Fuzzy adjoint equations.

Self-adjoint differential-algebraic equations

Integrating factors, adjoint equations and Lagrangians

Integrating factors and adjoint equations are determined for linear and nonlinear differential equations of an arbitrary order. The new concept of an adjoint equation is used for construction of a Lagrangian for an arbitrary differential equation and for any system of differential equations where the number of equations is equal to the number of dependent variables. The method is illustrated by...

Adjoint Fuzzy Partition and Generalized Sampling Theorem

A new notion of adjoint fuzzy partition is introduced and the reconstruction of a function from its F-transform components is analyzed. An analogy with the Nyquist-Shannon-Kotelnikov sampling theorem is discussed.

Factorization of self-adjoint ordinary differential equations

Keyword: Factorization method Self-adjoint differential equations Eigenvalue problems This paper deals with the factorization of self-adjoint differential operators Lð2nÞ 1⁄4 1 q d n dx qb d n dx , and their spectral type differential equations. Sufficient conditions of factorization are reported. A large class of differential operators and equations that can be factorized is obtained. The fact...

Adjoint Equations and Random Walks for Illumination

In this paper we introduce the potential equation which along with the rendering equation forms an adjoint system of equations and provides the mathematical framework for all known approaches to illumination computation. The potential equation is more natural for illumination computations which simulate light propagation starting from the light sources, such as, progressive radiosity and partic...