Algorithm of search identification with forced search for extremum

We provide one of possible ways to reduce the time of transitive process of models tuning in the identification problems, which is: forced search for extremum of system state criterion.

Construction of approximate solution and stability map of one set of differential equations with periodic coefficients, which can be reduced to canonical form

We construct the approximate solution and stability map of one set of differential equations with periodic coefficients.

On the best choice of nodes at interpolation of functions by even Hermitian splines

We have found exact values of deviation of even Hermitian splines on some classes of functions and pointed out the best choice of nodes at approximation of concrete functions by these splines.

On solution of one linear problem with initial and boundary conditions

We solve one boundary problem of fourth order with initial conditions, that appears, for example, when one solves the problem about lateral oscillations of elastic-viscous-relaxating rod of variable profile with variable momentum of inertia with freely supported ends.

Algorithm of forced search for extremum of unimodal criterion

We construct the algorithm that implements forced search for extremum of unimodal criterion. We provide results of mathematical modelling on a computer.

Absolute and strong summability in degree $p \geqslant 1$ of $r$ times differentiated Fourier series and $r$ times differentiated conjugate Fourier series by matrix methods

We establish conditions of $|\gamma|_p$- and $[\gamma]_p$-summability in degree $p \geqslant 1$ of $r$ times differentiated Fourier series at the point where $\gamma = \| \gamma_{nk} \|$ is the matrix of transformation of series to sequence. Analogous conditions are considered also for $r$ times differentiated conjugate Fourier series.

Absolute summability of power $p$ of series, associated with conjugate Fourier series, by triangular matrix methods

We establish conditions of absolute summability of powers of series that are associated with conjugate Fourier series, by triangular matrix methods, and provide the application of the theorems proved to Voronoi-Nerlund method.

On multidimensional Jackson's theorem

We have found the best linear polynomial methods of approximation of continuous periodic functions of multiple variables in uniform metric with concave modulus of continuity.

On widths of one class of periodic functions

In the paper, we have found the A.N. Kolmogorov's width of the class $W^r L^+_p$ ($r=1,2,\ldots$, $1 \leqslant p \leqslant \infty$) of all $2\pi$-periodic functions $f(x)$ whose $(r-1)$-th derivative $f^{(r-1)}(x)$ is absolutely continuous and $\| f^{(r)}_+ \|_p \leqslant 1$.

Tauberian theorems in the case of strong summability in degree $p$ of double series

We establish a Tauberian theorem in the case of strong summability in degree $p$ of double series by matrix methods, give its application to Abel methods.