In this paper we study a classical optimization problem in heat conduction, which may briefly be described as follows: given a surface ∂D in R, and a positive function φ defined on it (the temperature distribution), we want to surround ∂D with a prescribed volume of insulating material so as to minimize the loss of heat in a stationary situation. Mathematically speaking, we want to find a funct...

We study the complexity of proving the Pigeon Hole Principle (PHP) in a monotone variant of the Gentzen Calculus, also known as Geometric Logic. We show that the standard encoding of the PHP as a monotone sequent admits quasipolynomial-size proofs in this system. This result is a consequence of deriving the basic properties of certain quasipolynomial-size monotone formulas computing the boolean...

Passivity and dissipativity, in Jan Willems’s sense, are known to be powerful tools for stability analysis feedback control design. For instance, passive systems negative interconnection with slope-restricted, static, single-valued, smooth nonlinearities, as Lur’e systems, have been thoroughly studied automatic control, yielding the so-called absolute problem (with famous Popov circle criteria)...

We consider the forward-backward splitting method for nding a zero of the sum of two maximal monotone mappings. This method is known to converge when the inverse of the forward mapping is strongly monotone. We propose a modiication to this method, in the spirit of the extragradient method for monotone variational inequalities, under which the method converges assuming only the forward mapping i...

We consider a non-smooth system which models front motion in a noisy, excitable media. Standard methods from matched asymptotics permit the construction of a family of traveling front solutions. Similar constructions have been carried out in [5] and [2], where travelling wave solutions of non-smooth systems with piecewise linear but discontinuous nonlinearity with fixed jump are constructed for...

In this paper, a monotone positive solution is studied for buckling of a distributed model of multi walled carbon nanotube (MWCNT) cantilevers in the vicinity of thin and thick graphite sheets subject to intermolecular forces. In the modeling of intermolecular forces, Van der Waals forces are taken into account. A hybrid nano-scale continuum model based on Lennard–Jones potential is applied to ...

This paper is concerned with solving nonlinear monotone difference schemes of the parabolic type. The monotone Jacobi and monotone Gauss– Seidel methods are constructed. Convergence rates of the methods are compared and estimated. The proposed methods are applied to solving nonlinear singularly perturbed parabolic problems. Uniform convergence of the monotone methods is proved. Numerical experi...

We consider several questions about monotone AC-tree automata, a class of equational tree automata [21] whose transition rules correspond to rules in Kuroda normal form of context-sensitive grammars. Whereas it is known that this class has a decision procedure to determine if a given monotone AC-tree automaton accepts no term [23], other decidability and complexity results have not been well-in...