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991.
Annie Burns-Childers Draga Vidakovic 《International Journal of Mathematical Education in Science & Technology》2018,49(5):660-679
The purpose of this study was to gain insight into 30, first year calculus students’ understanding of the relationship between the concept of vertex of a quadratic function and the concept of the derivative. APOS (action-process-object-schema) theory was applied as a guiding framework of analysis on student written work, think-aloud and follow up group interviews. Students’ personal meanings of the vertex, including misconceptions, were explored, along with students’ understanding to solve problems pertaining to the derivative of a quadratic function. Results give evidence of students’ weak schema of the vertex, lack of connection between different problem types and the importance of linguistics in relation to levels of APOS theory. A preliminary genetic decomposition was developed based on the results. Future research is suggested as a continuation to improve student understanding of the relationship between the vertex of quadratic functions and the derivative. 相似文献
992.
Kousuke Kuto Tatsuki Mori Tohru Tsujikawa Shoji Yotsutani 《Journal of Differential Equations》2018,264(9):5928-5949
We consider the Neumann problem of a 1D stationary Allen–Cahn equation with nonlocal term. Our previous paper [4] obtained a local branch of asymmetric solutions which bifurcates from a point on the branch of odd-symmetric solutions. This paper derives the global behavior of the branch of asymmetric solutions, and moreover, determines the set of all solutions to the nonlocal Allen–Cahn equation. Our proof is based on a level set analysis for an integral map associated with the nonlocal term. 相似文献
993.
994.
Krzysztof Kurdyka Olivier Le Gal 《Journal of Mathematical Analysis and Applications》2018,457(1):978-990
Let be a connected locally closed set which is definable in an o-minimal structure. We prove that the following three statements are equivalent: (i) X is a manifold, (ii) the tangent cone and the paratangent cone of X coincide at every point in X, (iii) for every , the tangent cone of X at the point x is a k-dimensional linear subspace of (k does not depend on x) varies continuously in x, and the density . 相似文献
995.
Thomas Lorenz 《Journal of Mathematical Analysis and Applications》2018,457(2):1502-1567
Applications in robust control problems and shape evolution motivate the mathematical interest in control problems whose states are compact (possibly non-convex) sets rather than vectors. This leads to evolutions in a basic set which can be supplied with a metric (like the well-established Pompeiu–Hausdorff distance), but it does not have an obvious linear structure. This article extends differential inclusions with state constraints to compact-valued states in a separable Hilbert space H. The focus is on sufficient conditions such that a given constraint set (of compact subsets) is viable a.k.a. weakly invariant. Our main result extends the tangential criterion in the well-known viability theorem (usually for differential inclusions in a vector space) to the metric space of non-empty compact subsets of H. 相似文献
996.
Chris Le Sueur 《Annals of Pure and Applied Logic》2018,169(1):83-115
In this paper we develop a technique for proving determinacy of classes of the form (a refinement of the difference hierarchy on lying between and ) from weak principles, establishing upper bounds for the determinacy-strength of the classes for all computable α and of . This bridges the gap between previously known hypotheses implying determinacy in this region. 相似文献
997.
《Mathematical Methods in the Applied Sciences》2018,41(9):3282-3293
This paper investigates the problem of exponential H∞ synchronization of discrete‐time chaotic neural networks with time delays and stochastic perturbations. First, by using the Lyapunov‐Krasovskii (Lyapunov) functional and output feedback controller, we establish the H∞ performance of exponential synchronization in the mean square of master‐slave systems, which is analyzed using a matrix inequality approach. Second, the parameters of a desired output feedback controller can be achieved by solving a linear matrix inequality. Finally, 2 simulated examples are presented to show the effectiveness of the theoretical results. 相似文献
998.
《Mathematical Methods in the Applied Sciences》2018,41(10):3684-3695
The paper formulates effective and nonimprovable stability conditions for a linear difference system involving 2 integer delays. The used technique combines algorithm of the discrete D‐decomposition method with some procedures of the polynomial theory. Contrary to the related existing results, the derived conditions are fully explicit with respect to both delays, which enables their simple applicability in various scientific and engineering areas. As an illustration, we show their importance in delayed feedback controls of discrete dynamical systems, with a particular emphasis put on stabilization of unstable steady states of the discrete logistic map. 相似文献
999.
《Mathematical Methods in the Applied Sciences》2018,41(14):5423-5458
We investigate lp boundedness, the topological structure of solutions set and the asymptotic periodicity of Volterra functional difference equations. The theoretical results are complemented with a set of applications. 相似文献
1000.
Yuto Ogata Tamaki Tanaka Yutaka Saito Gue Myung Lee Jae Hyoung Lee 《Optimization》2018,67(7):1067-1075
AbstractThis paper contains a generalized Gordan-type alternative theorem for set-valued maps which characterizes set relations without any convexity assumptions using certain evaluation functions. As a direct consequence and as a good example, we discuss robustness (or stability) of linear programming problems for modelling error. Moreover, this theorem can be utilized for that of general vector optimization problems in special cases due to reformation of the evaluation functions. 相似文献