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Clash Royale CLAN TAG #URR8PPP up vote 0 down vote favorite I am trying to replicate the analysis from the paper Brock, W. A., and S. R. Carpenter. 2006. Variance as a leading indicator of regime shift in ecosystem services. Ecology and Society 11(2): 9. [online] URL: http://www.ecologyandsociety.org/vol11/iss2/art9/ A system of stochastic differential equations is provided $$dP_i = [M_i + D(P_j - P_i)-cP_i - sf(P_i)]dt + sigma dW_i$$ $$f(P) equiv fracm^qm^q + P^q$$ $$dS_i = left(fracrkP_i-hS_iright)dt $$ where "$dW$ is a Wiener noise process that is N(0,dt) and independent for each i" Later, it is stated: "To study the dynamics of variance, we simulated time series of P and S using the Euler method adapted for the Ito solution of stochastic differential equations (Horsthemke and Lefever 1984). We do this by iteratively computing using Eq. 2 below. Each time step dt is of length 1/n. Over each small increment we compute" $$dP_i,t approxeq [M_i,t + D(P_j...

Clash Royale CLAN TAG #URR8PPP up vote 1 down vote favorite Let $f: X to Y$ be a homeomorphism between two topological spaces. Let $U subset X$ be a regular open connected set, i.e., $textint(barU) = U$. Let $V = f(U)$. Then $f|_U: U to V$ is a homeomorphism on the two subspaces. Is it true $V$ is also regular open? I know $f(barU) = barV$ and $f(partial U) = partial V$ if $f$ is homeomorphism. But how do we conclude $V = barV setminus partial V$? general-topology continuity share | cite | improve this question asked Aug 3 at 20:02 user9527 923 5 24 add a comment  |  up vote 1 down vote favorite Let $f: X to Y$ be a homeomorphism between two topological spaces. Let $U subset X$ be a regular open connected set, i.e., $textint(barU) = U$. Let $V = f(U)$. Then $f|_U: U to V$ is a homeomorphism on the two subspaces. Is it true $V$ is also regular open? I know $f(barU) = barV$ and $f(partial U) = partial V$ if ...

Clash Royale CLAN TAG #URR8PPP up vote 0 down vote favorite a1=18, r=4/3, 8th term 1.Find the indicated term of the geometric sequence algebraically. geometric-series share | cite | improve this question asked Aug 3 at 20:07 Lala 1 1 put on hold as off-topic by amWhy, Leucippus, Henrik, Isaac Browne, Xander Henderson Aug 3 at 22:22 This question appears to be off-topic. The users who voted to close gave this specific reason: " This question is missing context or other details : Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, Leucippus, Henrik, Isaac Browne, Xander Henderson If this question can be reworded to fit the rules in the help center, please edit the question. 1...