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GR23_HW02 - Vernacular and Climate sensitive Architecture
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ANTEPROYECTO APLICACIÓN MÓVIL
Análisis cicloestratigráfico cicloestratigráfico de registros de pozo usando una aproximación combinada de análisis espectral y de ondícula
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Ch. 8 Production by Firms (micro)
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Generalization in Deep Learning - Reading notes
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Web Design: GUI
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10/19/2017 math econ
Ch. 13.5-13.6 (Math Econ)
Max \(U = f(x, y, \phi)\)
\(f_x (x, y, \phi) = f_y(x, y, \phi) = 0\)
\(x^* = x^*(\phi)\) and \(y^* = y^*(\phi)\)
\(V(\phi) = f(x^*(\phi), y^*(\phi), \phi)\)
\(\frac{dV}{d \phi} = f_x \frac{\partial x^*}{\partial \phi} + f_y \frac{\partial y^*}{\partial \phi} + f_\phi\)
\(\frac{dV}{d \phi} = f_\phi\)
\(\pi = Pf(K, L) - wL - rK\)
\(\pi _L = Pf_L(K, L) - w = 0\)\(\pi _K = Pf_K(K, L) - r = 0\)
\(L^* = L^* (w, r, P)\)\(K^* = K^* (w, r, P)\)
\(\pi ^* (w, r, P) = Pf(K^*, L^*) - wL^* - rK^*\)
\(\frac{\partial \pi}{\partial w} = -L\)
\(\frac{\partial \pi^*}{\partial w} = (Pf_L - w) \frac{\partial L^*}{\partial w} + (Pf_K - r) \frac{\partial K^*}{\partial w} - L^*\)
\(\frac{\partial \pi^*}{\partial w} = - L^* (w, r, P)\)
Max \(U = f(x, y, \phi)\)
\(V(\phi) = f(x^*(\phi), y^*(\phi), \phi)\)
\(\Omega (x, y, \phi) = f(x, y, \phi) - V(\phi)\)
\(\Omega _x(x, y, \phi) = f_x = 0\)\(\Omega _y(x, y, \phi) = f_y = 0\)\(\Omega _\phi(x, y, \phi) = f_\phi - V_\phi = 0\)
\(V_{\phi \phi} = f_{\phi x} \frac{\partial x^*}{\partial \phi} + f_{\phi y} \frac{\partial y^*}{\partial \phi} + f_{\phi \phi}\)
\(V_{\phi \phi} - f_{\phi \phi} = f_{x \phi} \frac{\partial x^*}{\partial \phi} + f_{\phi y} \frac{\partial y^*}{\partial \phi} > 0\)
\(f_{x \phi} \frac{\partial x^*}{\partial \phi} > 0\)
\(\frac{\partial L^*}{\partial r} = \frac{\partial K^*}{\partial w}\)
Max \(U = f(x, y; \phi)\)subject to \(g(x, y; \phi) = 0\)
\(Z = f(x, y; \phi) + \lambda [0 - g(x, y; \phi)]\)
\(Z_x = f_x - \lambda g_x = 0\)\(Z_y = f_y - \lambda g_y = 0\)\(Z_\lambda = -g (x, y; \phi) = 0\)
\(x = x^*(\phi) \)\(y = y^*(\phi)\)\(\lambda = \lambda^*(\phi)\)
\(U^* = f(x^* (\phi), y^*(\phi), \phi) = V(\phi)\)
\(\frac{dV}{d \phi} = f_x \frac{\partial x^*}{\partial \phi} + f_y \frac{\partial y^*}{\partial \phi} + f_\phi\)
\(g(x^*(\phi), y^*(\phi), \phi) \equiv 0\)
\(g_x \frac{\partial x^*}{\partial \phi} + g_y \frac{\partial y^*}{\partial \phi} + g_\phi \equiv 0\)
\(\frac{dV}{d \phi} = (f_x - \lambda g_x) \frac{\partial x^*}{\partial \phi} + (f_y - \lambda g_y) \frac{\partial y^*}{\partial \phi} + f_\phi - \lambda g_\phi = Z_\phi\)
\(\frac{dV}{d \phi} = Z_\phi\)
Max \(U = f(x, y)\)subject to \(g(x, y) = c\)
\(Z = f(x, y) + \lambda [c - g(x, y)]\)
\(Z_x = f_x(x, y) - \lambda g_x (x, y) = 0\)\(Z_y = f_y(x, y) - \lambda g_y(x, y) = 0\)\(Z_\lambda = c - g(x,y) = 0\)
\(\lambda = \frac{f_x}{g_x} = \frac{f_y}{g_y}\)
\(x^* = x^*(c)\)\(y^* = y^*(c)\)\(\lambda^* = \lambda^*(c)\)
\(V(c) = Z^*(c) = f(x^*(c), y^*(c)) + \lambda ^*(c) [c - g(x_1^*(c), y^*(c))] \)
\(\frac{dZ^*}{dc} = [f_x - \lambda ^* g_x] \frac{\partial x^*}{\partial c} + [f_y - \lambda ^* g_y] \frac{\partial y^*}{\partial c} + [c - g(x^*, y^*)] \frac{\partial \lambda ^*}{\partial c} + \lambda ^*\)
\(\frac{dV}{dc} = \frac{dZ^*}{dc} = \lambda^*\)
Max \(U = U(x, y)\)subject to \(P_x x + P_y y = B\)
\(Z = U(x, y) + \lambda (B - P_x x - P_y y)\)
Micro Lecture Ch. 6
\(U = f( \pi)\)
\(Q = f(\bar {land}, \bar {labor})\)
Romer Question Ch. 4
\(\frac{dy_i(t)}{dt} = - \lambda [y_i(t) - y^*]\)
\(y_i(t) - y^* = e^{-\lambda t} [y_i(0) - y^*]\)
\(y_i(t) = e^{-\lambda t} y_i(0) + (1 - e^{- \lambda t}) y^* \)
\(y_i(t) = e^{-\lambda t} y_i(0) + (1 - e^{- \lambda t}) y^* + \mu _i (t)\)
\(y_i(t) - y_i(0) = \alpha + \beta y_i(0) + \epsilon _i\)\(\beta = \frac{cov[y_i(t) - y_i(0), y_i(0)]}{var[y_i(0)]}\)
\(cov [ (X - Y), Y] = cov [X, Y] - var [Y]\), we have:\(\beta = \frac{cov[y_i(t), y_i(0)]}{var[y_i(0)]} - 1\)
\(cov[y_i(t), y_i(0)] = cov[(1 - e^{-\lambda t}) y^* + e^{-\lambda t} y_i(0) + \mu _i (t), y_i(0)]\)
\(cov[y_i(t), y_i(0)] = e^{-\lambda t} var[y_i(0)]\)
\(\beta = \frac{e^{-\lambda t} var[y_i(0)]}{var[y_i(0)]} - 1\)
\(\lambda \equiv -\frac{\ln (1 + \beta)}{t}\)
\(var[y_i(t)] = e^{-2 \lambda t} var[y_i(0)] + var[\mu_i(t)]\)
\(y_i(t) = e^{-\lambda t} y_i(0) + (1 - e^{- \lambda t}) (a + bX_i)\)
\(\beta = \frac{cov[y_i(t), y_i(0)]}{var[y_i(0)]} - 1\)
\(y_i(t) = (1 - e^{-\lambda t}) y_i^* + e^{-\lambda t} y_i(0) + \epsilon _i\)
\(cov[y_i(t), y_i(0)] = (1 - e^{-\lambda t}) cov[ y_i^* , y_i(0)] + e^{-\lambda t} var[y_i(0)] \)
\(var[y_i(0)] = b^2 var[X_i] + var[\mu _i]\), and\(cov[y_i ^*, y_i(0)] = cov[a + bX_i, a + bX_i + \mu] = b^2 var[X_i]\)
\(cov[y_i ^*, y_i(0)] = b^2 var[X_i] + e^{- \lambda t} var[\mu_i]\)
\(\beta = \frac{b^2 var[X_i] + e^{- \lambda t} var[\mu_i]}{b^2 var[X_i] + var[\mu_i]} - 1\)\(e^{- \lambda t} = 1 + \frac{b^2 var[X_i] + var[\mu_i]}{var[\mu_i]} \beta\)\(\lambda = -\ln \frac{[1 + \frac{b^2 var[X_i] + var[\mu_i]}{var[\mu_i]} \beta]}{t}\)
\(y_i(t) - y_i(0)= (1 - e^{-\lambda t}) y_i^*- (1 - e^{-\lambda t}) y_i(0) + \epsilon _i\)
\(y_i(t) - y_i(0)= (1 - e^{-\lambda t}) y_i^*- (1 - e^{-\lambda t})(y_i^* - \mu_i) + \epsilon _i\)\(y_i(t) - y_i(0)= (e^{-\lambda t} - 1) \mu_i + \epsilon _i\)
\(y_i(t) - y_i(0)= \alpha + \beta y_i(0) + \gamma X_i + \epsilon _i\)
\(\mu _i = - a + y_i(0) - bX_i\)
\(- \frac{\gamma}{\beta} = -\frac{-Qb}{Q} = b\)
Dispositivo por medio de sensores para la medición de carga eléctrica y amperaje existente en una subestación móvil eléctrica en minera Sabinas en un periodo de Agosto-2017 a Enero-2018.
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Eclesiates 12:1
Romer Ch. 4
\(Y = K(t) ^\alpha [A(t)H(t)]^{1 - \alpha}\)
\(\dot K(t) = sY(t) - \delta K(t)\)\(\dot A(t) = gA(t)\)
\(H(t) = L(t) G(E)\)
\(\dot L(t) = nL(t)\)
\(G(E) = e^{\phi E} , \phi > 0\)
\(\dot k(t) = sk(t)^\alpha - (n + g + \delta)k(t)\)
\(k* = \frac{s}{(n + g + \delta)}^{\frac{1}{1 - \alpha}}\)
\(AG(E) = \frac{Y}{L} = AG(E) y\)
\(N(t) = \int_{\tau = 0} ^T B(t - \tau) d \tau\)\(= \int_{\tau = 0} ^T B(t) e^{- n \tau} d \tau\)\(= \frac{1 - e^{-n T}}{n} B(t)\)
\(L(t) = \int_{\tau = E} ^T B(t - \tau) d \tau\)\(= \int_{\tau = E} ^T B(t) e^{- n \tau} d \tau\)\(\frac{L(t)}{N(t)} = \frac{e^{-nE} - e^{-n T}}{n} B(t)\)
\(\frac{L(t)}{N(t)} = \frac{e^{-nE} - e^{-n T}}{1 - e^{-nT}}\)
\((\frac{Y}{N})^* = y^* A(t) G(E) \frac{e^{-nE} - e^{-n T}}{1 - e^{-nT}}\)
\(G(E)[\frac{(e^{-nE} - e^{-nT})}{(1 - e^{-nT})}]\)
\(Y_i = K_i ^\alpha (A_i H_i)^{1 - \alpha}\)
\(\ln \frac{Y_i}{L_i} = \alpha \ln \frac{K_i}{L_i} + ( 1 - \alpha) \ln \frac{H_i}{L_i} + (1 - \alpha) \ln A_i\)
\((1 - \alpha) \ln \frac{Y_i}{L_i} = (\alpha \ln \frac{K_i}{L_i} - \alpha \ln \frac{Y_i}{L_i}) + (1 - \alpha) \ln \frac{H_i}{L_i} + (1 - \alpha) \ln A_i\)\(\ln \frac{Y_i}{L_i} = \frac{\alpha}{1 - \alpha} \ln \frac{K_i}{Y_i} + \ln \frac{H_i}{L_i} + \ln A_i\)
\(\ln (\frac{Y_i}{L_i}) = a + bSI_i + e_i\)
\(\ln (\frac{Y_i}{L_i}) = a + b \hat {SI_i} + b(SI_i - \hat {SI_i}_i) + e_i\)\(\equiv a + b \hat {SI_i} + u_i\)
\(\frac{Y_i(t)}{L_i(t)} = A(t) f(k_i(t))\)
\(\dot k_i = \lambda [k_i * - k_i(t)]\)
\(\Delta k_{it + 1} = \lambda (k^* _{it} - k_{it})\)
\(k_i(T) - k_i(0) = (1 - e^{-\lambda T}) [k_i ^* (0) - k_i (0)] + \int _{\tau = 0} ^T (1 - e^{-\lambda (T - \tau)} \dot k_i ^* (\tau) d \tau\)
Project plan
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- Angle of attack, \(\alpha\)
IDT 617 Matel Trend: Identifying Game Play as an Instructional Tool
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