In this work, it is demonstrated that the existence and topology of the recently observed interfacial singularities driven by Marangoni effects can be deduced using mean-curvature flow theory extended to account for variations of interfacial tension. This suggests that some of the physical mechanisms underlying the formation of these interfacial singularities may originate from/be modeled by th...

Divisors with minimal discrepancy over cA points are classified. The problem of birational classification of algebraic varieties is highly interconnected with the problem of description of singularities on them. One of the most important class of three-dimensional singularities is terminal singularities, which arise within minimal models programm. Despite the analytical classification of the si...

We study the question of existence of a Riemannian metric of positive scalar curvature metric on manifolds with the Sullivan–Baas singularities. The manifolds we consider are Spin and simply connected. We prove an analogue of the Gromov–Lawson Conjecture for such manifolds in the case of particular type of singularities. We give an affirmative answer when such manifolds with singularities accep...

Let X be a proper complex variety with Du Bois singularities. Then Hi(X,C) → H(X,OX) is surjective for all i. This property makes this class of singularities behave well with regard to Kodaira type vanishing theorems. Steenbrink conjectured that rational singularities are Du Bois and Kollár conjectured that log canonical singularities are Du Bois. Kollár also conjectured that under some reasona...

Current image representation schemes have limited capability of representing 2D singularities (e.g., edges in an image). Wavelet transform has better performance in representing 1D singularities than Fourier transform. Recently invented ridgelet and curvelet transform achieve better performance in resolving 2D singularities than wavelet transform. To further improve the capability of representi...

It is known that the singularities of bounded invertible piecewise isometric dynamical systems in Euclidean plane can be classified as, removable, sliding and shuffling singularities, based upon their geometrical aspects. Moreover, it is known that the Devaney-chaos of the bounded invertible piecewise isometric systems can be generated only from the sliding singularities, while the other singul...

We prove that a Cohen-Macaulay normal variety X has Du Bois singularities if and only if π∗ωX′(G) ≃ ωX for a log resolution π : X ′ → X , where G is the reduced exceptional divisor of π. Many basic theorems about Du Bois singularities become transparent using this characterization (including the fact that Cohen-Macaulay log canonical singularities are Du Bois). We also give a straightforward an...

The workspace of a Robot is determined by an analytical method. The method is applicable to kinematic chains that can be modeled using the Denavit-Hartenberg representation for serial kinematic chains. This method is based upon analytical criteria for determining singular behavior of the mechanism. By manipulating the Jacobian of the robot by the row rank deficiency condition, the singularities...