Cycle-maximal triangle-free graphs

We conjecture that the balanced complete bipartite graph _{K⌊n/2⌋,⌈n/2⌉}$K_{\lfloor n/2\rfloor ,\lceil n/2\rceil }$ contains more cycles than any other n$n$-vertex triangle-free graph, and we make some progress toward proving this. We give equivalent conditions for cycle-maximal triangle-free graphs; show bounds on the numbers of cycles in graphs depending on numbers of vertices and edges, girth, and homomorphisms to small fixed graphs; and use the bounds to show that among regular graphs, the conjecture holds. We also consider graphs that are close to being regular, with the minimum and maximum degrees differing by at most a positive integer k$k$. For k=1$k=1$, we show that any such counterexamples have n≤91$n\le 91$ and are not homomorphic to _C5$C_5$; and for any fixed k$k$ there exists a finite upper bound on the number of vertices in a counterexample. Finally, we describe an algorithm for efficiently computing the matrix permanent (a #P$\#P$-complete problem in general) in a special case used by our bounds.     

Rational Design of Poly(2,7‐Carbazole) Derivatives for Photovoltaic Applications

A reliable model that can be used to estimate the electronic properties (i.e., the HOMO, LUMO, and band gap energies) of conjugated polymers would be a great tool for applications in organic electronics such as light‐emitting diodes, field‐effect transistors, and photovoltaic cells. Recently, poly(2,7‐carbazole) derivatives have shown promising results when used as an active donor layer in bulk heterojunction photovoltaic cells with power conversion efficiency exceeding 7%. By using a simple correlation between density functional theory (DFT) theoretical calculations performed on six model compounds (using the repeating unit) and experimental data from the six corresponding polymers, an accurate estimation of the HOMO energy level, the LUMO energy levels, and the band gap of several poly(2,7‐carbazole) derivatives was obtained. According to the theoretical data obtained for more than one hundred repeating units, fourteen new copolymers that can be used as p‐type materials in bulk heterojunction solar cells were selected and synthesized. Experimental data obtained from these materials were then used to refine the correlation between DFT and experimental data of poly(2,7‐carbazole) derivatives.

     

Hydrogen bonding,polarity and matrix effects on the spectroscopic and photophysical properties of some N- and 3-substituted derivatives of carbazoles

Fluorescence spectra and photophysical properties of N-cyano and N-carboethoxy carbazole derivatives have been compared to the equivalent 3-substituted compounds in fluid polar and unpolar solutions and in a low temperature rigid matrix at 77 K. The 3-carboethoxy derivatives have been shown to form an excited state complex (exciplex) with ethanol in fluid solutions. On the other hand the photophysical properties of the N-substituted derivatives are much affected by the solvent polarity in fluid solutions in that the radiationless decay rate constants show a marked increase in these media. A tentative explanation has been given in terms of the relative energy gap existing between the ¹L_b and the ¹L_a states of these molecules.     

EXTERNAL HEAVY ATOM EFFECTS ON THE S1 AND T1 ELECTRONIC STATES OF INDOLE

Abstract— The absorption, fluorescence and phosphorescence spectra along with the phosphorescence decay function of indole perturbed by various amounts of halocarbons have been studied in a 1:1 ethanol-ether glass at 77 K. For carbon tetrachloride. chloroform, halothane and methylene chloride used as quenchers. the biexponential nature of the phosphorescence decay prompted us to assume the existence of a triplet state complex (exciplex) between indole and the halocarbons. On the other hand. propyl bromide gives rise to a non-exponential decay and to an increase in the phosphorescence intensity suggesting the occurrence of a normal external spin-orbital coupling interaction between indole and the propyl bromide molecule.     

Temperature-induced structural and permeability changes in dioctadecyldimethylammonium bromide (DODAB) vesicles: a fluorescence investigation using 2-[(p-methylamino)phenyl]-3,3-dimethyl-5-carboethoxy-3H-indole as a probe

An investigation of the temperature dependence of the fluorescence spectral characteristics of 2-[(p-methyl-amino)phenyl]-3,3-dimethyl-5-carboethoxy-3H indole (I) in aqueous micelles(sodium dodecyl sulfate (SDS), cetyltrimethylammonium bromide (CTAB)) and surfactant vesicles (dioctadecyldimethylammonium bromide (DODAB)) is presented. The gel-to-liquid crystalline phase transition temperature T_c, determined to be approximately 309 K (36°C) for DODAB vesicles, is in close agreement with the value reported previously. A pretransition at 294 K (21°C) has also been obtained. The blue shift in the fluorescence maximum and the increase in bandwidth are accounted for by the displacement of molecule I towards the interior of the bilayer as a function of temperature. Arrhenius plots for the non-radiative decay processes competing with fluorescence as a function of temperature show relatively high values for the activation energy above the phase transition temperature, indicating the displacement of molecule I to a new, more viscous, less polar site compared with its initial location in DODAB. The highest value of the activation energy in water indicates that the decay dynamics of this molecule are different in water than in the organized media studied here.     

A first principles calculations and experimental study of the ground- and excited-state properties of ladder oligo(p-aniline)s

The molecular structure of three ladder oligo(p-aniline)s, 5,11-diethyl-6,12-dimethylindolo[3,2-b]carbazole (DIMER 2P), 14-ethyl-5,8-dihydro-diindolo[3,2-b:2',3'-h]carbazole (TRIMER 2P), and 5,8,14-triethyl-diindolo[3,2-b:2',3'-h]carbazole (TRIMER 3P) were investigated by first principles calculations at the Hartree-Fock (HF6-31G*) and density functional theory (DFTB3LYP6-31G*) levels. It is found that the agreement between theoretical and x-ray geometrical parameters is good and rather similar for both theoretical methods. The nature and the energy of the first two singlet-singlet electronic transitions have been obtained by Zerner intermediate neglect of differential overlap/spectroscopy semiempirical calculations performed on the HF6-31G* and DFTB3LYP6-31G* optimized geometries, as well as time-dependent density functional theory (TDDFT) calculations performed on the DFTB3LYP6-31G* optimized structures. For all the compounds and for all the theoretical approaches, it is observed that the S(1)<--S(0) electronic transition (pipi*) is weakly allowed and polarized along the short axis (y) of the molecule. On the other hand, the S(2)<--S(0) electronic transition of each oligomer possesses a much larger oscillator strength and is polarized along the long (x) molecular axis. It is found that TDDFT calculations provide the best overall agreement between the energies and the corresponding optical transitions obtained from the absorption bands (0-0 peaks) measured in dichloromethane as well as providing a good evaluation of the bathochromic shifts caused by the increase in the conjugation length or by the presence of extra alkyl chains on the nitrogen atoms in TRIMER 3P compared to TRIMER 2P.     

Is the Kβ/Kα x-ray intensity ratio dependent upon the energy of an inducing proton?

K_β/K_αX-ray intensity ratios have been measured for various elements between Z = 29 and Z = 79 for incident proton energies of 23.6, 32.1 and 43.6 MeV. The results yield no evidence for a variation in ratio with particle energy.