For a set S of real numbers, we introduce the concept of S-almost automorphic functions valued in a Banach space. It generalizes in particular the space of Z-almost automorphic functions. Considering the space of S-al...For a set S of real numbers, we introduce the concept of S-almost automorphic functions valued in a Banach space. It generalizes in particular the space of Z-almost automorphic functions. Considering the space of S-almost automorphic functions, we give sufficient conditions of the existence and uniqueness of almost automorphic solutions of a differential equation with a piecewise constant argument of generalized type. This is done using the Banach fixed point theorem.展开更多
In this paper, we investigate the existence, uniqueness and the asymptotic equiv- alence of a linear system and a perturbed system of differential equations with piecewise alternately advanced and retarded argument of...In this paper, we investigate the existence, uniqueness and the asymptotic equiv- alence of a linear system and a perturbed system of differential equations with piecewise alternately advanced and retarded argument of generalized type （DEPCAG）. This is based in the study of an equivalent integral equation with Cauchy and Green matrices type and in a solution of a DEPCAG integral inequality of Gronwall type. Several examples are also given to show the feasibility of results.展开更多
In this paper, the stability and bifurcation behaviors of a predator-prey model with the piecewise constant arguments and time delay are investigated. Technical approach is fully based on Jury criterion and bifurcatio...In this paper, the stability and bifurcation behaviors of a predator-prey model with the piecewise constant arguments and time delay are investigated. Technical approach is fully based on Jury criterion and bifurcation theory. The interesting point is that the model will produce two different branches by limiting branch parameters of different intervals. Besides, image simulation is also given.展开更多
Competence in academic writing in college is a challenging as well as an engaging task for many college students. Argumentative writing and acknowledging the counterargument is one of modes that is introduced in fresh...Competence in academic writing in college is a challenging as well as an engaging task for many college students. Argumentative writing and acknowledging the counterargument is one of modes that is introduced in freshman classes; however, college students approach writing with a certain mindset. Learning to write in different modes could be exciting when taught utilizing a film or a documentary. Using a documentary, such as Devil＇s Playground, writing professors not only initiate interest in culture learning and cultural understanding but also motivate students to use argumentation to foster critical thinking as well as cultural understanding.展开更多
Using geometric techniques, formulas for the number of squares that require k moves in order to be reached by a sole knight from its initial position on an infinite chessboard are derived. The number of squares reacha...Using geometric techniques, formulas for the number of squares that require k moves in order to be reached by a sole knight from its initial position on an infinite chessboard are derived. The number of squares reachable in exactly k moves are 1, 8, 32, 68, and 96 for k = 0, 1, 2, 3, and 4, respectively, and 28k – 20 for k ≥ 5. The cumulative number of squares reachable in k or fever moves are 1, 9, 41, and 109 for k = 0, 1, 2, and 3, respectively, and 14k2 – 6k + 5 for k ≥ 4. Although these formulas are known, the proofs that are presented are new and more mathematically accessible then preceding proofs.展开更多
文摘For a set S of real numbers, we introduce the concept of S-almost automorphic functions valued in a Banach space. It generalizes in particular the space of Z-almost automorphic functions. Considering the space of S-almost automorphic functions, we give sufficient conditions of the existence and uniqueness of almost automorphic solutions of a differential equation with a piecewise constant argument of generalized type. This is done using the Banach fixed point theorem.
文摘In this paper, we investigate the existence, uniqueness and the asymptotic equiv- alence of a linear system and a perturbed system of differential equations with piecewise alternately advanced and retarded argument of generalized type （DEPCAG）. This is based in the study of an equivalent integral equation with Cauchy and Green matrices type and in a solution of a DEPCAG integral inequality of Gronwall type. Several examples are also given to show the feasibility of results.
基金supported by Beijing Higher Education Young Elite Teacher(YETP0458)
文摘In this paper, the stability and bifurcation behaviors of a predator-prey model with the piecewise constant arguments and time delay are investigated. Technical approach is fully based on Jury criterion and bifurcation theory. The interesting point is that the model will produce two different branches by limiting branch parameters of different intervals. Besides, image simulation is also given.
文摘Competence in academic writing in college is a challenging as well as an engaging task for many college students. Argumentative writing and acknowledging the counterargument is one of modes that is introduced in freshman classes; however, college students approach writing with a certain mindset. Learning to write in different modes could be exciting when taught utilizing a film or a documentary. Using a documentary, such as Devil＇s Playground, writing professors not only initiate interest in culture learning and cultural understanding but also motivate students to use argumentation to foster critical thinking as well as cultural understanding.
文摘Using geometric techniques, formulas for the number of squares that require k moves in order to be reached by a sole knight from its initial position on an infinite chessboard are derived. The number of squares reachable in exactly k moves are 1, 8, 32, 68, and 96 for k = 0, 1, 2, 3, and 4, respectively, and 28k – 20 for k ≥ 5. The cumulative number of squares reachable in k or fever moves are 1, 9, 41, and 109 for k = 0, 1, 2, and 3, respectively, and 14k2 – 6k + 5 for k ≥ 4. Although these formulas are known, the proofs that are presented are new and more mathematically accessible then preceding proofs.
