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abstracts" class="reveal-all-trigger mr-2 small" data-reveal-text="Open all abstracts" data-link-purpose-append="in this tab" data-link-purpose-append-open="in this tab"> Open all abstracts<span class="offscreen-hidden">, in this tab</span> </button> </p>  <div class="art-list"> <div class="art-list-item reveal-container reveal-closed"> <div class="art-list-item-body"> <a href="/article/10.1070/SM9427" class="art-list-item-title event_main-link">On uniqueness of probability solutions of the Fokker-Planck-Kolmogorov equation</a> <p class="small art-list-item-meta"> V. I. Bogachev <em>et al</em> 2021 <em>Sb. Math.</em> <b>212</b> 745 </p> <div class="art-list-item-tools small wd-abstr-upper"> <button type="button" class="reveal-trigger mr-2 nowrap"> <svg aria-hidden="true" class="fa-icon fa-icon--left fa-icon--flip" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 320 512"><path d="M137.4 374.6c12.5 12.5 32.8 12.5 45.3 0l128-128c9.2-9.2 11.9-22.9 6.9-34.9s-16.6-19.8-29.6-19.8L32 192c-12.9 0-24.6 7.8-29.6 19.8s-2.2 25.7 6.9 34.9l128 128z"/></svg><span class="reveal-trigger-label" data-reveal-text="Open abstract" data-reveal-label-alt="Close abstract" data-link-purpose-append="On uniqueness of probability solutions of the Fokker-Planck-Kolmogorov equation" data-link-purpose-append-open="On uniqueness of probability solutions of the Fokker-Planck-Kolmogorov equation">Open abstract</span> </button> <a href="/article/10.1070/SM9427/meta" class="mr-2 mb-0 nowrap event_mini-link" data-event-action="View article"> <span class="icon-article"></span>View article<span class="offscreen-hidden">, On uniqueness of probability solutions of the Fokker-Planck-Kolmogorov equation</span></a> <a href="/article/10.1070/SM9427/pdf" class="mr-2 mb-0 nowrap event_mini-link" data-event-action="PDF"><span class="icon-file-pdf"></span>PDF<span class="offscreen-hidden">, On uniqueness of probability solutions of the Fokker-Planck-Kolmogorov equation</span></a> </div> <div class="reveal-content"> <div class="article-text view-text-small"><p> The paper gives a solution to the long-standing problem of uniqueness for probability solutions to the Cauchy problem for the Fokker- Planck-Kolmogorov equation with an unbounded drift coefficient and unit diffusion coefficient. It is proved that in the one-dimensional case uniqueness holds and in all other dimensions it fails. The case of nonconstant diffusion coefficients is also investigated. </p><p> Bibliography: 70 titles. </p></div> <div class="art-list-item-tools small wd-abstr-lower"> <a class="mr-2" href="https://doi.org/10.1070/SM9427">https://doi.org/10.1070/SM9427</a> </div> </div> </div> </div> <div class="art-list-item reveal-container reveal-closed"> <div class="art-list-item-body"> <a href="/article/10.1070/SM9410" class="art-list-item-title event_main-link">A Viskovatov algorithm for Hermite-Pad茅 polynomials</a> <p class="small art-list-item-meta"> N. R. Ikonomov and S. P. Suetin 2021 <em>Sb. Math.</em> <b>212</b> 1279 </p> <div class="art-list-item-tools small wd-abstr-upper"> <button type="button" class="reveal-trigger mr-2 nowrap"> <svg aria-hidden="true" class="fa-icon fa-icon--left fa-icon--flip" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 320 512"><path d="M137.4 374.6c12.5 12.5 32.8 12.5 45.3 0l128-128c9.2-9.2 11.9-22.9 6.9-34.9s-16.6-19.8-29.6-19.8L32 192c-12.9 0-24.6 7.8-29.6 19.8s-2.2 25.7 6.9 34.9l128 128z"/></svg><span class="reveal-trigger-label" data-reveal-text="Open abstract" data-reveal-label-alt="Close abstract" data-link-purpose-append="A Viskovatov algorithm for Hermite-Pad茅 polynomials" data-link-purpose-append-open="A Viskovatov algorithm for Hermite-Pad茅 polynomials">Open abstract</span> </button> <a href="/article/10.1070/SM9410/meta" class="mr-2 mb-0 nowrap event_mini-link" data-event-action="View article"> <span class="icon-article"></span>View article<span class="offscreen-hidden">, A Viskovatov algorithm for Hermite-Pad茅 polynomials</span></a> <a href="/article/10.1070/SM9410/pdf" class="mr-2 mb-0 nowrap event_mini-link" data-event-action="PDF"><span class="icon-file-pdf"></span>PDF<span class="offscreen-hidden">, A Viskovatov algorithm for Hermite-Pad茅 polynomials</span></a> </div> <div class="reveal-content"> <div class="article-text view-text-small"><p> We propose and justify an algorithm for producing Hermite- Pad茅 polynomials of type I for an arbitrary tuple of <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/212/9/1279/revision1/MSB_212_9_1279ieqn1.gif" style="max-width: 100%;" alt="$m+1$" align="top"></img></span><script type="math/tex">m+1</script></span></span> formal power series <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/212/9/1279/revision1/MSB_212_9_1279ieqn2.gif" style="max-width: 100%;" alt="$[f_0,\dots,f_m]$" align="top"></img></span><script type="math/tex">[f_0,\dots,f_m]</script></span></span>, <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/212/9/1279/revision1/MSB_212_9_1279ieqn3.gif" style="max-width: 100%;" alt="$m\geq1$" align="top"></img></span><script type="math/tex">m\geq1</script></span></span>, about the point <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/212/9/1279/revision1/MSB_212_9_1279ieqn4.gif" style="max-width: 100%;" alt="$z=0$" align="top"></img></span><script type="math/tex">z=0</script></span></span> (<span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/212/9/1279/revision1/MSB_212_9_1279ieqn5.gif" style="max-width: 100%;" alt="$f_j\in\mathbb{C}[[z]]$" align="top"></img></span><script type="math/tex">f_j\in\mathbb{C}[[z]]</script></span></span>) under the assumption that the series have a certain ('general position') nondegeneracy property. This algorithm is a straightforward extension of the classical Viskovatov algorithm for constructing Pad茅 polynomials (for <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/212/9/1279/revision1/MSB_212_9_1279ieqn6.gif" style="max-width: 100%;" alt="$m=1$" align="top"></img></span><script type="math/tex">m=1</script></span></span> our algorithm coincides with the Viskovatov algorithm). </p><p> The algorithm is based on a recurrence relation and has the following feature: all the Hermite-Pad茅 polynomials corresponding to the multi- indices <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/212/9/1279/revision1/MSB_212_9_1279ieqn7.gif" style="max-width: 100%;" alt="$(k,k,k,\dots,k,k)$" align="top"></img></span><script type="math/tex">(k,k,k,\dots,k,k)</script></span></span>, <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/212/9/1279/revision1/MSB_212_9_1279ieqn8.gif" style="max-width: 100%;" alt="$(k+1,k,k,\dots,k,k)$" align="top"></img></span><script type="math/tex">(k+1,k,k,\dots,k,k)</script></span></span>, <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/212/9/1279/revision1/MSB_212_9_1279ieqn9.gif" style="max-width: 100%;" alt="$(k+1,k+1,k,\dots,k,k)$" align="top"></img></span><script type="math/tex">(k+1,k+1,k,\dots,k,k)</script></span></span>, <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/212/9/1279/revision1/MSB_212_9_1279ieqn10.gif" style="max-width: 100%;" alt="$\dots$" align="top"></img></span><script type="math/tex">\dots</script></span></span>, <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/212/9/1279/revision1/MSB_212_9_1279ieqn11.gif" style="max-width: 100%;" alt="$(k+1,k+1,k+1,\dots,k+1,k)$" align="top"></img></span><script type="math/tex">(k+1,k+1,k+1,\dots,k+1,k)</script></span></span> are already known at the point when the algorithm produces the Hermite-Pad茅 polynomials corresponding to the multi- index <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/212/9/1279/revision1/MSB_212_9_1279ieqn12.gif" style="max-width: 100%;" alt="$(k+1,k+1,k+1,\dots,k+1,k+1)$" align="top"></img></span><script type="math/tex">(k+1,k+1,k+1,\dots,k+1,k+1)</script></span></span>. </p><p> We show how the Hermite-Pad茅 polynomials corresponding to different multi-indices can be found recursively via this algorithm by changing the initial conditions appropriately. </p><p> At every step <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/212/9/1279/revision1/MSB_212_9_1279ieqn13.gif" style="max-width: 100%;" alt="$n$" align="top"></img></span><script type="math/tex">n</script></span></span>, the algorithm can be parallelized in <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/212/9/1279/revision1/MSB_212_9_1279ieqn1.gif" style="max-width: 100%;" alt="$m+1$" align="top"></img></span><script type="math/tex">m+1</script></span></span> independent evaluations. </p><p> Bibliography: 30 titles. </p></div> <div class="art-list-item-tools small wd-abstr-lower"> <a class="mr-2" href="https://doi.org/10.1070/SM9410">https://doi.org/10.1070/SM9410</a> </div> </div> </div> </div> <div class="art-list-item reveal-container reveal-closed"> <div class="art-list-item-body"> <a href="/article/10.1070/SM9445" class="art-list-item-title event_main-link">Uniform convergence criterion for non-harmonic sine series</a> <p class="small art-list-item-meta"> K. A. Oganesyan 2021 <em>Sb. Math.</em> <b>212</b> 70 </p> <div class="art-list-item-tools small wd-abstr-upper"> <button type="button" class="reveal-trigger mr-2 nowrap"> <svg aria-hidden="true" class="fa-icon fa-icon--left fa-icon--flip" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 320 512"><path d="M137.4 374.6c12.5 12.5 32.8 12.5 45.3 0l128-128c9.2-9.2 11.9-22.9 6.9-34.9s-16.6-19.8-29.6-19.8L32 192c-12.9 0-24.6 7.8-29.6 19.8s-2.2 25.7 6.9 34.9l128 128z"/></svg><span class="reveal-trigger-label" data-reveal-text="Open abstract" data-reveal-label-alt="Close abstract" data-link-purpose-append="Uniform convergence criterion for non-harmonic sine series" data-link-purpose-append-open="Uniform convergence criterion for non-harmonic sine series">Open abstract</span> </button> <a href="/article/10.1070/SM9445/meta" class="mr-2 mb-0 nowrap event_mini-link" data-event-action="View article"> <span class="icon-article"></span>View article<span class="offscreen-hidden">, Uniform convergence criterion for non-harmonic sine series</span></a> <a href="/article/10.1070/SM9445/pdf" class="mr-2 mb-0 nowrap event_mini-link" data-event-action="PDF"><span class="icon-file-pdf"></span>PDF<span class="offscreen-hidden">, Uniform convergence criterion for non-harmonic sine series</span></a> </div> <div class="reveal-content"> <div class="article-text view-text-small"><p> We show that for a nonnegative monotonic sequence <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/212/1/70/revision5/MSB_212_1_70ieqn1.gif" style="max-width: 100%;" alt="$\{c_k\}$" align="top"></img></span><script type="math/tex">\{c_k\}</script></span></span> the condition <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/212/1/70/revision5/MSB_212_1_70ieqn2.gif" style="max-width: 100%;" alt="$c_kk\to 0$" align="top"></img></span><script type="math/tex">c_kk\to 0</script></span></span> is sufficient for the series <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/212/1/70/revision5/MSB_212_1_70ieqn3.gif" style="max-width: 100%;" alt="$\sum_{k=1}^{\infty}c_k\sin k^{\alpha} x$" align="top"></img></span><script type="math/tex">\sum_{k=1}^{\infty}c_k\sin k^{\alpha} x</script></span></span> to converge uniformly on any bounded set for <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/212/1/70/revision5/MSB_212_1_70ieqn4.gif" style="max-width: 100%;" alt="$\alpha\in (0,2)$" align="top"></img></span><script type="math/tex">\alpha\in (0,2)</script></span></span>, and for any odd <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/212/1/70/revision5/MSB_212_1_70ieqn5.gif" style="max-width: 100%;" alt="$\alpha$" align="top"></img></span><script type="math/tex">\alpha</script></span></span> it is sufficient for it to converge uniformly on the whole of <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/212/1/70/revision5/MSB_212_1_70ieqn6.gif" style="max-width: 100%;" alt="$\mathbb{R}$" align="top"></img></span><script type="math/tex">\mathbb{R}</script></span></span>. Moreover, the latter assertion still holds if we replace <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/212/1/70/revision5/MSB_212_1_70ieqn7.gif" style="max-width: 100%;" alt="$k^{\alpha}$" align="top"></img></span><script type="math/tex">k^{\alpha}</script></span></span> by any polynomial in odd powers with rational coefficients. On the other hand, in the case of even <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/212/1/70/revision5/MSB_212_1_70ieqn5.gif" style="max-width: 100%;" alt="$\alpha$" align="top"></img></span><script type="math/tex">\alpha</script></span></span> it is necessary that <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/212/1/70/revision5/MSB_212_1_70ieqn8.gif" style="max-width: 100%;" alt="$\sum_{k=1}^{\infty}c_k<\infty$" align="top"></img></span><script type="math/tex">\sum_{k=1}^{\infty}c_k<\infty</script></span></span> for the above series to converge at the point <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/212/1/70/revision5/MSB_212_1_70ieqn9.gif" style="max-width: 100%;" alt="$\pi/2$" align="top"></img></span><script type="math/tex">\pi/2</script></span></span> or at <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/212/1/70/revision5/MSB_212_1_70ieqn10.gif" style="max-width: 100%;" alt="$2\pi/3$" align="top"></img></span><script type="math/tex">2\pi/3</script></span></span>. As a consequence, we obtain uniform convergence criteria. Furthermore, the results for natural numbers <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/212/1/70/revision5/MSB_212_1_70ieqn5.gif" style="max-width: 100%;" alt="$\alpha$" align="top"></img></span><script type="math/tex">\alpha</script></span></span> remain true for sequences in the more general class <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/212/1/70/revision5/MSB_212_1_70ieqn11.gif" style="max-width: 100%;" alt="$\mathrm{RBVS}$" align="top"></img></span><script type="math/tex">\mathrm{RBVS}</script></span></span>. </p><p> Bibliography: 17 titles. </p></div> <div class="art-list-item-tools small wd-abstr-lower"> <a class="mr-2" href="https://doi.org/10.1070/SM9445">https://doi.org/10.1070/SM9445</a> </div> </div> </div> </div> <div class="art-list-item reveal-container reveal-closed"> <div class="art-list-item-body"> <a href="/article/10.1070/SM9402" class="art-list-item-title event_main-link">Critical Galton-Watson branching processes with a countable set of types and infinite second moments</a> <p class="small art-list-item-meta"> V. A. Vatutin <em>et al</em> 2021 <em>Sb. Math.</em> <b>212</b> 1 </p> <div class="art-list-item-tools small wd-abstr-upper"> <button type="button" class="reveal-trigger mr-2 nowrap"> <svg aria-hidden="true" class="fa-icon fa-icon--left fa-icon--flip" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 320 512"><path d="M137.4 374.6c12.5 12.5 32.8 12.5 45.3 0l128-128c9.2-9.2 11.9-22.9 6.9-34.9s-16.6-19.8-29.6-19.8L32 192c-12.9 0-24.6 7.8-29.6 19.8s-2.2 25.7 6.9 34.9l128 128z"/></svg><span class="reveal-trigger-label" data-reveal-text="Open abstract" data-reveal-label-alt="Close abstract" data-link-purpose-append="Critical Galton-Watson branching processes with a countable set of types and infinite second moments" data-link-purpose-append-open="Critical Galton-Watson branching processes with a countable set of types and infinite second moments">Open abstract</span> </button> <a href="/article/10.1070/SM9402/meta" class="mr-2 mb-0 nowrap event_mini-link" data-event-action="View article"> <span class="icon-article"></span>View article<span class="offscreen-hidden">, Critical Galton-Watson branching processes with a countable set of types and infinite second moments</span></a> <a href="/article/10.1070/SM9402/pdf" class="mr-2 mb-0 nowrap event_mini-link" data-event-action="PDF"><span class="icon-file-pdf"></span>PDF<span class="offscreen-hidden">, Critical Galton-Watson branching processes with a countable set of types and infinite second moments</span></a> </div> <div class="reveal-content"> <div class="article-text view-text-small"><p> We consider an indecomposable Galton-Watson branching process with a countable set of types. Assuming that the process is critical and may have infinite variance of the offspring sizes of some (or all) types of particles we describe the asymptotic behaviour of the survival probability of the process and establish a Yaglom-type conditional limit theorem for the infinite-dimensional vector of the number of particles of all types. </p><p> Bibliography: 20 titles. </p></div> <div class="art-list-item-tools small wd-abstr-lower"> <a class="mr-2" href="https://doi.org/10.1070/SM9402">https://doi.org/10.1070/SM9402</a> </div> </div> </div> </div> <div class="art-list-item reveal-container reveal-closed"> <div class="art-list-item-body"> <a href="/article/10.1070/SM9193" class="art-list-item-title event_main-link">Spectral representations of topological groups and near-openly generated groups</a> <p class="small art-list-item-meta"> V. M. Valov and K. L. Kozlov 2020 <em>Sb. Math.</em> <b>211</b> 258 </p> <div class="art-list-item-tools small wd-abstr-upper"> <button type="button" class="reveal-trigger mr-2 nowrap"> <svg aria-hidden="true" class="fa-icon fa-icon--left fa-icon--flip" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 320 512"><path d="M137.4 374.6c12.5 12.5 32.8 12.5 45.3 0l128-128c9.2-9.2 11.9-22.9 6.9-34.9s-16.6-19.8-29.6-19.8L32 192c-12.9 0-24.6 7.8-29.6 19.8s-2.2 25.7 6.9 34.9l128 128z"/></svg><span class="reveal-trigger-label" data-reveal-text="Open abstract" data-reveal-label-alt="Close abstract" data-link-purpose-append="Spectral representations of topological groups and near-openly generated groups" data-link-purpose-append-open="Spectral representations of topological groups and near-openly generated groups">Open abstract</span> </button> <a href="/article/10.1070/SM9193/meta" class="mr-2 mb-0 nowrap event_mini-link" data-event-action="View article"> <span class="icon-article"></span>View article<span class="offscreen-hidden">, Spectral representations of topological groups and near-openly generated groups</span></a> <a href="/article/10.1070/SM9193/pdf" class="mr-2 mb-0 nowrap event_mini-link" data-event-action="PDF"><span class="icon-file-pdf"></span>PDF<span class="offscreen-hidden">, Spectral representations of topological groups and near-openly generated groups</span></a> </div> <div class="reveal-content"> <div class="article-text view-text-small"><p> Near-openly generated groups are introduced. They form a topological and multiplicative subclass of <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/211/2/258/revision1/MSB_211_2_258ieqn1.gif" style="max-width: 100%;" alt="$\mathbb R$" align="top"></img></span><script type="math/tex">\mathbb R</script></span></span>-factorizable groups. Dense and open subgroups, quotients and the Raikov completion of a near-openly generated group are near-openly generated. Almost connected pro-Lie groups, Lindel枚f almost metrizable groups and the spaces <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/211/2/258/revision1/MSB_211_2_258ieqn2.gif" style="max-width: 100%;" alt="$C_p(X)$" align="top"></img></span><script type="math/tex">C_p(X)</script></span></span> of all continuous real-valued functions on a Tychonoff space with pointwise convergence topology are near-openly generated. </p><p> We provide characterizations of near-openly generated groups using methods of inverse spectra and topological game theory. </p><p> Bibliography: 24 titles. </p></div> <div class="art-list-item-tools small wd-abstr-lower"> <a class="mr-2" href="https://doi.org/10.1070/SM9193">https://doi.org/10.1070/SM9193</a> </div> </div> </div> </div> <div class="art-list-item reveal-container reveal-closed"> <div class="art-list-item-body"> <a href="/article/10.1070/SM9340" class="art-list-item-title event_main-link">Asymptotic analysis of solutions of ordinary differential equations with distribution coefficients</a> <p class="small art-list-item-meta"> A. M. Savchuk and A. A. Shkalikov 2020 <em>Sb. Math.</em> <b>211</b> 1623 </p> <div class="art-list-item-tools small wd-abstr-upper"> <button type="button" class="reveal-trigger mr-2 nowrap"> <svg aria-hidden="true" class="fa-icon fa-icon--left fa-icon--flip" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 320 512"><path d="M137.4 374.6c12.5 12.5 32.8 12.5 45.3 0l128-128c9.2-9.2 11.9-22.9 6.9-34.9s-16.6-19.8-29.6-19.8L32 192c-12.9 0-24.6 7.8-29.6 19.8s-2.2 25.7 6.9 34.9l128 128z"/></svg><span class="reveal-trigger-label" data-reveal-text="Open abstract" data-reveal-label-alt="Close abstract" data-link-purpose-append="Asymptotic analysis of solutions of ordinary differential equations with distribution coefficients" data-link-purpose-append-open="Asymptotic analysis of solutions of ordinary differential equations with distribution coefficients">Open abstract</span> </button> <a href="/article/10.1070/SM9340/meta" class="mr-2 mb-0 nowrap event_mini-link" data-event-action="View article"> <span class="icon-article"></span>View article<span class="offscreen-hidden">, Asymptotic analysis of solutions of ordinary differential equations with distribution coefficients</span></a> <a href="/article/10.1070/SM9340/pdf" class="mr-2 mb-0 nowrap event_mini-link" data-event-action="PDF"><span class="icon-file-pdf"></span>PDF<span class="offscreen-hidden">, Asymptotic analysis of solutions of ordinary differential equations with distribution coefficients</span></a> </div> <div class="reveal-content"> <div class="article-text view-text-small"><p> Ordinary differential equations of the form <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/211/11/1623/revision4/MSB_211_11_1623ieqn1.gif" style="max-width: 100%;" alt="$ \tau(y)- \lambda ^{2m} \varrho(x) y=0, \qquad \tau(y) =\sum_{k,s=0}^m(\tau_{k,s}(x)y^{(m-k)}(x))^{(m-s)}, $" align="top"></img></span><script type="math/tex">\tau(y)- \lambda ^{2m} \varrho(x) y=0, \qquad \tau(y) =\sum_{k,s=0}^m(\tau_{k,s}(x)y^{(m-k)}(x))^{(m-s)},</script></span></span> on the finite interval <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/211/11/1623/revision4/MSB_211_11_1623ieqn2.gif" style="max-width: 100%;" alt="$x\in[0,1]$" align="top"></img></span><script type="math/tex">x\in[0,1]</script></span></span> are under consideration. Here the functions <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/211/11/1623/revision4/MSB_211_11_1623ieqn3.gif" style="max-width: 100%;" alt="$\tau_{0,0}$" align="top"></img></span><script type="math/tex">\tau_{0,0}</script></span></span> and <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/211/11/1623/revision4/MSB_211_11_1623ieqn4.gif" style="max-width: 100%;" alt="$\varrho$" align="top"></img></span><script type="math/tex">\varrho</script></span></span> are absolutely continuous and positive and the coefficients of the differential expression <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/211/11/1623/revision4/MSB_211_11_1623ieqn5.gif" style="max-width: 100%;" alt="$\tau(y)$" align="top"></img></span><script type="math/tex">\tau(y)</script></span></span> are subject to the conditions <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/211/11/1623/revision4/MSB_211_11_1623ieqn6.gif" style="max-width: 100%;" alt="$ \tau_{k,s}^{(-l)}\in L_2[0,1], \qquad 0\leqslant k,s \leqslant m, \quad l=\min\{k,s\}, $" align="top"></img></span><script type="math/tex">\tau_{k,s}^{(-l)}\in L_2[0,1], \qquad 0\leqslant k,s \leqslant m, \quad l=\min\{k,s\},</script></span></span> where <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/211/11/1623/revision4/MSB_211_11_1623ieqn7.gif" style="max-width: 100%;" alt="$f^{(-k)}$" align="top"></img></span><script type="math/tex">f^{(-k)}</script></span></span> denotes the <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/211/11/1623/revision4/MSB_211_11_1623ieqn8.gif" style="max-width: 100%;" alt="$k$" align="top"></img></span><script type="math/tex">k</script></span></span>th antiderivative of the function <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/211/11/1623/revision4/MSB_211_11_1623ieqn9.gif" style="max-width: 100%;" alt="$f$" align="top"></img></span><script type="math/tex">f</script></span></span> in the sense of distributions. Our purpose is to derive analogues of the classical asymptotic Birkhoff-type representations for the fundamental system of solutions of the above equation with respect to the spectral parameter as <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/211/11/1623/revision4/MSB_211_11_1623ieqn10.gif" style="max-width: 100%;" alt="$\lambda \to \infty$" align="top"></img></span><script type="math/tex">\lambda \to \infty</script></span></span> in certain sectors of the complex plane <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/211/11/1623/revision4/MSB_211_11_1623ieqn11.gif" style="max-width: 100%;" alt="$\mathbb C$" align="top"></img></span><script type="math/tex">\mathbb C</script></span></span>. We reduce this equation to a system of first-order equations of the form <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/211/11/1623/revision4/MSB_211_11_1623ieqn12.gif" style="max-width: 100%;" alt="$ \mathbf y'=\lambda\rho(x)\mathrm B\mathbf y+\mathrm A(x)\mathbf y+\mathrm C(x,\lambda)\mathbf y, $" align="top"></img></span><script type="math/tex">\mathbf y'=\lambda\rho(x)\mathrm B\mathbf y+\mathrm A(x)\mathbf y+\mathrm C(x,\lambda)\mathbf y,</script></span></span> where <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/211/11/1623/revision4/MSB_211_11_1623ieqn13.gif" style="max-width: 100%;" alt="$\rho$" align="top"></img></span><script type="math/tex">\rho</script></span></span> is a positive function, <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/211/11/1623/revision4/MSB_211_11_1623ieqn14.gif" style="max-width: 100%;" alt="$\mathrm B$" align="top"></img></span><script type="math/tex">\mathrm B</script></span></span> is a matrix with constant elements, the elements of the matrices <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/211/11/1623/revision4/MSB_211_11_1623ieqn15.gif" style="max-width: 100%;" alt="$\mathrm A(x)$" align="top"></img></span><script type="math/tex">\mathrm A(x)</script></span></span> and <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/211/11/1623/revision4/MSB_211_11_1623ieqn16.gif" style="max-width: 100%;" alt="$\mathrm C(x,\lambda)$" align="top"></img></span><script type="math/tex">\mathrm C(x,\lambda)</script></span></span> are integrable functions, and <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/211/11/1623/revision4/MSB_211_11_1623ieqn17.gif" style="max-width: 100%;" alt="$\|\mathrm C(x,\lambda)\|_{L_1}=o(1)$" align="top"></img></span><script type="math/tex">\|\mathrm C(x,\lambda)\|_{L_1}=o(1)</script></span></span> as <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/211/11/1623/revision4/MSB_211_11_1623ieqn10.gif" style="max-width: 100%;" alt="$\lambda \to \infty$" align="top"></img></span><script type="math/tex">\lambda \to \infty</script></span></span>. For systems of this kind, we obtain new results concerning the asymptotic representation of the fundamental solution matrix, which we use to make an asymptotic analysis of the above scalar equations of high order. </p><p> Bibliography: 44 titles. </p></div> <div class="art-list-item-tools small wd-abstr-lower"> <a class="mr-2" href="https://doi.org/10.1070/SM9340">https://doi.org/10.1070/SM9340</a> </div> </div> </div> </div> <div class="art-list-item reveal-container reveal-closed"> <div class="art-list-item-body"> <a href="/article/10.1070/SM9275" class="art-list-item-title event_main-link">Kripke semantics for the logic of problems and propositions</a> <p class="small art-list-item-meta"> A. A. Onoprienko 2020 <em>Sb. Math.</em> <b>211</b> 709 </p> <div class="art-list-item-tools small wd-abstr-upper"> <button type="button" class="reveal-trigger mr-2 nowrap"> <svg aria-hidden="true" class="fa-icon fa-icon--left fa-icon--flip" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 320 512"><path d="M137.4 374.6c12.5 12.5 32.8 12.5 45.3 0l128-128c9.2-9.2 11.9-22.9 6.9-34.9s-16.6-19.8-29.6-19.8L32 192c-12.9 0-24.6 7.8-29.6 19.8s-2.2 25.7 6.9 34.9l128 128z"/></svg><span class="reveal-trigger-label" data-reveal-text="Open abstract" data-reveal-label-alt="Close abstract" data-link-purpose-append="Kripke semantics for the logic of problems and propositions" data-link-purpose-append-open="Kripke semantics for the logic of problems and propositions">Open abstract</span> </button> <a href="/article/10.1070/SM9275/meta" class="mr-2 mb-0 nowrap event_mini-link" data-event-action="View article"> <span class="icon-article"></span>View article<span class="offscreen-hidden">, Kripke semantics for the logic of problems and propositions</span></a> <a href="/article/10.1070/SM9275/pdf" class="mr-2 mb-0 nowrap event_mini-link" data-event-action="PDF"><span class="icon-file-pdf"></span>PDF<span class="offscreen-hidden">, Kripke semantics for the logic of problems and propositions</span></a> </div> <div class="reveal-content"> <div class="article-text view-text-small"><p> In this paper we study the propositional fragment <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/211/5/709/revision1/MSB_211_5_709ieqn1.gif" style="max-width: 100%;" alt="$\mathrm{HC}$" align="top"></img></span><script type="math/tex">\mathrm{HC}</script></span></span> of the joint logic of problems and propositions introduced by Melikhov. We provide Kripke semantics for this logic and show that <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/211/5/709/revision1/MSB_211_5_709ieqn1.gif" style="max-width: 100%;" alt="$\mathrm{HC}$" align="top"></img></span><script type="math/tex">\mathrm{HC}</script></span></span> is complete with respect to those models and has the finite model property. We consider examples of the use of <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/211/5/709/revision1/MSB_211_5_709ieqn1.gif" style="max-width: 100%;" alt="$\mathrm{HC}$" align="top"></img></span><script type="math/tex">\mathrm{HC}</script></span></span>-models usage. In particular, we prove that <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/211/5/709/revision1/MSB_211_5_709ieqn1.gif" style="max-width: 100%;" alt="$\mathrm{HC}$" align="top"></img></span><script type="math/tex">\mathrm{HC}</script></span></span> is a conservative extension of the logic <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/211/5/709/revision1/MSB_211_5_709ieqn2.gif" style="max-width: 100%;" alt="$\mathrm{H4}$" align="top"></img></span><script type="math/tex">\mathrm{H4}</script></span></span>. We also show that the logic <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/211/5/709/revision1/MSB_211_5_709ieqn1.gif" style="max-width: 100%;" alt="$\mathrm{HC}$" align="top"></img></span><script type="math/tex">\mathrm{HC}</script></span></span> is complete with respect to Kripke frames with sets of audit worlds introduced by Artemov and Protopopescu (who called them audit set models). </p><p> Bibliography: 31 titles. </p></div> <div class="art-list-item-tools small wd-abstr-lower"> <a class="mr-2" href="https://doi.org/10.1070/SM9275">https://doi.org/10.1070/SM9275</a> </div> </div> </div> </div> <div class="art-list-item reveal-container reveal-closed"> <div class="art-list-item-body"> <a href="/article/10.1070/SM9446" class="art-list-item-title event_main-link">Singularities on toric fibrations</a> <p class="small art-list-item-meta"> C. Birkar and Y. Chen 2021 <em>Sb. Math.</em> <b>212</b> 288 </p> <div class="art-list-item-tools small wd-abstr-upper"> <button type="button" class="reveal-trigger mr-2 nowrap"> <svg aria-hidden="true" class="fa-icon fa-icon--left fa-icon--flip" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 320 512"><path d="M137.4 374.6c12.5 12.5 32.8 12.5 45.3 0l128-128c9.2-9.2 11.9-22.9 6.9-34.9s-16.6-19.8-29.6-19.8L32 192c-12.9 0-24.6 7.8-29.6 19.8s-2.2 25.7 6.9 34.9l128 128z"/></svg><span class="reveal-trigger-label" data-reveal-text="Open abstract" data-reveal-label-alt="Close abstract" data-link-purpose-append="Singularities on toric fibrations" data-link-purpose-append-open="Singularities on toric fibrations">Open abstract</span> </button> <a href="/article/10.1070/SM9446/meta" class="mr-2 mb-0 nowrap event_mini-link" data-event-action="View article"> <span class="icon-article"></span>View article<span class="offscreen-hidden">, Singularities on toric fibrations</span></a> <a href="/article/10.1070/SM9446/pdf" class="mr-2 mb-0 nowrap event_mini-link" data-event-action="PDF"><span class="icon-file-pdf"></span>PDF<span class="offscreen-hidden">, Singularities on toric fibrations</span></a> </div> <div class="reveal-content"> <div class="article-text view-text-small"><p> In this paper we investigate singularities on toric fibrations. In this context we study a conjecture of Shokurov (a special case of which is due to M<span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/212/3/288/revision3/MSB_212_3_288ieqn1.gif" style="max-width: 100%;" alt="$^c$" align="top"></img></span><script type="math/tex">^c</script></span></span>Kernan which roughly says that if <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/212/3/288/revision3/MSB_212_3_288ieqn2.gif" style="max-width: 100%;" alt="$(X,B)\to Z$" align="top"></img></span><script type="math/tex">(X,B)\to Z</script></span></span> is an <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/212/3/288/revision3/MSB_212_3_288ieqn3.gif" style="max-width: 100%;" alt="$\varepsilon$" align="top"></img></span><script type="math/tex">\varepsilon</script></span></span>-lc Fano-type log Calabi-Yau fibration, then the singularities of the log base <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/212/3/288/revision3/MSB_212_3_288ieqn4.gif" style="max-width: 100%;" alt="$(Z,B_Z+M_Z)$" align="top"></img></span><script type="math/tex">(Z,B_Z+M_Z)</script></span></span> are bounded in terms of <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/212/3/288/revision3/MSB_212_3_288ieqn3.gif" style="max-width: 100%;" alt="$\varepsilon$" align="top"></img></span><script type="math/tex">\varepsilon</script></span></span> and <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/212/3/288/revision3/MSB_212_3_288ieqn5.gif" style="max-width: 100%;" alt="$\dim X$" align="top"></img></span><script type="math/tex">\dim X</script></span></span> where <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/212/3/288/revision3/MSB_212_3_288ieqn6.gif" style="max-width: 100%;" alt="$B_Z$" align="top"></img></span><script type="math/tex">B_Z</script></span></span> and <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/212/3/288/revision3/MSB_212_3_288ieqn7.gif" style="max-width: 100%;" alt="$M_Z$" align="top"></img></span><script type="math/tex">M_Z</script></span></span> are the discriminant and moduli divisors of the canonical bundle formula. A corollary of our main result says that if <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/212/3/288/revision3/MSB_212_3_288ieqn8.gif" style="max-width: 100%;" alt="$X\to Z$" align="top"></img></span><script type="math/tex">X\to Z</script></span></span> is a toric Fano fibration with <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/212/3/288/revision3/MSB_212_3_288ieqn9.gif" style="max-width: 100%;" alt="$X$" align="top"></img></span><script type="math/tex">X</script></span></span> being <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/212/3/288/revision3/MSB_212_3_288ieqn3.gif" style="max-width: 100%;" alt="$\varepsilon$" align="top"></img></span><script type="math/tex">\varepsilon</script></span></span>-lc, then the multiplicities of the fibres over codimension one points are bounded depending only on <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/212/3/288/revision3/MSB_212_3_288ieqn3.gif" style="max-width: 100%;" alt="$\varepsilon$" align="top"></img></span><script type="math/tex">\varepsilon</script></span></span> and <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/212/3/288/revision3/MSB_212_3_288ieqn5.gif" style="max-width: 100%;" alt="$\dim X$" align="top"></img></span><script type="math/tex">\dim X</script></span></span>. </p><p> Bibliography: 20 titles. </p></div> <div class="art-list-item-tools small wd-abstr-lower"> <a class="mr-2" href="https://doi.org/10.1070/SM9446">https://doi.org/10.1070/SM9446</a> </div> </div> </div> </div> <div class="art-list-item reveal-container reveal-closed"> <div class="art-list-item-body"> <a href="/article/10.1070/SM9108" class="art-list-item-title event_main-link">Letter to the editors</a> <p class="small art-list-item-meta"> V. A. Kozlov and S. A. Nazarov 2018 <em>Sb. Math.</em> <b>209</b> 919 </p> <div class="art-list-item-tools small wd-abstr-upper"> <a href="/article/10.1070/SM9108/meta" class="mr-2 mb-0 nowrap event_mini-link" data-event-action="View article"> <span class="icon-article"></span>View article<span class="offscreen-hidden">, Letter to the editors</span></a> <a href="/article/10.1070/SM9108/pdf" class="mr-2 mb-0 nowrap event_mini-link" data-event-action="PDF"><span class="icon-file-pdf"></span>PDF<span class="offscreen-hidden">, Letter to the editors</span></a> </div> <div class="reveal-content"> <div class="article-text view-text-small"></div> <div class="art-list-item-tools small wd-abstr-lower"> <a class="mr-2" href="https://doi.org/10.1070/SM9108">https://doi.org/10.1070/SM9108</a> </div> </div> </div> </div> <div class="art-list-item reveal-container reveal-closed"> <div class="art-list-item-body"> <a href="/article/10.1070/SM2013v204n09ABEH004339" class="art-list-item-title event_main-link">Conformally flat Lorentzian manifolds with special holonomy groups</a> <p class="small art-list-item-meta"> A. S. Galaev 2013 <em>Sb. Math.</em> <b>204</b> 1264 </p> <div class="art-list-item-tools small wd-abstr-upper"> <button type="button" class="reveal-trigger mr-2 nowrap"> <svg aria-hidden="true" class="fa-icon fa-icon--left fa-icon--flip" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 320 512"><path d="M137.4 374.6c12.5 12.5 32.8 12.5 45.3 0l128-128c9.2-9.2 11.9-22.9 6.9-34.9s-16.6-19.8-29.6-19.8L32 192c-12.9 0-24.6 7.8-29.6 19.8s-2.2 25.7 6.9 34.9l128 128z"/></svg><span class="reveal-trigger-label" data-reveal-text="Open abstract" data-reveal-label-alt="Close abstract" data-link-purpose-append="Conformally flat Lorentzian manifolds with special holonomy groups" data-link-purpose-append-open="Conformally flat Lorentzian manifolds with special holonomy groups">Open abstract</span> </button> <a href="/article/10.1070/SM2013v204n09ABEH004339/meta" class="mr-2 mb-0 nowrap event_mini-link" data-event-action="View article"> <span class="icon-article"></span>View article<span class="offscreen-hidden">, Conformally flat Lorentzian manifolds with special holonomy groups</span></a> <a href="/article/10.1070/SM2013v204n09ABEH004339/pdf" class="mr-2 mb-0 nowrap event_mini-link" data-event-action="PDF"><span class="icon-file-pdf"></span>PDF<span class="offscreen-hidden">, Conformally flat Lorentzian manifolds with special holonomy groups</span></a> </div> <div class="reveal-content"> <div class="article-text view-text-small"><p>We obtain a local classification of conformally flat Lorentzian manifolds with special holonomy groups. The corresponding local metrics are certain extensions of Riemannian spaces of constant sectional curvature to Walker metrics.</p><p>Bibliography: 28 titles.</p></div> <div class="art-list-item-tools small wd-abstr-lower"> <a class="mr-2" href="https://doi.org/10.1070/SM2013v204n09ABEH004339">https://doi.org/10.1070/SM2013v204n09ABEH004339</a> </div> </div> </div> </div> </div>  </div> </div> </div>   <div tabindex="0" role="tabpanel" id="latest-articles-tab" aria-labelledby="latest-articles"> <div class=" reveal-container reveal-closed reveal-enabled reveal-container--jnl-tab"> <h2 class="tabpanel__title"> <button type="button" class="reveal-trigger event_tabs-accordion" aria-expanded="false"> <svg aria-hidden="true" class="fa-icon fa-icon--left fa-icon--flip" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 320 512"><path d="M137.4 374.6c12.5 12.5 32.8 12.5 45.3 0l128-128c9.2-9.2 11.9-22.9 6.9-34.9s-16.6-19.8-29.6-19.8L32 192c-12.9 0-24.6 7.8-29.6 19.8s-2.2 25.7 6.9 34.9l128 128z"/></svg>Latest articles</button> </h2> <div class="reveal-content tabpanel__content" style="display: none"> <p> <button data-reveal-label-alt="Close all abstracts" class="reveal-all-trigger mr-2 small" data-reveal-text="Open all abstracts" data-link-purpose-append="in this tab" data-link-purpose-append-open="in this tab"> Open all abstracts<span class="offscreen-hidden">, in this tab</span> </button> </p>  <div class="art-list"> <div class="art-list-item reveal-container reveal-closed"> <div class="art-list-item-body"> <a href="/article/10.1070/SM9542" class="art-list-item-title event_main-link">Configuration spaces of hinged mechanisms, and their projections</a> <p class="small art-list-item-meta"> M. D. Kovalev 2022 <em>Sb. Math.</em> <b>213</b> 512 </p> <div class="art-list-item-tools small wd-abstr-upper"> <button type="button" class="reveal-trigger mr-2 nowrap"> <svg aria-hidden="true" class="fa-icon fa-icon--left fa-icon--flip" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 320 512"><path d="M137.4 374.6c12.5 12.5 32.8 12.5 45.3 0l128-128c9.2-9.2 11.9-22.9 6.9-34.9s-16.6-19.8-29.6-19.8L32 192c-12.9 0-24.6 7.8-29.6 19.8s-2.2 25.7 6.9 34.9l128 128z"/></svg><span class="reveal-trigger-label" data-reveal-text="Open abstract" data-reveal-label-alt="Close abstract" data-link-purpose-append="Configuration spaces of hinged mechanisms, and their projections" data-link-purpose-append-open="Configuration spaces of hinged mechanisms, and their projections">Open abstract</span> </button> <a href="/article/10.1070/SM9542/meta" class="mr-2 mb-0 nowrap event_mini-link" data-event-action="View article"> <span class="icon-article"></span>View article<span class="offscreen-hidden">, Configuration spaces of hinged mechanisms, and their projections</span></a> <a href="/article/10.1070/SM9542/pdf" class="mr-2 mb-0 nowrap event_mini-link" data-event-action="PDF"><span class="icon-file-pdf"></span>PDF<span class="offscreen-hidden">, Configuration spaces of hinged mechanisms, and their projections</span></a> </div> <div class="reveal-content"> <div class="article-text view-text-small"><p> Our subject is the geometry of planar hinged mechanisms. The article contains a formalization of basic concepts of the theory of hinged-lever constructions, as well as some information from real algebraic geometry needed for their study. We consider mechanisms with variable number of degrees of freedom and mechanisms that have more than one degree of freedom but each hinge of which moves with one degree of freedom. For the last type we find the dimension of the configuration space. We give a number of examples of mechanisms with unusual geometric properties and formulate open questions. </p><p> Bibliography: 17 titles. </p></div> <div class="art-list-item-tools small wd-abstr-lower"> <a class="mr-2" href="https://doi.org/10.1070/SM9542">https://doi.org/10.1070/SM9542</a> </div> </div> </div> </div> <div class="art-list-item reveal-container reveal-closed"> <div class="art-list-item-body"> <a href="/article/10.1070/SM9559" class="art-list-item-title event_main-link">How many roots of a system of random Laurent polynomials are real?</a> <p class="small art-list-item-meta"> B. Ya. Kazarnovskii 2022 <em>Sb. Math.</em> <b>213</b> 466 </p> <div class="art-list-item-tools small wd-abstr-upper"> <button type="button" class="reveal-trigger mr-2 nowrap"> <svg aria-hidden="true" class="fa-icon fa-icon--left fa-icon--flip" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 320 512"><path d="M137.4 374.6c12.5 12.5 32.8 12.5 45.3 0l128-128c9.2-9.2 11.9-22.9 6.9-34.9s-16.6-19.8-29.6-19.8L32 192c-12.9 0-24.6 7.8-29.6 19.8s-2.2 25.7 6.9 34.9l128 128z"/></svg><span class="reveal-trigger-label" data-reveal-text="Open abstract" data-reveal-label-alt="Close abstract" data-link-purpose-append="How many roots of a system of random Laurent polynomials are real?" data-link-purpose-append-open="How many roots of a system of random Laurent polynomials are real?">Open abstract</span> </button> <a href="/article/10.1070/SM9559/meta" class="mr-2 mb-0 nowrap event_mini-link" data-event-action="View article"> <span class="icon-article"></span>View article<span class="offscreen-hidden">, How many roots of a system of random Laurent polynomials are real?</span></a> <a href="/article/10.1070/SM9559/pdf" class="mr-2 mb-0 nowrap event_mini-link" data-event-action="PDF"><span class="icon-file-pdf"></span>PDF<span class="offscreen-hidden">, How many roots of a system of random Laurent polynomials are real?</span></a> </div> <div class="reveal-content"> <div class="article-text view-text-small"><p> We say that a zero of a Laurent polynomial that lies on the unit circle with centre <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/213/4/466/revision1/MSB_213_4_466ieqn1.gif" style="max-width: 100%;" alt="$0\in\mathbb C$" align="top"></img></span><script type="math/tex">0\in\mathbb C</script></span></span> is real. We also say that a Laurent polynomial that is real on this circle is real. In contrast with ordinary polynomials, it is known that for random real Laurent polynomials of increasing degree the average proportion of real roots tends to <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/213/4/466/revision1/MSB_213_4_466ieqn2.gif" style="max-width: 100%;" alt="$1/\sqrt 3$" align="top"></img></span><script type="math/tex">1/\sqrt 3</script></span></span> rather than to <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/213/4/466/revision1/MSB_213_4_466ieqn3.gif" style="max-width: 100%;" alt="$0$" align="top"></img></span><script type="math/tex">0</script></span></span>. We show that this phenomenon of the asymptotically nonvanishing proportion of real roots also holds for systems of Laurent polynomials of several variables. The corresponding asymptotic formula is obtained in terms of the mixed volumes of certain convex compact sets determining the growth of the system of polynomials. </p><p> Bibliography: 11 titles. </p></div> <div class="art-list-item-tools small wd-abstr-lower"> <a class="mr-2" href="https://doi.org/10.1070/SM9559">https://doi.org/10.1070/SM9559</a> </div> </div> </div> </div> <div class="art-list-item reveal-container reveal-closed"> <div class="art-list-item-body"> <a href="/article/10.1070/SM9579" class="art-list-item-title event_main-link">Realization of Fomenko-Zieschang invariants in closed symplectic manifolds with contact singularities</a> <p class="small art-list-item-meta"> D. B. Zot'ev and V. I. Sidel'nikov 2022 <em>Sb. Math.</em> <b>213</b> 443 </p> <div class="art-list-item-tools small wd-abstr-upper"> <button type="button" class="reveal-trigger mr-2 nowrap"> <svg aria-hidden="true" class="fa-icon fa-icon--left fa-icon--flip" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 320 512"><path d="M137.4 374.6c12.5 12.5 32.8 12.5 45.3 0l128-128c9.2-9.2 11.9-22.9 6.9-34.9s-16.6-19.8-29.6-19.8L32 192c-12.9 0-24.6 7.8-29.6 19.8s-2.2 25.7 6.9 34.9l128 128z"/></svg><span class="reveal-trigger-label" data-reveal-text="Open abstract" data-reveal-label-alt="Close abstract" data-link-purpose-append="Realization of Fomenko-Zieschang invariants in closed symplectic manifolds with contact singularities" data-link-purpose-append-open="Realization of Fomenko-Zieschang invariants in closed symplectic manifolds with contact singularities">Open abstract</span> </button> <a href="/article/10.1070/SM9579/meta" class="mr-2 mb-0 nowrap event_mini-link" data-event-action="View article"> <span class="icon-article"></span>View article<span class="offscreen-hidden">, Realization of Fomenko-Zieschang invariants in closed symplectic manifolds with contact singularities</span></a> <a href="/article/10.1070/SM9579/pdf" class="mr-2 mb-0 nowrap event_mini-link" data-event-action="PDF"><span class="icon-file-pdf"></span>PDF<span class="offscreen-hidden">, Realization of Fomenko-Zieschang invariants in closed symplectic manifolds with contact singularities</span></a> </div> <div class="reveal-content"> <div class="article-text view-text-small"><p> The topological bifurcations of Liouville foliations on invariant <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/213/4/443/revision1/MSB_213_4_443ieqn1.gif" style="max-width: 100%;" alt="$3$" align="top"></img></span><script type="math/tex">3</script></span></span>-manifolds that are induced by attaching toric <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/213/4/443/revision1/MSB_213_4_443ieqn2.gif" style="max-width: 100%;" alt="$\Theta$" align="top"></img></span><script type="math/tex">\Theta</script></span></span>-handles are investigated. It is shown that each marked molecule (Fomenko-Zieschang invariant) can be realized on an invariant submanifold of a closed symplectic manifold with contact singularities which is obtained by attaching toric <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/213/4/443/revision1/MSB_213_4_443ieqn2.gif" style="max-width: 100%;" alt="$\Theta$" align="top"></img></span><script type="math/tex">\Theta</script></span></span>-handles sequentially to a set of symplectic manifolds, while these latter have the structures of locally trivial fibrations over <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/213/4/443/revision1/MSB_213_4_443ieqn3.gif" style="max-width: 100%;" alt="$S^1$" align="top"></img></span><script type="math/tex">S^1</script></span></span> associated with atoms. </p><p> Bibliography: 10 titles. </p></div> <div class="art-list-item-tools small wd-abstr-lower"> <a class="mr-2" href="https://doi.org/10.1070/SM9579">https://doi.org/10.1070/SM9579</a> </div> </div> </div> </div> <div class="art-list-item reveal-container reveal-closed"> <div class="art-list-item-body"> <a href="/article/10.1070/SM9609" class="art-list-item-title event_main-link">Time minimization problem on the group of motions of a plane with admissible control in a half-disc</a> <p class="small art-list-item-meta"> A. P. Mashtakov 2022 <em>Sb. Math.</em> <b>213</b> 534 </p> <div class="art-list-item-tools small wd-abstr-upper"> <button type="button" class="reveal-trigger mr-2 nowrap"> <svg aria-hidden="true" class="fa-icon fa-icon--left fa-icon--flip" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 320 512"><path d="M137.4 374.6c12.5 12.5 32.8 12.5 45.3 0l128-128c9.2-9.2 11.9-22.9 6.9-34.9s-16.6-19.8-29.6-19.8L32 192c-12.9 0-24.6 7.8-29.6 19.8s-2.2 25.7 6.9 34.9l128 128z"/></svg><span class="reveal-trigger-label" data-reveal-text="Open abstract" data-reveal-label-alt="Close abstract" data-link-purpose-append="Time minimization problem on the group of motions of a plane with admissible control in a half-disc" data-link-purpose-append-open="Time minimization problem on the group of motions of a plane with admissible control in a half-disc">Open abstract</span> </button> <a href="/article/10.1070/SM9609/meta" class="mr-2 mb-0 nowrap event_mini-link" data-event-action="View article"> <span class="icon-article"></span>View article<span class="offscreen-hidden">, Time minimization problem on the group of motions of a plane with admissible control in a half-disc</span></a> <a href="/article/10.1070/SM9609/pdf" class="mr-2 mb-0 nowrap event_mini-link" data-event-action="PDF"><span class="icon-file-pdf"></span>PDF<span class="offscreen-hidden">, Time minimization problem on the group of motions of a plane with admissible control in a half-disc</span></a> </div> <div class="reveal-content"> <div class="article-text view-text-small"><p> The time minimization problem with admissible control in a half-disc is considered on the group of motions of a plane. The control system under study provides a model of a car on the plane that can move forwards or rotate in place. Optimal trajectories of such a system are used to detect salient curves in image analysis. In particular, in medical image analysis such trajectories are used for tracking vessels in retinal images. The problem is of independent interest in geometric control theory: it provides a model example when the set of values of the control parameters contains zero at the boundary. The problem of controllability and existence of optimal trajectories is studied. By analysing the Hamiltonian system of the Pontryagin maximum principle the explicit form of extremal controls and trajectories is found. Optimality of the extremals is partially investigated. The structure of the optimal synthesis is described. </p><p> Bibliography: 33 titles. </p></div> <div class="art-list-item-tools small wd-abstr-lower"> <a class="mr-2" href="https://doi.org/10.1070/SM9609">https://doi.org/10.1070/SM9609</a> </div> </div> </div> </div> <div class="art-list-item reveal-container reveal-closed"> <div class="art-list-item-body"> <a href="/article/10.1070/SM9628" class="art-list-item-title event_main-link">Extremal functional <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="https://content.cld.iop.org/journals/1064-5616/213/4/556/revision1/MSB_213_4_556ieqn1.gif" alt="$L_p$" align="top"></img></span><script type="math/tex">L_p</script></span></span>-interpolation on an arbitrary mesh on the real axis</a> <p class="small art-list-item-meta"> Yu. N. Subbotin and V. T. Shevaldin 2022 <em>Sb. Math.</em> <b>213</b> 556 </p> <div class="art-list-item-tools small wd-abstr-upper"> <button type="button" class="reveal-trigger mr-2 nowrap"> <svg aria-hidden="true" class="fa-icon fa-icon--left fa-icon--flip" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 320 512"><path d="M137.4 374.6c12.5 12.5 32.8 12.5 45.3 0l128-128c9.2-9.2 11.9-22.9 6.9-34.9s-16.6-19.8-29.6-19.8L32 192c-12.9 0-24.6 7.8-29.6 19.8s-2.2 25.7 6.9 34.9l128 128z"/></svg><span class="reveal-trigger-label" data-reveal-text="Open abstract" data-reveal-label-alt="Close abstract" data-link-purpose-append="Extremal functional -interpolation on an arbitrary mesh on the real axis" data-link-purpose-append-open="Extremal functional -interpolation on an arbitrary mesh on the real axis">Open abstract</span> </button> <a href="/article/10.1070/SM9628/meta" class="mr-2 mb-0 nowrap event_mini-link" data-event-action="View article"> <span class="icon-article"></span>View article<span class="offscreen-hidden">, Extremal functional -interpolation on an arbitrary mesh on the real axis</span></a> <a href="/article/10.1070/SM9628/pdf" class="mr-2 mb-0 nowrap event_mini-link" data-event-action="PDF"><span class="icon-file-pdf"></span>PDF<span class="offscreen-hidden">, Extremal functional -interpolation on an arbitrary mesh on the real axis</span></a> </div> <div class="reveal-content"> <div class="article-text view-text-small"><p> The Golomb-de Boor problem of extremal interpolation of infinite real sequences with smallest <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/213/4/556/revision1/MSB_213_4_556ieqn1.gif" style="max-width: 100%;" alt="$L_p$" align="top"></img></span><script type="math/tex">L_p</script></span></span>-norm of the <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/213/4/556/revision1/MSB_213_4_556ieqn2.gif" style="max-width: 100%;" alt="$n$" align="top"></img></span><script type="math/tex">n</script></span></span>th derivative of the interpolant, <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/213/4/556/revision1/MSB_213_4_556ieqn3.gif" style="max-width: 100%;" alt="$1\leqslant p\leqslant \infty$" align="top"></img></span><script type="math/tex">1\leqslant p\leqslant \infty</script></span></span>, on an arbitrary mesh on the real axis is studied under constraints on the norms of the corresponding divided differences. For this smallest norm, lower estimates are obtained for any <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/213/4/556/revision1/MSB_213_4_556ieqn4.gif" style="max-width: 100%;" alt="$n\in \mathbb N$" align="top"></img></span><script type="math/tex">n\in \mathbb N</script></span></span> in terms of <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/213/4/556/revision1/MSB_213_4_556ieqn5.gif" style="max-width: 100%;" alt="$B$" align="top"></img></span><script type="math/tex">B</script></span></span>-splines. For the second derivative, this quantity is estimated from below and above by constants depending on the parameter <span xmlns:xlink="http://www.w3.org/1999/xlink" class="inline-eqn"><span class="tex"><span class="texImage"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mNkYAAAAAYAAjCB0C8AAAAASUVORK5CYII=" data-src="https://content.cld.iop.org/journals/1064-5616/213/4/556/revision1/MSB_213_4_556ieqn6.gif" style="max-width: 100%;" alt="$p$" align="top"></img></span><script type="math/tex">p</script></span></span>. </p><p> Bibliography: 13 titles. </p></div> <div class="art-list-item-tools small wd-abstr-lower"> <a class="mr-2" href="https://doi.org/10.1070/SM9628">https://doi.org/10.1070/SM9628</a> </div> </div> </div> </div> </div>  </div> </div> </div>                  </div>  </div>  </div> </main> <div class="db2 tb2"> <div class="side-and-below">  <div class="sidebar-list" id="wd-jnl-links"> <h2 class="sidebar-list__heading">Journal 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