Many problems in image analysis, digital processing and shape optimization can be expressed as variational problems involving the discretization of the Laplace-Beltrami operator. Such discretizations have have been widely studied for meshes or polyhedral surfaces. On digital surfaces, direct applications of classical operators are usually not satisfactory (lack of multigrid convergence, lack of...

Piezoelectric, magnetostrictive, and shape memory alloy actuators are gaining importance in high-frequency precision applications constrained by space. Their intrinsic hysteretic behavior makes control difficult. The Prandtl–Ishlinskii (PI) operator can model hysteresis well, albeit a major inadequacy: the inverse operator does not exist when the hysteretic curve gradient is not positive defini...

In this paper we present a method of evolving the contrast characteristics of a satellite image by employing a real-coded genetic algorithm with subjective fitness. The contrast properties of an image are given by its contrast-stretching curve, and the task of the Genetic Algorithm is to evolve this curve in order to find the best shape according to some subjective fitness. The subjective fitne...

We introduce a new concept of general $G$-$eta$-monotone operator generalizing the general $(H,eta)$-monotone operator cite{arvar2, arvar1}, general $H-$ monotone operator cite{xiahuang} in Banach spaces, and also generalizing $G$-$eta$-monotone operator cite{zhang}, $(A, eta)$-monotone operator cite{verma2}, $A$-monotone operator cite{verma0}, $(H, eta)$-monotone operator cite{fanghuang}...

This paper considers Schrödinger operators, and presents a probabilistic interpretation of the variation (or shape derivative) of the Dirichlet groundstate energy when the associated domain is perturbed. This interpretation relies on the distribution on the boundary of a stopped random process with Feynman-Kac weights. Practical computations require in addition the explicit approximation of the...

A tool is needed to track several mode shape estimates from iterative or repeated (variability) testing. Modal Assurance Criterion (MAC) is a well known modal vector comparison tool, however it can compare only two modal vectors at a time. A method to compare multiple samples of modal vector is presented The approach begins with mode shape correlation and correspondence. Pseudo orthogonality is...

Real-world data structures are often enhanced with additional pointers capturing alternative paths through a basic inductive skeleton (e.g., back pointers, head pointers). From the static analysis point of view, we must obtain several interlocking shape invariants. At the same time, it is well understood in abstract interpretation design that supporting a separation of concerns is critically im...