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...

In this paper, we study the existence of generalized solutions for the infinite dimensional nonlinear stochastic differential inclusions $dx(t) in F(t,x(t))dt +G(t,x(t))dW_t$ in which the multifunction $F$ is semimonotone and hemicontinuous and the operator-valued multifunction $G$ satisfies a Lipschitz condition. We define the It^{o} stochastic integral of operator set-valued stochastic pr...

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...

We show that if a Boolean function f : {0, 1}n → {0, 1} can be computed by a monotone real circuit of size s using k-ary monotone gates then f can be computed by a monotone real circuit of size O(snk−2) which uses unary or binary monotone gates only. This partially solves an open problem presented in [2]. In fact, in size O(snk−1), the circuit uses only unary monotone gates and binary addition....

This paper deals with discrete monotone iterative algorithms for solving a nonlinear singularly perturbed parabolic problem. A block monotone domain decomposition algorithm based on a Schwarz alternating method and on a block iterative scheme is constructed. This monotone algorithm solves only linear discrete systems at each time level and converges monotonically to the exact solution of the no...

We study monotonicity properties for minimizers of transport problems. In the one-dimensional case, we present an algorithm to construct minimizing monotone transport plans by “monotonizing” a given minimizing transport plan. This method applies in particular to the case of the L1-Wasserstein metric where we prove the existence of monotone minimizers for arbitrary marginals. We find that monoto...

We study the learnability of monotone term decision lists in the exact model of equivalence and membership queries. We show that, for any constant k 0, k-term monotone decision lists are exactly and properly learnable with n O(k) membership queries in O(n k 3) time. We also show n (k) membership queries are necessary for exact learning. In contrast, both k-term monotone decision lists (k 2) and...

The subject is the overview of the use of quasi-entropy in finite dimensional spaces. Operator monotone functions and relative modular operators are used. The origin is the relative entropy, and the f -divergence, monotone metrics, covariance and the χ2-divergence are the most important particular cases. The extension of monotone metrics to those with two parameters is a new concept. Monotone m...