WE CONSTRUCT compact hyperbolic 3-manifolds M,, M, and an irreducible representation p I : T-C, (M,) + SO(3) so that singularity of the representation variety of n,(M,) into SO(3) at pr is not quadratic. We prove that for any semi-simple Lie group G the singularity of the representation variety of sr (A4,) into G at the trivial representation is not quadratic. Copyright

A bulk viscosity is introduced in the formalism of modified gravity. It is shown that, based on a natural scaling law for the viscosity, a simple solution can be found for quantities such as the Hubble parameter and the energy density. These solutions may incorporate a viscosity-induced Big Rip singularity. By introducing a phase transition in the cosmic fluid, the future singularity can nevert...

At a two-fold singularity, the velocity vector of a flow switches discontinuously across a codimension one switching manifold, between two directions that both lie tangent to the manifold. Particularly intricate dynamics arises when the local flow curves towards the switching manifold from both sides, a case referred to as the Teixeira singularity. The flow locally performs two different action...

We investigate various dark energy models by taking into account the thermal effects induced from Hawking radiation on apparent horizon of Universe, for example near a finite-time future singularity. If density increases as Universe expands, Universe's evolution reaches singularity II type (or sudden singularity). The second derivative scale factor diverges but first remains finite. Quasi-de Si...

Mammals sense odors through the gene family of olfactory receptors (ORs). Despite the enormous number of OR genes (∼1,400 in mouse), each olfactory sensory neuron expresses one, and only one, of them. In neurobiology, it remains a long-standing mystery how this singularity can be achieved despite intrinsic stochasticity of gene expression. Recent experiments showed an epigenetic mechanism for m...

The singularity in Hawking and Turok’s model of open inflation has some appealing properties. We suggest that this singularity should be regularized with matter. The singular instanton can then be obtained as the limit of a family of “no-boundary” solutions where both the geometry and the scalar field are regular. Using this procedure, the contribution of the singularity to the Euclidean action...

In this survey paper some issues concerning a singularity concept in robotics are addressed. Singularities analyzed the scope of inverse kinematics for serial manipulator, motion planning task nonholonomic systems and optimal control covering large area practical robotic systems. An attempt has been made to define term singularity, which is independent on specific task. A few classifications si...

Higher order simple-pole type operators, that is, higher order linear ordinary differential operators with a large parameter η whose coefficients have simple poles at the origin, are discussed from the viewpoint of the exact WKB analysis. Making use of the technique of microdifferential operators, we clarify the singularity structure of the Borel transform of their WKB solutions.

We give a full exceptional collection in the triangulated category of singularities in the sense of Orlov [16] for a hypersurface singularity of Fermat type, and discuss its relation with homological mirror symmetry for simple elliptic hypersurface singularities.