We derive the first closed-form optimal refinancing rule: Refinance when the current mortgage interest rate falls below the original rate by at least [Formula: see text] In this formula W(.) is the Lambert W-function, [Formula: see text]ρ is the real discount rate, λ is the expected real rate of exogenous mortgage repayment, σ is the standard deviation of the mortgage rate, κ/M is the ratio of ...

Numerical simulation, phase-space analysis, and analytic techniques are three methods used to solve quantitative differential equations . Most work in Qualitative Reasoning has dealt with analogs of the first two techniques, producing capabilities applicable to a wide range of systems . Although potentially of benefit, little has been done to provide closedform, analytic solution techniques for...

In this paper, we present a novel solution for implementing Head-Eye coordination which is an intelligent human behavior. We develop the principle of determining a third unknown view from two known views and apply it to solve Head-Eye coordination problem. The advantages of our solution are: (a) a closed-form solution is obtained and (b) "one-step" or "two-step" control algorithm can be impleme...

We address the problem of 3D reconstruction from image features tracked along a sequence. The most precise algorithms compute the Maximum Likelihood (ML) estimate and are iterative. They need an approximate 3D reconstruction as starting position. For that purpose, we propose a closed-form expression of paraperspective reconstruction. A matrix that approximately verifies the properties of a para...

In this paper, we study the solution of difference equation Ω m + 1 = − 7 q 6 / ∏</...

The optimization problem for a column, loaded by compression forces is studied in this article. direction of the applied coincides until buckling moment with axis column. critical values are equal among all competitive designs columns. dimensional analysis eases mathematical technique problem. introduces two dimensionless factors, one total material volume and stiffness With method analysis, so...