Storrer introduced the epimorphic hull of a commutative semiprime ring R and showed that it is (up to isomorphism) the unique essential epic von Neumann regular extension of R. In the case when R = C(X) with X a Tychonoff space, we show that the embedding induced by a dense subspace of X is always essential. This simplifies the search for spaces whose epimorphic hull is a full ring of continuou...

This article presents a new subspace-based technique for reducing the noise of signals in time-series. In the proposed approach, the signal is initially represented as a data matrix. Then using Singular Value Decomposition (SVD), noisy data matrix is divided into signal subspace and noise subspace. In this subspace division, each derivative of the singular values with respect to rank order is u...

The topological space of linear, time-invariant systems is considered. A properly of linear systems is called generic if the systems equipped with this property occupy an open and dense subspace of the space of systems. Several generic properties of linear systems are reviewed, including controllability, observability, invertibility, structural stability, as well as some topological properties ...

We show that if an infinite-dimensional Banach space X has a symmetric basis then there exists a bounded, linear operator R : X −→ X such that the set A = {x ∈ X : ||R(x)|| → ∞} is non-empty and nowhere dense in X . Moreover, if x ∈ X \ A then some subsequence of (R(x)) n=1 converges weakly to x. This answers in the negative a recent conjecture of Prǎjiturǎ. The result can be extended to any Ba...

The R-linear Beltrami equation appears in applications, such as in the inverse problem of recovering the electrical conductivity distribution in the plane. In this paper, a new way to discretize the R-linear Beltrami equation is considered. This gives rise to large and dense R-linear systems of equations with structure. For their iterative solution, norm minimizing Krylov subspace methods are d...

Let X be a geometrically irreducible closed subvariety of an abelian variety A over a number field k such that X generates A. Let V be a finite-dimensional subspace of A(k) ⊗R, and let π : A(k) → V be the orthogonal projection relative to a Néron-Tate pairing 〈 , 〉 : A(k) × A(k) → R. For V = A(k) ⊗R, we prove that π(X(k)) = A(k) ⊗Q, and moreover, there exist c, c′ > 0 such that for any a ∈ A(k)...

We construct the solution φ(t,x) of the quantum wave equation 2φ+m2φ+λ : φ3:= 0 as a bilinear form which can be expanded over Wick polynomials of the free in-field, and where :φ3(t,x) : is defined as the normal ordered product with respect to the free in-field. The constructed solution is correctly defined as a bilinear form on Dθ×Dθ, whereDθ is a dense linear subspace in the Fock space of the ...

This paper is concerned with Schrödinger equations whose principal operators are elliptic. Under certain degenerate condition we show the estimate of an oscillatory integral related to the solution operator in free case, and then employ fractionally integrated groups to obtain the Lp estimate of solutions for the initial data belonging to a dense subspace of Lp in the case of integrable potenti...

We give an overview of the Invariant Subspace Decomposition Algorithm for dense symmetric matrices (SYISDA) by rst describing the algorithm, followed by a discussion of a parallel implementation of SYISDA on the Intel Delta. Our implementation utilizes an optimized parallel matrix multiplication implementation we have developed. Load balancing in the costly early stages of the algorithm is acco...

In the topology of coordinatewise convergence ∇∞ is a compact, metrizable and separable space. Denote by C(∇∞) the algebra of real continuous functions on ∇∞ with pointwise operations and the supremum norm. In C(∇∞) there is a distinguished dense subspace F := R [q1, q2, . . . ] generated (as a commutative unital algebra) by algebraically independent continuous functions qk(x) := ∑∞ i=1 x k+1 i...