The provided materials present the results of the diagnostic application of polarization-correlation cartography of microscopic images of the polycrystalline component of biological tissues for the differential diagnosis of benign (adenoma) and malignant (adenocarcinoma) prostate tumors. For microscopic images of histological sections of adenoma and adenocarcinoma biopsies, integral and layered maps, as well as histograms of the distributions of the following parameters are provided: 1. The modulus of the fourth parameter |ππΎ4 12| of the polarization-correlation vector. 2. The argument of the fourth parameter π΄ππ(π4 12) of the polarization-correlation vector. Systematized tables contain the values of central statistical moments of the 1st to 4th order, which characterize the polarization-correlation, wavelet, and multifractal parameters of the polarization-correlation maps |ππΎ4 12|(π Γ π) and π΄ππ(π4 12) (π Γ π). Additionally, a set of the most sensitive diagnostic markers has been determined, representing statistical parameters that are highly responsive to changes in the polycrystalline structure of biological samples.
The paper presents the structural-logical diagram and research design of the newest method of 3D Mueller-matrix microscopy of the layer-by-layer structure of the polycrystalline component [1-9] of depolarizing histological sections of the brain. Principles of differential diagnosis of the formation of hemorrhages of traumatic genesis, cerebral infarction ischemic and hemorrhagic genesis by the method of 3D Mueller-matrix microscopy. Layer-by-layer azimuthal-invariant Mueller-matrix images of circular birefringence (MMI OA) of histological brain sections and operational characteristics of the method of their statistical analysis were determined.
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 Foxβs 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.
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.
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