The results of a complex statistical, correlation and fractal analysis of distributions of the magnitude of the real component of the elements of the Jones matrix polycrystalline films of biological fluids of different biochemical composition are presented. The magnitudes and ranges of changes in the set of statistical, correlation, and fractal moments of the 1st to 4th orders, which characterize the Jones-matrix images of dendritic, spherolithic, and combined networks of biological crystals, are determined. A classification system is proposed for the polarization manifestations of the optically anisotropic properties of such polycrystalline structures for the development of the principles for the differential diagnosis of pathological conditions of human organs.
We present a formula for classical solutions for time- and space-fractional kinetic equation (also known as fractional diffusion equation) and deviation time variable is given in terms of the Fox’s H-function, using the step by step method. This equations describe fractal properties of real data arising in applied fields such as turbulence, hydrology, ecology, geographic, air pollution, economics and finance.
A theoretical basis for the method of polarization-interference mapping of optically thin polycrystalline films of human biological fluids is given. The coordinate distributions of the value of the local contrast of the interference distributions of the polarization-inhomogeneous microscopic images of polycrystalline films of the synovial fluid of the human joint are investigated. In the framework of the statistical (statistical moments of the 1st-4th order) approaches, objective criteria for the distribution of the values of local contrast are established. The possibility of differentiation of weak changes in the optical anisotropy of blood films of healthy and patients with breast cancer patients is determined.
The given data on the optical arrangement, in which the coordinate distributions of the real and imaginary component of the elements of the Jones matrix of optically thin polycrystalline layers are determined. Algorithms are presented and an experimental method for measuring the real and imaginary component of Jones-matrix images is analyzed. The experimental results of the study of statistical, correlation, and fractal parameters, which characterize the real component of the Jones-matrix image of polycrystalline networks of flat layers of the main types of human amino acids, are presented.
This paper contains structural and logical scheme of the research; theoretical information about the set of azimuthally invariant Mueller-matrix elements and their combinations; The work is aimed at the development of a set of techniques that form a new method of azimuthally invariant differential polarimetry of partially-depolarizing optically anisotropic biological layers. This method is based on the determination and diagnostic use of a set of physical relationships between the distributions of azimuthally invariant polarization parameters characterizing the optical anisotropy of partially depolarizing layers of biological tissues, and the distributions of the parameters of linear and circular birefringence of such objects.
Experimental studies within the statistical approach of the coordinate structure of the distributions of the intensity of own fluorescence of polycrystalline blood plasma films of patients of the following groups: control group of donors - group 1; patients with non-alcoholic fatty liver disease - group 2; patients with chronic hepatitis - group 3: The average values and ranges of variation of statistical moments of the 1st - 4th orders determined within the representative samples, which characterize the coordinate distributions of the intensity values of autofluorescent microscopic images of samples of polycrystalline blood plasma films within groups 1, 2, 3. The analysis of the operating characteristics of the power of the method of laser polarization mapping of two-dimensional distributions of the intensity values of its own fluorescence of microscopic images based on the determination of the sensitivity values, specificity and accuracy of the diagnostic test.
We prove the solvability of the Cauchy problem for a nonlocal heat equation which is of fractional order both in space and time. The representation formula for classical solutions for time- and space- fractional partial differential operator Dat + a2 (-Δ) γ/2 (0 ≤ α ≤ 1, γ ε (0, 2]) and deviation time variable is given in terms of the Fox H-function, using the step by step method.
Solvability of nonlocal multipoint on time problem is proved for evolutionary equations with differentiation operator on the time variable where the marginal function is the Gevrey ultradistribution.
The solvability of nonlocal multi-point problems is proved for the time evolution equation with an operator of differentiation in the time variable and pseudo-differential operator for the case when the limit function is an element of the space of generalized functions of ultradistributions.
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