The failure by the court to take measures to return the criminal case to the prosecutor in accordance with art. 237 of the code of criminal procedure of the Russian federation as an unconditional basis for canceling the sentence

Part 2 of Article 389.17 of the Criminal Procedure Code of the Russian Federation establishes a list of unconditionally significant violations of the norms of the criminal procedure law, the identification of which in a case entails the cancellation or change of the sentence in every case without exception. The range of these violations was determined by the legislator during the development of the Code of Criminal Procedure of the Russian Federation in 2001, and has not changed since then. However, the rules, violation of which can affect the quality of the sentence and lead to its cancellation in each case, have changed more than once. Including the norms governing the institution of returning the case to the prosecutor in accordance with Art. 237 of the Code of Criminal Procedure of the Russian Federation and determining the significance of this institution for the issuance of a legal, reasonable and fair sentence. In this regard, this article discusses the feasibility of expanding the list of unconditional grounds for canceling a sentence by including a violation associated with the failure of the court to take measures to return the criminal case to the prosecutor in accordance with Art. 237 of the Criminal Procedure Code of the Russian Federation, if there are grounds for that.

On two long standing open problems on $L_p$-spaces

The present note was written during the preparation of the talk at the International Conference dedicated to 70-th anniversary of Professor O. Lopushansky, September 16-19, 2019, Ivano-Frankivsk (Ukraine). We focus on two long standing open problems. The first one, due to Lindenstrauss and Rosenthal (1969), asks of whether every complemented infinite dimensional subspace of $L_1$ is isomorphic to either $L_1$ or $\ell_1$. The second problem was posed by Enflo and Rosenthal in 1973: does there exist a nonseparable space $L_p(\mu)$ with finite atomless $\mu$ and $1<p<\infty$, $p \neq 2$ having an unconditional basis? We analyze partial results and discuss on some natural ideas to solve these problems.

Spectral properties of ordinary differential operators with involuton

Let P and Q be ordinary differential operators of order n and m generated by s = max{n; m} boundary conditions on a nite interval [a; b]. We study operators of the form L = JP + Q, where J is the involution operator in the space L2[a; b]. We consider three cases n > m, n < m, and n = m, for which we dene concepts of regular, almost regular, and normal boundary conditions. We announce theorems on unconditional basis and completeness of the root functions of operator L depending on the type of boundary conditions from selected classes.