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7  Articles
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We establish sharp estimates of the LqL_q-norms on any finite interval for the polynomials and splines and their derivatives with the help of local LpL_p-norms of these polynomials and splines.

For given n,r?Nn, r \in \mathbb{N}; p,A>0p, A > 0 and any fixed interval [a,b]?R[a,b] \subset \mathbb{R} we solve the extremal problem b?a|x(t)|qdt?sup\int\limits_a^b |x(t)|^q dt \rightarrow \sup, q?pq \geqslant p, over sets of trigonometric polynomial... see more

The shaping of structural elements in the area of mechanical design is a recurrent problem. The mechanical designer, as a rule, chooses what is believed to be the “simplest” shapes, such as the geometric primitives: lines, circles and, occasionally, conic... see more

For any q>p>0q > p > 0, ?>0,\omega > 0, d=2?,d \ge 2 \omega,  we obtain the following sharp inequality of various metrics?x?Lq(Id)=?f+c?Lq(I2?)?f+c?Lp(I2?)?x?Lp(Id) \|x\|_{L_q(I_{d})} \le \frac{\|\varphi + c\|_{L_q(I_{2\omega})}}{\|\varphi +... see more

Genetic parameters of Montbeliarde cows were estimated for test-day milk yield with a random regression spline model. The spline model has been considered as a good alternative to Legendre polynomials to direct interpretation of parameters. With this mode... see more

We prove new sharp Remez-type inequalities of various metrics for periodic functions, polynomials and splines.

The paper is dedicated to the 50th anniversary of the Grinberg theorem. The main works of Emanuel Grinberg (1911-1982) in applied mathematics are described, following the stages of his life path, namely: the design of radio receivers and the calculation o... see more

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