General Functions Method in Transport Boundary Value Problems of Elasticity Theory

The Lame system describing the dynamics of an isotropic elastic medium affected by a steady transport load moving at subsonic, transonic, and supersonic speed is considered. Its fundamental and generalized solutions in a moving frame of reference tied to the transport load are analyzed. Shock waves arising in the medium at supersonic speeds are studied. Conditions on the jump in the stress, displacement rate, and energy across the shock front are obtained using distribution theory. Transport boundary value problem for an elastic medium bounded by a cylindrical surface of arbitrary cross section and subjected to transport loads is considered in the subsonic and supersonic case with regard to shock waves. To solve problems, the generalized functions method is developed. In the space of generalized functions, generalized solutions are constructed and their regular integral presentations are obtained. Singular boundary equations solving the boundary value problems are presented

Generalized and Fundamental Solutions of Motion Equations of Two-Component Biot’s Medium

Here processes of wave propagation in a two-component Biot’s medium are considered, which are generated by arbitrary forces actions. By using Fourier transformation of generalized functions, a fundamental solution, Green tensor, of motion equations of this medium has been constructed in a non-stationary case and in the case of stationary harmonic oscillation. These tensors describe the processes of wave propagation (in spaces of dimensions 1, 2, 3) under an action of power sources concentrated at coordinates origin, which are described by a singular delta-function. Based on them, generalized solutions of these equations are constructed under the action of various sources of periodic and non-stationary perturbations, which are described by both regular and singular generalized functions. For regular acting forces, integral representations of solutions are given that can be used to calculate the stress-strain state of a porous water-saturated medium

Application and comparison of different classification methods based on symptom analysis with traditional classification technique for breast cancer diagnosis

Novel approach for classification technique such as Artificial Neural Network (ANN), Linear Discriminant Analysis (LDA) and Random Forest (RF) using factor or dichotomic variables has been introduced. This study searches for the highly informative finitely linear combinations (symptoms) of variables in the finite field on the based of the Fisher’s exact test and accurately predict the target class for each case in the data. There are several super symptoms have comparable p-values. In this case, it becomes possible to choose as a nominative representative the factor which is more accessible for interpretation. The super symptom means a linear combination of various multiplications of k dichotomous variables over a field of characteristic 2 without repeating. In algebra, such functions are called Zhegalkin polynomials or algebraic normal forms