The solvability and optimal controls for some fractional impulsive equation

This paper is concerned with the existence and uniqueness of mild solution of some fractional impulsive equations. Firstly, we introduce the fractional calculus, Gronwall inequality, and Leray-Schauder’s fixed point theorem. Secondly with the help of them, the sufficient condition for the existence and uniqueness of solutions is presented. Finally we give an example to illustrate our main results

Action Research on the Effects of an Innovative Use of CALL (Computer Assisted Language Learning) on the Listening and Speaking Abilities of Chinese University Intermediate Level English Students

This research aims to explore the effective use of modern technology and the encouragement of learner autonomy in support of English language teaching and learning at a university in Northeastern China in order to address a number of learning and teaching problems, in particular, the so-called “time-consuming, low efficiency” and “deaf and dumb English” problems. Action research was employed as a research methodology in this study. The action research project consisted of three cycles: the teaching time of each cycle was six weeks, with two teaching hours each week in each class. The 102 research participants were the second-year undergraduate non-English major students who had (or had nearly) reached an intermediate level in terms of English proficiency. Research methods included questionnaires, pre-testing and post-testing, interviews, classroom observation, learning diaries and research journal. All the data were analyzed using qualitative and quantitative techniques as appropriate. SPSS (Statistical Package for the Social Sciences) was used for statistical analysis. The research findings from the qualitative and quantitative data analysis show that the students made greater progress and improvements within a very short time (6 weeks) in each cycle in terms of listening and speaking skills by the effective use of modern technologies such as computers and the internet, which were used in ways designed to promote learner autonomy and effective learning strategies. More importantly, a more novel and more effective approach to teach listening from the intermediate level to the advanced level has been discovered from this project and a new teaching model using CALL (Computer Assisted Language Learning) environments in a Chinese context has come into being. On the whole, the students benefitted a great deal from autonomous learning by using modern technologies, dependent upon the quantitative data such as test score changes and qualitative data such as interview and learning diaries. In the meantime, the student learning experiences, my “teacher as researcher” teaching experience, and my professional development have been improved. This study is of great significance, particularly in the Chinese context, in contributing to the current literature on English teaching and learning research, CALL research and applications such as the novel listening teaching approach and the new teaching model using the CALL environments mentioned above. Finally, pedagogical implications are discussed and some suggestions on further research are also proposed

Some Antiperiodic Boundary Value Problem for Nonlinear Fractional Impulsive Differential Equations

This paper is concerned with the sufficient conditions for the existence of solutions for a class of generalized antiperiodic boundary value problem for nonlinear fractional impulsive differential equations involving the Riemann-Liouville fractional derivative. Firstly, we introduce the fractional calculus and give the generalized R-L fractional integral formula of R-L fractional derivative involving impulsive. Secondly, the sufficient condition for the existence and uniqueness of solutions is presented. Finally, we give some examples to illustrate our main results

Precision Higgs physics at the CEPC

The discovery of the Higgs boson with its mass around 125 GeV by the ATLAS and CMS Collaborations marked the beginning of a new era in high energy physics. The Higgs boson will be the subject of extensive studies of the ongoing LHC program. At the same time, lepton collider based Higgs factories have been proposed as a possible next step beyond the LHC, with its main goal to precisely measure the properties of the Higgs boson and probe potential new physics associated with the Higgs boson. The Circular Electron Positron Collider~(CEPC) is one of such proposed Higgs factories. The CEPC is an $e^+e^-$ circular collider proposed by and to be hosted in China. Located in a tunnel of approximately 100~km in circumference, it will operate at a center-of-mass energy of 240~GeV as the Higgs factory. In this paper, we present the first estimates on the precision of the Higgs boson property measurements achievable at the CEPC and discuss implications of these measurements.Comment: 46 pages, 37 figure

On the finite approximate controllability for Hilfer fractional evolution systems with nonlocal conditions

The aim of this study is to investigate the finite approximate controllability of certain Hilfer fractional evolution systems with nonlocal conditions. To achieve this, we first transform the mild solution of the Hilfer fractional evolution system into a fixed point problem for a condensing map. Then, by using the topological degree approach, we present sufficient conditions for the existence and uniqueness of the solution of the Hilfer fractional evolution systems. Using the variational approach, we obtain sufficient conditions for the finite approximate controllability of semilinear controlled systems. Finally, an example is provided to illustrate main results

The Solvability and Optimal Controls for Some Fractional Impulsive Equations of Order 1< α<2

We study the existence of solutions and optimal controls for some fractional impulsive equations of order 1< α<2. By means of Gronwall’s inequality and Leray-Schauder’s fixed point theorem, the sufficient condition for the existence of solutions and optimal controls is presented. Finally, an example is given to illustrate our main results

The convergence analysis of P-type iterative learning control with initial state error for some fractional system

Abstract In this paper, the convergence of iterative learning control with initial state error for some fractional equation is studied. According to the Laplace transform and the M-L function, the concept of mild solutions is showed. The sufficient conditions of convergence for the open and closed P-type iterative learning control are obtained. Some examples are given to illustrate our main results

The convergence of iterative learning control for some fractional system

Abstract In this paper, we study the convergence of iterative learning control for some fractional equation. Firstly, by using the Laplace transform and the M-L function, we show the concept of mild solutions. Secondly, by using the Gronwall inequality, we show the sufficient conditions of convergence for the open P-type and the close P-type iterative learning control. At last, we give some examples to illustrate our main results

Multimedia Technology and Learner Autonomy: An Experimental Study for Asymmetric Effects

One of the advantages of multimedia-assisted instruction is that it makes students more interested in sustainable learning and assists them to access information and learn more effectively. This research sought to explore the asymmetric effects of the development of sustainable multimedia-assisted instruction (MAI) on student reading practice in areas such as the implementation of learner autonomy and the improvement of reading ability, primarily based on multimedia technology-assisted instruction. This experiment was conducted in a junior high school in China. Eighty-six students from two parallel grade two classes were selected as research participants. Class One was set as the experimental class (EC) and Class Two was symmetrically designed as the control class (CC). The research results indicate that MAI encouraged students in the EC to adopt reading strategies more frequently and helped them to improve their level of learner autonomy, from a low level to an intermediate level, for the use of an asymmetrical technology, in comparison with the control class. Furthermore, the EC&rsquo;s reading ability was significantly enhanced. Additionally, there is a discussion of pedagogical implications and constructive suggestions considered to be beneficial for sustainable learning skills, teaching and for further research on the symmetrical application of technology in education. Finally, one of the most significant findings from this study is the effectiveness of combining modern sustainable technology and advanced educational concepts with symmetry in promoting learner autonomy within a sustainable learning model