Probability Space of Stochastic Fractals

We develop a general method for the construction of a probability structure on the space F of random sets in ℝ. For this purpose, by using the introduced notion of c-system, we prove a theorem on the unique extension of a finite measure from a c-system to the minimal c-algebra. The obtained structure of measurability enables one to determine probability distributions of the c-algebra of random events sufficient, e.g., for the so-called fractal dimensionality of random realizations to be considered as a measurable functional on F.__________Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, No. 11, pp. 1467–1483, November, 2004.     

Whole-field determination of isoclinic parameter by five-step color phase shifting and its error analysis

Combining color imaging with phase shifting, a technique named five-step color phase shifting is presented to determine the whole-field isoclinic parameter. Relevant theory is derived and explicit conditions for directly determining the isoclinic parameter in the range of [0,π/2] are given. The unloaded light intensity of the model is systematically studied. A color camera recorded five isoclinic images coupled with isochromatics from a plane polariscope with five different settings, respectively. Experiments have been carried out with a circular disk under diametral compression and errors have been analyzed and estimated. This technique utilizes white light, which avoids undefined isoclinics near the locations where the isochromatics exist and will have active effect on experimental stress analysis and structural strength design.     

Effect of External Acidity of Mordenite-Supported Catalysts on the 2,2-Dimethylbutane Content in Hydroisomerization Products of n-Hexane

We have used potentiometric titration with tetrabutylammonium hydroxide to determine the acid center content on the outer surface of dealuminated natural and synthetic mordenites. We have established a symbatic relationship between the 2,2-dimethylbutane content in the hydroisomerization products of n-hexane on dealuminated palladium-containing mordenites and the number of their external acid centers. We have studied the possibility of partial deactivation of such centers during ion-exchange deposition of palladium on the catalysts, using a tetraammine palladium solution.     

Two-color resonance photoionization spectrum of nickelocene in a supersonic jet

Two-color photoionization of nickelocene molecules cooled in a supersonic jet is performed using a tunable nanosecond pulsed laser. The first stage of the multiphoton excitation is the transition from the highest occupied molecular orbital of nickelocene to the lowest Rydberg level. Conditions are found under which molecular ions (η ⁵-C₅H₅)₂Ni⁺ are the only product of the multiphoton ionization in the one-color experiment. Irradiation of an excited molecule by an intense pulse of another laser increases significantly the yield of molecular ions. The dependence of the yield of (η⁵-C₅H₅)₂Ni⁺ ions on the frequency of the second laser makes it possible to determine the adiabatic ionization potential of nickelocene as 6.138±0.012eV.     

Plastic multipliers as driving variables of numerical simulation in elastoplasticity

Statics of elasto-plastic media is stated in terms of eigenstrains acting upon a background elastic problem with fixed (initial) stiffness. In order to minimize the number of unknowns and to provide computationally cheap algorithms plastic multipliers are used as main driving variables. Fixed-point type iterations are suggested for computing plastic multipliers within the load increment. Numerical experiments results are shown to be in good correlation with other software results. A range of problems is outlined where the usage of the proposed algorithms can be advantageous.     

Bessel框架及其摄动

本文进一步研究了Bessel框架的性质,给出其稳定性和摄动的几个有意义的结果。     

Some Computational Aspects of Processing and Classification of Observations of Mental Impairments during the Acute Period of Concussion

A number of fast computer procedures are described to find the minimum error vectors for observations of patients with cranial-cerebral traumas of a special type.     

Reflection spectrum of a cholesteric liquid crystal with structural defects

An expression is obtained for the reflection coefficient of circularly polarized light normally incident on the film of a cholesteric liquid crystal with a variable helix pitch. It is shown that, in the case of a single defect (local change in the helix pitch), the spectrum of light reflection from a cholesteric acquires a dip corresponding to the defect mode. New qualitative features appear in the reflection spectrum of a cholesteric with two defects as the distance between them varies.     

Spectral Analysis of Powers of the Operator (Vf)(x)=q(x)∫0 xw(t)f(t),dt

Mathematical Notes -