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It is shown that the Belle and LHCb data on the interference of the amplitudes of the S- and D-partial waves in the decays $D_{s1}(2536 )^+\to D^{*+}K^0_S$ and $D_{s1}(2536)^-\to\bar D^{*0}K^-$ allow us to obtain an estimate of the S-wave $D^*K$ scattering length in the channel with isospin $I=0$: $|a^{(0)}_{D^*K}|=(0.94\pm0.06)$ fm. The possibility of explaining the found value by the contribution of the $D_{s1}(2460)$ resonance is discussed. The decay of $B_{s1}(5830)\to B^*\bar K$ is also briefly discussed., Comment: 8 pages

We construct an Anick type wild automorphism $\delta$ in a 3-generated free Poisson algebra which induces a tame automorphism in a 3-generated polynomial algebra. We also show that $\delta$ is stably tame. Dedicated to the memory of professor V.A.Roman'kov

The Conditional Gradient (or Frank-Wolfe) method is one of the most well-known methods for solving constrained optimization problems appearing in various machine learning tasks. The simplicity of iteration and applicability to many practical problems helped the method to gain popularity in the community. In recent years, the Frank-Wolfe algorithm received many different extensions, including stochastic modifications with variance reduction and coordinate sampling for training of huge models or distributed variants for big data problems. In this paper, we present a unified convergence analysis of the Stochastic Frank-Wolfe method that covers a large number of particular practical cases that may have completely different nature of stochasticity, intuitions and application areas. Our analysis is based on a key parametric assumption on the variance of the stochastic gradients. But unlike most works on unified analysis of other methods, such as SGD, we do not assume an unbiasedness of the real gradient estimation. We conduct analysis for convex and non-convex problems due to the popularity of both cases in machine learning. With this general theoretical framework, we not only cover rates of many known methods, but also develop numerous new methods. This shows the flexibility of our approach in developing new algorithms based on the Conditional Gradient approach. We also demonstrate the properties of the new methods through numerical experiments., Comment: Appears in: The 27th International Conference on Artificial Intelligence and Statistics (AISTATS 2024). 42 pages, 13 algorithms, 8 figures, 3 tables. Reference: https://proceedings.mlr.press/v238/nazykov24a.html

It is shown that the values of the ratios $\mathcal{B}(D^0\to a_0(980)^+\pi^-)/\mathcal{B} (D^0\to a_0(980)^-\pi^+ )$ and $\mathcal{B}(D^+\to a_0(980)^+\pi^0)/\mathcal{B} (D^+\to a_0(980)^0 \pi^+)$, recently measured by the BESIII Collaboration, are naturally explained in the four-quark model of the $a_0(980) $ resonance., Comment: 4 pages, 5 figures, v2, clarifications and references added, published in Phys. Rev. D

The rates of the $X(3872)\to\pi^0\pi^0\chi_{c1}$ and $X(3872)\to \pi^+\pi^-\chi_{c1}$ decays are estimated in the model of the triangle loop diagrams with charmed $D^*\bar DD$ and $\bar D^*D\bar D$ mesons in the loops. There are the triangle logarithmic singularities in the physical region of the $X(3872)\to\pi^0\pi^0 \chi_{c1}$ decay which manifest themselves as narrow peaks in the $\pi^0\chi_{c1}$ mass spectrum near the $D^0\bar D^0$ threshold. The model predicts approximately the same branching fractions of the $X(3872)\to\pi^0\pi^0 \chi_{c1}$ and $X(3872)\to\pi^+\pi^-\chi_{c1}$ decays at the level of about (0.8-1.7)$\times10^{-4}$. A distinct prediction of the model is the value of the ratio $\mathcal{R}= \mathcal{B}(X(3872)\to\pi^+\pi^-\chi_{c1})/\mathcal{B}(X(3872) \to\pi^0\pi^0\chi_{c1})\approx1.1$. It weakly depends on the $X(3872)$ resonance parameters and indicates a significant violation of the isotopic symmetry according to which one would expect $\mathcal{R}=2$., Comment: 11 pages, 6 figures; v2, clarifications added, published in Phys. Rev. D

The Jacobson Coordinatization Theorem describes the structure of unitary Jordan algebras containing the algebra $H_n(F)$ of symmetric nxn matrices over a field F with the same identity element, for $n\geq 3$. In this paper we extend the Jacobson Coordinatization Theorem for n=2. Specifically, we prove that if J is a unitary Jordan algebra containing the Jordan matrix algebra $H_2(F)$ with the same identity element, then J has a form $J=H_2(F)\otimes A_0+k\otimes A_1$, where $A=A_0+A_1$ is a $Z_2$-graded Jordan algebra with a partial odd Leibniz bracket {,} an $k=e_{12}-e_{21}\in M_2(F)$ with the multiplication given by $(a\otimes b)(c\otimes d)=ac\otimes bd + [a,c]\otimes \{b,d\},$ the commutator [a,c] is taken in $M_2(F)$., Comment: 24 pages

The well-known model of the triangle diagrams with $D^*\bar DD^*$ and $\bar D^*D\bar D^*$ mesons in the loops is compared with the modern data on the amplitude of the $X(3872)\to\pi^0\chi_{c1}(1P)$ decay. Considering the $X(3872)$ object as a $\chi_{c1}(2P)$ charmonium state, we introduce a parameter $\xi$ characterizing the scale of the isotopic symmetry violation in this decay and find a lower limit of $\xi\simeq0.0916$. The model incorporates the only fitted parameter associated with the form factor. We analyze in detail the influence of the form factor on the amplitude $X(3872)\to\pi^0 \chi_{c1}(1P)$ and on the parameter $\xi$. As the suppression of the amplitude by the form factor increases, $\xi$ increases. Due to the fact that the $X(3872)$ resonance is located practically at the threshold of the $D^0\bar D^{*0}$ channel, the amplitude of $X(3872) \to\pi^0\chi_{c1}(1P)$ turns out to be proportional to $\sqrt{m_d -m_u}$. Using the estimating values for the coupling constants $g_{XD\bar D^*}$, $g_{\chi_{ c1}D\bar D^*}$, and $g_{D^{*0}D^{*0}\pi^0}$, we show that the model of the triangle loop diagrams is in reasonable agreement with the available data. Apart from the difference in the masses of neutral and charged charmed mesons, any additional exotic sources of isospin violation in $X(3872)\to\pi^0\chi_{c1}(1P)$ (such as a significant difference between the coupling constants $g_{XD^0\bar D^{*0}}$ and $g_{XD^+ D^{*-}}$) are not required to interpret the data. This indirectly confirms the isotopic neutrality of the $X(3872)$, which is naturally realized for the $c\bar c$ state $\chi_{c1}(2P)$., Comment: 12 pages, 7 figures, v2, published version, clarifications and references added

It is proved that for any natural number $n$ the subalgebra of a free finitely generated alternative algebra generated by all the words on generators whose length is a multiple of $n$ (the Veronese $n$-subalgebra), is finitely generated.

Major results of researches conducted by Russian geodesists in 2019-2022 on the topics of the International Association of Geodesy (IAG) of the International Union of Geodesy and Geophysics (IUGG) are presented in this issue. This report is prepared by the Section of Geodesy of the National Geophysical Committee of Russia. In the report prepared for the XXVII General Assembly of IUGG (Germany, Berlin, 11-20 July 2023), the results of principal researches in geodesy, geodynamics, gravimetry, in the studies of geodetic reference frame creation and development, Earth's shape and gravity field, Earth's rotation, geodetic theory, its application and some other directions are briefly described. For some objective reasons not all results obtained by Russian scientists on the field of geodesy are included in the report., Comment: Misprint in the title of the arXiv record has been corrected. The submission content is not affected

Using the result of the VES Collaboration for $Br(J/\psi\to\gamma f_0(1710))$, we estimate the absolute branching fractions for the $f_0(1710)$ decays into $\pi\pi$, $K\bar K$, $\eta\eta$, $\omega\omega$, and $\omega\phi$. In addition, we estimate $Br(\psi(2S)\to\gamma f_0(1710))\approx3.5\times10^{-5}$ and $Br(\Upsilon(1S)\to\gamma f_0(1710))\approx1\times10^{-5}$., Comment: 2 pages; v3: version as published in JETP Letters

The current situation with the recently discovered $a_0(1700/1800)$ resonance is very paradoxical: it is believed that $a_0(1700/1800)$ must be strongly coupled with two vector mesons, but there is no direct experimental confirmation of this yet. Based on the assumption that the $a_0(1700/1800)$ is a state similar to the four-quark state from the MIT bag, belonging to either the $\underline{9}^*$ or the $\underline{36}^*$ $q^2\bar q^2$ multiplet, we analyze the influence of the strong $a_0(1700/1800)$ coupling to the vector channels $K^* \bar K^*$, $\rho\phi$, and $\rho \omega$ on its line shape in the decay channels into pseudoscalar mesons $K\bar K$, $\pi\eta$, and $\pi\eta'$. This effect depends on the location of the resonance mass $m_{a_0}$ relative to the nominal thresholds of vector channels. For example, if $m_{a_0}\approx 1700$ MeV, then the influence turns out to be hidden in a fairly wide range of coupling constants. On the whole, our analysis shows that, to confirm the presence of the strong $a_0(1700/1800)$ coupling to the vector channels, utterly required is the direct detection of the decays $a_0(1700/1800)\to K^*\bar K^*$, $\rho\phi$, $\rho\omega$. The appearance of even certain hints at the existence of these decays would make it possible to fundamentally advance in understanding the nature of the new $a_0$ state., Comment: 11 pages, 5 figures; v2 clarifications and references added

Recently V.H.L\'opez Sol\'is and I.Shestakov solved an old problem by N.Jacobson on describing of unital alternative algebras containing the $2\times 2$ matrix algebra $M_2$ as a unital subalgebra. Here we give another description of $M_2$-algebras via the 6-dimensional alternative superalgebra $B(4,2)$ and an auxiliar $\mathbf {\mit Z}_2$-graded algebra $\mit\Gamma$. It occurs that the category of alternative $M_2$-algebras is isomorphic to the category of $\mit\Gamma$-algebras. For any associative and commutative algebra $A$, we give a construction of a ${\mit \Gamma}$-algebra $\mit\Gamma(A)$, which turns to be a Jordan superalgebra; if $A$ is a domain then $\mit\Gamma(A)$ is a prime superalgebra. We describe also the free $\mit\Gamma$-algebras and construct their bases.

We present a phenomenological description of the LHCb data for the magnitudes and phases of the $\pi^-\pi^+$ $S$-wave amplitudes in the $D^+\to\pi^-\pi^+\pi^+$ and $D^+_s\to\pi^-\pi^+\pi^+$ decays. We operate within a simple model that takes into account the known pair interactions of particles in coupled channels. The seed complex amplitudes for various intermediate state production are assumed to be independent of the energy. Their values are determined by fitting. This model gives the satisfactorily description of virtually all features of the energy dependence of the experimentally measured $S$-wave amplitudes in the $D^+\to\pi^-\pi^+ \pi^+$ and $D^+_s\to \pi^-\pi^+\pi^+$ decays in the regions $2m_\pi

A variety of associative algebras is called nonmatrix if it does not contain the algebra of 2 x 2 matrices over the given field. Nonmatrix varieties were introduced and studied by V.N.Latyshev in relation with the Specht problem. Some characterizations of nonmatrix varieties were obtained in the paper [10]. In the given paper the notion of nonmatrix variety is extended for nonassociative algebras, and the characterization from [10] is generalized for alternative, Jordan, and some other varieties of algebras.

A brief review of the available experimental and theoretical results on the production of the $\chi_{Q1}$ states in $e^+e^-$ annihilation and photon-photon $\gamma\gamma^*$ interactions is presented. Future data on the production of the $\chi_{c1}(1P)$, $\chi_{c1}(3872)$, $\chi_{c1} (4140)$, $\chi_{c1}(4274)$, $\chi_{c1}(4685)$, $\chi_{b1} (1P)$, $\chi_{b1}(2P )$, and $\chi_{b1}(3P)$ resonances in $e^+e^-$ annihilation and $\gamma\gamma^*$ interactions will help the development and unification of theoretical predictions related to the electroweak decays of heavy quarkonia, the reduction of their spread and model uncertainties., Comment: 6 pages; v2: published version, corrections and clarifications made, new references and a paragraph on polarized electron beam added