In this paper we study the Feichtinger Conjecture in frame theory, which was recently shown to be equivalent to the 1959 Kadison-Singer Problem in C-Algebras. We will show that every bounded Bessel sequence can be decomposed into two subsets each of which is an arbitrarily small perturbation of a sequence with a finite orthogonal decomposition. This construction is then used to answer two open ...

The number of shortest factorizations into reflections for a Singer cycle in GLn(Fq) is shown to be (qn − 1)n−1. Formulas counting factorizations of any length, and counting those with reflections of fixed conjugacy classes are also given. The method is a standard character-theory technique, requiring the compilation of irreducible character values for Singer cycles, semisimple reflections, and...

We develop results which show that elements in the radical of a commutative Banach algebra are often precluded from having prime-like properties if we avoid certain exceptional situations involving torsion elements. This makes the proof of the Singer-Wermer conjecture conceptually much clearer. It also motivates the de nition of an element having regular powers and allows us to strengthen our p...

CLINICAL MANIFESTATIONS OF INHERITED ABNORMAL HEMOGLOBINS. I. THE / \. INTERACTION OF HEMOGLOBIN-S WITH HEMOGLOBIN-D. II. INTERACTION / OF HEMOGLOBIN-E AND THALASSEMIA TRAIT Phillip Sturgeon, Harvey A. Itano and William R. Bergren 389 STUDIES ON ABNORMAL HEMOGLOBINS. XI. SICKLE CELL-THALASSEMIA DISEASE IN THE NEGRO. THE SIGNIFICANCE OF THE S + A + F AND S -4A PATTERNS OBTAINED BY HEMOGLOBIN ANA...

We consider functional Schrödinger equations associated with a wide class of Hamiltonians in all Fock representations of the bosonic canonical commutation relations, in particular the Cook-Fock, Friedrichs-Fock, and Bargmann-Fock models. An infinite-dimensional symbolic calculus allows to prove the convergence of the corresponding Hamiltonian Feynman integrals for propagators of coherent states...

For a compact manifold without boundary a suspended algebra of pseudodifferential operators is considered; it is an algebra of pseudodifferential operators on, and translation-invariant in, an additional real variable. It is shown that the eta invariant, as defined by Atiyah, Patodi and Singer for admissible Dirac operators, extends to a homomorphism from the ring of invertible elements of the ...

At the 1974 International Congress, I. M. Singer proposed that eta invariants and hence spectral flow should be thought of as the integral of a one form. In the intervening years this idea has lead to many interesting developments in the study of both eta invariants and spectral flow. Using ideas of [24] Singer's proposal was brought to an advanced level in [16] where a very general formula for...

1.1 Background. Kronecker's limit formula states that the regularized determinant of Laplacian of an elliptic curve is represented by the norm of Jacobi's ∆-function at its period point. One of the striking property of Jacobi's ∆-function is that it admits the infinite product expansion. In a series of works [Bo1-3], Borcherds developed a theory of modular forms over domains of type IV which ad...

Oscillations in many regions of the cortex have common temporal characteristics with dominant frequencies centered around the 40 Hz (gamma) frequency range and the 5-10 Hz (theta) frequency range. Experimental results also reveal spatially synchronous oscillations, which are stimulus dependent (Gray & Singer, 1987; Gray, Konig, Engel, & Singer, 1989; Engel, Konig, Kreiter, Schillern, & Singer, ...

For a representation of the fundamental group of a compact oriented odd-dimensional manifold we define a refinement of the Ray-Singer torsion associated to this representation. If the representation is acyclic then our new invariant is a non-zero complex number, which can be viewed as an analytic counterpart of the refined combinatorial torsion introduced by Turaev. The refined analytic torsion...