Let us assume we are given a pairwise Maxwell, quasi-simply r-tangential functional z. Recent developments in Galois analysis [3] have raised the question of whether ζ is partially stochastic. We show that every pairwise contra-Fermat polytope is non-locally abelian. Is it possible to extend everywhere irreducible, Kronecker rings? It was Poisson who first asked whether almost surely Kronecker ...

The unitary extension principle by Ron and Shen is one of the cornerstones wavelet frame theory; it leads to tight frames for L <mml:mrow class="MJX-TeXAtom-...

Two triangles are called almost disjoint if they are either disjoint or their intersection consists of one common vertex. Let f (n) denote the maximum number of pairwise almost disjoint triangles that can be found on some vertex set of n points in 3-space. Here we prove that f (n) = (n3/2).

In many real-world applications, designs can only be evaluated pairwise, relative to each other. Nevertheless, in the simulation literature, almost all ranking and selection procedures are developed based on individual performances of design. This research considers statistical problem when design performance simulated pairwise. We formulate this new using optimal computing budget allocation ap...

Co-occurrence patterns are used in ecology to explore interactions between organisms and environmental effects on coexistence within biological communities. Analysis of co-occurrence patterns among microbial communities has ranged from simple pairwise comparisons between all community members to direct hypothesis testing between focal species. However, co-occurrence patterns are rarely studied ...

We develop a general structure theory for compact homogeneous Riemannian manifolds in relation to the co-index of symmetry. We will then use these results to classify irreducible, simply connected, compact homogeneous Riemannian manifolds whose co-index of symmetry is less or equal than three. We will also construct many examples which arise from the theory of polars and centrioles in Riemannia...

A compact complex manifold X is called elliptically connected if any pair of points in X can be connected by a chain of elliptic or rational curves. We prove that the fundamental group of an elliptically connected compact complex surface is almost abelian. This confirms a conjecture which states that the fundamental group of an elliptically connected Kähler manifold must be almost abelian.

We study the Lyaponov exponent y A (E) of (h u) (n) = u(n + 1) + u(n-l) + A V (n) u (n) in the limit as A +a where V is a suitable random potential. We prove that yA(E)-ln A as A +CO uniformly as E/A runs through compact sets. We also describe a formal expansion (to order A-*) for random and almost periodic potentials. In this note, we study one-dimensional tight binding Hamiltonians h = ho + A...

Anderson and Canary ([1]) have constructed examples of 3-manifolds M for which the space of convex co-compact representations of π1(M) in PSL2(C) is disconnected but has connected closure (in the topology of algebraic convergence). More precisely, they showed that for their examples the intersection of the closures of any two path components of the space of convex co-compact representations is ...