COVID-19 disease dynamics: Interaction between immune system and SARS-CoV-2 within host
- Author
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J Chowdhury, Shams Forruque Ahmed, S. Chowdhury, Irfan Anjum Badruddin, Sarfaraz Kamangar, and Praveen Agarwal
- Subjects
General Mathematics ,viruses ,mers-cov ,Context (language use) ,Disease ,Computational biology ,Biology ,medicine.disease_cause ,Virus ,sars-cov-2 ,immune system ,Immune system ,Viral replication ,covid-19 ,basic reproduction number ,medicine ,QA1-939 ,Viral load ,Host (network) ,mathematical model ,Mathematics ,Coronavirus - Abstract
SARS-COV-2 (Coronavirus) viral growth kinetics within-host become a key fact to understand the COVID-19 disease progression and disease severity since the year 2020. Quantitative analysis of the viral dynamics has not yet been able to provide sufficient information on the disease severity in the host. The SARS-CoV-2 dynamics are therefore important to study in the context of immune surveillance by developing a mathematical model. This paper aims to develop such a mathematical model to analyse the interaction between the immune system and SARS-CoV-2 within the host. The model is developed to explore the viral load dynamics within the host by considering the role of natural killer cells and T-cell. Through analytical simplifications, the model is found well-posed and asymptotically stable at disease-free equilibrium. The numerical results demonstrate that the influx of external natural killer (NK) cells alone or integrating with anti-viral therapy plays a vital role in suppressing the SARS-CoV-2 growth within-host. Also, within the host, the virus can not grow if the virus replication rate is below a threshold limit. The developed model will contribute to understanding the disease dynamics and help to establish various potential treatment strategies against COVID-19.
- Published
- 2022
65. The common Re-nonnegative definite and Re-positive definite solutions to the matrix equations $ A_1XA_1^\ast = C_1 $ and $ A_2XA_2^\ast = C_2 $
- Author
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Lina Liu and Yinlan Chen
- Subjects
Pure mathematics ,General Mathematics ,re-nonnegative definite solution ,Positive-definite matrix ,Linear matrix ,Matrix (mathematics) ,matrix equation ,QA1-939 ,moore-penrose inverse ,Generalized singular value decomposition ,re-positive definite solution ,Moore–Penrose pseudoinverse ,Mathematics ,generalized singular value decomposition - Abstract
In this paper, we consider the common Re-nonnegative definite (Re-nnd) and Re-positive definite (Re-pd) solutions to a pair of linear matrix equations $ A_1XA_1^\ast = C_1, \ A_2XA_2^\ast = C_2 $ and present some necessary and sufficient conditions for their solvability as well as the explicit expressions for the general common Re-nnd and Re-pd solutions when the consistent conditions are satisfied.
- Published
- 2022
66. Adaptive event-triggered state estimation for complex networks with nonlinearities against hybrid attacks
- Author
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Zhenhai Meng, Yahan Deng, and Hongqian Lu
- Subjects
Estimation ,Computer science ,General Mathematics ,complex networks ,denial-of-service attacks ,Complex network ,adaptive event-triggered scheme ,Control theory ,deception attacks ,QA1-939 ,State (computer science) ,state estimation ,Event triggered ,Mathematics ,Computer Science::Cryptography and Security - Abstract
This paper investigates the event-triggered state estimation problem for a class of complex networks (CNs) suffered by hybrid cyber-attacks. It is assumed that a wireless network exists between sensors and remote estimators, and that data packets may be modified or blocked by malicious attackers. Adaptive event-triggered scheme (AETS) is introduced to alleviate the network congestion problem. With the help of two sets of Bernoulli distribution variables (BDVs) and an arbitrary function related to the system state, a mathematical model of the hybrid cyber-attacks is developed to portray randomly occurring denial-of-service (DoS) attacks and deception attacks. CNs, AETS, hybrid cyber-attacks, and state estimators are then incorporated into a unified architecture. The system state is cascaded with state errors as an augmented system. Furthermore, based on Lyapunov stability theory and linear matrix inequalities (LMIs), sufficient conditions to ensure the asymptotic stability of the augmented system are derived, and the corresponding state estimator is designed. Finally, the effectiveness of the theoretical method is demonstrated by numerical examples and simulations.
- Published
- 2022
67. On the boundedness stepsizes-coefficients of A-BDF methods
- Author
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Kamal Kaveh, Dumitru Baleanu, Mohammad Mehdizadeh Khalsaraei, and Ali Shokri
- Subjects
a-bdf method ,total-variation-diminishing ,General Mathematics ,total-variation-bounded ,method of lines ,QA1-939 ,linear multistep method ,monotonicity ,Mathematics - Abstract
Physical constraints must be taken into account in solving partial differential equations (PDEs) in modeling physical phenomenon time evolution of chemical or biological species. In other words, numerical schemes ought to be devised in a way that numerical results may have the same qualitative properties as those of the theoretical results. Methods with monotonicity preserving property possess a qualitative feature that renders them practically proper for solving hyperbolic systems. The need for monotonicity signifies the essential boundedness properties necessary for the numerical methods. That said, for many linear multistep methods (LMMs), the monotonicity demands are violated. Therefore, it cannot be concluded that the total variations of those methods are bounded. This paper investigates monotonicity, especially emphasizing the stepsize restrictions for boundedness of A-BDF methods as a subclass of LMMs. A-stable methods can often be effectively used for stiff ODEs, but may prove inefficient in hyperbolic equations with stiff source terms. Numerical experiments show that if we apply the A-BDF method to Sod's problem, the numerical solution for the density is sharp without spurious oscillations. Also, application of the A-BDF method to the discontinuous diffusion problem is free of temporal oscillations and negative values near the discontinuous points while the SSP RK2 method does not have such properties.
- Published
- 2022
68. Some properties for certain class of bi-univalent functions defined by q-Cătaş operator with bounded boundary rotation
- Author
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S. M. Madian
- Subjects
Class (set theory) ,Pure mathematics ,General Mathematics ,Operator (physics) ,q-analogue cătaş operator ,Boundary (topology) ,bi-univalent functions ,bazilevič functions ,Bounded function ,bounded boundary rotation ,QA1-939 ,Rotation (mathematics) ,Mathematics - Abstract
Throughout the paper, we introduce a new subclass $ \mathcal{H}_{\alpha, \mu, \rho, m, \beta }^{n, q, \lambda, l}\ f(z)$ by using the Bazilevič functions with the idea of bounded boundary rotation and $ q $-analogue Cătaş operator. Also we find the estimate of the coefficients for functions in this class. Finally, in the concluding section, we have chosen to reiterate the well-demonstrated fact that any attempt to produce the rather straightforward $ (p, q) $-variations of the results, which we have presented in this article, will be a rather trivial and inconsequential exercise, simply because the additional parameter $ p $ is obviously redundant.
- Published
- 2022
69. On a boundary value problem for fractional Hahn integro-difference equations with four-point fractional integral boundary conditions
- Author
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Sotiris K. Ntouyas, Thanin Sitthiwirattham, and Varaporn Wattanakejorn
- Subjects
Mathematics::Functional Analysis ,boundary value problems ,General Mathematics ,Mathematics::Classical Analysis and ODEs ,existence ,Fixed-point theorem ,fractional hahn difference ,Fixed point ,Quantum number ,Nonlinear system ,Operator (computer programming) ,QA1-939 ,Applied mathematics ,fractional hahn integral ,Point (geometry) ,Boundary value problem ,Uniqueness ,Mathematics - Abstract
In this paper, we study a boundary value problem consisting of Hahn integro-difference equation supplemented with four-point fractional Hahn integral boundary conditions. The novelty of this problem lies in the fact that it contains two fractional Hahn difference operators and three fractional Hahn integrals with different quantum numbers and orders. Firstly, we convert the given nonlinear problem into a fixed point problem, by considering a linear variant of the problem at hand. Once the fixed point operator is available, we make use the classical Banach's and Schauder's fixed point theorems to establish existence and uniqueness results. An example is also constructed to illustrate the main results. Several properties of fractional Hahn integral that will be used in our study are also discussed.
- Published
- 2022
70. Mathematical modeling approach to predict COVID-19 infected people in Sri Lanka
- Author
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I. H. K. Premarathna, H. M. Srivastava, Z. A. M. S. Juman, Ali AlArjani, Md Sharif Uddin, and Shib Sankar Sana
- Subjects
model validation method ,covid-19 ,sir and logistic growth models ,General Mathematics ,QA1-939 ,stochastic model ,Mathematics - Abstract
The novel corona virus (COVID-19) has badly affected many countries (more than 180 countries including China) in the world. More than 90% of the global COVID-19 cases are currently outside China. The large, unanticipated number of COVID-19 cases has interrupted the healthcare system in many countries and created shortages for bed space in hospitals. Consequently, better estimation of COVID-19 infected people in Sri Lanka is vital for government to take suitable action. This paper investigates predictions on both the number of the first and the second waves of COVID-19 cases in Sri Lanka. First, to estimate the number of first wave of future COVID-19 cases, we develop a stochastic forecasting model and present a solution technique for the model. Then, another solution method is proposed to the two existing models (SIR model and Logistic growth model) for the prediction on the second wave of COVID-19 cases. Finally, the proposed model and solution approaches are validated by secondary data obtained from the Epidemiology Unit, Ministry of Health, Sri Lanka. A comparative assessment on actual values of COVID-19 cases shows promising performance of our developed stochastic model and proposed solution techniques. So, our new finding would definitely be benefited to practitioners, academics and decision makers, especially the government of Sri Lanka that deals with such type of decision making.
- Published
- 2022
71. Regularity results of solutions to elliptic equations involving mixed local and nonlocal operators
- Author
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CaiDan LaMao, Shuibo Huang, Qiaoyu Tian, and Canyun Huang
- Subjects
fractional elliptic equations ,General Mathematics ,mixed local and nonlocal operators ,summability ,QA1-939 ,Mathematics - Abstract
In this paper, we study the summability of solutions to the following semilinear elliptic equations involving mixed local and nonlocal operators \begin{document}$ \left\{ \begin{matrix} - \Delta u(x)+{{(-\Delta )}^{s}}u(x)=f(x), & x\in \Omega , \\ u(x)\ge 0,~~~~~ & x\in \Omega , \\ u(x)=0,~~~~~ & x\in {{\mathbb{R}}^{N}}\setminus \Omega , \\ \end{matrix} \right. $\end{document} where $ 0 < s < 1 $, $ \Omega\subset \mathbb{R}^N $ is a smooth bounded domain, $ (-\Delta)^s $ is the fractional Laplace operator, $ f $ is a measurable function.
- Published
- 2022
72. Note on r-central Lah numbers and r-central Lah-Bell numbers
- Author
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Hye Kyung Kim
- Subjects
Combinatorics ,lah-bell numbers ,General Mathematics ,QA1-939 ,r-lah-bell polynomials ,central factorial numbers of the second kind ,Lah number ,lah numbers ,Mathematics ,Bell number ,r-lah numbers - Abstract
The $ r $-Lah numbers generalize the Lah numbers to the $ r $-Stirling numbers in the same sense. The Stirling numbers and the central factorial numbers are one of the important tools in enumerative combinatorics. The $ r $-Lah number counts the number of partitions of a set with $ n+r $ elements into $ k+r $ ordered blocks such that $ r $ distinguished elements have to be in distinct ordered blocks. In this paper, the $ r $-central Lah numbers and the $ r $-central Lah-Bell numbers ($ r\in \mathbb{N} $) are introduced parallel to the $ r $-extended central factorial numbers of the second kind and $ r $-extended central Bell polynomials. In addition, some identities related to these numbers including the generating functions, explicit formulas, binomial convolutions are derived. Moreover, the $ r $-central Lah numbers and the $ r $-central Lah-Bell numbers are shown to be represented by Riemann integral, respectively.
- Published
- 2022
73. Single valued neutrosophic (m,n)-ideals of ordered semirings
- Author
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Mariam Hariri, Madeline Al Tahan, Saba Al-Kaseasbeh, and Bijan Davvaz
- Subjects
(m,n)-ideal ,single valued neutrosophic set ,General Mathematics ,ordered semiring ,QA1-939 ,semiring ,single valued neutrosophic (m,n)-ideal ,Mathematics - Abstract
The aim of this paper is to combine the innovative concept of single valued neutrosophic sets and ordered semirings. It studies ordered semirings by the properties of their single valued neutrosphic subsets. In this regard, we define single valued neutrosophic $ (m, n) $-ideals (SVN-$ (m, n) $-ideals) of ordered semirings. First, we illustrate our new definition by non-trivial examples. Second, we study these SVN-$ (m, n) $-ideals under different operations of SVNS. Finally, we find a relationship between the $ (m, n) $-ideals of ordered semirings and level sets by finding a necessary and sufficient condition for an SVNS of an ordered semiring $ R $ to be an SVN-$ (m, n) $-ideal of $ R $.
- Published
- 2022
74. Semilattice strongly regular relations on ordered n-ary semihypergroups
- Author
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Sorasak Leeratanavalee and Jukkrit Daengsaen
- Subjects
Combinatorics ,hyperideal ,hyperfilter ,General Mathematics ,QA1-939 ,Congruence (manifolds) ,Semilattice ,n-ary semihypergroup ,ordered semihypergroup ,Prime (order theory) ,Mathematics ,Counterexample - Abstract
In this paper, we introduce the concept of $ j $-hyperfilters, for all positive integers $ 1\leq j \leq n $ and $ n \geq 2 $, on (ordered) $ n $-ary semihypergroups and establish the relationships between $ j $-hyperfilters and completely prime $ j $-hyperideals of (ordered) $ n $-ary semihypergroups. Moreover, we investigate the properties of the relation $ \mathcal{N} $, which is generated by the same principal hyperfilters, on (ordered) $ n $-ary semihypergroups. As we have known from [21] that the relation $ \mathcal{N} $ is the least semilattice congruence on semihypergroups, we illustrate by counterexample that the similar result is not necessarily true on $ n $-ary semihypergroups where $ n\geq 3 $. However, we provide a sufficient condition that makes the previous conclusion true on $ n $-ary semihypergroups and ordered $ n $-ary semihypergroups where $ n\geq 3 $. Finally, we study the decomposition of prime hyperideals and completely prime hyperideals by means of their $ \mathcal{N} $-classes. As an application of the results, a related problem posed by Tang and Davvaz in [31] is solved.
- Published
- 2022
75. Integral presentations of the solution of a boundary value problem for impulsive fractional integro-differential equations with Riemann-Liouville derivatives
- Author
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Donal O’Regan, Snezhana Hristova, and Ravi P. Agarwal
- Subjects
riemann-liouville fractional derivative ,impulses ,Differential equation ,General Mathematics ,boundary value problem ,Mathematical analysis ,QA1-939 ,Boundary value problem ,Riemann liouville ,Mathematics ,riemann-liouville integral - Abstract
Riemann-Liouville fractional differential equations with impulses are useful in modeling the dynamics of many real world problems. It is very important that there are good and consistent theoretical proofs and meaningful results for appropriate problems. In this paper we consider a boundary value problem for integro-differential equations with Riemann-Liouville fractional derivative of orders from $ (1, 2) $. We consider both interpretations in the literature on the presence of impulses in fractional differential equations: With fixed lower limit of the fractional derivative at the initial time point and with lower limits changeable at each impulsive time point. In both cases we set up in an appropriate way impulsive conditions which are dependent on the Riemann-Liouville fractional derivative. We establish integral presentations of the solutions in both cases and we note that these presentations are useful for furure studies of existence, stability and other qualitative properties of the solutions.
- Published
- 2022
76. Ulam-Hyers-Rassias stability for a class of nonlinear implicit Hadamard fractional integral boundary value problem with impulses
- Author
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Kaihong Zhao and Shuang Ma
- Subjects
Class (set theory) ,Mathematics::Functional Analysis ,General Mathematics ,Stability (learning theory) ,stability ,hadamard fractional integral bvp ,contraction mapping principle ,Nonlinear system ,Hadamard transform ,QA1-939 ,Applied mathematics ,Boundary value problem ,Mathematics ,existence and uniqueness - Abstract
This paper considers a class of nonlinear implicit Hadamard fractional differential equations with impulses. By using Banach's contraction mapping principle, we establish some sufficient criteria to ensure the existence and uniqueness of solution. Furthermore, the Ulam-Hyers stability and Ulam-Hyers-Rassias stability of this system are obtained by applying nonlinear functional analysis technique. As applications, an interesting example is provided to illustrate the effectiveness of main results.
- Published
- 2022
77. On the eccentric connectivity coindex in graphs
- Author
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Ber-Lin Yu, Xianhao Shi, and Hongzhuan Wang
- Subjects
Physics ,Vertex (graph theory) ,General Mathematics ,eccentric connectivity coindex ,Unicyclic graphs ,Order (ring theory) ,trees ,Graph ,Combinatorics ,unicyclic graphs ,Topological index ,QA1-939 ,Astrophysics::Earth and Planetary Astrophysics ,cactus ,Eccentricity (mathematics) ,diameter ,Connectivity ,Mathematics - Abstract
The well-studied eccentric connectivity index directly consider the contribution of all edges in a graph. By considering the total eccentricity sum of all non-adjacent vertex, Hua et al. proposed a new topological index, namely, eccentric connectivity coindex of a connected graph. The eccentric connectivity coindex of a connected graph $ G $ is defined as \begin{document}$ \overline{\xi}^{c}(G) = \sum\limits_{uv\notin E(G)} (\varepsilon_{G}(u)+\varepsilon_{G}(v)). $\end{document} Where $ \varepsilon_{G}(u) $ (resp. $ \varepsilon_{G}(v) $) is the eccentricity of the vertex $ u $ (resp. $ v $). In this paper, some extremal problems on the $ \overline{\xi}^{c} $ of graphs with given parameters are considered. We present the sharp lower bounds on $ \overline{\xi}^{c} $ for general connecteds graphs. We determine the smallest eccentric connectivity coindex of cacti of given order and cycles. Also, we characterize the graph with minimum and maximum eccentric connectivity coindex among all the trees with given order and diameter. Additionally, we determine the smallest eccentric connectivity coindex of unicyclic graphs with given order and diameter and the corresponding extremal graph is characterized as well.
- Published
- 2022
78. Jordan matrix algebras defined by generators and relations
- Author
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Huihui Wang, Yingyu Luo, Junjie Gu, and Yu Wang
- Subjects
Jordan matrix ,symbols.namesake ,Pure mathematics ,generator ,General Mathematics ,Mathematics::Rings and Algebras ,symbols ,QA1-939 ,matrix algebra ,jordan matrix algebra ,Mathematics - Abstract
In the present paper we describe Jordan matrix algebras over a field by generators and relations. We prove that the minimun number of generators of some special Jordan matrix algebras over a field is $ 2 $.
- Published
- 2022
79. Fractional order COVID-19 model with transmission rout infected through environment
- Author
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Yao, Shao-Wen, Farman, Muhammad, Amin, Maryam, İnç, Mustafa, Akgül, Ali, Ahmad, Aqeel, and Mühendislik ve Doğa Bilimleri Fakültesi
- Subjects
fractal fractional ,General Mathematics ,QA1-939 ,uniqueness ,adams-moulton rule ,covid-19 model ,stability ,sumudu transform ,transmission rout ,Mathematics - Abstract
In this paper, we study a fractional order COVID-19 model using different techniques and analysis. The sumudu transform is applied with the environment as a route of infection in society to the proposed fractional-order model. It plays a significant part in issues of medical and engineering as well as its analysis in community. Initially, we present the model formation and its sensitivity analysis. Further, the uniqueness and stability analysis has been made for COVID-19 also used the iterative scheme with fixed point theorem. After using the Adams-Moulton rule to support our results, we examine some results using the fractal fractional operator. Demonstrate the numerical simulations to prove the efficiency of the given techniques. We illustrate the visual depiction of sensitive parameters that reveal the decrease and triumph over the virus within the network. We can reduce the virus by the appropriate recognition of the individuals in community of Saudi Arabia.
- Published
- 2022
80. Codimension two 1:1 strong resonance bifurcation in a discrete predator-prey model with Holling Ⅳ functional response
- Author
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Xianyi Li, Mianjian Ruan, and Chang Li
- Subjects
Physics ,holling ⅳ functional response ,codimension two ,General Mathematics ,Mathematical analysis ,Functional response ,Codimension ,Resonance (particle physics) ,transcritical bifurcation ,Predation ,1:1 strong resonance bifurcation ,Nonlinear Sciences::Adaptation and Self-Organizing Systems ,QA1-939 ,Quantitative Biology::Populations and Evolution ,predator-prey model ,Nonlinear Sciences::Pattern Formation and Solitons ,Bifurcation ,Mathematics - Abstract
In this paper we revisit a discrete predator-prey model with Holling Ⅳ functional response. By using the method of semidiscretization, we obtain new discrete version of this predator-prey model. Some new results, besides its stability of all fixed points and the transcritical bifurcation, mainly for codimension two 1:1 strong resonance bifurcation, are derived by using the center manifold theorem and bifurcation theory, showing that this system possesses complicate dynamical properties.
- Published
- 2022
81. Long-time dynamics of a stochastic multimolecule oscillatory reaction model with Poisson jumps
- Author
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Zongbin Yin and Yongchang Wei
- Subjects
Physics ,singleton sets ,random attractors ,General Mathematics ,multimolecule oscillatory reaction model ,uniqueness ,Poisson distribution ,Oscillatory reaction ,symbols.namesake ,Time dynamics ,symbols ,QA1-939 ,Statistical physics ,Mathematics - Abstract
This paper reveals dynamical behaviors in the stochastic multimolecule oscillatory reaction model with Poisson jumps. First, this system is proved to have a unique global positive solution via the Lyapunov technique. Second, the existence and uniqueness of general random attractors for its stochastic homeomorphism flow is proved by the comparison theorem, and meanwhile, a criterion for the existence of singleton sets is obtained. Finally, numerical simulations are used to illustrate the predicted random attractors.
- Published
- 2022
82. Fuzzy-interval inequalities for generalized convex fuzzy-interval-valued functions via fuzzy Riemann integrals
- Author
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Hari M. Srivastava, Taghreed M. Jawa, Pshtiwan Othman Mohammed, Muhammad Bilal Khan, and Dumitru Baleanu
- Subjects
Discrete mathematics ,hermite-hadamard inequality ,jense's type inequality ,General Mathematics ,p-convex fuzzy-interval-valued function ,Regular polygon ,Fuzzy logic ,schur's type inequality ,Interval valued ,hermite-hadamard-fejér inequality ,Riemann hypothesis ,symbols.namesake ,symbols ,QA1-939 ,Interval (graph theory) ,fuzzy riemann integral ,Mathematics - Abstract
The objective of the authors is to introduce the new class of convex fuzzy-interval-valued functions (convex-FIVFs), which is known as $ p $-convex fuzzy-interval-valued functions ($ p $-convex-FIVFs). Some of the basic properties of the proposed fuzzy-interval-valued functions are also studied. With the help of $ p $-convex FIVFs, we have presented some Hermite-Hadamard type inequalities ($ H-H $ type inequalities), where the integrands are FIVFs. Moreover, we have also proved the Hermite-Hadamard-Fejér type inequality ($ H-H $ Fejér type inequality) for $ p $-convex-FIVFs. To prove the validity of main results, we have provided some useful examples. We have also established some discrete form of Jense's type inequality and Schur's type inequality for $ p $-convex-FIVFs. The outcomes of this paper are generalizations and refinements of different results which are proved in literature. These results and different approaches may open new direction for fuzzy optimization problems, modeling, and interval-valued functions.
- Published
- 2022
83. Overtaking optimality in a discrete-time advertising game
- Author
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Poom Kumam, Jewaidu Rilwan, and Idris Ahmed
- Subjects
advertising game ,nash equilibrium ,Sequential game ,Present value ,General Mathematics ,Advertising ,Competition (economics) ,symbols.namesake ,Discrete time and continuous time ,Nash equilibrium ,Overtaking ,Convergence (routing) ,Economics ,symbols ,QA1-939 ,Market share ,overtaking optimality ,Mathematics - Abstract
In this paper, advertising competition among $ m $ firms is studied in a discrete-time dynamic game framework. Firms maximize the present value of their profits which depends on their advertising strategy and their market share. The evolution of market shares is determined by the firms' advertising activities. By employing the concept of the discrete-time potential games of González-Sánchez and Hernández-Lerma (2013), we derived an explicit formula for the Nash equilibrium (NE) of the game and obtained conditions for which the NE is an overtaking optimal. Moreover, we analyze the asymptotic behavior of the overtaking NE where the convergence towards a unique steady state (turnpike) is established.
- Published
- 2022
84. The extended Weibull–Fréchet distribution: properties, inference, and applications in medicine and engineering
- Author
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Ekramy A. Hussein, Ahmed Z. Afify, and Hassan M. Aljohani
- Subjects
Distribution (number theory) ,engineering data ,General Mathematics ,Inference ,Failure rate ,Probability density function ,maximum product of spacing estimators ,cramér–von mises estimation ,Frequentist inference ,fréchet distribution ,Generalized extreme value distribution ,QA1-939 ,Fréchet distribution ,Applied mathematics ,simulations ,Mathematics ,Weibull distribution ,extreme value distribution - Abstract
In this paper, a flexible version of the Fréchet distribution called the extended Weibull–Fréchet (EWFr) distribution is proposed. Its failure rate has a decreasing shape, an increasing shape, and an upside-down bathtub shape. Its density function can be a symmetric shape, an asymmetric shape, a reversed-J shape and J shape. Some mathematical properties of the EWFr distribution are explored. The EWFr parameters are estimated using several frequentist estimation approaches. The performance of these methods is addressed using detailed simulations. Furthermore, the best approach for estimating the EWFr parameters is determined based on partial and overall ranks. Finally, the performance of the EWFr distribution is studied using two real-life datasets from the medicine and engineering sciences. The EWFr distribution provides a superior fit over other competing Fréchet distributions such as the exponentiated-Fréchet, beta-Fréchet, Lomax–Fréchet, and Kumaraswamy Marshall–Olkin Fréchet.
- Published
- 2022
85. Decay properties for evolution-parabolic coupled systems related to thermoelastic plate equations
- Author
-
Baiping Ouyang, Zihan Cai, and Yan Liu
- Subjects
Physics ,Thermoelastic damping ,thermoelastic plate equations ,General Mathematics ,decay properties ,fractional power operators ,QA1-939 ,regularity-loss ,Mechanics ,non-local operator ,wentzel-kramers-brillouin (wkb) analysis ,Mathematics - Abstract
In this paper, we consider the Cauchy problem for a family of evolution-parabolic coupled systems, which are related to the classical thermoelastic plate equations containing non-local operators. By using diagonalization procedure and WKB analysis, we derive representation of solutions in the phase space. Then, sharp decay properties in a framework of $ L^p-L^q $ are investigated via these representations. Particularly, some thresholds for the regularity-loss type decay properties are found.
- Published
- 2022
86. Some new Hardy-Hilbert-type inequalities with multiparameters
- Author
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Ruiyun Yang, Environment, Zhengzhou , China, and Limin Yang
- Subjects
Pure mathematics ,Mathematics::Functional Analysis ,Inequality ,General Mathematics ,media_common.quotation_subject ,Mathematics::Classical Analysis and ODEs ,Type (model theory) ,beta function ,hardy–hilbert-type inequality ,QA1-939 ,Mathematics ,media_common ,hölder's inequality - Abstract
The purpose of this paper is to build some new Hardy-Hilbert-type inequalities with multiparameters and their equivalent forms and variants, which generalize some existing results. Similarly, the corresponding Hardy-Hilbert-type integral inequalities are also given.
- Published
- 2022
87. Promote sign consistency in cure rate model with Weibull lifetime
- Author
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Jianping Zhu and Chenlu Zheng
- Subjects
Cure rate ,General Mathematics ,cure rate model ,survival analysis ,sign consistency ,regularization ,Consistency (statistics) ,Statistics ,QA1-939 ,weibull distribution ,Mathematics ,Sign (mathematics) ,Weibull distribution - Abstract
In survival analysis, the cure rate model is widely adopted when a proportion of subjects have long-term survivors. The cure rate model is composed of two parts: the first part is the incident part which describes the probability of cure (infinity survival), and the second part is the latency part which describes the conditional survival of the uncured subjects (finite survival). In the standard cure rate model, there are no constraints on the relations between the coefficients in the two model parts. However, in practical applications, the two model parts are quite related. It is desirable that there may be some relations between the two sets of the coefficients corresponding to the same covariates. Existing works have considered incorporating a joint distribution or structural effect, which is too restrictive. In this paper, we consider a more flexible model that allows the two sets of covariates can be in different distributions and magnitudes. In many practical cases, it is hard to interpret the results when the two sets of the coefficients of the same covariates have conflicting signs. Therefore, we proposed a sign consistency cure rate model with a sign-based penalty to improve interpretability. To accommodate high-dimensional data, we adopt a group lasso penalty for variable selection. Simulations and a real data analysis demonstrate that the proposed method has competitive performance compared with alternative methods.
- Published
- 2022
88. A class of hypersurfaces in $ \mathbb{E}^{n+1}_{s} $ satisfying $ \Delta \vec{H} = \lambda\vec{H} $
- Author
-
Jinchao Yu, Dan Yang, Xiaoying Zhu, and Jingjing Zhang
- Subjects
Physics ,Class (set theory) ,Mean curvature ,Conjecture ,principal curvatures ,General Mathematics ,linear weingarten hypersurfaces ,Diagonalizable matrix ,Space (mathematics) ,Lambda ,Combinatorics ,Hypersurface ,Principal curvature ,QA1-939 ,Mathematics::Differential Geometry ,proper mean curvature vector ,Nuclear Experiment ,Mathematics - Abstract
A nondegenerate hypersurface in a pseudo-Euclidean space $ \mathbb{E}^{n+1}_{s} $ is called to have proper mean curvature vector if its mean curvature $ \vec{H} $ satisfies $ \Delta \vec{H} = \lambda \vec{H} $ for a constant $ \lambda $. In 2013, Arvanitoyeorgos and Kaimakamis conjectured [1]: any hypersurface satisfying $ \Delta \vec{H} = \lambda \vec{H} $ in pseudo-Euclidean space $ \mathbb E_{s}^{n+1} $ has constant mean curvature. This paper will give further support evidences to this conjecture by proving that a linear Weingarten hypersurface $ M^{n}_{r} $ in $ \mathbb E^{n+1}_{s} $ satisfying $ \Delta \vec{H} = \lambda \vec{H} $ has constant mean curvature if $ M^{n}_{r} $ has diagonalizable shape operator with less than seven distinct principal curvatures.
- Published
- 2022
89. Numerical simulation of time partial fractional diffusion model by Laplace transform
- Author
-
Thabet Abdeljawad, Abdullah, Iyad Suwan, and Amjad Ali
- Subjects
matlab ,Computer simulation ,Laplace transform ,General Mathematics ,Mathematical analysis ,Fractional diffusion ,QA1-939 ,laplace transform ,partial fraction diffusion equations ,numerical approximation ,Mathematics - Abstract
In the present work, the authors developed the scheme for time Fractional Partial Diffusion Differential Equation (FPDDE). The considered class of FPDDE describes the flow of fluid from the higher density region to the region of lower density, macroscopically it is associated with the gradient of concentration. FPDDE is used in different branches of science for the modeling and better description of those processes that involve flow of substances. The authors introduced the novel concept of fractional derivatives in term of both time and space independent variables in the proposed FPDDE. We provided the approximate solution for the underlying generalized non-linear time PFDDE in the sense of Caputo differential operator via Laplace transform combined with Adomian decomposition method known as Laplace Adomian Decomposition Method (LADM). Furthermore, we established the general scheme for the considered model in the form of infinite series by aforementioned techniques. The consequent results obtained by the proposed technique ensure that LADM is an effective and accurate technique to handle nonlinear partial differential equations as compared to the other available numerical techniques. At the end of this paper, the obtained numerical solution is visualized graphically by Matlab to describe the dynamics of desired solution.
- Published
- 2022
90. Frenet curves in 3-dimensional δ-Lorentzian trans Sasakian manifolds
- Author
-
Muslum Aykut Akgun
- Subjects
Physics ,Pure mathematics ,Quantitative Biology::Biomolecules ,General Mathematics ,Frenet–Serret formulas ,frenet curves ,δ-lorentzian manifold ,almost contact metric manifold ,QA1-939 ,Mathematics::Mathematical Physics ,Mathematics::Differential Geometry ,lorentzian metric ,Mathematics::Symplectic Geometry ,frenet elements ,Mathematics - Abstract
In this paper, we give some characterizations of Frenet curves in 3-dimensional $ \delta $-Lorentzian trans-Sasakian manifolds. We compute the Frenet equations and Frenet elements of these curves. We also obtain the curvatures of non-geodesic Frenet curves on 3-dimensional $ \delta $-Lorentzian trans-Sasakian manifolds. Finally, we give some results for these curves.
- Published
- 2022
91. An efficient modified hybrid explicit group iterative method for the time-fractional diffusion equation in two space dimensions
- Author
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Nur Nadiah Abd Hamid, Fouad Mohammad Salama, Norhashidah Hj. Mohd. Ali, and Umair Ali
- Subjects
fractional diffusion equation ,Group (mathematics) ,Iterative method ,General Mathematics ,caputo fractional derivative ,Space (mathematics) ,Fractional diffusion ,QA1-939 ,Applied mathematics ,laplace transform ,stability and convergence ,grouping strategy ,finite difference scheme ,Mathematics - Abstract
In this paper, a new modified hybrid explicit group (MHEG) iterative method is presented for the efficient and accurate numerical solution of a time-fractional diffusion equation in two space dimensions. The time fractional derivative is defined in the Caputo sense. In the proposed method, a Laplace transformation is used in the temporal domain, and, for the spatial discretization, a new finite difference scheme based on grouping strategy is considered. The unique solvability, unconditional stability and convergence are thoroughly proved by the matrix analysis method. Comparison of numerical results with analytical and other approximate solutions indicates the viability and efficiency of the proposed algorithm.
- Published
- 2022
92. Discrete Temimi-Ansari method for solving a class of stochastic nonlinear differential equations
- Author
-
Mourad S. Semary, M. T. M. Elbarawy, and Aisha F. Fareed
- Subjects
stochastic nonlinear differential equations ,langevin's equation ,temimi-ansari method ,davis-skodje and brusselator systems ,General Mathematics ,ginzburg-landau equation ,QA1-939 ,Mathematics - Abstract
In this paper, a numerical method to solve a class of stochastic nonlinear differential equations is introduced. The proposed method is based on the Temimi-Ansari method. The special states of the four systems are studied to show that the proposed method is efficient and applicable. These systems are stochastic Langevin's equation, Ginzburg-Landau equation, Davis-Skodje, and Brusselator systems. The results clarify the accuracy and efficacy of the presented new method with no need for any restrictive assumptions for nonlinear terms.
- Published
- 2022
93. On stochastic accelerated gradient with non-strongly convexity
- Author
-
Xingxing Zha, Yongquan Zhang, Dongyin Wang, and Yiyuan Cheng
- Subjects
least-square regression ,General Mathematics ,Carry (arithmetic) ,logistic regression ,Supervised learning ,Regular polygon ,Lipschitz continuity ,Stochastic approximation ,accelerated stochastic approximation ,Convexity ,Stochastic programming ,convergence rate ,Rate of convergence ,QA1-939 ,Applied mathematics ,Mathematics - Abstract
In this paper, we consider stochastic approximation algorithms for least-square and logistic regression with no strong-convexity assumption on the convex loss functions. We develop two algorithms with varied step-size motivated by the accelerated gradient algorithm which is initiated for convex stochastic programming. We analyse the developed algorithms that achieve a rate of $ O(1/n^{2}) $ where $ n $ is the number of samples, which is tighter than the best convergence rate $ O(1/n) $ achieved so far on non-strongly-convex stochastic approximation with constant-step-size, for classic supervised learning problems. Our analysis is based on a non-asymptotic analysis of the empirical risk (in expectation) with less assumptions that existing analysis results. It does not require the finite-dimensionality assumption and the Lipschitz condition. We carry out controlled experiments on synthetic and some standard machine learning data sets. Empirical results justify our theoretical analysis and show a faster convergence rate than existing other methods.
- Published
- 2022
94. Two self-adaptive inertial projection algorithms for solving split variational inclusion problems
- Author
-
Zheng Zhou, Bing Tan, and Songxiao Li
- Subjects
inertial technique ,General Mathematics ,split variational inclusion problem ,QA1-939 ,projection algorithm ,self-adaptive stepsize ,Mathematics - Abstract
This paper is to analyze the approximation solution of a split variational inclusion problem in the framework of Hilbert spaces. For this purpose, inertial hybrid and shrinking projection algorithms are proposed under the effect of a self-adaptive stepsize which does not require information of the norms of the given operators. The strong convergence properties of the proposed algorithms are obtained under mild constraints. Finally, a numerical experiment is given to illustrate the performance of proposed methods and to compare our algorithms with an existing algorithm.
- Published
- 2022
95. On generalized fractional integral operator associated with generalized Bessel-Maitland function
- Author
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Shahid Mubeen, Saba Batool, Asad Ali, Kottakkaran Sooppy Nisar, Rana Safdar Ali, Muhammad Samraiz, Roshan Noor Mohamed, and Gauhar Rahman
- Subjects
General Mathematics ,Operator (physics) ,integral transform ,Mathematical analysis ,Mathematics::Classical Analysis and ODEs ,Function (mathematics) ,symbols.namesake ,extended bessel-maitland function ,riemann-liouville fractional integral operator ,symbols ,QA1-939 ,Bessel function ,Mathematics - Abstract
In this paper, we describe generalized fractional integral operator and its inverse with generalized Bessel-Maitland function (BMF-Ⅴ) as its kernel. We discuss its convergence, boundedness, its relation with other well known fractional operators (Saigo fractional integral operator, Riemann-Liouville fractional operator), and establish its integral transform. Moreover, we have given the relationship of BMF-Ⅴ with Mittag-Leffler functions.
- Published
- 2022
96. Weighted proportional mean inactivity time model
- Author
-
Mohamed Kayid and Adel Alrasheedi
- Subjects
mixture ,hazard rate order ,mean inactivity time order ,General Mathematics ,increasing concave order ,QA1-939 ,likelihood ratio order ,reversed hazard rate order ,Mathematics - Abstract
In this paper, a mean inactivity time frailty model is considered. Examples are given to calculate the mean inactivity time for several reputable survival models. The dependence structure between the population variable and the frailty variable is characterized. The classical weighted proportional mean inactivity time model is considered as a special case. We prove that several well-known stochastic orderings between two frailties are preserved for the response variables under the weighted proportional mean inactivity time model. We apply this model on a real data set and also perform a simulation study to examine the accuracy of the model.
- Published
- 2022
97. Liapounoff type inequality for pseudo-integral of interval-valued function
- Author
-
Tatjana Grbić, Slavica Medić, Nataša Duraković, Sandra Buhmiler, Slaviša Dumnić, and Janja Jerebic
- Subjects
liapounoff type inequality ,interval-valued central g-moment of order n ,General Mathematics ,interval-valued function ,QA1-939 ,pseudo-integral of an interval-valued function ,semiring ,Mathematics - Abstract
In this paper, two new Liapounoff type inequalities in terms of pseudo-analysis dealing with set-valued functions are given. The first one is given for a pseudo-integral of set-valued function where pseudo-operations are given by a generator $ g:[0, \infty]\to [0, \infty] $ and the second one is given for the semiring $ ([0, \infty], \sup, \odot) $ with generated pseudo-multiplication. The interval Liapounoff inequality is applied for estimation of interval-valued central $ g $-moment of order $ n $ for interval-valued functions in a $ g $-semiring.
- Published
- 2022
98. Estimation of finite population mean using dual auxiliary variable for non-response using simple random sampling
- Author
-
Sohaib Ahmad, Sardar Hussain, Muhammad Aamir, Faridoon Khan, Mohammed N Alshahrani, and Mohammed Alqawba
- Subjects
bias ,numerical comparisons ,non-response ,General Mathematics ,population mean ,QA1-939 ,auxiliary information ,mean square error ,Mathematics - Abstract
This paper addresses the issue of estimating the population mean for non-response using simple random sampling. A new family of estimators is proposed for estimating the population mean with auxiliary information on the sample mean and the rank of the auxiliary variable. Bias and mean square errors of existing and proposed estimators are obtained using the first order of measurement. Theoretical comparisons are made of the performance of the proposed and existing estimators. We show that the proposed family of estimators is more efficient than existing estimators in the literature under the given constraints using these theoretical comparisons.
- Published
- 2022
99. Multiplicity result to a system of over-determined Fredholm fractional integro-differential equations on time scales
- Author
-
Yongkun Li and Xing Hu
- Subjects
Differential equation ,critical points ,General Mathematics ,time scales ,Mathematical analysis ,variational methods ,QA1-939 ,multiplicity ,Multiplicity (mathematics) ,riemann-liouville derivatives ,fractional boundary value problem ,Mathematics - Abstract
In present paper, several conditions ensuring existence of three distinct solutions of a system of over-determined Fredholm fractional integro-differential equations on time scales are derived. Variational methods are utilized in the proofs.
- Published
- 2022
100. Ready-made short basis for GLV+GLS on high degree twisted curves
- Author
-
Yi Ouyang, Honggang Hu, Songsong Li, and Bei Wang
- Subjects
Pure mathematics ,Basis (linear algebra) ,General Mathematics ,Scalar (mathematics) ,Lattice (group) ,Twists of curves ,Scalar multiplication ,Quartic function ,twist ,QA1-939 ,glv+gls ,endomorphism ,ready-made short basis ,Lattice reduction ,Eigenvalues and eigenvectors ,Mathematics - Abstract
The crucial step in elliptic curve scalar multiplication based on scalar decompositions using efficient endomorphisms—such as GLV, GLS or GLV+GLS—is to produce a short basis of a lattice involving the eigenvalues of the endomorphisms, which usually is obtained by lattice basis reduction algorithms or even more specialized algorithms. Recently, lattice basis reduction is found to be unnecessary. Benjamin Smith (AMS 2015) was able to immediately write down a short basis of the lattice for the GLV, GLS, GLV+GLS of quadratic twists using elementary facts about quadratic rings. Certainly it is always more convenient to use a ready-made short basis than to compute a new one by some algorithm. In this paper, we extend Smith's method on GLV+GLS for quadratic twists to quartic and sextic twists, and give ready-made short bases for $ 4 $-dimensional decompositions on these high degree twisted curves. In particular, our method gives a unified short basis compared with Hu et al.'s method (DCC 2012) for $ 4 $-dimensional decompositions on sextic twisted curves.
- Published
- 2022
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