We give upper and lower bounds for the consistency strength of the failure of a combinatorial principle introduced by Jensen, Square on singular cardinals. A combinatorial principle of great importance in set theory is the Global principle of Jensen [6]: Global : There exists 〈Cα | α a singular ordinal 〉 such that for each α, Cα is a closed unbounded subset of α of ordertype less than α, the li...

The problem of obtaining network coding maps for the physical layer network coded two-way relay channel is considered, using the denoise-and-forward forward protocol. It is known that network coding maps used at the relay node which ensure unique decodability at the end nodes form Latin Squares. Also, it is known that minimum distance of the effective constellation at the relay node becomes zer...

We give a method for constructing transcendental entire functions with good control of both the singular values of f and the geometry of the level-set {|f | > R}. The method consists of first building a quasiregular map by “gluing together” copies of the right half-plane that have each been quasiconformally “folded” into themselves. The measurable Riemann mapping theorem is then invoked to prod...

The purpose of this paper is to propose a definition of a set of singular values and a singular value decomposition associated with a linear operator defined on arbitrary normed linear spaces. This generalizes the usual notion of singular values and singular value decompositions to operators defined on spaces equipped with the p-norm, where p is arbitrary. Basic properties of these generalized ...

The quaternionic representation of ham images, treating RGB colour components as a single unit instead of as separate components, is very effective. The advantage of using quaternion arithmetic is that the perceptually richer colour images can be represented and analyzed as a single entity, improving the accuracy of pattern recognition models. The quaternionic singular value decomposition (SVD)...

Spectral approximations for ODEs in unbounded domains have only received limited attention. In many applicable problems, singular initial value problems arise. In solving these problems, most of numerical methods have difficulties and often could not pass the singular point successfully. In this paper, we apply the sinc-collocation method for solving singular initial value problems. The ability...

A general canonical curve X ⊂ P determines a finite set θ(X) of hyperplanes that are tangent to X at g − 1 points. Such a set is in bijective correspondence with the set of odd theta-characteristics of X. We generalize the definition of θ(X) to certain singular curves (including Deligne-Mumford stable curves) in a way that is compatible with degenerations. We give the explicit description of θ(...

We prove an a priori lower bound for the pressure, or p-norm joint spectral radius, of a measure on the set of d × d real matrices which parallels a result of J. Bochi for the joint spectral radius. We apply this lower bound to give new proofs of the continuity of the affinity dimension of a selfaffine set and of the continuity of the singular-value pressure for invertible matrices, both of whi...

We construct Colding-Minicozzi limit minimal laminations in open domains in R with the singular set of C-convergence being any properly embedded C-curve. By Meeks’ C-regularity theorem, the singular set of convergence of a Colding-Minicozzi limit minimal lamination L is a locally finite collection S(L) of C-curves that are orthogonal to the leaves of the lamination. Thus, our existence theorem ...

We consider a class of transcendental meromorphic functions f : C → C with infinitely many poles. Under some regularity assumption on the location of poles and the behavior of the function near the poles, we provide explicite lower bounds for the hyperbolic dimension (Hausdorff dimension of radial points) of the Julia set and upper bounds for the Hausdorff dimension of the set of escaping point...