The maximal correlation problem (MCP) aiming at optimizing correlation between sets of variables plays a very important role in many areas of statistical applications. Currently, algorithms for the general MCP stop at solutions of the multivariate eigenvalue problem (MEP) for a related matrix A. The MEP is a necessary condition for the global solutions of the MCP. Up to date, there is no algori...

We define a basis of solutions of a system of linear inequalities and present a general algorithm for finding such a basis. Our algorithm relies on an algorithm for finding a Hilbert basis for the set of nonnegative solutions of a system of linear inequalities and can be used in conjunction with any such algorithm.

We consider the Dirichlet problem −∆∞u = f(u) in Ω , u = 0 on ∂Ω , where ∆∞u = uxiuxjuxixj and f is a nonnegative continuous function. We investigate whether the solutions to this equation inherit geometrical properties from the domain Ω. We obtain results concerning convexity of level sets and symmetry of solutions.

In this paper, we study one-dimensional Newtonian filtration equation including unbounded sources with multiple delays. The existence of nonnegative non-trivial time periodic solutions will be established by the Leray-Schauder fixed point theorem based on some suitable Lyapunov functionals and some a priori estimates for all possible periodic solutions.

We consider the generalized variational inequality and construct certain merit functions associated with this problem. In particular, those merit functions are everywhere nonnegative and their zero-sets are precisely solutions of the variational inequality. We further use those functions to obtain error bounds, i.e., upper estimates for the distance to solutions of the problem.  2003 Elsevier ...

The paper develops a sub-supersolution approach for quasilinear elliptic equations driven by degenerated p-Laplacian and containing convection term. presence of the operator forces substantial change to functional setting previous works. existence location solutions through is established. abstract result applied find nontrivial, nonnegative bounded solutions.

We consider the Cauchy problem for a doubly nonlinear parabolic equation, obtaining optimal estimates both for the sup norm of nonnegative solutions, and for their support for large times.

For a coagulation equation with Becker-Döring type interactions and time-independent monomer input we study the detailed long-time behaviour of nonnegative solutions and prove the convergence to a selfsimilar function.

In this paper we study the classification of solutions of delay difference equation y,,= A, for n= N-(m+ 1),...N-1 where A,,, n =/V(m + 1), -, Nare given, m is a nonnegative integer.