Related papers: Real intersection theory (I)
These notes aim to give a first introduction to intersection cohomology and perverse sheaves with applications to representation theory or quantum groups in mind.
We investigate the collision of two vortex lines moving with viscous dynamics and driven towards each other by an applied current. Using London theory in the approach phase we observe a non-trivial vortex conformation producing…
Present article deals with trajectorial intersections in linear fractional systems ('systems'). We propose a classification of intersections of trajectories in three classes viz. trajectories intersecting at same time(EIST), trajectories…
We determine sets of elements which, under certain conditions, generate an intersection of ideals up to radical.
Observable currents are spacetime local objects that induce physical observables when integrated on an auxiliary codimension one surface. Since the resulting observables are independent of local deformations of the integration surface, the…
We investigate the viability of defining an intersection product on algebraic cycles on a singular algebraic variety by pushing forward intersection products formed on a resolution of singularities. For varieties with resolutions having a…
We investigate the behaviour of concepts from dependent theories when applied to real closed fields. Our main focus is on the concept of perpendicular indiscernible sequences, a concept first introduced in section 4 of math.LO/0009056 .…
Lebesgue's dominated convergence theorem is a crucial pillar of modern analysis, but there are certain areas of the subject where this theorem is deficient. Deeper criteria for convergence of integrals are described in this article.
We generalize two classical formulas for complete intersection curves by introducing the the complete intersection discrepancy of a curve as a correction term. The first is a well-known multiplicity formula in singularity theory, due to…
The interaction of metal-molecule-metal junctions with light is considered within a simple generic model. We show, for the first time, that light induced current in unbiased junctions can take place when the bridging molecule is…
This is an introduction to the theory of disconjugacy for a second order linear differential equation. We give new proofs of some of basic results and obtain new sufficient conditions for disconjugacy (in particular, on the whole real…
We prove the existence of non-trivial phase transitions for the intersection of two independent random interlacements and the complement of the intersection. Some asymptotic results about the phase curves are also obtained. Moreover, we…
We study the question of the continuity of slices of currents and explain how it relates to several seemingly unrelated problems in tropical geometry. On the one hand, through this lens, we show that the continuity of superpotentials…
We develop a tropical intersection formalism of forms and currents that extends classical tropical intersection theory in two ways. First, it allows to work with arbitrary polytopes, also non-rational ones. Second, it allows for smooth…
A tropical complete intersection curve C in R^(n+1) is a transversal intersection of n smooth tropical hypersurfaces. We give a formula for the number of vertices of C given by the degrees of the tropical hypersurfaces. We also compute the…
A survey of special curves, special subvarieties of $\mathcal{M}_g$, and related topics. A large portion of the text discusses various possible interpretation of the word 'special' in this context by giving also concrete examples. One…
The asynchronous systems $f$ are the models of the asynchronous circuits from digital electrical engineering. They are multi-valued functions that associate to each input $u:\mathbf{R}\to \{0,1\}^{m}$ a set of states $x\in f(u),$ where…
Oriented closed curves on an orientable surface with boundary are described up to continuous deformation by reduced cyclic words in the generators of the fundamental group and their inverses. By self-intersection number one means the…
In this short note, we give a new sufficient condition for the existence of long cycles in graphs involving Fan-type degree condition and neighborhood intersection.
We study the probability distribution of a current flowing through a diffusive system connected to a pair of reservoirs at its two ends. Sufficient conditions for the occurrence of a host of possible phase transitions both in and out of…