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1.
In this study, we explored how a sample of eight students used variational reasoning while discussing ordinary differential equations (DEs). Our analysis of variational reasoning draws on the literature with regard to student thinking about derivatives and rate, students’ covariational reasoning, and different multivariational structures that can exist between multiple variables. First, we found that while students can think of “derivative” as a variable in and of itself and also unpack derivative as a rate of change between two variables, the students were often able to think of “derivative” in these two ways simultaneously in the same explanation. Second, we found that students made significant usage of covariational reasoning to imagine relationships between pairs of variables in a DE, and that mental actions pertaining to recognizing dependence/independence were especially important. Third, the students also conceptualized relationships between multiple variables in a DE that matched different multivariational structures. Fourth, importantly, we identified a type of variational reasoning, which we call “feedback variation”, that may be unique to DEs because of the recursive relationship between a function’s value and its own rate of change.  相似文献   
2.
The present paper describes the applicability of the active flow control device, mini electromagnetic flap actuators attached on the leading edge of an airfoil, for the flow separation under both the steady and the unsteady flow conditions in the low Reynolds number region. At first, lift and drag have been measured for a wide variety of the wind speed Reynolds numbers and the angles of attack for the steady flow condition. Then, effects of some simple feedback flow controls, where the time-dependent signal of the lift-drag ratio have been used to detect the stall and served as a trigger to start the actuation, have been explored under the unsteady flow condition for evading the stall. In every low Reynolds number ranging from 30 000 to 80 000, the present actuators worked quite well to delay the stall, increasing in the lift and delaying the stall angle of attack. These aerodynamic modifications by the flap actuators obtained from the steady flow were found to be available even if the manipulation of the actuators started after the stall. Activation threshold of the lift-drag ratio as the input for the feedback control was determined from a stall classification map obtained under the steady flow experiment. Effectiveness of this feedback control was then demonstrated under the condition of the wind speed decrease (Reynolds number from 80 000 to 40 000) keeping the angle of attack constant at 11°, at which the stall occurs without the active control. Immediately after the sudden velocity decrease, the decrease in the lift-drag ratio were detected and the dynamic actuations were successfully started, resulting in evading the stall and keeping high and stable lift. An additional operation of the feedback, in which the running actuation is turned off when the lift-drag ratio shows lower than the second threshold value after operation, was revealed to be effective to keep the high lift force under the condition combined with the wind speed increase and decrease within the low Reynolds number range treated in this study.  相似文献   
3.
We study the approximation of a multiscale reaction–diffusion system posed on both macroscopic and microscopic space scales. The coupling between the scales is done through micro–macro flux conditions. Our target system has a typical structure for reaction–diffusion flow problems in media with distributed microstructures (also called, double porosity materials). Besides ensuring basic estimates for the convergence of two-scale semi-discrete Galerkin approximations, we provide a set of a priori feedback estimates and a local feedback error estimator that help in designing a distributed-high-errors strategy to allow for a computationally e?cient zooming in and out from microscopic structures. The error control on the feedback estimates relies on two-scale-energy, regularity, and interpolation estimates as well as on a fine bookeeping of the sources responsible with the propagation of the (multiscale) approximation errors. The working technique based on a priori feedback estimates is in principle applicable to a large class of systems of PDEs with dual structure admitting strong solutions.  相似文献   
4.
5.
A low-cost optical feedback system using dynamic mirrors has been developed at the NSLS for stabilizing the position and direction of an infrared synchrotron beam against thermal drift and mechanical noise. The system design has some unique features that potentially simplify installation into an existing infrared beamline. We describe the system and its features along with some performance results.  相似文献   
6.
We consider the minimization problem of an integral functional with integrand that is not convex in the control on solutions of a control system described by fractional differential equation with mixed nonconvex constraints on the control. A relaxation problem is treated along with the original problem. It is proved that, under general assumptions, the relaxation problem has an optimal solution, and that for each optimal solution there is a minimizing sequence of the original problem that converges to the optimal solution with respect to the trajectory, the control, and the functional in appropriate topologies simultaneously.  相似文献   
7.
Nonlinear filter generators are commonly used as keystream generators in stream ciphers. A nonlinear filter generator utilizes a nonlinear filtering function to combine the outputs of a linear feedback shift register (LFSR) to improve the linear complexity of keystream sequences. However, the LFSR-based stream ciphers are still potentially vulnerable to algebraic attacks that recover the key from some keystream bits. Although the known algebraic attacks only require polynomial time complexity of computations, all have their own constraints. This paper uses the linearization of nonlinear filter generators to cryptanalyze LFSR-based stream ciphers. Such a method works for any nonlinear filter generators. Viewing a nonlinear filter generator as a Boolean network that evolves as an automaton through Boolean functions, we first give its linearization representation. Compared to the linearization representation in Limniotis et al. (2008), this representation requires lower spatial complexity of computations in most cases. Based on the representation, the key recoverability is analyzed via the observability of Boolean networks. An algorithm for key recovery is given as well. Compared to the exhaustive search to recover the key, using this linearization representation requires lower time complexity of computations, though it leads to exponential time complexity.  相似文献   
8.
In this article the local stability of the Rabinovich–Fabrikant (R–F) chaotic system with fractional order time derivative is analyzed using fractional Routh–Hurwitz stability criterion. Feedback control method is used to control chaos in the considered fractional order system and after controlling the chaos the authors have introduced the synchronization between fractional order non-chaotic R–F system and the chaotic R–F system at various equilibrium points. The fractional derivative is described in the Caputo sense. Numerical simulation results which are carried out using Adams–Boshforth–Moulton method show that the method is effective and reliable for synchronizing the systems.  相似文献   
9.
《Optimization》2012,61(3-4):205-232
Various optimal control problems for linear parabolic systems with multiple constant time delays are considered. Necessary and sufficient conditions of optimality are derived for the Neumann problem. The optimal control is obtained in the feedback formMaking use of the results of Schwartz's, the representation of the optimal feedback control is given. A simple example of application is also provided  相似文献   
10.
We present an extension from two dimensions to three dimensions of a boundary control law, which stabilizes the parabolic profile of an infinite channel flow. The controller acts on the normal component of the velocity only. The stability is achieved without any a priori condition on the viscosity coefficient, that is on Reynolds number.  相似文献   
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