This article deals with Wishart process which is defined as matrix generalization of a squared Bessel process. We consider a single risky asset pricing model whose volatility is described by Wishart affine diffusion processes. The multifactor volatility specification enables this model to be flexible enough to describe the market prices for short or long maturities. The aim of the study is to derive the log-asset returns dynamic under the double Wishart stochastic volatility model. The corrected Euler–Maruyama discretization technique is applied in order to obtain the numerical solution of the log-asset return dynamic under Bi-Wishart processes. The numerical examples show the effect of the model parameters on the asset returns under the double Wishart volatility model.
{"title":"The Log-Asset Dynamic with Euler-Maruyama Scheme under Wishart Processes","authors":"Raphael Naryongo, P. Ngare, A. Waititu","doi":"10.1155/2021/4050722","DOIUrl":"https://doi.org/10.1155/2021/4050722","url":null,"abstract":"This article deals with Wishart process which is defined as matrix generalization of a squared Bessel process. We consider a single risky asset pricing model whose volatility is described by Wishart affine diffusion processes. The multifactor volatility specification enables this model to be flexible enough to describe the market prices for short or long maturities. The aim of the study is to derive the log-asset returns dynamic under the double Wishart stochastic volatility model. The corrected Euler–Maruyama discretization technique is applied in order to obtain the numerical solution of the log-asset return dynamic under Bi-Wishart processes. The numerical examples show the effect of the model parameters on the asset returns under the double Wishart volatility model.","PeriodicalId":301406,"journal":{"name":"Int. J. Math. Math. Sci.","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130489192","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we consider the Darboux frame of a curve lying on an arbitrary regular surface and we use its unit osculator Darboux vector , unit rectifying Darboux vector , and unit normal Darboux vector to define some direction curves such as -direction curve,
Pub Date : 2021-11-05DOI: 10.21203/rs.3.rs-1017049/v1
Maryam Farzam, M. A. Kermani, T. Allahviranloo, A. Aminataei
Since real-world data is often inaccurate and working with fuzzy data and Z-numbers are very important and necessary, in the real world we need to rank and compare data. In this paper, we introduce a new method for ranking Z-numbers. This ranking algorithm is based on centroid point.We evaluate distance between centroid point, and based on this distance, we rank the Z-numbers.We use this method in two practical examples. First in ranking the return on assets of Tehran stock exchange, and second, in ranking of factors affecting the productivity of tourism security.The advantage of this method over conventional fuzzy methods is considering uncertainty, and allocating credit in the opinion of experts to estimate fuzzy parameters.
{"title":"Ranking the Return on Assets of Tehran Stock Exchange by a New Method Based on Z-Numbers Data","authors":"Maryam Farzam, M. A. Kermani, T. Allahviranloo, A. Aminataei","doi":"10.21203/rs.3.rs-1017049/v1","DOIUrl":"https://doi.org/10.21203/rs.3.rs-1017049/v1","url":null,"abstract":"\u0000 Since real-world data is often inaccurate and working with fuzzy data and Z-numbers are very important and necessary, in the real world we need to rank and compare data. In this paper, we introduce a new method for ranking Z-numbers. This ranking algorithm is based on centroid point.We evaluate distance between centroid point, and based on this distance, we rank the Z-numbers.We use this method in two practical examples. First in ranking the return on assets of Tehran stock exchange, and second, in ranking of factors affecting the productivity of tourism security.The advantage of this method over conventional fuzzy methods is considering uncertainty, and allocating credit in the opinion of experts to estimate fuzzy parameters.","PeriodicalId":301406,"journal":{"name":"Int. J. Math. Math. Sci.","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125963982","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
K. R. Cheneke, Koya Purnachandra Rao, G. K. Edessa
In this study, the mathematical model of the cholera epidemic is formulated and analyzed to show the impact of Vibrio cholerae in reserved freshwater. Moreover, the results obtained from applying the new fractional derivative method show that, as the order of the fractional derivative increases, cholera-preventing behaviors also increase. Also, the finding of our study shows that the dynamics of Vibrio cholerae can be controlled if continuous treatment is applied in reserved freshwater used for drinking purposes so that the intrinsic growth rate of Vibrio cholerae in water is less than the natural death of Vibrio cholerae. We have applied the stability theory of differential equations and proved that the disease-free equilibrium is asymptotically stable if R 0 < 1 , and the intrinsic growth rate of the Vibrio cholerae bacterium population is less than its natural death rate. The center manifold theory is applied to show the existence of forward bifurcation at the point R 0 = 1 and the local stability of endemic equilibrium if R 0 > 1 . Furthermore, the performed numerical simulation results show that, as the rank of control measures applied increases from no control, weak control, and strong control measures, the recovered individuals are 55.02, 67.47, and 674.7, respectively. Numerical simulations are plotted using MATLAB software package.
{"title":"Application of a New Generalized Fractional Derivative and Rank of Control Measures on Cholera Transmission Dynamics","authors":"K. R. Cheneke, Koya Purnachandra Rao, G. K. Edessa","doi":"10.1155/2021/2104051","DOIUrl":"https://doi.org/10.1155/2021/2104051","url":null,"abstract":"In this study, the mathematical model of the cholera epidemic is formulated and analyzed to show the impact of Vibrio cholerae in reserved freshwater. Moreover, the results obtained from applying the new fractional derivative method show that, as the order of the fractional derivative increases, cholera-preventing behaviors also increase. Also, the finding of our study shows that the dynamics of Vibrio cholerae can be controlled if continuous treatment is applied in reserved freshwater used for drinking purposes so that the intrinsic growth rate of Vibrio cholerae in water is less than the natural death of Vibrio cholerae. We have applied the stability theory of differential equations and proved that the disease-free equilibrium is asymptotically stable if \u0000 \u0000 \u0000 \u0000 R\u0000 \u0000 \u0000 0\u0000 \u0000 \u0000 <\u0000 1\u0000 \u0000 , and the intrinsic growth rate of the Vibrio cholerae bacterium population is less than its natural death rate. The center manifold theory is applied to show the existence of forward bifurcation at the point \u0000 \u0000 \u0000 \u0000 R\u0000 \u0000 \u0000 0\u0000 \u0000 \u0000 =\u0000 1\u0000 \u0000 and the local stability of endemic equilibrium if \u0000 \u0000 \u0000 \u0000 R\u0000 \u0000 \u0000 0\u0000 \u0000 \u0000 >\u0000 1\u0000 \u0000 . Furthermore, the performed numerical simulation results show that, as the rank of control measures applied increases from no control, weak control, and strong control measures, the recovered individuals are 55.02, 67.47, and 674.7, respectively. Numerical simulations are plotted using MATLAB software package.","PeriodicalId":301406,"journal":{"name":"Int. J. Math. Math. Sci.","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116031367","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
S. Shah, S. Hussain, Saima Noor, M. Darus, Ibrar Ahmad
In this present paper, we introduce and explore certain new classes of uniformly convex and starlike functions related to the Liu–Owa integral operator. We explore various properties and characteristics, such as coefficient estimates, rate of growth, distortion result, radii of close-to-convexity, starlikeness, convexity, and Hadamard product. It is important to mention that our results are a generalization of the number of existing results in the literature.
{"title":"Multivalent Functions Related with an Integral Operator","authors":"S. Shah, S. Hussain, Saima Noor, M. Darus, Ibrar Ahmad","doi":"10.1155/2021/5882343","DOIUrl":"https://doi.org/10.1155/2021/5882343","url":null,"abstract":"In this present paper, we introduce and explore certain new classes of uniformly convex and starlike functions related to the Liu–Owa integral operator. We explore various properties and characteristics, such as coefficient estimates, rate of growth, distortion result, radii of close-to-convexity, starlikeness, convexity, and Hadamard product. It is important to mention that our results are a generalization of the number of existing results in the literature.","PeriodicalId":301406,"journal":{"name":"Int. J. Math. Math. Sci.","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125017432","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we are interested in the inverse problem of the determination of the unknown part of the boundary of a uniformly Lipschitzian domain included in from the measurement of the normal derivative on suitable part of its boundary, where is the solution of the wave equation
在本文中，我们感兴趣的是确定未知部分∂Ω的逆问题，在一个均匀Lipschitzian域Ω中包含的边界Γ 0N从∂N v在合适部分的法向导数的测量中得到其边界为Γ 0，v是波动方程∂t t v的解X t - Δ v X，T + p x v x = 0在Ω × 0, T和给定的Dirichlet边界数据。我们使用形状优化工具来检索∂Ω的边界部分Γ。从必要条件出发，我们估计了一个拉格朗日乘子k Ω，它在定义域上通过求导得到。利用双曲型方程的极大原理理论，在几何假设条件下，证明了该反问题的唯一性结果。利普希茨稳定性是通过增加系统的能量来建立的。一些数值模拟说明了最优形状。
{"title":"Inverse Problem Related to Boundary Shape Identification for a Hyperbolic Differential Equation","authors":"F. Ndiaye, I. Ly","doi":"10.1155/2021/1716027","DOIUrl":"https://doi.org/10.1155/2021/1716027","url":null,"abstract":"<jats:p>In this paper, we are interested in the inverse problem of the determination of the unknown part <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\">\u0000 <mo>∂</mo>\u0000 <mi mathvariant=\"normal\">Ω</mi>\u0000 <mo>,</mo>\u0000 <msub>\u0000 <mi mathvariant=\"normal\">Γ</mi>\u0000 <mrow>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 </msub>\u0000 </math>\u0000 </jats:inline-formula> of the boundary of a uniformly Lipschitzian domain <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\">\u0000 <mi mathvariant=\"normal\">Ω</mi>\u0000 </math>\u0000 </jats:inline-formula> included in <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M3\">\u0000 <msup>\u0000 <mrow>\u0000 <mi>ℝ</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>N</mi>\u0000 </mrow>\u0000 </msup>\u0000 </math>\u0000 </jats:inline-formula> from the measurement of the normal derivative <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M4\">\u0000 <msub>\u0000 <mrow>\u0000 <mo>∂</mo>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </msub>\u0000 <mi>v</mi>\u0000 </math>\u0000 </jats:inline-formula> on suitable part <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M5\">\u0000 <msub>\u0000 <mi mathvariant=\"normal\">Γ</mi>\u0000 <mrow>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 </msub>\u0000 </math>\u0000 </jats:inline-formula> of its boundary, where <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M6\">\u0000 <mi>v</mi>\u0000 </math>\u0000 </jats:inline-formula> is the solution of the wave equation <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M7\">\u0000 <msub>\u0000 <mrow>\u0000 <mo>∂</mo>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>t</mi>\u0000 <mi>t</mi>\u0000 </mrow>\u0000 ","PeriodicalId":301406,"journal":{"name":"Int. J. Math. Math. Sci.","volume":"65 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122895434","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Peidong Liang, H. T. Likassa, Chentao Zhang, Jielong Guo
In this paper, we propose a novel robust algorithm for image recovery via affine transformations, the weighted nuclear, L ∗ , w , and the L 2,1 norms. The new method considers the spatial weight matrix to account the correlated samples in the data, the L 2,1 norm to tackle the dilemma of extreme values in the high-dimensional images, and the L ∗ , w norm newly added to alleviate the potential effects of outliers and heavy sparse noises, enabling the new approach to be more resilient to outliers and large variations in the high-dimensional images in signal processing. The determination of the parameters is involved, and the affine transformations are cast as a convex optimization problem. To mitigate the computational complexity, alternating iteratively reweighted direction method of multipliers (ADMM) method is utilized to derive a new set of recursive equations to update the optimization variables and the affine transformations iteratively in a round-robin manner. The new algorithm is superior to the state-of-the-art works in terms of accuracy on various public databases.
{"title":"New Robust PCA for Outliers and Heavy Sparse Noises' Detection via Affine Transformation, the L ∗ , w and L 2, 1 Norms, and Spatial Weight Matrix in High-Dimensional Images: From the Perspective of Signal Processing","authors":"Peidong Liang, H. T. Likassa, Chentao Zhang, Jielong Guo","doi":"10.1155/2021/3047712","DOIUrl":"https://doi.org/10.1155/2021/3047712","url":null,"abstract":"In this paper, we propose a novel robust algorithm for image recovery via affine transformations, the weighted nuclear, \u0000 \u0000 \u0000 \u0000 L\u0000 \u0000 \u0000 ∗\u0000 ,\u0000 w\u0000 \u0000 \u0000 \u0000 , and the \u0000 \u0000 \u0000 \u0000 L\u0000 \u0000 \u0000 2,1\u0000 \u0000 \u0000 \u0000 norms. The new method considers the spatial weight matrix to account the correlated samples in the data, the \u0000 \u0000 \u0000 \u0000 L\u0000 \u0000 \u0000 2,1\u0000 \u0000 \u0000 \u0000 norm to tackle the dilemma of extreme values in the high-dimensional images, and the \u0000 \u0000 \u0000 \u0000 L\u0000 \u0000 \u0000 ∗\u0000 ,\u0000 w\u0000 \u0000 \u0000 \u0000 norm newly added to alleviate the potential effects of outliers and heavy sparse noises, enabling the new approach to be more resilient to outliers and large variations in the high-dimensional images in signal processing. The determination of the parameters is involved, and the affine transformations are cast as a convex optimization problem. To mitigate the computational complexity, alternating iteratively reweighted direction method of multipliers (ADMM) method is utilized to derive a new set of recursive equations to update the optimization variables and the affine transformations iteratively in a round-robin manner. The new algorithm is superior to the state-of-the-art works in terms of accuracy on various public databases.","PeriodicalId":301406,"journal":{"name":"Int. J. Math. Math. Sci.","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126864893","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The study recognized the worth of understanding the how’s of handling censoring and censored data in survival analysis and the potential biases it might cause if researchers fail to identify and handle the concepts with utmost care. We systematically reviewed the concepts of censoring and how researchers have handled censored data and brought all the ideas under one umbrella. The review was done on articles written in the English language spanning from the late fifties to the present time. We googled through NCBI, PubMed, Google scholar and other websites and identified theories and publications on the research topic. Revelation was that censoring has the potential of biasing results and reducing the statistical power of analyses if not handled with the appropriate techniques it requires. We also found that, besides the four main approaches (complete-data analysis method; imputation approach; dichotomizing the data; the likelihood-based approach) to handling censored data, there were several other innovative approaches to handling censored data. These methods include censored network estimation; conditional mean imputation method; inverse probability of censoring weighting; maximum likelihood estimation; Buckley-Janes least squares algorithm; simple multiple imputation strategy; filter algorithm; Bayesian framework; β -substitution method; search-and-score-hill-climbing algorithm and constraint-based conditional independence algorithm; frequentist; Markov chain Monte Carlo for imputed data; quantile regression; random effects hierarchical Cox proportional hazards; Lin’s Concordance Correlation Coefficient; classical maximum likelihood estimate. We infer that the presence of incomplete information about subjects does not necessarily mean that such information must be discarded, rather they must be incorporated into the study for they might carry certain relevant information that holds the key to the understanding of the research. We anticipate that through this review, researchers will develop a deeper understanding of this concept in survival analysis and select the appropriate statistical procedures for such studies devoid of biases.
{"title":"Handling Censoring and Censored Data in Survival Analysis: A Standalone Systematic Literature Review","authors":"A. J. Turkson, Francis Ayiah-Mensah, Vivian Nimoh","doi":"10.1155/2021/9307475","DOIUrl":"https://doi.org/10.1155/2021/9307475","url":null,"abstract":"The study recognized the worth of understanding the how’s of handling censoring and censored data in survival analysis and the potential biases it might cause if researchers fail to identify and handle the concepts with utmost care. We systematically reviewed the concepts of censoring and how researchers have handled censored data and brought all the ideas under one umbrella. The review was done on articles written in the English language spanning from the late fifties to the present time. We googled through NCBI, PubMed, Google scholar and other websites and identified theories and publications on the research topic. Revelation was that censoring has the potential of biasing results and reducing the statistical power of analyses if not handled with the appropriate techniques it requires. We also found that, besides the four main approaches (complete-data analysis method; imputation approach; dichotomizing the data; the likelihood-based approach) to handling censored data, there were several other innovative approaches to handling censored data. These methods include censored network estimation; conditional mean imputation method; inverse probability of censoring weighting; maximum likelihood estimation; Buckley-Janes least squares algorithm; simple multiple imputation strategy; filter algorithm; Bayesian framework; \u0000 \u0000 β\u0000 \u0000 -substitution method; search-and-score-hill-climbing algorithm and constraint-based conditional independence algorithm; frequentist; Markov chain Monte Carlo for imputed data; quantile regression; random effects hierarchical Cox proportional hazards; Lin’s Concordance Correlation Coefficient; classical maximum likelihood estimate. We infer that the presence of incomplete information about subjects does not necessarily mean that such information must be discarded, rather they must be incorporated into the study for they might carry certain relevant information that holds the key to the understanding of the research. We anticipate that through this review, researchers will develop a deeper understanding of this concept in survival analysis and select the appropriate statistical procedures for such studies devoid of biases.","PeriodicalId":301406,"journal":{"name":"Int. J. Math. Math. Sci.","volume":"2021 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129427252","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we present and establish a new result on the stability analysis of solutions for fuzzy nonlinear fractional differential equations by extending Lyapunov’s direct method from the fuzzy ordinary case to the fuzzy fractional case. As an application, several examples are presented to illustrate the proposed stability result.
{"title":"A Note on the Stability Analysis of Fuzzy Nonlinear Fractional Differential Equations Involving the Caputo Fractional Derivative","authors":"Ali El Mfadel, S. Melliani, M. Elomari","doi":"10.1155/2021/7488524","DOIUrl":"https://doi.org/10.1155/2021/7488524","url":null,"abstract":"In this paper, we present and establish a new result on the stability analysis of solutions for fuzzy nonlinear fractional differential equations by extending Lyapunov’s direct method from the fuzzy ordinary case to the fuzzy fractional case. As an application, several examples are presented to illustrate the proposed stability result.","PeriodicalId":301406,"journal":{"name":"Int. J. Math. Math. Sci.","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134526706","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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