an infinitely long hollow cylinder containing isotropic linear elastic material is considered under the effect of arbitrary boundary stress and thermal condition. the two-dimensional coupled thermoelastodynamic pdes are specified based on equations of motion and energy equation, which are uncoupled using nowacki potential functions. the laplace integral transform and bessel-fourier series are u...

1 Plane Curves 2 1.1 Computation of Topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.1.1 Expansion at Simple Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.1.2 Expansion at Singular Points . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.1.3 Newton Factorization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.1.4 Local...

We study the notion of singular tropical hypersurfaces of any dimension. We characterize the singular points in terms of tropical Euler derivatives and we give an algorithm to compute all singular points. We also describe non-transversal intersection points of planar tropical curves.

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...

In this paper, linear second-order differential equations of Sturm-Liouville type having a finite number of singularities and turning points in a finite interval are investigated. First, we obtain the dual equations associated with the Sturm-Liouville equation. Then, we prove the uniqueness theorem for the solutions of dual initial value problems.

This paper presents a novel algorithm for detection of singular points, the core and delta points, in fingerprint images. The number and location of singular points, are used to classify fingerprint images in to five general groups; and therefore to narrow down the search space in large fingerprint databases. Using the proposed directional masks in the first step, detects the neighborhood of th...

Context: Recently, the singular points of neural networks have attracted attention from the artificial intelligence community, and their interesting properties have been demonstrated. The objective of this study is to provide an overview of studies on the singularities of complex-valued neural networks. Evidence Acquisition: This review is based on the relevant literature on complex-valued neur...

We compare and contrast various notions of the “critical locus” of a complex analytic function on a singular space. After choosing a topological variant as our primary notion of the critical locus, we justify our choice by generalizing Lê and Saito’s result that constant Milnor number implies that Thom’s af condition is satisfied.

— 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).