Discrete and Continuous Time Modulated Random Walks with Heavy-Tailed Increments

We consider a modulated process S which, conditional on a background process X, has independent increments. Assuming that S drifts to −∞ and that its increments (jumps) are heavy-tailed (in a sense made precise in the paper), we exhibit natural conditions under which the asymptotics of the tail distribution of the overall maximum of S can be computed. We present results in discrete and in continuous time. In particular, in the absence of modulation, the process S in continuous time reduces to a Lévy process with heavy-tailed Lévy measure. A central point of the paper is that we make full use of the so-called “principle of a single big jump” in order to obtain both upper and lower bounds. Thus, the proofs are entirely probabilistic. The paper is motivated by queueing and Lévy stochastic networks.     

Lévy processes and Fourier multipliers

We study Fourier multipliers which result from modulating jumps of Lévy processes. Using the theory of martingale transforms we prove that these operators are bounded in Lp(Rd) for 1<p<∞ and we obtain the same explicit bound for their norm as the one known for the second order Riesz transforms.     

Calculation of the van der Waals volumes of organic molecules

A new and more precise method is proposed for calculating van der Waals atomic and molecular volumes of organic compounds. The method provides for intersections of three or more spheres at one point of space. Such a possibility is essential for calculating the volumes of sterically overcrowded molecules and of molecules with intramolecular hydrogen bonds. A computer program for IBM PC/AT(XT) is developed. Depending on the atomic environment in the molecule, the average values of the volume increments for atoms C, N, O, H, F, Cl, and S are obtained using the data from the Cambridge Structural Database.N. S. Kurnakov Institute of General and Inorganic Chemistry, Russian Academy of Sciences, Moscow 117071. Translated from Izvestiya Akademii Nauk, Seriya Khimicheskaya, No. 4, pp. 922–931, April, 1992.     

A law of the iterated logarithm for processes with independent increments

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103Rh-NMR-spektroskopischer Nachweis der gemischten Nonahalogenodirhodate(III), [Rh2ClnBr9–n]3−, n = 0–9

¹⁰³Rh NMR Spectroscopic Evidence of Mixed Nonahalogenodirhodates(III), [Rh₂Cl_nBr_9–n]^3?, n = 0–9 On heating a mixture of the tetrabutylammonium salts (TBA)₃[Rh₂Cl₉] and (TBA)₃[Rh₂Br₉] at 60°C in propylenecarbonate the complete system of the mixed nonahalogenodirhodates(III) [Rh₂Cl_nBr_9–n]^3?, n = 0–9 is formed. In the ¹⁰³Rh nmr spectra 40 different species have been detected, 16 with two equivalent ¹⁰³Rh atoms each resulting in one singlet and 24 with inequivalent ¹⁰³Rh atoms each pair giving two resonances. The signals of the geometric isomeres are not resolved. All 64 expected resonances are really observed. By additional measuring of the ¹⁰³Rh nmr spectra of the fractions n = 0–4 separable by ion exchange chromatography on DEAE cellulose, and utilizing characteristic increments of chemical shifts the complete and unambiguous assignment of all signals is achieved.     

Persistence of sums of correlated increments and clustering in cellular automata

Let $T$ be the first return time to $(?\infty ,0]$ of sums of increments given by a functional of a stationary Markov chain. We determine the asymptotic behavior of the survival probability, $\mathbb{P}(T\ge t)～C{t}^{?1∕2}$ for an explicit constant $C$. Our analysis is based on a connection between the survival probability and the running maximum of the time-reversed process, and relies on a functional central limit theorem for Markov chains. As applications, we recover known clustering results for the 3-color cyclic cellular automaton and the Greenberg–Hastings model, and we prove a new clustering result for the 3-color firefly cellular automaton.     

Experimental and Theoretical Investigation on the Thermochemistry of 3-Methyl-2-benzoxazolinone and 6-Nitro-2-benzoxazolinone

The determination of the reliable thermodynamic properties of 2-benzoxazolinone derivatives is the main goal of this work. Some correlations are established between the energetic properties determined and the structural characteristics of the title compounds, and the reactivity of this class of compounds is also evaluated. Static-bomb combustion calorimetry and high-temperature Calvet microcalorimetry were used to determine, respectively, the standard molar enthalpies of formation in the solid state and the standard molar enthalpies of sublimation, both at T = 298.15 K. Using the results obtained for each compound, the respective gas-phase standard molar enthalpy of formation was derived. High-level quantum chemical calculations were performed to estimate the same property and the results evidence good accordance. Moreover, the gas-phase relative thermodynamic stability of 2-benzoxazolinone derivatives was also evaluated using the respective gas-phase standard molar Gibbs energy of formation. In addition, the relationship between the energetic and structural characteristics of the benzoxazolinones is presented, evidencing the enthalpic increments associated with the presence of a methyl and a nitro groups in the molecule, and this effect is compared with similar ones in other structurally related compounds.     

Uniform dimension results of multi-parameter stable processes

The problem of uniform dimensions for multi-parameter processes, which may not possess the uniform stochastic Hölder condition, is investigated. The problem of uniform dimension for multi-parameter stable processes is solved. That is, ifZ is a stable (N,d, α)-process and αN ?d, then $\forall E \subseteq \mathbb{R}_ + ^N , \dim Z\left( E \right) = \alpha \cdot \dim E$ holds with probability 1, whereZ(E) = {x : ?t ∈E,Z _t =x} is the image set ofZ onE. The uniform upper bounds for multi-parameter processes with independent increments under general conditions are also given. Most conclusions about uniform dimension can be considered as special cases of our results.     

Gas-chromatographic method of evaluation ofn-alkanol ability for self-association in pure liquid

The values of the gas-chromatographic indicator reflecting the capacity of analytes for self-association in pure liquids, δT _b.p., were estimated for C₁–C₉ and C₁₁ n-alkanols by capillary gas chromatography on a nonpolar stationary phase under isothermal conditions. The δT _b.p. values ofn-alkanols, found as the difference between the boiling points measured directly and those calculated from GC data, are correlated with thermodynamic characteristics of the formation ofn-alkanol associates in pure liquids. Usingn-alkanols as analytes with insignificant temperature increments of the retention indices, it was shown that the δT _b.p. values can be determined under conditions used in gas chromatography with temperature programming. In this way a single chromatographic run can be used to compare the capacities for self-association of analytes boiling over a wide temperature range. The C₂–C₉ n-alkanethiols, which are not associated in neat liquids, have negative δT _b.p. values. An interpretation of this finding is proposed. Translated fromIzvestiya Akademii Nauk, Seriya Khimicheskaya, No. 2, pp. 315–318 February, 2000.