Obstacle Numbers of Planar Graphs

Given finitely many connected polygonal obstacles $O_1,\dots,O_k$ in the plane and a set $P$ of points in general position and not in any obstacle, the {\em visibility graph} of $P$ with obstacles $O_1,\dots,O_k$ is the (geometric) graph with vertex set $P$, where two vertices are adjacent if the straight line segment joining them intersects no obstacle. The obstacle number of a graph $G$ is the smallest integer $k$ such that $G$ is the visibility graph of a set of points with $k$ obstacles. If $G$ is planar, we define the planar obstacle number of $G$ by further requiring that the visibility graph has no crossing edges (hence that it is a planar geometric drawing of $G$). In this paper, we prove that the maximum planar obstacle number of a planar graph of order $n$ is $n-3$, the maximum being attained (in particular) by maximal bipartite planar graphs. This displays a significant difference with the standard obstacle number, as we prove that the obstacle number of every bipartite planar graph (and more generally in the class PURE-2-DIR of intersection graphs of straight line segments in two directions) of order at least $3$ is $1$.Comment: Appears in the Proceedings of the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017

On colouring point visibility graphs

In this paper we show that it can be decided in polynomial time whether or not the visibility graph of a given point set is 4-colourable, and such a 4-colouring, if it exists, can also be constructed in polynomial time. We show that the problem of deciding whether the visibility graph of a point set is 5-colourable, is NP-complete. We give an example of a point visibility graph that has chromatic number 6 while its clique number is only 4

Biodecolorization of acid violet 19 by Alternaria solani

Microorganisms are the nature’s tools for cleaning the environment. Bioremediation using bacteria, fungi and algae is becoming an attractive option for the treatment of industrial effluents containing awide spectrum of pollutants including dyes and heavy metal ions. In the current research work, the potential of a deuteromycete fungus, Alternaria solani for the removal of a dye, Acid Violet 19 from aqueous solution was studied. The fungus showed promising potential for the decolorization of the dye (88.6%) at a dye concentration of 30 mg/L within a relatively short period of time (four days). But with increase in the contact time, the % decolorization decreased showing that some of the adsorbed dye was desorbed especially in case of higher dye concentrations. The desorption of the dye from the fungal cells at long contact time and higher dye concentrations was considered to be due to higher molecular mass, structural complexity and the presence of inhibitory groups, SO3Na in the dye

Accretion Disks Around Black Holes: Twenty Five Years Later

We study the progress of the theory of accretion disks around black holes in last twenty five years and explain why advective disks are the best bet in explaining varied stationary and non-stationary observations from black hole candidates. We show also that the recently proposed advection dominated flows are incorrect.Comment: 30 Latex pages including figures. Kluwer Style files included. Appearing in `Observational Evidence for Black Holes in the Universe', ed. Sandip K. Chakrabarti, Kluwer Academic Publishers (DORDRECHT: Holland

On the Concept of a Notational Variant

In the study of modal and nonclassical logics, translations have frequently been employed as a way of measuring the inferential capabilities of a logic. It is sometimes claimed that two logics are “notational variants” if they are translationally equivalent. However, we will show that this cannot be quite right, since first-order logic and propositional logic are translationally equivalent. Others have claimed that for two logics to be notational variants, they must at least be compositionally intertranslatable. The definition of compositionality these accounts use, however, is too strong, as the standard translation from modal logic to first-order logic is not compositional in this sense. In light of this, we will explore a weaker version of this notion that we will call schematicity and show that there is no schematic translation either from first-order logic to propositional logic or from intuitionistic logic to classical logic

IMPLEMENTASI FUZZY LOGIC CONTROLLER - MCS 51 UNTUK PENGATURAN TEMPERATUR RUANG DAN PUTARAN MOTOR DC

In this research is method implementation conduct logic fuzzy - MCS 51 and used for roomtemperature arrangement and DC motor rotation were applied Incubator Baby machine. The research desired room temperature arrangement used to heater element and motor rotation arrangement as stabilize room temperature. The condition is wanted in this research is although trouble at fickle burden, but room temperature stability remain to earn to be defended according to desire. Advantages are system will become more stable, this will seen at respond of yielded output as well as system resilience to trouble. With easier system controller logic fuzzy to be adapted for various condition of yielding reliable and stable control syste

Is the expressive vocabulary of young Cantonese speakers noun or verb dominated?

The spontaneous utterances produced by 492 Cantonese-speaking children aged 36-60 months in 30-minute toy play contexts were collected. The incidence and percentage of different lexical classes, the ratio of noun and verb types and tokens were calculated. A statistically significant predominance of verb usage was found in the expressive utterances of the children. No similar predominance was found for nouns. Linguistic, cultural and contextual variables possibly underlying these outcomes are explored and discussed.postprin

The acquisition of Cantonese classifiers by preschool children in Hong Kong

The Cantonese language has a complex classifier system and young learners need to pay attention to both the semantics and syntax of classifiers. This study investigated the repertoire of classifiers produced by 492 Cantonese-speaking preschoolers in three age groups (3 ;0, 4 ;0 and 5 ;0). Spontaneous utterances produced in 30-mmute toy-play contexts were collected and transcribed. Analyses identified a productive repertoire of 73 classifiers in the utterances, which could be appropriately classified into the typology proposed in the present study. An age-related increase in the number of classifier types per child as well as the repertoire size of each group was found. g03 (CL) was widely used as the general classifier by the young children. It was also discovered that the three-year-olds were already showing signs of grasping the basic syntax of classifiers. Cognitive, linguistic and contextual influences presumed to shape the evidence are discussed. © 2007 Cambridge University Press.published_or_final_versio

On local structures of cubicity 2 graphs

A 2-stab unit interval graph (2SUIG) is an axes-parallel unit square intersection graph where the unit squares intersect either of the two fixed lines parallel to the $X$-axis, distance $1 + \epsilon$ ($0 < \epsilon < 1$) apart. This family of graphs allow us to study local structures of unit square intersection graphs, that is, graphs with cubicity 2. The complexity of determining whether a tree has cubicity 2 is unknown while the graph recognition problem for unit square intersection graph is known to be NP-hard. We present a polynomial time algorithm for recognizing trees that admit a 2SUIG representation