Let $\cal{R}$ be the set of all finite graphs $G$ with the Ramsey property that every coloring of the edges of $G$ by two colors yields a monochromatic triangle. In this paper we establish a sharp ...threshold for random graphs with this property. Let $G(n,p)$ be the random graph on $n$ vertices with edge probability $p$. We prove that there exists a function $\widehat c=\widehat c(n)=\Theta(1)$ such that for any $\varepsilon > 0$, as $n$ tends to infinity, $Pr\leftG(n,(1-\varepsilon)\widehat c/\sqrt{n}) \in \cal{R} \right \rightarrow 0$ and $Pr \leftG(n,(1+\varepsilon)\widehat c/\sqrt{n}) \in \cal{R}\ \right \rightarrow 1. A crucial tool that is used in the proof and is of independent interest is a generalization of Szemeredi's Regularity Lemma to a certain hypergraph setting.
In 1963 Oystein Ore wrote this classic volume, which was published in the New Mathematical Library Series. This elegant book has provided students and teachers with an excellent introduction to the ...field of graph theory for close to thirty years. Robin Wilson's revision adds strength to the book by updating the terminology and notation, bringing them in line with contemporary usage. Wilson has added new material on interval graphs, the traveling salesman problem, bracing frameworks, shortest route problems, and coloring maps on surfaces. Most of the diagrams in the book have been redrawn.
The abstract nature of group theory makes its exposition, at an elementary level, difficult. The authors of the present volume have overcome this obstacle by leading the reader slowly from the ...concrete to the abstract, from the simple to the complex, employing effectively graphs or Cayley diagrams to hlep the student visualize some of the structural properties of groups. Among the concrete examples of groups, the authors include groups of congruence motions and groups of permutations. A conscientious reader will acquire a good intuitive grasp of this pwerful subject.
Tisak grafena na tekstroničke uređaje Puchalski, Michal; Skrzetuska, Ewa; Draczynski, Zbigniew ...
Tekstil,
09/2016, Letnik:
65, Številka:
5-6
Conference Proceeding
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Grafen se dokazao kao izvrstan nanomaterijal za suvremene elektroničke namjene kao što su biosenzori, tranzistori ili grijači. Nastojanja su da se ovaj novi nanomaterijal upotrebljava za razvoj ...jedinstvenih tekstroničkih uređaja. Trenutno stanje znanosti o materijalima pokazuje mogućnosti dizajna pametnih tekstila s grafenom. Autori iznose rezultate primjene 2D ugljikove strukture u tekstroničkim uređajima. Primjena novorazvijenih tinti i pasta daju zanimljiva svojstva tekstilu kao što su električna vodljivost i osjetljivost na hlapljive organske spojeve.
This book develops a method to obtain limit theorems for various functionals of random graphs. The method is based on a certain orthogonal decomposition. Janson's results include limit theorems for ...the two standard random graph models, G_{n,p} and G_{n,m}, as well as functional limit theorems for the evolution of a random graph and results on the maximum of a function during the evolution. Janson obtains both normal and nonnormal limits, and the method provides an explanation for the appearance of nonnormal limits. Applications to subgraph counts and to vertex degrees are presented as examples.
U ovom radu istraživano je toplinsko starenje nitril-butadienskog kaučuka (NBR) uz različite udjele grafena (GE). Kompoziti NBR i NBR-GE bili su izloženi ubrzanom toplinskom starenju koje je ...proizvodila zračna cirkulacijska pećnica tijekom sedam dana. Ispitivana su mehanička svojstva, kemijske promjene i toplinska stabilnost uzoraka starenja i čistih uzoraka. Rezultati su pokazali veliko i nehomogeno površinsko oštećenje NBR-a. Stupanj starenja bio je najozbiljniji na rubnom dijelu praznina, dok su se kompoziti NBR-GE prije i poslije starenja neznatno promijenili. S povećanjem koncentracije GE, vlačna čvrstoća se uvećala do maksimalne vrijednosti i smanjila s daljnjim povećanjem koncentracije GE. Ugrađena GE mreža ograničila je kretanje lanaca u smjeru rastezanja i odigrala ulogu u svojstvima kompozita i slojevima GE (sadržavali su funkcionalne skupine −OH, −C=O i C=C) nakon starenja. Ta pojava može ukazivati na veću međupovršinsku adheziju GE i NBR. Dodatno, rezultati dobiveni termogravimetrijskom analizom (TGA) pokazuju da se termička stabilnost NBR-a znatno promijenila s ubrzanim uvjetima toplinskog starenja, ali uz dodatak određene količine GE u NBR, može se poboljšati toplinska stabilnost NBR-a. Kompoziti NBR-GE pokazali su dobra sveobuhvatna svojstva s masenim udjelom GE od 10 %. Prije i nakon toplinskog starenja, mehanizam kvara kompozita NBR-GE pokazao je intergranularne i duktilne prijelome.
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Graphene is foreseen to be the basis of future electronics owing to its ultra thin structure, extremely high charge carrier mobility, high thermal conductivity etc., which are expected to overcome ...the size limitation and heat dissipation problem in silicon based transistors. But these great prospects are hindered by the metallic nature of pristine graphene even at charge neutrality point, which allows to flow current even when a transistor is switched off. A part of the thesis is dedicated to invoke electronic band gaps in graphene to overcome this problem. The concept of quantum confinement has been employed to tune the band gaps in graphene by dimensional confinement along with the functionalization of the edges of these confined nanostructures. Thermodynamic stability of the functionalized zigzag edges with hydrogen, fluorine and reconstructed edges has been presented in the thesis. Keeping an eye towards the same goal of band gap opening, a different route has been considered by admixing insulating hexagonal boron nitride (h-BN) with semimetal graphene. The idea has been implemented in two dimensional h-BN-graphene composites and three dimensional stacked heterostructures. The study reveals the possibility of tuning band gaps by controlling the admixture. Occurrence of defects in graphene has significant effect on its electronic properties. By random insertion of defects, amorphous graphene is studied, revealing a semi-metal to a metal transition. The field of molecular electronics and spintronics aims towards device realization at the molecular scale. In this thesis, different aspects of magnetic bistability in organometallic molecules have been explored in order to design practical spintronics devices. Manipulation of spin states in organometallic molecules, specifically metal porphyrin molecules, is achieved by controlling surface–molecule interaction. It has been shown that by strain engineering in defected graphene, the magnetic state of adsorbed molecules can be changed. The spin crossover between different spin states can also be achieved by chemisorption on magnetic surfaces. A significant part of the thesis demonstrates that the surface-molecule interaction not only changes the spin state of the molecule, but allows to manipulate magnetic anisotropies and spin dipole moments via modified ligand fields. Finally, in collaboration with experimentalists, a practical realization of switching surface–molecule magnetic interactions by external magnetic fields is demonstrated.
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