In this paper, we study new classes of operators on separable Banach spaces which are called extended-cyclic operators and extended-transitive operators. We study some properties of their vectors which are called extended-cyclic vectors. We show that if x is an extended-cyclic vector for T, then T^n x is also an extended-cyclic vector for T for all n∈N. Then, we show the extended-cyclicity is preserved under qsuasi-similarity. Moreover, we prove that an operator is extended-cyclic if and only if it is extended-transitive. As a consequence, the set of all extended-cyclic vectors is a dense and G_δ set. Finally, we find some spectral properties of these operators. Particularly, the point spectrum of the adjoint of an extended-cyclic operator has at most one element of modules greater than one. Moreover, if the spectrum of an operator has a connected component subset of B_0 (1), then T is not extended-cyclic.
{"title":"Extended-Cyclic Operators","authors":"N. Bamerni","doi":"10.31972/ticma22.01","DOIUrl":"https://doi.org/10.31972/ticma22.01","url":null,"abstract":"In this paper, we study new classes of operators on separable Banach spaces which are called extended-cyclic operators and extended-transitive operators. We study some properties of their vectors which are called extended-cyclic vectors. We show that if x is an extended-cyclic vector for T, then T^n x is also an extended-cyclic vector for T for all n∈N. Then, we show the extended-cyclicity is preserved under qsuasi-similarity. Moreover, we prove that an operator is extended-cyclic if and only if it is extended-transitive. As a consequence, the set of all extended-cyclic vectors is a dense and G_δ set. Finally, we find some spectral properties of these operators. Particularly, the point spectrum of the adjoint of an extended-cyclic operator has at most one element of modules greater than one. Moreover, if the spectrum of an operator has a connected component subset of B_0 (1), then T is not extended-cyclic.","PeriodicalId":269628,"journal":{"name":"Proceeding of 3rd International Conference of Mathematics and its Applications","volume":"61 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130247935","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}
Let R be a ring with 1 and D be unitary left Module over R. In this paper, we present purely semi small compressible Modules. Also, we give remarks and examples, many properties of such Modules are investigated.
{"title":"Purely semismall Compressible Modules","authors":"Mukdad Hussain, Zahraa. J. Kadhim, Shahad Mahmood","doi":"10.31972/ticma22.02","DOIUrl":"https://doi.org/10.31972/ticma22.02","url":null,"abstract":"Let R be a ring with 1 and D be unitary left Module over R. In this paper, we present purely semi small compressible Modules. Also, we give remarks and examples, many properties of such Modules are investigated.","PeriodicalId":269628,"journal":{"name":"Proceeding of 3rd International Conference of Mathematics and its Applications","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115615005","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 main goal of this thesis is to determine the most important effective factors for student admission and his/her interests in the specialization by using multivariate methods. Therefore, it focused on using factor analysis by identifying a number of the obtained factors and cluster analysis by classifying them into five clusters. Furthermore, the factor analysis and cluster analysis results will be compared to each other. Moreover, this study depends on the analysis of 350 questionnaire forms, distributed by random stratified sample method on students in the first stage of three different colleges, including Scientific colleges and Humanity colleges of Salahaddin University in Northern Iraq for the academic year 2018-2019. Thus, the IBM SPSS Statistics V: 25 software programs have been used in data analysis. Additionally, the results have demonstrated that Reliability is accepted, and also in factor analysis, the rate of the total variance interpretation is %62.157. Moreover, the most common variables between the factor analysis and cluster analysis can be considered the most important and influential variables for student admission and their interests in choosing a specialization. Consequently, the first factor and the first cluster have five significant variables in common; they are V1, V2, V3, V4 and V5 (the system is helpful for student admission to colleges to get their desired professions). The second factor and the second cluster have four influential variables in common they are V24, V32, V35 and V37 (the new system may help master's and PhD students to be admitted to colleges and get competitive results by utilizing their accounts). In the fourth factor and the fourth cluster, there is one variable in common, which is V18 (decreasing the number of students admitted in the parallel system by using the graduated students who must not be able to refill admission forms). Ultimately, the conclusion has shown a kind of approach and similarity between factor analysis and cluster analysis.
{"title":"Comparison Between Factor Analysis and Cluster Analysis to Determine the Most Important Affecting Factors for Students' Admission and Their Interests in The Specializations: A Sample of Salahaddin University-Erbil","authors":"Mohammed Abdullah, R. Ahmed, Y. Altun","doi":"10.31972/ticma22.03","DOIUrl":"https://doi.org/10.31972/ticma22.03","url":null,"abstract":"The main goal of this thesis is to determine the most important effective factors for student admission and his/her interests in the specialization by using multivariate methods. Therefore, it focused on using factor analysis by identifying a number of the obtained factors and cluster analysis by classifying them into five clusters. Furthermore, the factor analysis and cluster analysis results will be compared to each other. Moreover, this study depends on the analysis of 350 questionnaire forms, distributed by random stratified sample method on students in the first stage of three different colleges, including Scientific colleges and Humanity colleges of Salahaddin University in Northern Iraq for the academic year 2018-2019. Thus, the IBM SPSS Statistics V: 25 software programs have been used in data analysis. Additionally, the results have demonstrated that Reliability is accepted, and also in factor analysis, the rate of the total variance interpretation is %62.157. Moreover, the most common variables between the factor analysis and cluster analysis can be considered the most important and influential variables for student admission and their interests in choosing a specialization. Consequently, the first factor and the first cluster have five significant variables in common; they are V1, V2, V3, V4 and V5 (the system is helpful for student admission to colleges to get their desired professions). The second factor and the second cluster have four influential variables in common they are V24, V32, V35 and V37 (the new system may help master's and PhD students to be admitted to colleges and get competitive results by utilizing their accounts). In the fourth factor and the fourth cluster, there is one variable in common, which is V18 (decreasing the number of students admitted in the parallel system by using the graduated students who must not be able to refill admission forms). Ultimately, the conclusion has shown a kind of approach and similarity between factor analysis and cluster analysis.","PeriodicalId":269628,"journal":{"name":"Proceeding of 3rd International Conference of Mathematics and its Applications","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115457862","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}
This paper investigates the study of L-complex fuzzy sets. The L-complex fuzzy set, where L is a completely distributive lattice, is a generalization of the complex fuzzy set. The fundamental set theoretic operations on L-complex fuzzy sets are discussed properly, including L-complex fuzzy complement, union and intersection. New procedures are presented to combine the novel concepts of L-complex fuzzy t-norms and t-conorms and look into the conditions that lead to a comparable representation theorem. We have used the axiomatic method, in the sense that our underlying assumptions, especially about L, are abstract; it can thus be ascertained to what extent our results apply to some new problem. On the other hand, our method shows that if mathematics, as we use it, is consistent, so is fuzziness, as we formulate it.
{"title":"Combinations of L-Complex Fuzzy t-Norms and t-Conorms","authors":"Pishtiwan O. Sabir, A. Qadir","doi":"10.31972/ticma22.16","DOIUrl":"https://doi.org/10.31972/ticma22.16","url":null,"abstract":"This paper investigates the study of L-complex fuzzy sets. The L-complex fuzzy set, where L is a completely distributive lattice, is a generalization of the complex fuzzy set. The fundamental set theoretic operations on L-complex fuzzy sets are discussed properly, including L-complex fuzzy complement, union and intersection. New procedures are presented to combine the novel concepts of L-complex fuzzy t-norms and t-conorms and look into the conditions that lead to a comparable representation theorem. We have used the axiomatic method, in the sense that our underlying assumptions, especially about L, are abstract; it can thus be ascertained to what extent our results apply to some new problem. On the other hand, our method shows that if mathematics, as we use it, is consistent, so is fuzziness, as we formulate it.","PeriodicalId":269628,"journal":{"name":"Proceeding of 3rd International Conference of Mathematics and its Applications","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131371846","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, some new results are introduced for the bi-domination in graphs. Some properties of bi-domination number and bounds according to maximum, minimum degrees, order, and size have been determined. The effects of removing a vertex and removing or adding an edge are discussed on the bi-domination number of a graph. This study is important to know affected graphs by the deletion or addition of components.
{"title":"New Results in Bi- Domination in Graphs","authors":"M. Al-harere, Athraa T. Breesam","doi":"10.31972/ticma22.10","DOIUrl":"https://doi.org/10.31972/ticma22.10","url":null,"abstract":"In this paper, some new results are introduced for the bi-domination in graphs. Some properties of bi-domination number and bounds according to maximum, minimum degrees, order, and size have been determined. The effects of removing a vertex and removing or adding an edge are discussed on the bi-domination number of a graph. This study is important to know affected graphs by the deletion or addition of components.","PeriodicalId":269628,"journal":{"name":"Proceeding of 3rd International Conference of Mathematics and its Applications","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125182435","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}
This paper introduces the Lasso and Ridge Regression methods, which are two popular regularization approaches. The method they give a penalty to the coefficients differs in both of them. L1 Regularization refers to Lasso linear regression, while L2 Regularization refers to Ridge regression. As we all know, regression models serve two main purposes: explanation and prediction of scientific phenomena. Where prediction accuracy will be optimized by balancing each of the bias and variance of predictions, while explanation will be gained by constructing interpretable regression models by variable selection. The penalized regression method, also known as Lasso regression, adds bias to the model's estimates and reduces variance to enhance prediction. Ridge regression, on the other hand, introduces a minor amount of bias in the data to get long-term predictions. In the presence of multicollinearity, both regression methods have been offered as an alternative to the least square approach (LS). Because they deal with multicollinearity, they have the appropriate properties to reduce numerical instability caused by overfitting. As a result, prediction accuracy can be improved. For this study, the Corona virus disease (Covid-19) dataset was used, which has had a significant impact on global life. Particularly in our region (Kurdistan), where life has altered dramatically and many people have succumbed to this deadly sickness. Our data is utilized to analyze the benefits of each of the two regression methods. The results show that the Lasso approach produces more accurate and dependable or reliable results in the presence of multicollinearity than Ridge and LS methods when compared in terms of accuracy of predictions by using NCSS10, EViews 12 and SPSS 25.
{"title":"Improving Prediction Accuracy of Lasso and Ridge Regression as an Alternative to LS Regression to Identify Variable Selection Problems","authors":"P. Omer","doi":"10.31972/ticma22.05","DOIUrl":"https://doi.org/10.31972/ticma22.05","url":null,"abstract":"This paper introduces the Lasso and Ridge Regression methods, which are two popular regularization approaches. The method they give a penalty to the coefficients differs in both of them. L1 Regularization refers to Lasso linear regression, while L2 Regularization refers to Ridge regression. As we all know, regression models serve two main purposes: explanation and prediction of scientific phenomena. Where prediction accuracy will be optimized by balancing each of the bias and variance of predictions, while explanation will be gained by constructing interpretable regression models by variable selection. The penalized regression method, also known as Lasso regression, adds bias to the model's estimates and reduces variance to enhance prediction. Ridge regression, on the other hand, introduces a minor amount of bias in the data to get long-term predictions. In the presence of multicollinearity, both regression methods have been offered as an alternative to the least square approach (LS). Because they deal with multicollinearity, they have the appropriate properties to reduce numerical instability caused by overfitting. As a result, prediction accuracy can be improved. For this study, the Corona virus disease (Covid-19) dataset was used, which has had a significant impact on global life. Particularly in our region (Kurdistan), where life has altered dramatically and many people have succumbed to this deadly sickness. Our data is utilized to analyze the benefits of each of the two regression methods. The results show that the Lasso approach produces more accurate and dependable or reliable results in the presence of multicollinearity than Ridge and LS methods when compared in terms of accuracy of predictions by using NCSS10, EViews 12 and SPSS 25.","PeriodicalId":269628,"journal":{"name":"Proceeding of 3rd International Conference of Mathematics and its Applications","volume":"207 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122782002","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}
This paper is devoted to studying the stability of the unique equilibrium point and the occurrence of the Hopf bifurcation as well as limit cycles of a three-dimensional chaotic system. We characterize the parameters for which a Hopf equilibrium point takes place at the equilibrium point. In addition, the system has only one equilibrium point which is E_0=(0,0,0). It was proved that E_0 is asymptotically stable and unstable when α<(-13)/7 and α>(-13)/7, respectively. Moreover, for studying the cyclicity of the system, two techniques are used which are dynamics on the center manifold and Liapunov quantities. It was shown that at most two limit cycles can be bifurcated from the origin. All the results presented in this paper have been verified by a program via Maple software.
{"title":"Hopf Bifurcation Analysis Of A Chaotic System","authors":"Rizgar H. Salih, B. Mohammed","doi":"10.31972/ticma22.11","DOIUrl":"https://doi.org/10.31972/ticma22.11","url":null,"abstract":"This paper is devoted to studying the stability of the unique equilibrium point and the occurrence of the Hopf bifurcation as well as limit cycles of a three-dimensional chaotic system. We characterize the parameters for which a Hopf equilibrium point takes place at the equilibrium point. In addition, the system has only one equilibrium point which is E_0=(0,0,0). It was proved that E_0 is asymptotically stable and unstable when α<(-13)/7 and α>(-13)/7, respectively. Moreover, for studying the cyclicity of the system, two techniques are used which are dynamics on the center manifold and Liapunov quantities. It was shown that at most two limit cycles can be bifurcated from the origin. All the results presented in this paper have been verified by a program via Maple software.","PeriodicalId":269628,"journal":{"name":"Proceeding of 3rd International Conference of Mathematics and its Applications","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128719296","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 look at several (trigonometric) stochastic differential equations , we find the general form for such nonlinear stochastic differential equation by using the I'to formula. Then we find the exact solution for the different trigonometric stochastic differential equations by the use of stochastic integrals. Ilustrate the approach with various examples. (precise solution using the Ito integral formula) and approximate solution (numerical approximation (the Euler-Maruyama technique and the Milstein method) were compared to the exact solutions with the error of those approaches.
{"title":"Studying Some Stochastic Differential Equations with trigonometric terms with Application","authors":"Abdulghafoor Jasim, Ali Asmael","doi":"10.31972/ticma22.13","DOIUrl":"https://doi.org/10.31972/ticma22.13","url":null,"abstract":"In this paper we look at several (trigonometric) stochastic differential equations , we find the general form for such nonlinear stochastic differential equation by using the I'to formula. Then we find the exact solution for the different trigonometric stochastic differential equations by the use of stochastic integrals. Ilustrate the approach with various examples. (precise solution using the Ito integral formula) and approximate solution (numerical approximation (the Euler-Maruyama technique and the Milstein method) were compared to the exact solutions with the error of those approaches.","PeriodicalId":269628,"journal":{"name":"Proceeding of 3rd International Conference of Mathematics and its Applications","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128830957","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 algorithm is presented to solve dynamical equations for excitation of molecular models with multiple energy levels. It uses only discrete structures: discrete orthogonal polynomials constructed specially in Fourier space of the probability amplitudes, discrete Fourier transform and leads to exact solution of the differential equations and to discrete distribution of the quantum systems by energy levels.
{"title":"Coherent Dynamics of Quantum Systems with Non-Uniform Fourier Space Excited by Laser Radiation","authors":"S. Banjak, V. Savva","doi":"10.31972/ticma22.09","DOIUrl":"https://doi.org/10.31972/ticma22.09","url":null,"abstract":"The algorithm is presented to solve dynamical equations for excitation of molecular models with multiple energy levels. It uses only discrete structures: discrete orthogonal polynomials constructed specially in Fourier space of the probability amplitudes, discrete Fourier transform and leads to exact solution of the differential equations and to discrete distribution of the quantum systems by energy levels.","PeriodicalId":269628,"journal":{"name":"Proceeding of 3rd International Conference of Mathematics and its Applications","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128080474","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}
All the world now is depending on networks to share information between the users, where different data types are transferred wirelessly from network to network. Using wireless LANs are important to connect the users and share the data, these Wireless LANs have different types of obstacles that affect the data sharing or the wireless signal, such as, compatibility wireless protocol types, range coverage, walls penetration, moving devices, different routing protocols, data transferred types, weak signal, and many more. In this paper a practical analysis will be made to the latest IEEE 802.11ax wireless protocol to be compared with two types of Wi-Fi booster’s networks, Mesh and Extender Wi-Fi, while transferring 4k video size data rate, inside a room and on different rooms for wall penetration analysis, while measuring the throughput, delay, and signal strength metrics. The main importance of this paper is to give a more practical understanding and avoid the main problems of using the wireless protocol 802.11ax in different network types.
{"title":"Practical Analysis of IEEE 802.11ax Wireless Protocol in Wi-Fi Boosters Environments","authors":"Ghassan A. QasMarrogy","doi":"10.31972/ticma22.04","DOIUrl":"https://doi.org/10.31972/ticma22.04","url":null,"abstract":"All the world now is depending on networks to share information between the users, where different data types are transferred wirelessly from network to network. Using wireless LANs are important to connect the users and share the data, these Wireless LANs have different types of obstacles that affect the data sharing or the wireless signal, such as, compatibility wireless protocol types, range coverage, walls penetration, moving devices, different routing protocols, data transferred types, weak signal, and many more. In this paper a practical analysis will be made to the latest IEEE 802.11ax wireless protocol to be compared with two types of Wi-Fi booster’s networks, Mesh and Extender Wi-Fi, while transferring 4k video size data rate, inside a room and on different rooms for wall penetration analysis, while measuring the throughput, delay, and signal strength metrics. The main importance of this paper is to give a more practical understanding and avoid the main problems of using the wireless protocol 802.11ax in different network types.","PeriodicalId":269628,"journal":{"name":"Proceeding of 3rd International Conference of Mathematics and its Applications","volume":"62 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133704439","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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