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In this work, we study a new implicit method to compute the solutions of ill-posed linear operator equations of the first kind under the setting of compact operators. The regularization theory can be used to demonstrate the stability and convergence of this scheme. Furthermore, we obtain convergence results and effective stopping criteria according to Morozov's discrepancy principle. Numerical performances are calculated to show the validity of our implicit method and demonstrate its applicability to deblurring problems.

The system of linear acoustic equations is hyperbolic. It describes the process of the acoustic wave propagation in deformable media. An important property of the schemes used for the numerical solution is their high approximation order. This property allows one to simulate the perturbation propagation process over sufficiently large distances. Another important property is monotonicity of the schemes used, which prevents the appearance of non-physical solution oscillations. In this paper, we present linear quasi-monotone and hybrid grid-characteristic schemes for a linear transport equation and a one-dimensional acoustic system. They are constructed by a method of analysis in the space of unknown coefficients proposed by A.S. Kholodov and a grid-characteristic monotonicity criterion. Wide spatial stencils with five to seven nodes of the computational grid are considered. Reflection of a longitudinal wave with a sharp front from the interface between media with different parameters is used to compare the numerical solutions.

In this study, we introduce multi-step collocation methods (MSCM) for solving the Volterra integral equation (VIE) of the auto-convolution type such that without increasing the computational cost, the order of convergence of the proposed one-step collocation methods will be increased. A convergence analysis of the MSCM is investigated using the Peano theorems for interpolation and, finally, two numerical examples are introduced to clarify the significant advantage of the MSCM.

The article presents the results of the analysis of the demographic structure of the coenotic populations of Hedysarum sangilense Krasnob. et Timoch. on the high-altitude Sangilen plateau (South-Eastern Tuva). The ecological-coenotic association, ontogenesis, ontogenetic and vital structure of 7 populations of this subendemic species were studied. It is established that in the studied territory the species is confined to the communities with Kobresia and dryad tundras within the alpine belt and to the shrubby thickets in the forest belt. Study of the demographic structure revealed that the majority of coenotic populations are characterized by left-sided age spectra with a predominance of juvenile, virginal and, most often, young generative plants. In conditions of disturbed phytocenoses (recovering from fires), left-sided spectra are formed with a maximum on generative young plants. Among the vitality of the types of populations of H. sangilense is dominated by depressive and equilibrium types. Sufficiently high real seed productivity and a long generative period ensure the self-maintenance of H. sangilense populations in the conditions of high-altitude plant communities of the Sangilen highlands.

The appearance of new collections from Eastern Siberia and the reanalysis of previously studied collections from Siberia and Mongolia stored in Herbariums LE, MW, NSK, as well as the analysis of virtual collections hosted in the international Jstor database, made it possible to describe a species new to science Lappula turczaninowii Ovczinnikova from the kinship L. redowskii (Hornem.) Greene from the Redowskianae Ovczinnikova series of the type section , validate the names of two varieties of L. anisacantha (Turcz. ex Bunge) Gürke var. sibirica Popov ex Ovczinnikova and L. anisacantha var. uniserialis Popov ex Ovczinnikova, proposed by M.G. Popov in “Flora of the USSR”, as well as to clarify the range of L. stricta (Ledeb.) Gürke in the Baikal region. L. turczaninowii is described from the Irkutsk region, found on stony and rocky steppe slopes in the Baikal region, Transbaikalia, Yakutia, and Mongolia. It differs from the closely related species L. redowskii in the sparse soft pubescence of all plant organs, more densely arranged fruits on the fruiting twigs, the ovoid shape of the eremocarp disc, and the number of glochids (13-15) along the edge of the disc. For all new taxa, a nomenclature citation is given, labels of type specimens are cited, information is given on ecological features and distribution, and a table of diagnostic characters of the new species and the species in which it was included is compiled. The main diagnostic features of the taxa are illustrated in the figures, and photographs of type specimens are given. The cited new localities of L. stricta from the Irkutsk region complement the natural range of this species.

For the first time for the flora of Omsk Region, a representative of the steppe halophyte complexes Camphorosma lessingii from the Chenopodiaceae family is indicated. The nearest findings of this species are known in Novosibirsk Region and in the north of the Republic of Kazakhstan. The article also contains data on the new locations of 7 rare and protected species of vascular plants for the territory of Omsk Region: Allium ramosum L., Campanula bononiensis L., Cleistogenes squarrosa (Trin.) Keng., Galatella divaricata (M. Bieb.) Novopokr., Nitraria sibirica Pall., Stipa praecapillata Alechin, Vincetoxicum sibiricum (L.) Decne., discovered during field studies in 2021-2022. The article justifies proposals to change or confirm the current security status for Allium ramosum, Camphorosma lessingii, Galatella divaricata, Nitraria sibirica, Stipa praecapillata - 1 (E), Campanula bononiensis - 2 (V). Due to poor knowledge and a small number of populations, it is proposed to include Cleistogenes squarrosa and Vincetoxicum sibiricum in the list of species that need special attention to their condition in the nature.

New localities of alien species rarely found in the Novosibirsk Region are reported: Acer tataricum L. subsp. ginnala (Maxim.) Wesm., Amelanchier ovalis Medik., Bromus tectorum L., Cornus alba L. f. argenteo-marginata (Rehd.) Schelle, Corylus heterophylla Fisch. ex Trautv., Hemerocallis fulva (L.) L., Iris × hybrida hort., Lamium galeobdolon (L.) L., Prunus fruticosa Pall., Rubus odoratus L., Schisandra chinensis (Turcz.) Baill., Sisymbrium volgense M. Bieb. ex E. Fourn., Symphytum caucasicum M. Bieb., Tilia cordata Mill., Veronica filiformis Sm., Viola tricolor L. Dispersal of 14 species, predominantly invasive or potentially invasive, was recorded in the Novosibirsk Region. Most of the discussed species are ergasiophytes - species that have left the culture.

The paper presents an analytical review of the multivolume floristic synopsis, “Conspectus Florae Asiae Mediae” (1968-1993), edited by the eminent Russian botanist, Professor Aleksei Ivanovich Vvedensky (1898-1972). Сheck-lists for new species as well as for new nomenclature combinations published in these books are compiled. Overall from 1968 to 1993, 10 volumes of synopsis of the Middle Asian flora were published with 8102 species, 1151 genera and 125 families. According to the materials published in the additional 11^th volume of the synopsis, the total number of vascular plants in Middle Asian flora is 9347 species.

The article is dedicated to the 90th anniversary of the birth of the famous Russian florist, algologist Tatiana Andreevna Safonova. Her work has made a great contribution to the study of the diversity, morphology and distribution of freshwater algae.

On February 15, 2023, Olga Dmitrievna Nikiforova, a well-known taxonomist of Siberian vascular plants, Doctor of Biological Sciences, a real ascetic of science and a person of great soul, passed away. All scientific activities of O.D. Nikiforova is associated with the Central Siberian Botanical Garden of the Siberian Branch of the Russian Academy of Sciences. For the multi-volume edition “Flora of Siberia” she studied the morphology, geography and ecology of more than 200 species from the families Poaceae, Fabaceae, Brassicaceae, Boraginaceae. She is the author of 114 scientific publications. In the study of the flora of Siberia and neighboring states, she described 24 new species and subspecies, 50 new sections, subsections and series in the system of genera Vicia, Mertensia, Myosotis.