An n-ary operation Q : Σ → Σ is called an n-ary quasigroup of order |Σ| if in the equation x0 = Q(x1, . . . , xn) knowledge of any n elements of x0, . . . , xn uniquely specifies the remaining one. An n-ary quasigroup Q is (permutably) reducible if Q(x1, . . . , xn) = P ( R(xσ(1), . . . , xσ(k)), xσ(k+1), . . . , xσ(n) ) where P and R are (n−k+1)-ary and k-ary quasigroups, σ is a permutation, a...

The theory of the nonlocal linear boundary value problems is still on the level of examples. Any attempt to encompass them by a unified scheme sticks upon the lack of general methods. Here we are to outline an algebraic approach to linear nonlocal boundary value problems. It is based on the notion of convolution of linear operator and on operational calculus on it. Our operators are right inver...

Introduction The Token Economy Advantages of Token Economies Problems of Token Economies Management/Control Goals Disruptive Behavior Ward Care Behavior Self-care Behavior Therapeutic/Educative Goals Verbal Behaviors Social Behaviors Implementation of the Token Economy Staff Training Backup Reinforcers Social Reinforcement Economic Balance and Savings Intermittant Reinforcement Su~ary and Concl...

The present paper intends to describe some classification methods based on computational kernels developed in the field of generalized eigenvalue problems. It will be illustrated how some numerical difficulties can be overcome and how to obtain a simple iterative algorithm for binary and n-ary classification. Finally, some hints will be given on how eigenvalues techniques can be used in mathema...

Solutions are obtained for the boundary value problem, y(n) + f(x, y) = 0, y(i)(0) = y(1) = 0, 0 ≤ i ≤ n − 2, where f(x, y) is singular at y = 0. An application is made of a fixed point theorem for operators that are decreasing with respect to a cone. §

It is shown that the non-homogeneous Dirichlet and Neuman problems for the 2-order Seiberg-Witten equation admit a regular solution once the H-condition 3.1.1 is satisfied. The approach consist in applying the elliptic techniques to the variational setting of the Seiberg-Witten equation.

In this chapter we discuss discrete variable methods for solving BVPs for ordinary differential equations. These methods produce solutions that are defined on a set of discrete points. Methods of this type are initial-value techniques, i.e., shooting and superposition, and finite difference schemes. We will discuss initialvalue and finite difference methods for linear and nonlinear BVPs, and th...

In the first part of this chapter we focus on the question of well-posedness of boundary-value problems for linear partial differential equations of elliptic type. The second part is devoted to the construction and the error analysis of finite difference schemes for these problems. It will be assumed throughout that the coefficients in the equation, the boundary data and the resulting solution ...

We consider the problem of solving equations over k-ary trees. Here an equation is a pair of labeled-ary trees, where is a function associating an arity to each label. A solution to an equation is a morphism from-ary trees to k-ary trees that maps the left and right hand side of the equation to the same k-ary tree. This problem is a generalization of the word uniication problem posed by A. Mark...

Consider a tree network T , where each edge acts as an independent copy of a given channel M , and information is propagated from the root. For which T and M does the configuration obtained at level n of T typically contain significant information on the root variable? This problem arose independently in biology, information theory and statistical physics. • For all b, we construct a channel fo...