# Vol 23, No 2 (2019)

**Year:**2019**Articles:**11**URL:**https://journals.eco-vector.com/1991-8615/issue/view/1232

### Duality equations on a 4-manifold of conformal torsion-free connection and some of their solutions for the zero signature

#### Abstract

On a 4-manifold of conformal torsion-free connection with zero signature (--++) we found conditions under which the conformal curvature matrix is dual (self-dual or anti-self-dual). These conditions are 5 partial differential equations of the 2nd order on 10 coefficients of the angular metric and 4 partial differential equations of the 1st order, containing also 3 coefficients of external 2-form of charge. (External 2-form of charge is one of the components of the conformal curvature matrix.) Duality equations for a metric of a diagonal type are composed. They form a system of five second-order differential equations on three unknown functions of all four variables. We found several series of solutions for this system. In particular, we obtained all solutions for a logarithmically polynomial diagonal metric, that is, for a metric whose coefficients are exponents of polynomials of four variables.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2019;23(2):207-228

### Solvability of a nonlocal problem for a hyperbolic equation with degenerate integral conditions

#### Abstract

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2019;23(2):229-245

### Asymmetric tensor representations in micropolar continuum mechanics theories

#### Abstract

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2019;23(2):246-255

### Estimation of mechanical characteristics of salt rock crystals based on the mathematical model of nanoindentation using scanning probe microscope Dimension Icon

#### Abstract

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2019;23(2):256-269

### Creep and plastic flow of a spherical viscoelastic layer material at its loading and unloading

#### Abstract

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2019;23(2):270-283

### Determination of elastic constants of rocks

#### Abstract

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2019;23(2):284-303

### Analysis of the linear viscoelasticity theory capabilities to simulate hydrostatic pressure influence on creep curves and lateral contraction ratio of rheonomous materials

#### Abstract

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2019;23(2):304-340

### Convective layered flows of a vertically whirling viscous incompressible fluid. Velocity field investigation

#### Abstract

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2019;23(2):341-360

### Effective computational procedure of the alternance optimization method

#### Abstract

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2019;23(2):361-377

### The existence of chaotic regimes of the fractional analogue of the Duffing-type oscillator

#### Abstract

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2019;23(2):378-393

### On singular solutions of a multidimensional differential equation of Clairaut-type with power and exponential functions

#### Abstract

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2019;23(2):394-401