Pub Date : 2023-06-23DOI: 10.28924/2291-8639-21-2023-57
M. Hasanov
Let (X, Z) be a bivariate random vector. A predictor of X based on Z is just a Borel function g(Z). The problem of "least squares prediction" of X given the observation Z is to find the global minimum point of the functional E[(X − g(Z))2] with respect to all random variables g(Z), where g is a Borel function. It is well known that the solution of this problem is the conditional expectation E(X|Z). We also know that, if for a nonnegative smooth function F: R×R → R, arg ming(Z)E[F(X, g(Z))] = E[X|Z], for all X and Z, then F(x, y) is a Bregmann loss function. It is also of interest, for a fixed ϕ to find F (x, y), satisfying, arg ming(Z)E[F(X, g(Z))] = ϕ(E[X|Z]), for all X and Z. In more general setting, a stronger problem is to find F (x, y) satisfying arg miny∈RE[F (X, y)] = ϕ(E[X]), ∀X. We study this problem and develop a partial differential equation (PDE) approach to solution of these problems.
{"title":"A PDE Approach to the Problems of Optimality of Expectations","authors":"M. Hasanov","doi":"10.28924/2291-8639-21-2023-57","DOIUrl":"https://doi.org/10.28924/2291-8639-21-2023-57","url":null,"abstract":"Let (X, Z) be a bivariate random vector. A predictor of X based on Z is just a Borel function g(Z). The problem of \"least squares prediction\" of X given the observation Z is to find the global minimum point of the functional E[(X − g(Z))2] with respect to all random variables g(Z), where g is a Borel function. It is well known that the solution of this problem is the conditional expectation E(X|Z). We also know that, if for a nonnegative smooth function F: R×R → R, arg ming(Z)E[F(X, g(Z))] = E[X|Z], for all X and Z, then F(x, y) is a Bregmann loss function. It is also of interest, for a fixed ϕ to find F (x, y), satisfying, arg ming(Z)E[F(X, g(Z))] = ϕ(E[X|Z]), for all X and Z. In more general setting, a stronger problem is to find F (x, y) satisfying arg miny∈RE[F (X, y)] = ϕ(E[X]), ∀X. We study this problem and develop a partial differential equation (PDE) approach to solution of these problems.","PeriodicalId":45204,"journal":{"name":"International Journal of Analysis and Applications","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45112015","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}
Pub Date : 2023-06-23DOI: 10.28924/2291-8639-21-2023-59
Aiyared Iampan, A. Satirad, R. Chinram, R. Prasertpong, P. Julatha
The aim of this paper is to apply the concept of L-fuzzy sets (LFSs) to UP (BCC)-algebras and introduce five types of LFSs in UP (BCC)-algebras: L-fuzzy UP (BCC)-subalgebras, L-fuzzy near UP (BCC)-filters, L-fuzzy UP (BCC)-filters, L-fuzzy UP (BCC)-ideals, and L-fuzzy strong UP (BCC)-ideals. Also, we study the characteristic LFSs, t-level subsets, and the Cartesian product of LFSs in UP (BCC)-algebras.
本文将l -模糊集(lfs)的概念应用于UP (BCC)-代数，并引入UP (BCC)-代数中的五种lfs: L-fuzzy UP (BCC)-子代数、L-fuzzy近UP (BCC)-滤波器、L-fuzzy UP (BCC)-滤波器、L-fuzzy UP (BCC)-理想和L-fuzzy强UP (BCC)-理想。此外，我们还研究了UP (BCC)-代数中的特征lfs、t-level子集以及lfs的笛卡尔积。
{"title":"Lattice Valued Fuzzy Sets in UP (BCC)-Algebras","authors":"Aiyared Iampan, A. Satirad, R. Chinram, R. Prasertpong, P. Julatha","doi":"10.28924/2291-8639-21-2023-59","DOIUrl":"https://doi.org/10.28924/2291-8639-21-2023-59","url":null,"abstract":"The aim of this paper is to apply the concept of L-fuzzy sets (LFSs) to UP (BCC)-algebras and introduce five types of LFSs in UP (BCC)-algebras: L-fuzzy UP (BCC)-subalgebras, L-fuzzy near UP (BCC)-filters, L-fuzzy UP (BCC)-filters, L-fuzzy UP (BCC)-ideals, and L-fuzzy strong UP (BCC)-ideals. Also, we study the characteristic LFSs, t-level subsets, and the Cartesian product of LFSs in UP (BCC)-algebras.","PeriodicalId":45204,"journal":{"name":"International Journal of Analysis and Applications","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42761809","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}
Pub Date : 2023-06-23DOI: 10.28924/2291-8639-21-2023-58
Elçin Çelik, Deniz Uçar
Early analysis of infectious diseases is very important in the spread of the disease. The main aim of this study is to make important predictions and inferences for Covid 19, which is the current epidemic disease, with mathematical modeling and numerical solution methods. So we deal with the logistic growth model. We obtain carrying capacity and growth rate with Turkey epidemic data. The obtained growth rate and carrying capacity is used in the Taylor collocation method. With this method, we estimate and making predictions close to reality with Maple. We also show the estimates made with the help of graphics and tables.
{"title":"Analysis of the Logistic Growth Model With Taylor Matrix and Collocation Method","authors":"Elçin Çelik, Deniz Uçar","doi":"10.28924/2291-8639-21-2023-58","DOIUrl":"https://doi.org/10.28924/2291-8639-21-2023-58","url":null,"abstract":"Early analysis of infectious diseases is very important in the spread of the disease. The main aim of this study is to make important predictions and inferences for Covid 19, which is the current epidemic disease, with mathematical modeling and numerical solution methods. So we deal with the logistic growth model. We obtain carrying capacity and growth rate with Turkey epidemic data. The obtained growth rate and carrying capacity is used in the Taylor collocation method. With this method, we estimate and making predictions close to reality with Maple. We also show the estimates made with the help of graphics and tables.","PeriodicalId":45204,"journal":{"name":"International Journal of Analysis and Applications","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46952886","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}
Pub Date : 2023-06-16DOI: 10.28924/2291-8639-21-2023-56
Safa Gherian, Abdelaziz Azeb Ahmed, F. Yazid, F.S. Djeradi
We consider a mathematical model which describes a dynamic frictional contact problem for thermo-viscoelastic materials with long memory and damage. The contact is modeled by the normal compliance condition and wear between surfaces are taken into account. We establish a variational formulation for the model and prove the existence and uniqueness of the weak solution. The proof is based on arguments of hyperbolic nonlinear differential equations, parabolic variational inequalities and Banach fixed point.
{"title":"Frictional Contact Problem With Wear for Thermo-Viscoelastic Materials With Damage","authors":"Safa Gherian, Abdelaziz Azeb Ahmed, F. Yazid, F.S. Djeradi","doi":"10.28924/2291-8639-21-2023-56","DOIUrl":"https://doi.org/10.28924/2291-8639-21-2023-56","url":null,"abstract":"We consider a mathematical model which describes a dynamic frictional contact problem for thermo-viscoelastic materials with long memory and damage. The contact is modeled by the normal compliance condition and wear between surfaces are taken into account. We establish a variational formulation for the model and prove the existence and uniqueness of the weak solution. The proof is based on arguments of hyperbolic nonlinear differential equations, parabolic variational inequalities and Banach fixed point.","PeriodicalId":45204,"journal":{"name":"International Journal of Analysis and Applications","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49592957","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}
Pub Date : 2023-06-16DOI: 10.28924/2291-8639-21-2023-55
N. Mangapathi, B. Rao, K. Rao, M. I. Pasha
Using C-class functions, we demonstrate a few popular common coupled fixed point theorems on Ab-metric spaces and discuss some implications of the main findings. Additionally, we provide examples to illustrate the findings and their applications to both homotopy theory and integral equations.
{"title":"Existence of Solutions via C-Class Functions in Ab-Metric Spaces With Applications","authors":"N. Mangapathi, B. Rao, K. Rao, M. I. Pasha","doi":"10.28924/2291-8639-21-2023-55","DOIUrl":"https://doi.org/10.28924/2291-8639-21-2023-55","url":null,"abstract":"Using C-class functions, we demonstrate a few popular common coupled fixed point theorems on Ab-metric spaces and discuss some implications of the main findings. Additionally, we provide examples to illustrate the findings and their applications to both homotopy theory and integral equations.","PeriodicalId":45204,"journal":{"name":"International Journal of Analysis and Applications","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41701640","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}
Pub Date : 2023-06-16DOI: 10.28924/2291-8639-21-2023-53
Bayan Albishry, Sarah O. Alshehri, N. Zeyada
Doubt m-polar subalgebras (ideals) were introduced and some properties were investigated. Also, doubt m-polar positive implicative (commutative) ideals were defined and related results were proved.
{"title":"Doubt m-Polar Fuzzy Sets Based on BCK-Algebras","authors":"Bayan Albishry, Sarah O. Alshehri, N. Zeyada","doi":"10.28924/2291-8639-21-2023-53","DOIUrl":"https://doi.org/10.28924/2291-8639-21-2023-53","url":null,"abstract":"Doubt m-polar subalgebras (ideals) were introduced and some properties were investigated. Also, doubt m-polar positive implicative (commutative) ideals were defined and related results were proved.","PeriodicalId":45204,"journal":{"name":"International Journal of Analysis and Applications","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48625702","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}
Pub Date : 2023-06-16DOI: 10.28924/2291-8639-21-2023-54
N. Beghersa, M. Benabdallah, Mohamed Hariri
The aim of this research is to study the exponential stability of the stationary implicit system: Ax’(t) + Bx(t) = 0, where A and B are bounded operators in Hilbert spaces. The achieved results are the generalization of Liapounov Theorem for the spectrum of the operator pencil λA + B. We also establish the exponential stability conditions for the corresponding perturbed and quasi-linear implicit systems.
{"title":"On the Exponential Stability of the Implicit Differential Systems in Hilbert Spaces","authors":"N. Beghersa, M. Benabdallah, Mohamed Hariri","doi":"10.28924/2291-8639-21-2023-54","DOIUrl":"https://doi.org/10.28924/2291-8639-21-2023-54","url":null,"abstract":"The aim of this research is to study the exponential stability of the stationary implicit system: Ax’(t) + Bx(t) = 0, where A and B are bounded operators in Hilbert spaces. The achieved results are the generalization of Liapounov Theorem for the spectrum of the operator pencil λA + B. We also establish the exponential stability conditions for the corresponding perturbed and quasi-linear implicit systems.","PeriodicalId":45204,"journal":{"name":"International Journal of Analysis and Applications","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42060621","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}
Pub Date : 2023-06-08DOI: 10.28924/2291-8639-21-2023-52
Abdelkader Dibes, L. Bouzettouta, Manel Abdelli, S. Zitouni
In the present work, we consider a one-dimensional Von kármán beam with infinite memory, we establish the well-posedness of the system using semigroup theory and prove the exponential stability under some conditions on the kernel of the infinite memory term.
{"title":"Well-Posedness and Exponential Stability of the Von Kármán Beam With Infinite Memory","authors":"Abdelkader Dibes, L. Bouzettouta, Manel Abdelli, S. Zitouni","doi":"10.28924/2291-8639-21-2023-52","DOIUrl":"https://doi.org/10.28924/2291-8639-21-2023-52","url":null,"abstract":"In the present work, we consider a one-dimensional Von kármán beam with infinite memory, we establish the well-posedness of the system using semigroup theory and prove the exponential stability under some conditions on the kernel of the infinite memory term.","PeriodicalId":45204,"journal":{"name":"International Journal of Analysis and Applications","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49103652","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}
Pub Date : 2023-06-08DOI: 10.28924/2291-8639-21-2023-51
Hichem Elmossaoui, N. Oukid
In this paper, we propose a new approach for building computer experiment designs using the continuum random cluster point process, also referred to as the connected component Markov point process. Our method involves generating designs through the Markov Chain Monte Carlo method (MCMC) and the Random Walk Metropolis Hastings algorithm (RWMH algorithm), which can be easily scaled to meet various objectives. We have conducted a comprehensive study on the convergence of the Markov chain and compared our approach with existing computer experiment designs. Overall, our approach offers a novel and flexible solution for constructing computer experiment designs.
在本文中，我们提出了一种新的方法来构建计算机实验设计，使用连续随机聚类点过程，也称为连接分量马尔可夫点过程。我们的方法包括通过Markov Chain Monte Carlo方法（MCMC）和Random Walk Metropolis Hastings算法（RWMH算法）生成设计，这些算法可以很容易地进行缩放以满足各种目标。我们对马尔可夫链的收敛性进行了全面的研究，并将我们的方法与现有的计算机实验设计进行了比较。总之，我们的方法为构建计算机实验设计提供了一种新颖而灵活的解决方案。
{"title":"New Computer Experiment Designs Using Continuum Random Cluster Point Process","authors":"Hichem Elmossaoui, N. Oukid","doi":"10.28924/2291-8639-21-2023-51","DOIUrl":"https://doi.org/10.28924/2291-8639-21-2023-51","url":null,"abstract":"In this paper, we propose a new approach for building computer experiment designs using the continuum random cluster point process, also referred to as the connected component Markov point process. Our method involves generating designs through the Markov Chain Monte Carlo method (MCMC) and the Random Walk Metropolis Hastings algorithm (RWMH algorithm), which can be easily scaled to meet various objectives. We have conducted a comprehensive study on the convergence of the Markov chain and compared our approach with existing computer experiment designs. Overall, our approach offers a novel and flexible solution for constructing computer experiment designs.","PeriodicalId":45204,"journal":{"name":"International Journal of Analysis and Applications","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49288026","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}
Pub Date : 2023-06-02DOI: 10.28924/2291-8639-21-2023-49
Yassin Alzubaidi
The main aim of this paper is to present our approach of obtaining sufficient conditions for convergence of sequences of Henstock-Kurzweil integrable functions. Our approach involves the use of the concept of multiplier functions, where we define a class Φ of multipliers for the Henstock-Kurzweil integral. We consider a sequence (fn) of Henstock-Kurzweil integrable functions on a non-degenerate interval [a, b] and we assume that (fn) converges point wise to a function f. Then we show that f is Henstock-Kurzweil integrable and its integral is equal to the limit of the sequence (∫abfn) if there exists φ∈Φ such that the defined functionals of the type F (φ, fn) satisfy the imposed conditions. Beside the fact that the results regarding the convergence under the integral sign are always of great importance, the method introduced here can be imitated and used to obtain other results on the related areas.
{"title":"Sufficient Conditions for Convergence of Sequences of Henstock-Kurzweil Integrable Functions","authors":"Yassin Alzubaidi","doi":"10.28924/2291-8639-21-2023-49","DOIUrl":"https://doi.org/10.28924/2291-8639-21-2023-49","url":null,"abstract":"The main aim of this paper is to present our approach of obtaining sufficient conditions for convergence of sequences of Henstock-Kurzweil integrable functions. Our approach involves the use of the concept of multiplier functions, where we define a class Φ of multipliers for the Henstock-Kurzweil integral. We consider a sequence (fn) of Henstock-Kurzweil integrable functions on a non-degenerate interval [a, b] and we assume that (fn) converges point wise to a function f. Then we show that f is Henstock-Kurzweil integrable and its integral is equal to the limit of the sequence (∫abfn) if there exists φ∈Φ such that the defined functionals of the type F (φ, fn) satisfy the imposed conditions. Beside the fact that the results regarding the convergence under the integral sign are always of great importance, the method introduced here can be imitated and used to obtain other results on the related areas.","PeriodicalId":45204,"journal":{"name":"International Journal of Analysis and Applications","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42255223","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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