All extremal solutions of the truncated L-problem of moments in two real variables , with support contained in a given compact set, are described as characteristic functions of semi-algebraic sets given by a single polynomial inequality. An exponential kernel, arising as the determinantal function of a naturally associated hyponormal operator with rank-one self-commutator, provides a natural de...

We consider a family of variational problems on a Hilbert manifold parameterized by an open subset of a Banach manifold, and we discuss the genericity of the nondegeneracy condition for the critical points. Based on an idea of B. White [24], we prove an abstract genericity result that employs the infinite dimensional Sard–Smale theorem. Applications are given by proving the genericity of metric...

BACKGROUND Outdoor ambient polycyclic aromatic hydrocarbon (PAH) concentrations are variable throughout an urban environment. However, little is known about how variation in semivolatile and nonvolatile PAHs related to the built environment (open space vs. semi-closed space) contributes to differences in concentrations. METHODS We simultaneously collected 14, two-week samples of PAHs from the...

We explore semi-complete self-similar solutions for the polytropic gas dynamics involving self-gravity under spherical symmetry, examine behaviours of the sonic critical curve, and present new asymptotic collapse solutions that describe ‘quasi-static’ asymptotic behaviours at small radii and large times. These new ‘quasi-static’ solutions with divergent mass density approaching the core can hav...

This paper studies the representations of a non-negative polynomial f on a non-compact semi-algebraic set K modulo its critical ideal. Under the assumption that the semi-algebraic set K is regular and f satisfies the boundary Hessian conditions (BHC) at each zero of f in K. We show that f can be represented as a sum of squares (SOS) of real polynomials modulo its critical ideal if f ≥ 0 on K. P...

State of the art set expansion algorithms produce varying quality expansions for different entity types. Even for the highest quality expansions, errors still occur and manual refinements are necessary for most practical uses. In this paper, we propose algorithms to aide this refinement process, greatly reducing the amount of manual labor required. The methods rely on the fact that most expansi...

In this paper, we introduce a new class of sets, namely semi*δ-open sets, using δ-open sets and the generalized closure operator. We find characterizations of semi*δ-open sets. We also define the semi*δ-interior of a subset. Further, we study some fundamental properties of semi*δ-open sets and semi*δ-interior.

This paper examines the impact of demographic factors on saving, investment, and external balances. We derive a number of semi-structural equations from national accounting principle and the principle that external balances for the world as a whole must sum to zero. The resulting equations embody both closed, partially open and completely open economies as special cases, and are arguably more p...

Given a symplectic space, equipped with a line bundle and a Hamiltonian group action satisfying certain compatibility conditions, it is a basic question to understand the decomposition of the quantization space in irreducible representations of the group. We derive weight multiplicity formulas for the quantization space in terms of data at the fixed points on the symplectic space, which apply t...