In this paper, we study the geometry of biharmonic curves in a strict Walker 3-manifold and we obtain explicit parametric equations for biharmonic curves and time-like biharmonic curves, respectively. We discuss the conditions for a speed curve to be a slant helix in a Walker manifold. We give an example of biharmonic curve for illustrating the main result.
{"title":"Biharmonic Curves in a Strict Walker 3-Manifold","authors":"Mamadou Gningue, A. Ndiaye, Rénovat Nkunzimana","doi":"10.1155/2022/3855033","DOIUrl":"https://doi.org/10.1155/2022/3855033","url":null,"abstract":"In this paper, we study the geometry of biharmonic curves in a strict Walker 3-manifold and we obtain explicit parametric equations for biharmonic curves and time-like biharmonic curves, respectively. We discuss the conditions for a speed curve to be a slant helix in a Walker manifold. We give an example of biharmonic curve for illustrating the main result.","PeriodicalId":301406,"journal":{"name":"Int. J. Math. Math. Sci.","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133702431","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 study the general Mandelbrot set of the family of polynomials , denoted by GM(). We construct the general Mandelbrot set for these polynomials by the escaping method. We determine the boundaries, areas, fractals, and symmetry of the previous polynomials. On the other hand, we study some topological properties of
在本文中，研究了多项式族np的一般Mandelbrot集Z = zn + Z + c;N≥2，用GM(pn)表示。我们用转义的方法构造了这些多项式的一般Mandelbrot集合。我们确定了前面多项式的边界、面积、分形和对称性。另一方面，研究了GM pn的一些拓扑性质。证明了GM P n是有界闭的;因此，它是紧凑的。此外，我们将一般曼德尔布罗集描述为吸引力盆地的结合。最后,我们比较了著名的Mandelbrot集合mz2 + c的性质和一般的曼德勃罗集。
{"title":"Generalized Mandelbrot Sets of a Family of Polynomials P n z = z n + z + c ; n ≥ 2","authors":"Salma M. Farris","doi":"10.1155/2022/4510088","DOIUrl":"https://doi.org/10.1155/2022/4510088","url":null,"abstract":"<jats:p>In this paper, we study the general Mandelbrot set of the family of polynomials <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\">\u0000 <mfenced open=\"{\" close=\"}\" separators=\"|\">\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>P</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </msub>\u0000 <mfenced open=\"(\" close=\")\" separators=\"|\">\u0000 <mrow>\u0000 <mi>z</mi>\u0000 </mrow>\u0000 </mfenced>\u0000 <mo>=</mo>\u0000 <msup>\u0000 <mrow>\u0000 <mi>z</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </msup>\u0000 <mo>+</mo>\u0000 <mi>z</mi>\u0000 <mo>+</mo>\u0000 <mi>c</mi>\u0000 <mo>;</mo>\u0000 <mfenced open=\"(\" close=\")\" separators=\"|\">\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>≥</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </mfenced>\u0000 </mrow>\u0000 </mfenced>\u0000 </math>\u0000 </jats:inline-formula>, denoted by GM(<jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M3\">\u0000 <msub>\u0000 <mrow>\u0000 <mi>P</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </msub>\u0000 </math>\u0000 </jats:inline-formula>). We construct the general Mandelbrot set for these polynomials by the escaping method. We determine the boundaries, areas, fractals, and symmetry of the previous polynomials. On the other hand, we study some topological properties of <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M4\">\u0000 <mtext>GM</mtext>\u0000 <mfenced open=\"(\" close=\")\" separators=\"|\">\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>P</mi>\u0000 ","PeriodicalId":301406,"journal":{"name":"Int. J. Math. Math. Sci.","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124466602","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 article, we implemented the Elzaki decomposition technique (EDM) to solve Volterra–Fredholm integro-differential equations of higher-order. Illustrations are used to test the technique’s accuracy and validity. Comparison among the acquired consequences by EDM and actual solutions have proven the power and accuracy of this technique. This technique is dependable and able to supply analytic remedies for solving such equations.
{"title":"On the Use of Elzaki Decomposition Method for Solving Higher-Order Integro-Differential Equations","authors":"Ekhlass S. Al-Rawi, Merna Samarchi","doi":"10.1155/2022/5638901","DOIUrl":"https://doi.org/10.1155/2022/5638901","url":null,"abstract":"In this article, we implemented the Elzaki decomposition technique (EDM) to solve Volterra–Fredholm integro-differential equations of higher-order. Illustrations are used to test the technique’s accuracy and validity. Comparison among the acquired consequences by EDM and actual solutions have proven the power and accuracy of this technique. This technique is dependable and able to supply analytic remedies for solving such equations.","PeriodicalId":301406,"journal":{"name":"Int. J. Math. Math. Sci.","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116995107","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}
Communication systems including AM and FM radio stations transmitting signals are capable of generating interference due to unwanted radio frequency signals. To avoid such interferences and maximize the number of channels for a predefined spectrum bandwidth, the radio-k-chromatic number problem is introduced. Let be a connected graph with diameter and radius . For any integer , , radio coloring of G is an assignment of color (positive integer) to the vertices of such that
为 k = d 和 k = ρ ,收音机 k − chromatic数字是美国termed收音机号码 ( r n G ) 无线电和径向当家 ( rr
{"title":"Radio and Radial Radio Numbers of Certain Sunflower Extended Graphs","authors":"Mohammed K. A. Kaabar, Kins Yenoke","doi":"10.1155/2022/9229409","DOIUrl":"https://doi.org/10.1155/2022/9229409","url":null,"abstract":"<jats:p>Communication systems including AM and FM radio stations transmitting signals are capable of generating interference due to unwanted radio frequency signals. To avoid such interferences and maximize the number of channels for a predefined spectrum bandwidth, the radio-k-chromatic number problem is introduced. Let <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\">\u0000 <mi>G</mi>\u0000 <mo>=</mo>\u0000 <mfenced open=\"(\" close=\")\" separators=\"|\">\u0000 <mrow>\u0000 <mi>V</mi>\u0000 <mo>,</mo>\u0000 <mi>E</mi>\u0000 </mrow>\u0000 </mfenced>\u0000 </math>\u0000 </jats:inline-formula> be a connected graph with diameter <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\">\u0000 <mi>d</mi>\u0000 </math>\u0000 </jats:inline-formula> and radius <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M3\">\u0000 <mi>ρ</mi>\u0000 </math>\u0000 </jats:inline-formula>. For any integer <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M4\">\u0000 <mi>k</mi>\u0000 </math>\u0000 </jats:inline-formula>, <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M5\">\u0000 <mn>1</mn>\u0000 <mo>≤</mo>\u0000 <mi>k</mi>\u0000 <mo>≤</mo>\u0000 <mi>d</mi>\u0000 </math>\u0000 </jats:inline-formula>, radio <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M6\">\u0000 <mi>k</mi>\u0000 <mo>−</mo>\u0000 </math>\u0000 </jats:inline-formula>coloring of G is an assignment <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M7\">\u0000 <mi>φ</mi>\u0000 </math>\u0000 </jats:inline-formula> of color (positive integer) to the vertices of <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M8\">\u0000 <mi>G</mi>\u0000 </math>\u0000 </jats:inline-formula> such that <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M9\">\u0000 <mi>d</mi>\u0000 <mfenced open=\"(\" close=\")\" separators=\"|\">\u0000 <mrow>\u0000 <mi>a</mi>\u0000 <mo>,</mo>\u0000 <mi>b</mi>\u0000 ","PeriodicalId":301406,"journal":{"name":"Int. J. Math. Math. Sci.","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131801009","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}
It is well established that people with diabetes are more likely to have serious complications from COVID-19. Nearly 1 in 5 COVID-19 deaths in the African region are linked to diabetes. World Health Organization (WHO) finds that 18.3% of COVID-19 deaths in Africa are among people with diabetes. In this paper, we have formulated and analysed a mathematical comorbidity model of diabetes-COVID-19 of the deterministic type. The basic properties of the model were explored. The basic reproductive number, equilibrium points, and stability of the equilibrium points were examined. Sensitivity analysis of the model was carried on to determine the impact of the model parameters on the basic reproductive number R 0 of the model. The model had a unique endemic equilibrium point, which was stable for R 0 > 1 . Time-dependent optimal controls were incorporated into the model with the sole aim of determining the best strategy for curtailing the spread of the disease. COVID-19 cases from March to September 2020 in Ghana were used to validate the model. Results of the numerical simulation suggest a greater number of individuals deceased when the infected individual had an underlying condition of diabetes. More so, the disease is endemic in Ghana with the basic reproduction number found to be R 0 = 1.4722 . The numerical simulation of the optimal control model reveals the lockdown control minimized the rate of decay of the susceptible individuals whereas the vaccination led to a number of susceptible individuals becoming immune to COVID-19 infections. In all, the two preventive control measures were both effective in curbing the spread of the disease as the number of COVID-19 infections was greatly reduced. We conclude that more attention should be paid to COVID-19 patients with an underlying condition of diabetes as the probability of death in this population was significantly higher.
{"title":"A Mathematical Model of Transmission Dynamics of SARS-CoV-2 (COVID-19) with an Underlying Condition of Diabetes","authors":"S. Okyere, J. Ackora-Prah","doi":"10.1155/2022/7984818","DOIUrl":"https://doi.org/10.1155/2022/7984818","url":null,"abstract":"It is well established that people with diabetes are more likely to have serious complications from COVID-19. Nearly 1 in 5 COVID-19 deaths in the African region are linked to diabetes. World Health Organization (WHO) finds that 18.3% of COVID-19 deaths in Africa are among people with diabetes. In this paper, we have formulated and analysed a mathematical comorbidity model of diabetes-COVID-19 of the deterministic type. The basic properties of the model were explored. The basic reproductive number, equilibrium points, and stability of the equilibrium points were examined. Sensitivity analysis of the model was carried on to determine the impact of the model parameters on the basic reproductive number \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 R\u0000 \u0000 \u0000 0\u0000 \u0000 \u0000 \u0000 \u0000 \u0000 of the model. The model had a unique endemic equilibrium point, which was stable for \u0000 \u0000 \u0000 \u0000 R\u0000 \u0000 \u0000 0\u0000 \u0000 \u0000 >\u0000 1\u0000 \u0000 . Time-dependent optimal controls were incorporated into the model with the sole aim of determining the best strategy for curtailing the spread of the disease. COVID-19 cases from March to September 2020 in Ghana were used to validate the model. Results of the numerical simulation suggest a greater number of individuals deceased when the infected individual had an underlying condition of diabetes. More so, the disease is endemic in Ghana with the basic reproduction number found to be \u0000 \u0000 \u0000 \u0000 R\u0000 \u0000 \u0000 0\u0000 \u0000 \u0000 =\u0000 1.4722\u0000 \u0000 . The numerical simulation of the optimal control model reveals the lockdown control minimized the rate of decay of the susceptible individuals whereas the vaccination led to a number of susceptible individuals becoming immune to COVID-19 infections. In all, the two preventive control measures were both effective in curbing the spread of the disease as the number of COVID-19 infections was greatly reduced. We conclude that more attention should be paid to COVID-19 patients with an underlying condition of diabetes as the probability of death in this population was significantly higher.","PeriodicalId":301406,"journal":{"name":"Int. J. Math. Math. Sci.","volume":"77 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115369871","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 purpose of this paper is to study the convergence analysis of an intermixed algorithm for finding the common element of the set of solutions of split monotone variational inclusion problem (SMIV) and the set of a finite family of variational inequality problems. Under the suitable assumption, a strong convergence theorem has been proved in the framework of a real Hilbert space. In addition, by using our result, we obtain some additional results involving split convex minimization problems (SCMPs) and split feasibility problems (SFPs). Also, we give some numerical examples for supporting our main theorem.
{"title":"An Iterative Method for Solving Split Monotone Variational Inclusion Problems and Finite Family of Variational Inequality Problems in Hilbert Spaces","authors":"Wanna Sriprad, Somnuk Srisawat","doi":"10.1155/2021/4273851","DOIUrl":"https://doi.org/10.1155/2021/4273851","url":null,"abstract":"The purpose of this paper is to study the convergence analysis of an intermixed algorithm for finding the common element of the set of solutions of split monotone variational inclusion problem (SMIV) and the set of a finite family of variational inequality problems. Under the suitable assumption, a strong convergence theorem has been proved in the framework of a real Hilbert space. In addition, by using our result, we obtain some additional results involving split convex minimization problems (SCMPs) and split feasibility problems (SFPs). Also, we give some numerical examples for supporting our main theorem.","PeriodicalId":301406,"journal":{"name":"Int. J. Math. Math. Sci.","volume":"133 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121293955","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}
We study determinants of the square-type Stirling matrix and the square-type Bell matrix . For this purpose, we prove that and have LU factorizations and
研究了方形斯特林矩阵S *和方形贝尔矩阵B *的行列式。为此目的，证明了S *和B *具有LU分解S * = l S uS和B * = L其中U的对角线元素S是k k−1，而U B的是k !(k≥1)。
{"title":"On the Determinants of the Square-Type Stirling Matrix and Bell Matrix","authors":"E. Choi, Jiin Jo","doi":"10.1155/2021/7959370","DOIUrl":"https://doi.org/10.1155/2021/7959370","url":null,"abstract":"<jats:p>We study determinants of the square-type Stirling matrix <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\">\u0000 <msup>\u0000 <mrow>\u0000 <mi>S</mi>\u0000 </mrow>\u0000 <mi>∗</mi>\u0000 </msup>\u0000 </math>\u0000 </jats:inline-formula> and the square-type Bell matrix <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\">\u0000 <msup>\u0000 <mrow>\u0000 <mi>B</mi>\u0000 </mrow>\u0000 <mi>∗</mi>\u0000 </msup>\u0000 </math>\u0000 </jats:inline-formula>. For this purpose, we prove that <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M3\">\u0000 <msup>\u0000 <mrow>\u0000 <mi>S</mi>\u0000 </mrow>\u0000 <mi>∗</mi>\u0000 </msup>\u0000 </math>\u0000 </jats:inline-formula> and <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M4\">\u0000 <msup>\u0000 <mrow>\u0000 <mi>B</mi>\u0000 </mrow>\u0000 <mi>∗</mi>\u0000 </msup>\u0000 </math>\u0000 </jats:inline-formula> have LU factorizations <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M5\">\u0000 <msup>\u0000 <mrow>\u0000 <mi>S</mi>\u0000 </mrow>\u0000 <mi>∗</mi>\u0000 </msup>\u0000 <mo>=</mo>\u0000 <msub>\u0000 <mrow>\u0000 <mi>L</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>S</mi>\u0000 </mrow>\u0000 </msub>\u0000 <msub>\u0000 <mrow>\u0000 <mi>U</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>S</mi>\u0000 </mrow>\u0000 </msub>\u0000 </math>\u0000 </jats:inline-formula> and <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M6\">\u0000 <msup>\u0000 <mrow>\u0000 <mi>B</mi>\u0000 </mrow>\u0000 <mi>∗</mi>\u0000 </msup>\u0000 ","PeriodicalId":301406,"journal":{"name":"Int. J. Math. Math. Sci.","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114363608","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}
Osteoporosis, a bone metabolic disease, is one of the major diseases occurring in aging population especially in postmenopausal women. A system of impulsive differential equations is developed in this paper in order to investigate the effects of parathyroid hormone and prolactin on bone-forming cells, namely, osteoblasts, and bone-resorbing cells, namely, osteoclasts, under the impulsive estrogen supplement. The theoretical analysis of the developed model is carried out so that we obtain the conditions on the system parameters in which the stability and permanence of the model can occur. Computer simulations are also provided to illustrate the theoretical predictions.
{"title":"Dynamical Modelling of Bone Formation and Resorption under Impulsive Estrogen Supplement: Effects of Parathyroid Hormone and Prolactin","authors":"Supassorn Aekthong, C. Rattanakul","doi":"10.1155/2021/5435876","DOIUrl":"https://doi.org/10.1155/2021/5435876","url":null,"abstract":"Osteoporosis, a bone metabolic disease, is one of the major diseases occurring in aging population especially in postmenopausal women. A system of impulsive differential equations is developed in this paper in order to investigate the effects of parathyroid hormone and prolactin on bone-forming cells, namely, osteoblasts, and bone-resorbing cells, namely, osteoclasts, under the impulsive estrogen supplement. The theoretical analysis of the developed model is carried out so that we obtain the conditions on the system parameters in which the stability and permanence of the model can occur. Computer simulations are also provided to illustrate the theoretical predictions.","PeriodicalId":301406,"journal":{"name":"Int. J. Math. Math. Sci.","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125399671","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 mechanical motion of a system consisting of simple springs is investigated from the viewpoint of two inertial observers with a relativistic relative velocity. It is shown that the final displacement of the springs is not measured the same by the observers. Indeed, it is demonstrated that there is an incompatibility between kinematics and dynamics in Einstein’s relativity regarding the force transformation.
{"title":"The Mechanical Behavior of a Multispring System Revealing Absurdity in the Relativistic Force Transformation","authors":"Mohammad Javanshiry","doi":"10.1155/2021/2706705","DOIUrl":"https://doi.org/10.1155/2021/2706705","url":null,"abstract":"The mechanical motion of a system consisting of simple springs is investigated from the viewpoint of two inertial observers with a relativistic relative velocity. It is shown that the final displacement of the springs is not measured the same by the observers. Indeed, it is demonstrated that there is an incompatibility between kinematics and dynamics in Einstein’s relativity regarding the force transformation.","PeriodicalId":301406,"journal":{"name":"Int. J. Math. Math. Sci.","volume":"126 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132206843","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 aim of this paper is to prove a common random fixed-point and some random fixed-point theorems for random weakly contractive operators in separable Banach spaces. A random Mann iterative process is introduced to approximate the fixed point. Finally, the main result is supported by an example and used to prove the existence and the uniqueness of a solution of a nonlinear stochastic integral equation system.
{"title":"Some Random Fixed-Point Theorems for Weakly Contractive Random Operators in a Separable Banach Space","authors":"Kenza Benkirane, A. Eladraoui, E. Marhrani","doi":"10.1155/2021/9484771","DOIUrl":"https://doi.org/10.1155/2021/9484771","url":null,"abstract":"The aim of this paper is to prove a common random fixed-point and some random fixed-point theorems for random weakly contractive operators in separable Banach spaces. A random Mann iterative process is introduced to approximate the fixed point. Finally, the main result is supported by an example and used to prove the existence and the uniqueness of a solution of a nonlinear stochastic integral equation system.","PeriodicalId":301406,"journal":{"name":"Int. J. Math. Math. Sci.","volume":"55 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127821179","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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