Linearizability is the commonly accepted notion of correctness for concurrent data structures. It requires that any execution of the data structure is justified by a linearization — a linear order on operations satisfying the data structure’s sequential specification. Proving linearizability is often challenging because an operation’s position in the linearization order may depend on future ope...

A sufficient condition for exact linearization of a nonlinear system via an exponential transformation is obtained as a Lagrange partial differential equation. When its solution can be found, the transformation is determined such that the nonlinear systemis exactly converted into a linear system with arbitrary dynamics. When the transformation is invertible, this technique can be applied to exa...

We discuss Fredholm properties of the linearization of partial differential equations on cylindrical domains about travelling and modulated waves. We show that the Fredholm index of each such linearization is given by a relative Morse index which depends only on the asymptotic coefficients. Several strategies are outlined that help to compute relative Morse indices using crossing numbers of spa...

The method of exact linearization nonlinear ordinary differential equations (ODE) of order n suggested by one of the authors is demonstrated in [1, 2]. This method is based on the factorization of nonlinear ODE through the first order nonlinear differential the operators, and is also based on using both point and nonpoint, local and nonlocal transformations. Exact linearization of autonomous th...

Linearizability is the commonly accepted notion of correctness for concurrent data structures. It requires that any execution of the data structure is justified by a linearization — a linear order on operations satisfying the data structure’s sequential specification. Proving linearizability is often challenging because an operation’s position in the linearization order may depend on future ope...

In the present work, we propose a novel polynomial approach to approximate the Input-State feedback linearization control. The aim of this new method is to simplify the implementation complexity of the exact InputState feedback linearization. Indeed, the present approach leads to an analytical control law via analytical nonlinear transformations without need to resolve a set of partial differen...

We study a class of fractional semilinear elliptic equations and formulate the corresponding Calder\'on problem. determine nonlinearity from exterior partial measurements Dirichlet-to-Neumann map by using first order linearization Runge approximation property.

Traditionally, the energy shaping for mechanical systems requires elimination of holonomic and nonholonomic constraints. In recent years, it was argued that such might be unnecessary, leading to a possible simplification matching conditions in shaping. On other hand, partial feedback linearization (PFL) approach has been widely applied unconstrained systems, but there is no general result const...

This paper presents a new solution technique for the tra c assignment problem. The approach is based on an iteratively improved nonlinear and separable approximation of the originally nonseparable objective function, and resembles the Frank-Wolfe algorithm in the sense that the subproblem separates with respect to commodities. Since the singlecommodity subproblems are strictly convex, the new a...

A an uncertainty model is presented that is useful to the robust control design. Under-actuated state affine systems are considered. A partially linear model is gotten taking into account the second and third order partial derivatives of the Taylor series expansion around a constant equilibrium point. This model includes the linear model and constant matrices multiplied by the quadratic and cub...