This paper introduces a technique for extracting structure and motion using directionally selective matches between linear features. A world-centered coordinate system is used to make these computations without the intermediate calculation of depth. In order to constrain the possible structure and motion conngurations, we assume that the three-dimensional direction of gravity relative to each i...

11.1 Prime fields of odd characteristic 201 Representations and reductions • Multiplication • Inversion and division • Exponentiation • Squares and square roots 11.2 Finite fields of characteristic 2 213 Representation • Multiplication • Squaring • Inversion and division • Exponentiation • Square roots and quadratic equations 11.3 Optimal extension fields 229 Introduction • Multiplication • Exp...

We derive Heisenberg equations for arbitrary high order moments of creation and annihilation operators in the case quantum master equation with a multimode generator which is quadratic obtain their solutions. Based on them we also similar equation, occur after averaging dynamics respect to classical Poisson process. This allows us show that finite-order fully defined by finite number linear dif...

We show in this paper that thirdand fourth-order low storage Runge-Kutta algorithms can be built specifically for quadratic nonlinear operators, at the expense of roughly doubling the time needed for evaluating the temporal derivatives. The resulting algorithms are especially well suited for computational fluid dynamics. Examples are given for the Hénon-Heiles Hamiltonian system and, in one and...

We consider control-constrained linear-quadratic optimal control problems on evolving hypersurfaces in R. In order to formulate well-posed problems, we prove existence and uniqueness of weak solutions for the state equation, in the sense of vector-valued distributions. We then carry out and prove convergence of the variational discretization of a distributed optimal control problem. In the proc...

A linear-like discrete-time fuzzy controller was designed to control and stabilize a single-pool irrigation canal. Saint Venant equations for open-channel flow were linearized using the Taylor series and a finite-difference approximation of the original nonlinear partial differential equations. Using the linear optimal control theory, a traditional linear quadratic regulator (LQR) was first dev...

A semilinear second-order parabolic equation is considered in a regular and a singularly perturbed regime. For this equation, we give computable a posteriori error estimates in the maximum norm. Semidiscrete and fully discrete versions of the backward Euler, Crank–Nicolson, and discontinuous Galerkin dG(r) methods are addressed. For their full discretizations, we employ elliptic reconstructions...

There is a question attributed to Irving Kaplansky concerning the solvability of the quadratic equation x2 − py2 = a in the case that the prime p = a2 + (2b)2. This question was answered in the affirmative by Mollin [1], although according to [3], this result is implicit in the work of Gauss and Legendre. The proof appearing in [1] was later simplified in [4], and it was also shown therein that...

In this paper, we introduce and study fuzzy variational-like inclusion, fuzzy resolvent equation and $H(cdot,cdot)$-$phi$-$eta$-accretive operator in real  uniformly smooth Banach spaces. It is established that fuzzy variational-like inclusion is equivalent to a fixed point problem as well as to a fuzzy resolvent equation. This equivalence is used to define an iterative algorithm for solving fu...

Orthogonal function approach (OFA) and the hybrid Taguchi-genetic algorithm (HTGA) are used to solve quadratic finite-horizon optimal controller design problems in both a fuzzy parallel distributed compensation (PDC) controller and a non-PDC controller (linear state feedback controller) for Takagi–Sugeno (TS) fuzzy-model-based control systems for dynamic ship positioning systems (TS-DSPS). Base...