As an important feature of fingerprints, singular points (includingcores and deltas) not only represent the local ridge pattern characteristics, but also determine the topological structure (i.e. fingerprint type). 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 relationship between cores and deltas in...

In this paper we construct the Poincare line bundle for stack of Higgs bundles on smooth projective curves and show that it induces a fully-faithful Fourier-Mukai transform category quasi-coherent sheaves.

We consider the mixing of similar, cohesionless granular materials in quasi-two-dimensional rotating containers by means of theory and experiment. A mathematical model is presented for the flow in containers of arbitrary shape but which are symmetric with respect to rotation by 180 degrees and half-filled with solids. The flow comprises a thin cascading layer at the flat free surface, and a fix...

We provide canonical forms for the homogeneous polynomials of degree five. Then we characterize all phase portraits in Poincare disk quartic polynomial differential systems. More precisely, there are exactly 23 different topological

In this research, dynamic analysis of the rotational slender axially moving string is investigated. String assumed as Euler Bernoulli beam. The axial motion of the string, gyroscopic force and mass eccentricity were considered in the study. Equations of motion are derived using Hamilton’s principle, resulting in two partial differential equations for the transverse motions. The equations are ch...

In a paper recently published in the Rendiconti del Circolo Matemático di Palermo (vol. 33, 1912, pp. 375-407) and entitled Sur un théorème de Géométrie, Poincaré enunciated a theorem of great importance, in particular for the restricted problem of three bodies; but, having only succeeded in treating a variety of special cases after long-continued efforts, he gave out the theorem for the consid...

The separating mechanisms occuring in a class of Poincar6 halfmaps that is induced by the flow of a saddle-focus are described quantitatively. The “critical spiral” is calculated explicitly inside the domain of the map. A complete hierarchy, consisting of three different types of separating mechanisms, is demonstrated. It is characterized in terms of the properties of the critical spiral, as it...

We propose and rigorously analyze two randomized algorithms to factor univariate polynomials over finite fields using rank 2 Drinfeld modules. The first algorithm estimates the degree of an irreducible factor of a polynomial from Euler-Poincare characteristics of random Drinfeld modules. Knowledge of a factor degree allows one to rapidly extract all factors of that degree. As a consequence, the...