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Using the matrix approach we prove that the sequence of sampling functions is always complete in the cases of critical sampling and oversampling.
      
At last, we discuss the series expressions of these functions and give a Box-counting dimension estimation of "critical" fractal interpolation functions by using our smoothness results.
      
there exists a C∞ rank-1 map f: I2→R1 such that f(A) has nonempty interior for some subset A ?I2 of critical points with finite Hausdorff dimension.
      
The modeling of defect outlines that exhibit a great variety of defect shapes is usually modeled as a circle, which causes the errors of critical area estimation.
      
The dependences of critical current density Jc on the interlayer coupling strength and magnetic field in Bi2212 crystals were obtained by measuring the magnetic loop of the crystals with different interlayer coupling strengths.
      
For the static model, direct and inverse problems of resource allocation were solved, and the set of critical resources was determined.
      
A Theoretical Graph Method for Search and Analysis of Critical Phenomena in Biochemical Systems.
      
A Theoretical Graph Method for Search and Analysis of Critical Phenomena in Biochemical Systems.
      
Experimental Determination of the Surface Energy of Critical Nuclei During the Nucleation of Supersaturated Vapor
      
Theoretical substantiation of the empirical method for determining the surface (or excess) energy of critical nuclei was performed within the framework of thermodynamic approach.
      
Characteristics of critical nuclei were determined based on the studies of the nucleation of supersaturated vapors of glycerol in the vicinity of its melting point and the critical temperature of carrier gas.
      
The effect of the specific features of physicochemical parameters of the studied substance and carrier gas on the parameters of critical nuclei was revealed.
      
Experimental values of the surface energy of critical nuclei were compared with those calculated by the droplet model.
      
The necessity for the allowance for the temperature dependence of the surface energy of critical nuclei was demonstrated.
      
The values of critical micellization concentration (CMC) and excess free energy of adsorption were determined from tensiometric measurements.
      
The aggregation numbers and radii of micelles, the hydrophilic group area, and the parameters of critical compaction of micelles are calculated from the data on fluorescence quenching by hexadecylpyridinium bromide.
      
Micellar and thermodynamics data were obtained from the temperature dependence of critical micelle concentrations in various aqueous mixtures of ethanol.
      
The choice of critical values for developing electron-stimulated discharges (ESDs) in insulator covers of spacecraft is substantiated.
      
Specifically, a bifurcation of optimal solutions is found, the existence of critical inclination is demonstrated, and a partial classification of the structure of optimal control is performed.
      
An experimental method for determination of critical conditions of condensation of metal propellants of electric jet engines (EJEs) on the surfaces of materials of spacecraft thermoregulating covers is presented.
      
 

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