Particle Tracking Velocimetry in Noisy Environment

The encoded Particle Tracking Velocimetry (ePTV) is introduce in this paper as a specific approach of Particle Tracking Velocimetry (PTV). This method is applied to track particles obtained from flow images that contain significant background noise and relatively low particle density. Encoding is achieved by illuminating the flow with a series of light pulses within individual image exposures. Dependent upon the velocity, each particle will be illuminated multiple times in each image frame with spacing determined by both the pulse train timing and the particle velocity. A search algorithm is used that identifies each particle and seeks the encoded pattern with other particles in the image, repeating this until all encoded particles are found. Based on probability analysis and finite image size an analytic model is developed to determine the ratio of true particles, false particles and those that are ‘lost’ by exiting the image frame. This ePTV technique has been experimentally implemented to track spherical particles suspended in stationary vortices. By using a suspension of micro-particles, subsequent imaging with encoded pulse trains provided snap-shots of the complex flow patterns. Typically, even after filtering, the images show around 100 to 200 particles from which encoded trajectories have been extracted and typically account for about 30% of the objects identified in the image.

Bipolar Fuzzy Structure of H-Ideals in BCI-Algebras

In this chapter, the concepts of bipolar fuzzy H-ideals of BCI-algebras are introduced and their natures are investigated. Relations between bipolar fuzzy subalgebras, bipolar fuzzy ideals, and bipolar fuzzy H-ideals are discussed. Conditions for a bipolar fuzzy ideal to be a bipolar fuzzy H-ideal are provided. Some characterization theorems of bipolar fuzzy H-ideals are established. A bipolar fuzzy H-ideal is established by using a finite collection of H-ideals. The authors have shown that if every bipolar fuzzy H-ideal has the finite image, then every descending chain of H-ideals terminates at finite step.

Finiteness for mapping class group representations from twisted Dijkgraaf–Witten theory

We show that any twisted Dijkgraaf–Witten representation of a mapping class group of an orientable, compact surface with boundary has finite image. This generalizes work of Etingof et al. showing that the braid group images are finite [P. Etingof, E. C. Rowell and S. Witherspoon, Braid group representations from twisted quantum doubles of finite groups, Pacific J. Math. 234 (2008)(1) 33–42]. In particular, our result answers their question regarding finiteness of images of arbitrary mapping class group representations in the affirmative. Our approach is to translate the problem into manipulation of colored graphs embedded in the given surface. To do this translation, we use the fact that any twisted Dijkgraaf–Witten representation associated to a finite group [Formula: see text] and 3-cocycle [Formula: see text] is isomorphic to a Turaev–Viro–Barrett–Westbury (TVBW) representation associated to the spherical fusion category [Formula: see text] of twisted [Formula: see text]-graded vector spaces. The representation space for this TVBW representation is canonically isomorphic to a vector space of [Formula: see text]-colored graphs embedded in the surface [A. Kirillov, String-net model of Turaev-Viro invariants, Preprint (2011), arXiv:1106.6033 ]. By analyzing the action of the Birman generators [J. Birman, Mapping class groups and their relationship to braid groups, Comm. Pure Appl. Math. 22 (1969) 213–242] on a finite spanning set of colored graphs, we find that the mapping class group acts by permutations on a slightly larger finite spanning set. This implies that the representation has finite image.

On Bipolar Fuzzy B-Subalgebras of B-Algebras

Based on the concept of bipolar fuzzy set, a theoretical approach of B-subalgebras of B-algebras are established. Some characterizations of bipolar fuzzy B-subalgebras of B-algebras are given. We have shown that the intersection of two bipolar fuzzy B-subalgebras is also a bipolar fuzzy B-subalgebra, but for the union it is not always true. We have also shown that if every bipolar fuzzy B-subalgebras has the finite image, then every descending chain of B-subalgebras terminates at finite step.

John Locke, ‘Hobbist’: of sleeping souls and thinking matter

In this paper, I consider Isaac Newton’s fevered accusation that John Locke is a ‘Hobbist.’ I suggest a number of ways in which Locke’s account of the mind–body relation could plausibly be construed as Hobbesian. Whereas Newton conceives of the human mind as an immaterial substance and venerates it as a finite image of the Divine Mind, I argue that Locke utterly deflates the religious, ethical, and metaphysical significance of an immaterial soul. Even stronger, I contend that there is good reason to suspect that Locke is a crypto-materialist, at least with respect to human beings, and in this respect, could reasonably be labeled a ‘Hobbist.’

On model-theoretic connected components in some group extensions

We analyze model-theoretic connected components in extensions of a given group by abelian groups which are defined by means of 2-cocycles with finite image. We characterize, in terms of these 2-cocycles, when the smallest type-definable subgroup of the corresponding extension differs from the smallest invariant subgroup. In some situations, we also describe the quotient of these two connected components. Using our general results about extensions of groups together with Matsumoto–Moore theory or various quasi-characters considered in bounded cohomology, we obtain new classes of examples of groups whose smallest type-definable subgroup of bounded index differs from the smallest invariant subgroup of bounded index. This includes the first known example of a group with this property found by Conversano and Pillay, namely the universal cover of [Formula: see text] (interpreted in a monster model), as well as various examples of different nature, e.g. some central extensions of free groups or of fundamental groups of closed orientable surfaces. As a corollary, we get that both non-abelian free groups and fundamental groups of closed orientable surfaces of genus [Formula: see text], expanded by predicates for all subsets, have this property, too. We also obtain a variant of the example of Conversano and Pillay for [Formula: see text] instead of [Formula: see text], which (as most of our examples) was not accessible by the previously known methods.

TWISTED ALEXANDER INVARIANTS OF TWISTED LINKS

Let L = ℓ1 ∪⋯∪ℓd+1 be an oriented link in 𝕊3, and let L(q) be the d-component link ℓ1 ∪⋯∪ℓd regarded in the homology 3-sphere that results from performing 1/q-surgery on ℓd+1. Results about the Alexander polynomial and twisted Alexander polynomials of L(q) corresponding to finite-image representations are obtained. The behavior of the invariants as q increases without bound is described.

Actions of higher-rank lattices on free groups

If G is a semisimple Lie group of real rank at least two and Γ is an irreducible lattice in G, then every homomorphism from Γ to the outer automorphism group of a finitely generated free group has finite image.