matlab monotonicity

时间: 2023-11-02 15:02:42 浏览: 41
Monotonicity refers to the property of a mathematical function where the function either increases or decreases in value as the input variables increase. In MATLAB, you can check the monotonicity of a function using the "ismonotonic" function. This function returns a logical value that indicates whether a given array is monotonic or not. For example, consider the following code: ``` x = [1 2 3 4 5]; y = [1 3 5 7 9]; ismonotonic(x) % returns true ismonotonic(y) % returns true ``` In this example, the arrays x and y are both monotonic, as they both increase in value as the input variables increase. The "ismonotonic" function returns true for both cases. Note that the "ismonotonic" function also has optional input arguments that allow you to specify whether the array should be strictly monotonic (i.e., strictly increasing or decreasing) or not.

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帮我地道的翻译:The differential variational inequalities ((DVIs), for short) are useful for the study of models involving both dynamics and constraints in the form of in￾equalities. They arise in many applications: electrical circuits with ideal diodes, Coulomb friction problems for contacting bodies, economical dynamics, dynamic traffic networks. Pang and Stewart [26], [27] established the existence, unique￾ness, and Lipschitz dependence of solutions subject to boundary conditions for (DVIs) in finite dimensional spaces. Han and Pang investigated a class of dif￾ferential quasi-variational inequalities in [11], and Li, Huang and O’Regan [18] studied a class of differential mixed variational inequalities in finite dimensional Well-Posedness of Differential Mixed Quasi-Variational-Inequalities 137 spaces. Gwinner [8] obtained an equivalence result between (DVIs) and projected dynamical systems. In [9] he also proved a stability property for (DVIs) by using the monotonicity method of Browder and Minty, and Mosco set convergence. Chen and Wang [4] studied dynamic Nash equilibrium problems which have the formulation of differential mixed quasi-variational inequalities. Elastoplastic contact problems can also be incorporated into (DMQVIs) formulation because general dynamic processes in the nonsmooth unilateral contact problems are governed by quasi-variational inequalities. A numerical study for nonsmooth contact problems with Tresca friction can be found in [10], Liu, Loi and Obukhovskii [19] studied the existence and global bifurcation for periodic solutions of a class of (DVIs) by using the topological degree theory for multivalued maps and the method of guiding functions. For more details about (DVIs) we refer to [3], [30], [12], [22]–[21].

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