In this paper the 5-dimensional contact SO(3)-manifolds are classified up to equivariant contactomorphisms. The construction of such manifolds with singular orbits requires the use of generalized Dehn twists. We show as an application that all simply connected 5-manifolds with singular orbits are realized by a Brieskorn manifold with exponents (k, 2, 2, 2). A 5-dimensional contact SO(3)-manifol...

‎This paper presents two main results that the singular values of the Hadamard product of normal matrices $A_i$ are weakly log-majorized by the singular values of the Hadamard product of $|A_{i}|$ and the singular values of the sum of normal matrices $A_i$ are weakly log-majorized by the singular values of the sum of $|A_{i}|$‎. ‎Some applications to these inequalities are also given‎. ‎In addi...

We consider the problem of constructing nonnegative matrices with prescribed extremal singular values. In particular, given 2n−1 real numbers σ ( j) 1 and σ ( j) j , j = 1, . . . , n, we construct an n×n nonnegative bidiagonal matrix B and an n×n nonnegative semi-bordered diagonal matrix C , such that σ ( j) 1 and σ ( j) j are, respectively, the minimal and the maximal singular values of certai...

Shelah proved recently that if κ > ω and S ⊆ κ+ is a stationary set of ordinals of cofinality different from cf(κ), then 2κ = κ+ implies ♦κ+ (S). We show that for singular κ, an elaboration on his argument allows us to derive ♦κ+ (T ) from 2κ = κ+ + κ where T = {δ < κ+ | cf(δ) = cf(κ)}. This gives a strong restriction on the existence of saturated ideals on κ+.

We prove certain L estimates (1 < p <∞) for non-isotropic singular integrals along surfaces of revolution. The singular integrals are defined by rough kernels. As an application we obtain L boundedness of the singular integrals under a sharp size condition on their kernels. We also prove a certain estimate for a trigonometric integral, which is useful in studying non-isotropic singular integrals.

A transcendental entire function f is called geometrically finite if the intersection of the set S(f) of singular values with the Fatou set F(f) is compact and the intersection of the postsingular set P (f) with the Julia set J (f) is finite. (In particular, this includes all entire functions with finite postsingular set.) If f is geometrically finite, then F(f) is either empty or consists of t...

This paper presents work that uses Transductive Latent Semantic Indexing (LSI) for text classification. In addition to relying on labeled training data, we improve classification accuracy by incorporating the set of test examples in the classification process. Rather than performing LSI’s singular value decomposition (SVD) process solely on the training data, we instead use an expanded term-by-...

In this paper we study the dynamics of the family of complex maps given by fλ(z) = z n + λ/(zh(z − a)d) where n, h and d are integers such that 1/n+1/h < 1 and d ≥ 1 and the pole a lies outside the unit circle. The parameter λ is complex and arbitrarily small. In spite of the large number of possibilities we prove that the Julia set of fλ(z) consists of a countable collection of Cantor sets of ...

Starting from the existence of many supercompact cardinals, we construct a model of ZFC + GCH in which the tree property holds at a countable segment of successor of singular cardinals.

In this paper we study singular values of a matrix whose one entry varies while all other entries are prescribed. In particular, we find the possible pth singular value of such a matrix, and we define explicitly the unknown entry such that the completed matrix has the minimal possible pth singular value. This in turn determines possible pth singular value of a matrix under rank one perturbation...