For a family of operator inclusions with convex closed-valued right-hand sides in Banach spaces, the existence of solutions is obtained by chieey using Ky Fan's xed point principle. The main result of the paper improves Theorem 1 in 16] as well as Theorem 2.2 of 3]. Some meaningful concrete cases are also presented and discussed. KEY WORDS: operator inclusions in Banach spaces, Ky Fan's xed poi...

The inequality Ffx;fy(qs) Fx;y(s) (s 0), where q 2 (0; 1), is generalized for multivalued mappings in many directions. Using Hausdor distance S.B. Nadler in [7] introduced a generalization of Banach contraction principle in metric spaces. In [3] the de nition of probabilistic Nadler q-contraction is given. Using some results given in [12] a xed point theorem on spaces with a convex structure is...

For every xed-point expression e of alternation-depth r, we construct a new xed-point expression e 0 of alternation-depth 2 and size O(r jej). Expression e 0 is equivalent to e whenever operators are distributive and the underlying complete lattice has a co-continuous least upper bound. We show that our transformation is optimal not only w.r.t. alternation-depth but also w.r.t. the increase in ...

We give a new proof for the existence of a non{Gaussian hierarchical renormalization group xed point, using what could be called a beta{function for this problem. We also discuss the asymptotic behavior of this xed point, and the connection between the hierarchical models of Dyson and Gallavotti. 1 Supported in Part by the National Science Foundation under Grant No. DMS{8802590. 2 Supported in ...

Resumen Background: With the 2-way mixed model, one a fi xed factor and the other random, the procedure followed to test statistical signifi cance of the random factor has been the focus of a heated controversy in theoretical and applied statistics, and the debating continues even now. One of the main consequences of this controversy is that the position defended in the classical ANOVA texts on...

We report on our recent studies of the large N renormalization group (RG) method which clariies phase structure of random matrix models. We derive an exact RG equation which enables us to obtain the exact locations of xed points and their scaling exponents. The classiication of phases is given by this analysis. A linear approximation visualizes the RG ow of crossover phenomena including several...

Xia’s algorithm consists of a reduction algorithm and a translation procedure both originally used to tackle the xed point property for ordered sets. We present results that show that the translation procedure allows access to a much wider range of problems and results showing that the algorithm is very e cient when applied to the xed point property in ordered sets or for order=graph isomorphis...

We report numerical and analytical studies of the nite size time scales in a system with microscopic stochastic dynamics which in the bulk limit corresponds to an evolution equation with an accumulation point of critical xed points. Our results suggest that the nite size behavior is dominated not by uctuations but by the bottleneck statistical weights at near-xed-point conditions in a nite-size...

During winter, aerial surveys are used to estimate densities of ducks that occupy open-water habitats. However, such surveys are ineffective for sampling forest-dwelling species, especially Aix sponsa (Wood Ducks), Anas platyrhynchos (Mallards), and Lophodytes cucullatus (Hooded Mergansers). We evaluated fi xed-radius plot (FRP) and Reynolds and Goodrum variable-radius plot (VRP) methods for es...

Aesthetic improvement is highly valued by patients seeking orthodontic treatment ( Dann et al. , 1995 ). Subjects with a Class II malocclusion are a good example of patients who are referred to orthodontists primarily for aesthetic improvement ( Dann et al. , 1995 ). In growing patients, two-phase treatment of Class II skeletal malocclusions, which includes growth modifi cation with functional ...