The ordering of liquid crystals (LCs) is known to be influenced by surfaces and contaminants. Here, we report that picogram per milliliter concentrations of endotoxin in water trigger ordering transitions in micrometer-size LC droplets. The ordering transitions, which occur at surface concentrations of endotoxin that are less than 10(-5) Langmuir, are not due to adsorbate-induced changes in the...

in addition to exploring constructions and properties of limits and colimits in categories of topologicalalgebras, we study special subcategories of topological algebras and their properties. in particular, undercertain conditions, reflective subcategories when paired with topological structures give rise to reflectivesubcategories and epireflective subcategories give rise to epireflective subc...

<p>Given an autohomeomorphism on ordered topological space or its subspace, we show that it is sometimes possible to introduce a new topology-compatible order so the same map monotonic with respect ordering. We note existence of such re-ordering for given equivalent being conjugate (topologically equivalent) some homeomorphic space. observe latter cannot always be chosen order-isomorphic ...

We present a simple algorithm which maintains the topological order of a directed acyclic graph with n nodes under an online edge insertion sequence in O(n) time, independent of the number of edges m inserted. For dense DAGs, this is an improvement over the previous best result of O(min{m 2 log n,m 3 2 + n log n}) by Katriel and Bodlaender. We also provide an empirical comparison of our algorit...

The paper is devoted to variational analysis of set-valued mappings acting from quasimetric spaces into topological spaces with variable ordering structures. Besides the mathematical novelty, our motivation comes from applications to adaptive dynamical models of behavioral sciences. We develop a unified dynamical approach to variational principles in such settings based on the new minimal point...

We present an Õ(n)-time algorithm for maintaining the topological order of a directed acyclic graph with n vertices while inserting m edges. This is an improvement over the previous result of O(n) by Ajwani, Friedrich, and Meyer.

We present a simple algorithm which maintains the topological order of a directed acyclic graph with n nodes under an online edge insertion sequence in O(n) time, independent of the number m of edges inserted. For dense DAGs, this is an improvement over the previous best result of O(min{m 3 2 logn, m 3 2 + n logn}) by Katriel and Bodlaender. We also provide an empirical comparison of our algori...

''Three is a crowd" is an old proverb that applies as much to social interactions as it does to frustrated configurations in statistical physics models. Accordingly, social relations within a triangle deserve special attention. With this motivation, we explore the impact of topological frustration on the evolutionary dynamics of the snowdrift game on a triangular lattice. This topology provides...