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The ExoMol database (www.exomol.com) provides molecular data for spectroscopic studies of hot atmospheres. These data are widely used to model atmospheres of exoplanets, cool stars and other astronomical objects, as well as a variety of terrestrial applications. The 2024 data release reports the current status of the database which contains recommended line lists for 91 molecules and 224 isotopologues giving a total of almost 10$^{12}$ individual transitions. New features of the database include extensive "MARVELization" of line lists to allow them to be used for high resolutions studies, extension of several line lists to ultraviolet wavelengths, provision of photodissociation cross sections and extended provision of broadening parameters. Some of the in-house data specifications have been rewritten in JSON and moved to conformity with other international standards. Data products, including specific heats, a database of lifetimes for plasma studies, and the ExoMolHR web app which allows exclusively high resolution data to be extracted, are discussed.

New ExoMol line lists AloHa for AlH and AlD are presented improving the previous line lists WYLLoT (Yurchenko et al., MNRAS 479, 1401 (2018)). The revision is motivated by the recent experimental measurements and astrophysical findings involving the highly excited rotational states of AlH in its $A\,^{1}\Pi-{X}\,^{1}\Sigma^{+}$ system. A new high-resolution emission spectrum of ten bands from the ${A}\,^{1}\Pi-{X}\,^{1}\Sigma^{+}$ system of AlD, in the region $17300 - 32000$ cm$^{-1}$ was recorded with a Fourier transform spectrometer, which probes the predissociative $A\,^1\Pi$ $v=2$ state. The AlD new line positions are combined with all available experimental data on AlH and AlD to construct a comprehensive set of empirical rovibronic energies of AlH and AlD covering the $X\,^1\Sigma^+$ and $A\,^1\Pi$ electronic states using the MARVEL approach. We then refine the spectroscopic model WYLLoT to our experimentally derived energies using the nuclear-motion code Duo and use this fit to produce improved line lists for $^{27}$AlH, $^{27}$AlD and $^{26}$AlH with a better coverage of the rotationally excited states of $A\,^1\Pi$ in the predissociative energy region. The lifetimes of the predissociative states are estimated and are included in the line list using the new ExoMol data structure, alongside the temperature-dependent continuum contribution to the photo-absorption spectra of AlH. The new line lists are shown to reproduce the experimental spectra of both AlH and AlD well, and to describe the AlH absorption in the recently reported Proxima Cen spectrum, including the strong predissociative line broadening. The line lists are included into the ExoMol database www.exomol.com.

Silicon mononitride ($^{28}$Si$^{14}$N, $^{29}$Si$^{14}$N, $^{30}$Si$^{14}$N, $^{28}$Si$^{15}$N) line lists covering infrared, visible and ultraviolet regions are presented. The \name\ line lists produced by ExoMol include rovibronic transitions between six electronic states: \XS, \AS, \BS, \DS, \asi, \bsi. The \ai\ potential energy and coupling curves, computed at the multireference configuration interaction (MRCI/aug-cc-pVQZ) level of theory, are refined for the observed states by fitting their analytical representations to 1052 experimentally derived SiN energy levels determined from rovibronic bands belonging to the $X$--$X$, $A$--$X$ and $B$--$X$ electronic systems through the MARVEL procedure. The SiNful line lists are compared to previously observed spectra, recorded and calculated lifetimes, and previously calculated partition functions. SiNful is available via the \url{www.exomol.com} database.

A new silicon monoxide ($^{28}$Si$^{16}$O) line list covering infrared, visible and ultraviolet regions called SiOUVenIR is presented. This line list extends the infrared EBJT ExoMol line list by including vibronic transitions to the $A\,{}^{1}\Pi$ and $E\,{}^{1}\Sigma^{+}$ electronic states. Strong perturbations to the $A\,{}^{1}\Pi$ band system are accurately modelled through the treatment of 6 dark electronic states: $C\,{}^{1}\Sigma^{-}$, $D\,{}^{1}\Delta$, $a\,{}^{3}\Sigma^{+}$, $b\,{}^{3}\Pi$, $e\,{}^{3}\Sigma^{-}$ and $d\,{}^{3}\Delta$. Along with the $X\,{}^{1}\Sigma^{+}$ ground state, these 9 electronic states were used to build a comprehensive spectroscopic model of SiO using a combination of empirical and ab initio curves, including the potential energy (PE), spin-orbit (SO), electronic angular momentum (EAM) and (transition) dipole moment curves. The ab initio PE and coupling curves, computed at the multireference configuration interaction (MRCI) level of theory, were refined by fitting their analytical representations to 2617 experimentally derived SiO energy levels determined from 97 vibronic bands belonging to the $X$-$X$, $E$-$X$ and $A$-$X$ electronic systems through the MARVEL procedure. 112 observed forbidden transitions from the $C$-$X$, $D$-$X$, $e$-$X$, and $d$-$X$ bands were assigned using our predictions, and these could be fed back into the MARVEL procedure. The SiOUVenIR line list was computed using published ab initio transition dipole moments for the $E$-$X$ and $A$-$X$ bands; the line list is suitable for temperatures up to 10,000 K and for wavelengths longer than 140 nm. SiOUVenIR is available from www.exomol.com and the CDS database.

We report an ab initio study on the rovibronic spectroscopy of the closed-shell diatomic molecule phosphorous mononitride, PN. The study considers the nine lowest electronic states, $X\,{}^{1}\Sigma^{+}$, $A\,{}^{1}\Pi$, $C\,{}^{1}\Sigma^{-}$, $D\,{}^{1}\Delta$, $E\,{}^{1}\Sigma^{-}$, $a\,{}^{3}\Sigma^{+}$, $b\,{}^{3}\Pi$, $d\,{}^{3}\Delta$ and $e\,{}^{3}\Sigma^{-}$ using high level electronic structure theory and accurate nuclear motion calculations. The ab initio data cover 9 potential energy, 14 spin-orbit coupling, 7 electronic angular momentum coupling, 9 electric dipole moment and 8 transition dipole moment curves. The Duo nuclear motion program is used to solve the coupled nuclear motion Schr\"{o}dinger equations for these nine electronic states and to simulate rovibronic absorption spectra of $^{31}$P$^{14}$N for different temperatures, which are compared to available spectroscopic studies. Lifetimes for all states are calculated and compared to previous results from the literature. The calculated lifetime of the $A\,{}^{1}\Pi$ state shows good agreement with an experimental value from the literature, which is an important quality indicator for the ab initio $A$-$X$ transition dipole moment.

The ExoMol database (www.exomol.com) provides molecular data for spectroscopic studies of hot atmospheres. While the data is intended for studies of exoplanets and other astronomical bodies, the dataset is widely applicable. The basic form of the database is extensive line lists; these are supplemented with partition functions, state lifetimes, cooling functions, Land\'e g-factors, temperature-dependent cross sections, opacities, pressure broadening parameters, $k$-coefficients and dipoles. This paper presents the latest release of the database which has been expanded to consider 80 molecules and 190 isotopologues totaling over 700 billion transitions. While the spectroscopic data is concentrated at infrared and visible wavelengths, ultraviolet transitions are being increasingly considered in response to requests from observers. The core of the database comes from the ExoMol project which primarily uses theoretical methods, albeit usually fine-tuned to reproduce laboratory spectra, to generate very extensive line lists for studies of hot bodies. The data has recently been supplemented by line lists deriving from direct laboratory observations, albeit usually with the use of ab initio transition intensities. A major push in the new release is towards accurate characterisation of transition frequencies for use in high resolution studies of exoplanets and other bodies.

In the paper, we use and investigate copulas models to represent multivariate dependence in financial time series. We propose the algorithm of risk measure computation using copula models. Using the optimal mean-$CVaR$ portfolio we compute portfolio's Profit and Loss series and corresponded risk measures curves. Value-at-risk and Conditional-Value-at-risk curves were simulated by three copula models: full Gaussian, Student's $t$ and regular vine copula. These risk curves are lower than historical values of the risk measures curve. All three models have superior prediction ability than a usual empirical method. Further directions of research are described., Comment: 13 pages, 5 figures

The portfolio optimization problem is a basic problem of financial analysis. In the study, an optimization model for constructing an options portfolio with a certain payoff function has been proposed. The model is formulated as an integer linear programming problem and includes an objective payoff function and a system of constraints. In order to demonstrate the performance of the proposed model, we have constructed the portfolio on the European call and put options of Taiwan Futures Exchange. The optimum solution was obtained using the MATLAB software. Our approach is quite general and has the potential to design options portfolios on financial markets., Comment: 10 pages, 2 figures

The program {\sc Duo} (Yurchenko {\it et al.}, Computer Phys. Comms., 202 (2016) 262) provides direct solutions of the nuclear motion Schr\"odinger equation for the (coupled) potential energy curves of open shell diatomic molecules. Wavefunctions from {\sc Duo} are used to compute Land\'e $g$-factors valid for weak magnetic fields, the results are compared with the idealized predictions of both Hund's case (a) and Hund's case (b) coupling schemes. Test calculations are performed for AlO, NO, CrH and C$_2$. The computed $g_J$'s both provide a sensitive test of the underlying spectroscopic model used to represent the system and an indication of whether states of the molecule are well-represented by the either of the Hund's cases considered. The computation of Land\'e $g$-factors is implemented as a standard option in the latest release of {\sc Duo}., Comment: This is a revised version which includes the correct Figure 5 (compared to the published version)

A mathematical model of plastic deformation in face-centered cubic (FCC) materials based on a balance model taking into account fundamental properties of deformation defects of a crystal lattice was developed. This model is based on a system of ordinary differential equations (ODE) accounting for various mechanisms of generation and annihilation of deformation defects for different external conditions. In-house developed software, SPFCC (Slip Plasticity of Face-Centered Cubic), was employed to solve the system of ordinary differential equations. The implemented code solves efficiently the stiff ODE system and provides a user-friendly interface for investigation of various features of plastic deformation in FCC materials. Simulation of plastic deformation in the FCC metals was performed for the case of constant strain rate. The modelling results were validated by comparing experimental data and simulation results (stress-strain curves) and good agreement was obtained., Comment: LaTeX, 10 pages, 4 figures, 23 references