Asymptotic expansions in the integral and local limit theorems in banach spaces with applications to ω-statistics

LetB be a real separable Banach space and letX,X ₁,X ₂,...∈B denote a sequence of independent identically distributed random variables taking values inB. DenoteS _n =n ^?1/2(X ₁+...X _n ). Let π:B→R be a polynomial. We consider (truncated) Edgeworth expansions and other asymptotic expansions for the distribution function of the r.v. π(S _n ) with uniform and nonuniform bounds for the remainder terms. Expansions for the density of π(S _n ) and its higher order derivatives are derived as well. As an application of the general results we get expansions in the integral and local limit theorems for ω-statistics $$\omega _n^p (q)\mathop { = n^{{p \mathord{\left/ {\vphantom {p 2}} \right. \kern-\nulldelimiterspace} 2}} }\limits^\Delta \smallint _{(0,1)} \{ F_n (x) - x\} ^p q(x)dx$$ and investigate smoothness properties of their distribution functions. Herep≥2 is an even number,q: [0, 1]→[0, ∞] is a measurable weight function, andF _n denotes the empirical distribution function. Roughly speaking, we show that in order to get an asymptotic expansion with remainder termO(n ^?α), α<p/2, for the distribution function of the ω-statistic, it is sufficient thatq is nontrivial, i.e., mes{t∈(0, 1):q(t)≠0}>0. Expansions of arbitrary length are available provided the weight functionq is absolutely continuous and positive on an nonempty subinterval of (0, 1). Similar results hold for the density of the distribution function and its derivatives providedq satisfies certain very mild smoothness condition and is bounded away from zero. The last condition is essential since the distribution function of the ω-statistic has no density whenq is vanishing on an nonempty subinterval of (0, 1).     

Electric field assisted charge carrier photogeneration in poly(spirobifluorene-co-benzothiadiazole)

The dynamics of charge carrier generation in poly(spirobifluorene-co-benzothiadiazole) was investigated by electric field-induced fluorescence quenching and differential absorption measurements. Three different time domains of carrier generation have been identified: an ultrafast phase, a subnanosecond phase, and an entire lifetime phase. The charge generation efficiencies during the first and second phases were found to be almost independent of temperature, being about 25% and 10%, respectively, at an applied electric field of 1.3×10(6)?V/cm, while the generation efficiency during the third phase increases from 2% at 80 K to 10% at room temperature. The results of transient spectroscopy measurements and quantum chemical calculations suggest an intramolecular charge transfer for about 1 ps from the alkoxy-substituted fluorene side group to the benzothiadiazole subunit of the main chain. The formation and evolution of the resulting charge transfer states determine the way of charge carrier generation.     

Elastic properties of chemically modified baker's yeast cells studied by AFM

Chemical pretreatment is widely used to facilitate transformation of living cells when foreign components are introduced into a cell through the cell wall. The influence of appropriate chemicals on the wall properties and mechanism of transformation is still a matter of intensive studies. Saccharomyces cerevisiae cells (also known as baker's yeast) were investigated by atomic force microscopy (AFM). The cell walls were modified by lithium acetate and dithiothreitol. The AFM imaging was performed in liquid water‐based environment. The living cells were fixed by trapping into the holes of a polycarbonate membrane. Mechanical and morphological properties of initial intact cells and treated cells were investigated. The increased stiffness of the chemically treated cells was observed. As deduced from the applied theoretical Hertz‐Sneddon model, the treated cells show completely different response mechanism to applied mechanical pressure in comparison with the intact cells. Also, the increased roughness of the cell wall of the treated yeasts was observed. Copyright © 2011 John Wiley & Sons, Ltd.     

Impact of intramolecular twisting and exciton migration on emission efficiency of multifunctional fluorene-benzothiadiazole-carbazole compounds

Novel donor-acceptor compounds consisting of singly bonded fluorene (Fl), benzothiadiazole (BT), and carbazole (Cz) functional units in the same molecule were investigated. Analysis of the optical spectra and fluorescence transients of the compounds revealed the domination of intramolecular charge transfer (ICT) states with high fluorescence quantum yield (72%-85%). A similar Cz-Fl-Cz compound exhibiting 100% fluorescence quantum yield and no ICT character was also studied as a reference to reveal the impact of electron-accepting BT groups. Thorough examination of the optical properties of the compounds in different media, i.e., dilute solution and polymer matrix, indicated their twisted conformations due to steric hindrance in the ground state and flattened geometry in the excited state for both reference and ICT compounds. Remarkable fluorescence efficiency losses (amounting to 70%) observed upon casting the molecular solutions into neat films were determined to originate from the low-fluorescent twisted conformers and migration-facilitated exciton quenching. The majority of emission efficiency losses (over 70%) were caused by the twisted conformers, whereas only less than 30% by exciton-migration-induced nonradiative deactivation.     

Multicoordinational excited state twisting of indan-1,3-dione derivatives

Excited state relaxation of indan-1,3-dione derivatives with different substituents attached to the phenyl ring and with the bridged amino group was investigated by means of the steady-state fluorescence and femtosecond time-resolved absorption pump–probe spectroscopy. Bridging of the amino group increases the fluorescence quantum yield and the excited state lifetime. Analysis of the results indicates that the phenyl ring twisting around a single central bond leads to the nonradiative state formation and to subsequent fast relaxation to the ground state. Double bond twisting takes place in molecules with the bridged amino group and causes a large Stokes shift and slightly slower excited state relaxation.     

Exciton diffusion and relaxation in methyl-substituted polyparaphenylene polymer films

Exciton diffusion in ladder-type methyl-substituted polyparaphenylene film and solution was investigated by means of femtosecond pump-probe spectroscopy using a combined approach, analyzing exciton-exciton annihilation, and transient absorption depolarization properties. We show that the different views on the exciton dynamics offered by anisotropy decay and annihilation are required in order to obtain a correct picture of the energy transfer dynamics. Comparison of the exciton diffusion coefficient and exciton diffusion radius obtained for polymer film with the two techniques reveals that there is substantial short-range order in the film. Also in isolated chains there is considerable amount of order, as revealed from only partial anisotropy decay, which shows that only a small fraction of the excitons move to differently oriented polymer segments. It is further concluded that interchain energy transfer is faster than intrachain transfer, mainly as a result of shorter interchain distances between chromophoric units.     

Dispersion of phase response of dye solutions using picosecond excitation

Dispersion of phase response (frequency-dependent light-induced variations of the refractive index) of a solution of bleachable dye 3955 due to variation in the populations of the ground and excited states of molecules is investigated using wavelength-tuned picosecond light pulses. On the wavelengths of the dye absorption band the refractive index increases under bleaching, and in the fluorescence band it decreases, what is in qualitative agreement with the expected picture.     

Triphenylamino or 9-phenyl carbazolyl-substituted pyrimidine-5-carbonitriles as bipolar emitters and hosts with triplet harvesting abilities

To obtain highly efficient organic semiconductors exhibiting fast emission decays, triplet-harvesting abilities and good bipolar charge-transporting properties for optoelectronic applications, compounds containing triphenylamine or 9-phenylcarbazole as donor moieties and pyrimidine-5-carbonitrile as electron-withdrawing unit were synthesised. Toluene solutions of the compounds demonstrated high photoluminescence quantum yields reaching 98%. As required for electroluminescent device applications, compound containing triphenylamino moiety showed high mobilities of both electrons and holes, which reached 4.4 × 10^?4 cm²/V × s and 7.3 × 10^?3 cm²/V × s, respectively at electric field of 3.6 × 10⁵ V/cm. This triplet-harvesting mechanism was confirmed by the theoretical and experimental studies including a femtosecond transient absorption pump?probe technique and time-resolved electroluminescence spectroscopy. Pure-blue and greenish-blue fluorescent organic light-emitting diodes (OLEDs) with external quantum efficiency (EQE) reaching 7% and 6%, corresposndingly, were obtained using the newly synthesised compounds as emitters. The operation time (T50) of ca. 650 h were observed for blue OLED and of ca. 3800 h for greenish-blue OLED until reaching the half initial brightness (100 cd/m²). EQE of more than 20% and T50 exceeding 20,000 h were observed for electroluminescent devices based on emitter characterised by triplet?triplet annihilation and thermally activated delayed fluorescence which was utilised to test hosting properties of the differently donor-substituted pyrimidine-5-carbonitriles.     

On the asymptotical behavior of the constant in the Berry-Esseen inequality

LetF be the distribution function of a sumS _n ofn independent centered random variables, denote the standard normal distribution function and its density. It follows from our results that

Mode-locking of neodymium lasers by glasses doped with PbS nanocrystals

Nonlinear optical absorption properties of silicate glasses doped by the PbS nanocrystals were investigated by means of the picosecond pump-probe absorption spectroscopy and absorption bleaching technique. The glass samples were used as saturable absorbers for passive mode-locking of Nd:YAG and Nd:glass lasers. Application of the PbS doped glass together with the active mode-locking and laser cavity quality control enabled the stable of generation of 28 ps and 5 ps duration pulses in Nd:YAG and Nd:glass lasers respectively. PACS 42.60.Fc; 42.70.Hj; 78.47.+p