When does the absolute continuity imply Lipschitz? How to prove whether or not a multivariable function is continuous or differentiable at a point? Suppose f and g are differentiable on (a, b). Prove that T (x) = F (x) - g (x) is differentiable on (a, b). ...
With q∗ being strictly increasing (and continuous) in internal funds, there exists a unique level A=AFB at which q∗=qFB. This tension between over- and underproduction is the main force behind the hump-shaped effect of internal funds on welfare, as illustrated in the right panel of ...
We consider the so-called Boussinesq contact problem for an isotropic elastic half-space (see Figure 1), which is indented by a frictionless cylindrical punch of radius a with a non-flat base described by a continuous shape function, Φ(𝑟,𝜑)Φ(r,φ). For the sake of simplicity we ...
Let us introduce the continuous, differentiable but non-analytic function f (t) = exp(−1/t) 0 0≤t t≤0 (15) that permits us to define for tR ∈ R the function gtR (t) = f (1/2 + t/tR) f (1/2 + t/tR) + f (1/2 − t/tR) (16) This function represents a ...
This model’s function is continuous, but its slope has a discontinuity at the kink or turning point. The structure of the model takes the following form: 𝑌𝑡=𝛽0+𝛽−1(𝑋𝑡−𝛾)−+𝛽+1(𝑋𝑡−𝛾)++𝑒𝑡Yt=β0+β1−(Xt−γ)−+β1+(Xt−γ)++et...
This model’s function is continuous, but its slope has a discontinuity at the kink or turning point. The structure of the model takes the following form: 𝑌𝑡=𝛽0+𝛽−1(𝑋𝑡−𝛾)−+𝛽+1(𝑋𝑡−𝛾)++𝑒𝑡Yt=β0+β1−(Xt−γ)−+β1+(Xt−γ)++et...