The concept of critical points in nuclear phase transitional regions is discussed from the standpoints of Q-invariants, simple observables and wave function entropy. It is shown that these critical points very closely coincide with the turning points of the discussed quantities, establishing the singular character of these points in nuclear phase transition regions between vibrational and rotat...

We deal with the following closely related problems: (i) For a germ of a reduced plane analytic curve, what is the minimal degree of an algebraic curve with a singular point analytically equivalent (isomorphic) to the given one? (ii) For a germ of a holomorphic function in two variables with an isolated critical point, what is the minimal degree of a polynomial, equivalent to the given function...

Defects or junctions in materials serve as a source of interactions for particles, and in idealized limits they may be treated as singular points yielding contact interactions. In quantum mechanics, these singularities accommodate an unexpectedly rich structure and thereby provide a variety of physical phenomena, especially if their properties are controlled properly. Based on our recent studie...

We compute the fundamental groups of five maximizing sextics with double singular points only; in four cases, the groups are as expected. The approach used would apply to other sextics as well, given their equations.

For the conceptual design of countercurrently operated reactive distillation columns, fast methods are needed to estimate potential top and bottom products. The possible column bottom product composition can be determined from the stable singular points of a batch reactive reboiler. In a similar manner the top product composition can be obtained from the stable singular points of a batch reacti...

Fingerprint classification is an important task for any large scale fingerprint recognition system. The high precision of detecting core point is crucial for most fingerprint classification operations. This paper provides an overview of the most well-known techniques for singular points detection fingerprint classification based on these singularities. The main purpose of singular points detect...

An adaptive unstructured grid generation scheme is introduced to use finite volume (FV) and finite element (FE) formulation to solve the heat equation with singular boundary conditions. Regular grids could not acheive accurate solution to this problem. The grid generation scheme uses an optimal time complexity frontal method for the automatic generation and delaunay triangulation of the grid po...

As an important feature of fingerprints, singular points ( core and delta) not only represent the local ridge pattern characteristics, but also determine the topological structure (i.e. fingerprint type) and largely influence the orientation field. In this paper, we have performed analysis for singular points in two aspects: (1) based on the topology theory in 2D manifold, we deduced the relati...