Abstract We show that for an area minimizing m ‐dimensional integral current T of codimension at least two inside a sufficiently regular Riemannian manifold, the upper Minkowski dimension interior singular set is most . This provides strengthening existing Hausdorff bound due to Almgren and De Lellis & Spadaro. As by‐product proof, we establish improvement on persistence singularities along...

— Given an intersection of two quadrics X ⊂ Pm−1, with m > 9, the quantitative arithmetic of the set X(Q) is investigated under the assumption that the singular locus of X consists of a pair of conjugate singular points defined over Q(i).

In this paper , by constructing a special set and utilizing fixed point theory in coin , we study the existence of solution of singular two points boundary value problem for second-order differential equation , which improved and generalize the result of related paper . Keywords—singular differential equation , boundary value problem, coin , fixed point theory .

The dynamics of the Bianchi IX cosmological model with minimally coupled massive real scalar field is studied. The possibility of non-singular transition from contraction to expansion is shown. A set of initial conditions that lead to non-singular solutions is studied numerically.

In this paper, we present an efficient method to compute singular points and singularity induced bifurcation points of differential-algebraic equations (DAEs) for a multimachine power system model. The algebraic part of the DAEs brings singularity issues into dynamic stability assessment of power systems. Roughly speaking, the singular points are points that satisfy the algebraic equations, but...

A new approach is presented for computing the interior medial axes of generic regions in R bounded by C-smooth parametric B-spline surfaces. The generic structure of the 3D medial axis is a set of smooth surfaces along with a singular set consisting of edge curves, branch curves, fin points and six junction points. In this work, the medial axis singular set is first computed directly from the B...

(1.4) H(x,∇u) = 1 in . Under suitable conditions we show that the (n−1)–dimensional Hausdorff measure of the singular set of solutions (the complement of the open set where u ∈ C) is finite. In addition, we prove the corresponding result for H(x, t, p) but under very special conditions. See Theorem 10.5 and its simple consequences, Propositions 1.8, 1.10, and 1.11. We were brought to the proble...