The Discounted Limit Theorems

The large deviation theorems, exponential inequalities and a non-uniform estimate of the Berry–Esséen theorem in a discounted version are proved.Dedicated to Professor Vytautas Statulevičius on the occasion of his 75th birthday.     

Changes of the solution pH due to exposure by high-voltage electric pulses

The change of the pH of a NaCl solution (139-149 mM NaCl) buffered with 5-15 mM sodium phosphates (pH 7.4) during electromanipulation was studied. It has been determined that an increase in the pH value of electroporation solution of a whole chamber volume, caused by the application of electric field pulses, commonly used in cell electromanipulation procedures, can exceed 1-2 pH units. Several materials for the cathode were tested. In all cases a stainless steel anode was utilized. The aluminum cathode gave a two-fold greater DeltapH in comparison with platinum, copper or stainless steel cathodes. In addition, a substantial release of aluminum (up to 1 mg/l) from the cathode was observed. It has also been found that the shift in pH depended on the medium conductivity: DeltapH of the solution, in which sucrose was substituted for NaCl, was about 5 times less. On the basis of the results obtained here, to avoid the plausible undesirable consequences of the cathodic electrolysis processes, in particular under the conditions of strong electric treatment, it could be recommended that chambers with aluminum electrodes not be utilized and one should use strongly buffered solutions of low conductivity and alternating current (sine or square wave) bipolar electric pulses.     

Femtosecond spectroscopy of optical excitations in single-walled carbon nanotubes: evidence for exciton-exciton annihilation

Frequency-resolved femtosecond transient absorption spectra and kinetics measured by optical excitation of the second and first electronic transitions of the (8,3) single-walled carbon nanotube species reveal a unique mutual response between these transitions. Based on the analysis of the spectra, kinetics, and their distinct amplitude dependence on the pump intensity observed at these transitions, we conclude that these observations originate from both the excitonic origin of the spectrum and nonlinear exciton annihilation.     

Asymptotic Expansion of the Distribution Density Function for the Sum of Random Variables in the Series Scheme in Large Deviation Zones

The work is designated for obtaining asymptotic expansions and determination of structures of the remainder terms that take into consideration large deviations both in the Cramer zone and Linnik power zones for the distribution density function of sums of independent random variables in a triangular array scheme. The result was obtained using general Lemma 6.1 of Saulis and Statuleviius in Limit Theorems for Large Deviations (Kluwer, 1991) and joining the methods of characteristic functions and cumulants. The work extends the theory of sums of random variables and in a special case, improves S. A.Book's results on sums of random variables with weights.     

Electrochemical modification of Bi2S3 coatings in a nickel plating electrolyte

The electrochemical behavior of Bi₂S₃ coatings in Watts nickel plating electrolyte was investigated using the cyclic voltammetry, electrochemical quartz crystal microbalance, X-ray diffraction, and energy dispersive X-ray analysis methods. During the bismuth sulfide coating reduction in Watts background electrolyte in the potential region from −0.4 to −0.6 V, the Bi₂S₃ and Bi(III) oxygen compounds are reduced to metallic Bi, and the decrease in coating mass is related to the transfer of S²⁻ ions from the electrode surface. When the bismuth sulfide coating is reduced in Watts nickel plating electrolyte, the observed increase in coating mass in the potential region −0.1 to −0.4 V is conditioned by Ni²⁺ ions reduction before the bulk deposition of Ni, initiated by Bi₂S₃. In this potential region, the reduction of Bi(III) oxygen compounds can occur. After the treatment of as-deposited bismuth sulfide coating in nickel plating electrolyte at E = −0.3 V, the sheet resistance of the layer decreases from 10¹³ to 500–700 Ω cm. A metal-rich mixed sulfide Ni₃Bi₂S₂–parkerite is obtained when as-deposited bismuth sulfide coating is treated in Watts nickel plating electrolyte at a potential close to the equilibrium potential of the Ni/Ni²⁺ system and then annealed at temperatures higher than 120 °C.     

Excited-state dynamics of carotenoids in light-harvesting complexes. 2. Dissecting pulse structures from optimal control experiments

Dispersed multipump-probe (PPP) spectroscopy was used to explore the role of saturation, annihilation, and structured pulses in recent coherent control experiments on the light-harvesting 2 complex from Rhodopseudomonas acidophila (Herek et al. Nature 2002, 417, 533). We discuss the complimentary aspects between the PPP technique and coherent control studies, in particular the ability to dissect complicated pulse structures and the utility in exploring incoherent mechanisms. With the aid of a simple multistate model involving only population dynamics, we illustrate how the optimized structured pulses may be explained in terms of an interplay between excited-state populations, saturation, and annihilation. Furthermore, we discuss the experimental conditions that are required for incoherent effects to contribute to control experimental signals, with particular emphasis on pulse intensities, and show that the optimization of a ratio of conservative signals (i.e., not modulated by external dynamics) is required to exclude saturation effects from coherent control studies.     

Temperature effects on femtosecond transient absorption kinetics of semiconducting single-walled carbon nanotubes

We report femtosecond transient absorption kinetics measured for selected semiconducting single-walled carbon nanotubes at different temperatures between 77 and 290 K. The nanotubes are embedded in a thin polymethylmethacrylate film, and the dominance of individual species enabled to probe selectively the kinetics associated with two desired tube types, the (6,5) and (7,5) tubes. A strikingly similar temperature dependence is found between the maximum change in the amplitude of transient absorption kinetics, the overall decay time and steady-state fluorescence emission intensity. The simplest explanation for our data is that the temperature dependence of the fluorescence intensity and the exciton decay kinetics are dominated by nonradiative decay and that the radiative decay rate is weakly temperature dependent.