Pub Date : 2023-10-31DOI: 10.29235/1561-8323-2023-67-5-433-440
V. M. Shapovalov, D. L. Podobed, S. V. Zotov, A. A. Boyka
The aim of the work is to obtain and study polymer composite materials based on mixtures of secondary polyolefins and modified polydisperse bentonite clay. The formation features of the structure of mixtures of waste polyolefins in the presence of this-type filler are studied. The data on the changes in the mechanical strength of mixed composites, as well as the results of physico-chemical studies are presented. Mixtures based on waste polymers in the presence of highly dispersed particles of modified polydisperse bentonite are characterized by the improvement of the strength of composites due to increased interfacial interaction in them and by the formation of structure uniformity of the material. This to some extent compensates for the loss of cohesive strength of secondary polymers due to thermal degradation processes. The following conclusions are made: at the phase boundaries, the molecular mobility of polymer chains decreases, which leads to changing the crystallization conditions and to appearing a nonequilibrium stress state; introducing bentonite increases crystalline due to the initiation of physico-chemical interaction; the strength grows due to increased interfacial interaction and structure uniformity; the formation mechanism of a complex of properties of composites consists of two-level adsorption – a modifier on filler particles and active polymer groups on the modified filler surface.
{"title":"Hardening mechanism of waste polyolefin mixtures in the presence of modified bentonite clay","authors":"V. M. Shapovalov, D. L. Podobed, S. V. Zotov, A. A. Boyka","doi":"10.29235/1561-8323-2023-67-5-433-440","DOIUrl":"https://doi.org/10.29235/1561-8323-2023-67-5-433-440","url":null,"abstract":"The aim of the work is to obtain and study polymer composite materials based on mixtures of secondary polyolefins and modified polydisperse bentonite clay. The formation features of the structure of mixtures of waste polyolefins in the presence of this-type filler are studied. The data on the changes in the mechanical strength of mixed composites, as well as the results of physico-chemical studies are presented. Mixtures based on waste polymers in the presence of highly dispersed particles of modified polydisperse bentonite are characterized by the improvement of the strength of composites due to increased interfacial interaction in them and by the formation of structure uniformity of the material. This to some extent compensates for the loss of cohesive strength of secondary polymers due to thermal degradation processes. The following conclusions are made: at the phase boundaries, the molecular mobility of polymer chains decreases, which leads to changing the crystallization conditions and to appearing a nonequilibrium stress state; introducing bentonite increases crystalline due to the initiation of physico-chemical interaction; the strength grows due to increased interfacial interaction and structure uniformity; the formation mechanism of a complex of properties of composites consists of two-level adsorption – a modifier on filler particles and active polymer groups on the modified filler surface.","PeriodicalId":41825,"journal":{"name":"DOKLADY NATSIONALNOI AKADEMII NAUK BELARUSI","volume":"17 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135869799","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-31DOI: 10.29235/1561-8323-2023-67-5-399-409
A. V. Spirydovich, N. B. Vlasava, A. D. Ahabalayeva, D. V. Dubovik, A. N. Skuratovich, Yu. K. Vinogradova, V. N. Reshetnikov
The history of intentional introduction of Rhamnus cathartica L. into the Midwestern regions of the USA is briefly described. The species abundance and structure of plant communities, in which Rhamnus cathartica, a native species for Belarus and invasive in the USA grows, has been studied. We compared the studied parameters (floristic description of the monitoring plots, field enumeration of Rhamnus cathartica individuals, average height, projective coverage of the accompanying herb species) at two permanent sample plots in Belarus and three permanent sample plots in the Midwestern regions of the USA. The data confirmed the hypothesis of increased competitiveness of non-native species in the secondary range (EICA). In American populations, compared to Belarusian populations, Rhamnus cathartica has larger sizes, higher seed production, higher number of juvenile individuals, and higher total number of individuals in the population up to the formation of single-species thickets. Invading Rhamnus cathartica into natural plant communities in the USA reduces the number of herbaceous species 8 times! As control measures, the Minnesota Arboretum has begun balding the areas invaded by Rhamnus cathartica, removing juvenile plants (one to five years old) and replanting native tree species.
{"title":"Сomparative analysis of the species abundance and structure of plant communities involving <i>Rhamnus cathartica</i> in Belarus and in the midwestern regions of the USA","authors":"A. V. Spirydovich, N. B. Vlasava, A. D. Ahabalayeva, D. V. Dubovik, A. N. Skuratovich, Yu. K. Vinogradova, V. N. Reshetnikov","doi":"10.29235/1561-8323-2023-67-5-399-409","DOIUrl":"https://doi.org/10.29235/1561-8323-2023-67-5-399-409","url":null,"abstract":"The history of intentional introduction of Rhamnus cathartica L. into the Midwestern regions of the USA is briefly described. The species abundance and structure of plant communities, in which Rhamnus cathartica, a native species for Belarus and invasive in the USA grows, has been studied. We compared the studied parameters (floristic description of the monitoring plots, field enumeration of Rhamnus cathartica individuals, average height, projective coverage of the accompanying herb species) at two permanent sample plots in Belarus and three permanent sample plots in the Midwestern regions of the USA. The data confirmed the hypothesis of increased competitiveness of non-native species in the secondary range (EICA). In American populations, compared to Belarusian populations, Rhamnus cathartica has larger sizes, higher seed production, higher number of juvenile individuals, and higher total number of individuals in the population up to the formation of single-species thickets. Invading Rhamnus cathartica into natural plant communities in the USA reduces the number of herbaceous species 8 times! As control measures, the Minnesota Arboretum has begun balding the areas invaded by Rhamnus cathartica, removing juvenile plants (one to five years old) and replanting native tree species.","PeriodicalId":41825,"journal":{"name":"DOKLADY NATSIONALNOI AKADEMII NAUK BELARUSI","volume":"59 43","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135870642","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-31DOI: 10.29235/1561-8323-2023-67-5-388-398
M. I. Shaladonova, Ya. V. Dzichenka, S. A. Usanov
The purpose of this study was to create a database of the chemical compounds – ligands of human steroid-hydroxylating cytochrome CYP19A1 (aromatase) in order to build a predictive model. The idea was to create a model on the basis of the machinery learning method such as random forest for two types of ligands – with steroidal (I type) and non-steroidal structure (II type). Two predictive models were built with the help of the KNIME analytical platform. Topological descriptors of the chemical structure were used as training data when building a model that takes into account their correlation between the structure of the molecule and the biological effect. The selection of the feature importance of the descriptors, optimal parameters of random forest and the definition of applicability domain of the models were carried out. The assessment of the ability to predict the results of a test sample was performed for each model. The quality marks of the obtained models indicated a rather high predictive ability of the models and the prospects of their use for identification of new human CYP19A1 ligands as potential drugs for treatment of hormone-dependent tumors.
{"title":"Predictive model for identifying new CYP19A1 ligands on the KNIME analytical platform","authors":"M. I. Shaladonova, Ya. V. Dzichenka, S. A. Usanov","doi":"10.29235/1561-8323-2023-67-5-388-398","DOIUrl":"https://doi.org/10.29235/1561-8323-2023-67-5-388-398","url":null,"abstract":"The purpose of this study was to create a database of the chemical compounds – ligands of human steroid-hydroxylating cytochrome CYP19A1 (aromatase) in order to build a predictive model. The idea was to create a model on the basis of the machinery learning method such as random forest for two types of ligands – with steroidal (I type) and non-steroidal structure (II type). Two predictive models were built with the help of the KNIME analytical platform. Topological descriptors of the chemical structure were used as training data when building a model that takes into account their correlation between the structure of the molecule and the biological effect. The selection of the feature importance of the descriptors, optimal parameters of random forest and the definition of applicability domain of the models were carried out. The assessment of the ability to predict the results of a test sample was performed for each model. The quality marks of the obtained models indicated a rather high predictive ability of the models and the prospects of their use for identification of new human CYP19A1 ligands as potential drugs for treatment of hormone-dependent tumors.","PeriodicalId":41825,"journal":{"name":"DOKLADY NATSIONALNOI AKADEMII NAUK BELARUSI","volume":"161 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135869923","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-31DOI: 10.29235/1561-8323-2023-67-5-410-416
E. I. Slobozhanina, E. V. Shamova, G. P. Zubritskaya, A. Yu. Kohan, E. I. Venskaya, I. Yu. Lendina, D. I. Suvorov, I. A. Iskrov
The relationship between the content of metallothioneins, copper and zinc ions in peripheral blood plasma in chronic lymphocytic leukemia (CLL) depending on the disease progression was studied. It was shown that in patients with CLL in blood plasma with a progressive disease, partial and complete remission, the values of the zinc-to-copper ratios significantly decreased in comparison to similar indicators of practically healthy donors. It was established that in patients with CLL, the level of metallothioneins in blood plasma decreases with the disease progression compared to other studied groups, which indicates a reduced function of cysteine-containing metallothionein proteins. Based on the obtained data, it can be concluded that the zinc-to-copper concentration ratio and the level of metallothionenins in peripheral blood plasma are potential diagnostic and prognostic markers in chronic leukemia.
{"title":"Changes in the level of metallothioneins, zinc and copper in blood plasma of patients with chronic lymphocytic leukemia","authors":"E. I. Slobozhanina, E. V. Shamova, G. P. Zubritskaya, A. Yu. Kohan, E. I. Venskaya, I. Yu. Lendina, D. I. Suvorov, I. A. Iskrov","doi":"10.29235/1561-8323-2023-67-5-410-416","DOIUrl":"https://doi.org/10.29235/1561-8323-2023-67-5-410-416","url":null,"abstract":"The relationship between the content of metallothioneins, copper and zinc ions in peripheral blood plasma in chronic lymphocytic leukemia (CLL) depending on the disease progression was studied. It was shown that in patients with CLL in blood plasma with a progressive disease, partial and complete remission, the values of the zinc-to-copper ratios significantly decreased in comparison to similar indicators of practically healthy donors. It was established that in patients with CLL, the level of metallothioneins in blood plasma decreases with the disease progression compared to other studied groups, which indicates a reduced function of cysteine-containing metallothionein proteins. Based on the obtained data, it can be concluded that the zinc-to-copper concentration ratio and the level of metallothionenins in peripheral blood plasma are potential diagnostic and prognostic markers in chronic leukemia.","PeriodicalId":41825,"journal":{"name":"DOKLADY NATSIONALNOI AKADEMII NAUK BELARUSI","volume":"43 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135870740","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-31DOI: 10.29235/1561-8323-2023-67-5-425-432
E. A. Kukharik, A. V. Matveyev
The article presents the results of assessment of technogenic transformation of the geological environment in the territory of the southwestern region of Belarus under the influence of various human economic activities. The research was based on the application of a complex methodology, including the study of published and fund sources, geological, geomorphological, topographic and cadastral maps, plans of settlements, remote survey data and materials of field and route observations, cartometric and cartographic works. It is shown that over the past 150 years, a noticeable restructuring of the earth’s surface, the structure and composition of the cover deposits has taken place in the region. This is due to a hydro-reclamation and residential development of the territory, road and railway construction, mining, accumulation of solid waste and other activities. The total volume of technogenically displaced soils in this area is 780.7 million m3, and the calculated indicator of the intensity of technogenic geological processes is 182 m3/km2/year. It is 2.4 times higher than the total impact on the earth’s surface of the region of modern exogenous geological processes.
{"title":"Integrated assessment of technogenic transformation of the geological environment in the southwestern region of Belarus","authors":"E. A. Kukharik, A. V. Matveyev","doi":"10.29235/1561-8323-2023-67-5-425-432","DOIUrl":"https://doi.org/10.29235/1561-8323-2023-67-5-425-432","url":null,"abstract":"The article presents the results of assessment of technogenic transformation of the geological environment in the territory of the southwestern region of Belarus under the influence of various human economic activities. The research was based on the application of a complex methodology, including the study of published and fund sources, geological, geomorphological, topographic and cadastral maps, plans of settlements, remote survey data and materials of field and route observations, cartometric and cartographic works. It is shown that over the past 150 years, a noticeable restructuring of the earth’s surface, the structure and composition of the cover deposits has taken place in the region. This is due to a hydro-reclamation and residential development of the territory, road and railway construction, mining, accumulation of solid waste and other activities. The total volume of technogenically displaced soils in this area is 780.7 million m3, and the calculated indicator of the intensity of technogenic geological processes is 182 m3/km2/year. It is 2.4 times higher than the total impact on the earth’s surface of the region of modern exogenous geological processes.","PeriodicalId":41825,"journal":{"name":"DOKLADY NATSIONALNOI AKADEMII NAUK BELARUSI","volume":"227 7","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135871681","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-31DOI: 10.29235/1561-8323-2023-67-5-373-379
V. V. Pilko (jr.), F. F. Komarov, V. V. Pilko
The results on the tolerance of several construction materials (D16T alloy, Zr, ЭИ-847, 12Х18Н9Т steels) and polycrystаlline SiC to blistering and flecking after irradiation with 500 keV He+ ions and following annealing have been high-lighted. Samples of stainless steels, zirconium, D16T alloy and silicon carbide were irradiated with helium ions in the range from 1016 to 3 · 1018 ion/cm 2 . Immediately after irradiation and annealing under temperatures from 300 to 750 °C, the optical microscopy was used to study the structure of surface layers. Temperature and fluence ranges of tolerance to blistering and flecking were determined for all examined materials. Primary types of material structure distortions were reviewed.
{"title":"Tolerance of several construction materials and polycrystalline SiC to blistering and flecking due to ion implantation and annealing","authors":"V. V. Pilko (jr.), F. F. Komarov, V. V. Pilko","doi":"10.29235/1561-8323-2023-67-5-373-379","DOIUrl":"https://doi.org/10.29235/1561-8323-2023-67-5-373-379","url":null,"abstract":"The results on the tolerance of several construction materials (D16T alloy, Zr, ЭИ-847, 12Х18Н9Т steels) and polycrystаlline SiC to blistering and flecking after irradiation with 500 keV He+ ions and following annealing have been high-lighted. Samples of stainless steels, zirconium, D16T alloy and silicon carbide were irradiated with helium ions in the range from 1016 to 3 · 1018 ion/cm 2 . Immediately after irradiation and annealing under temperatures from 300 to 750 °C, the optical microscopy was used to study the structure of surface layers. Temperature and fluence ranges of tolerance to blistering and flecking were determined for all examined materials. Primary types of material structure distortions were reviewed.","PeriodicalId":41825,"journal":{"name":"DOKLADY NATSIONALNOI AKADEMII NAUK BELARUSI","volume":"52 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135813431","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-31DOI: 10.29235/1561-8323-2023-67-5-380-387
A. V. Kulsha, O. A. Ivashkevich
The possibility of theoretical calculation of the ionization constants of strong organic bases in dimethyl sulfoxide and hexametapole was studied by the DLPNO-CCSD (T) and DFT methods. By comparison with the experimental data available in the literature, it has been established that the error of such calculations lies within 1–2 pKa units. The stability of some ionizing solvents against strong organic bases is investigated, the mechanisms of decomposition of solvent molecules in strongly basic media are predicted, and the corresponding energy barriers are estimated. According to the calculations, among ionizing solvents, hexamethylphosphoramide has the highest resistance to superbases, being able to maintain pH > 50 at room temperature. At the same time, 1,3-dimethyl-2-imidazolidinone gradually decomposes under these conditions, while tetrahydrofuran and pivalonitrile are even less stable.
{"title":"Quantum-chemical study of the stability of solvents with respect to strong organic bases","authors":"A. V. Kulsha, O. A. Ivashkevich","doi":"10.29235/1561-8323-2023-67-5-380-387","DOIUrl":"https://doi.org/10.29235/1561-8323-2023-67-5-380-387","url":null,"abstract":"The possibility of theoretical calculation of the ionization constants of strong organic bases in dimethyl sulfoxide and hexametapole was studied by the DLPNO-CCSD (T) and DFT methods. By comparison with the experimental data available in the literature, it has been established that the error of such calculations lies within 1–2 pKa units. The stability of some ionizing solvents against strong organic bases is investigated, the mechanisms of decomposition of solvent molecules in strongly basic media are predicted, and the corresponding energy barriers are estimated. According to the calculations, among ionizing solvents, hexamethylphosphoramide has the highest resistance to superbases, being able to maintain pH > 50 at room temperature. At the same time, 1,3-dimethyl-2-imidazolidinone gradually decomposes under these conditions, while tetrahydrofuran and pivalonitrile are even less stable.","PeriodicalId":41825,"journal":{"name":"DOKLADY NATSIONALNOI AKADEMII NAUK BELARUSI","volume":"9 10","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135863309","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-31DOI: 10.29235/1561-8323-2023-67-5-417-424
E. I. Lebedeva, A. T. Shchastniy, A. S. Babenka
The aim of the work was to evaluate the role of stellate macrophages in a large number of points of toxic liver fibrosis in rats. Liver fibrosis and cirrhosis in male Wistar rats were induced with thioacetamide at a dose of 200 mg/kg animal weight for 17 weeks. Histological preparations of the liver were stained with hematoxylin and eosin according to the Mallory method. Immunohistochemical examination was performed on paraffin sections using monoclonal mouse antibodies CD68 and polyclonal rabbit antibodies CD206. The fibrosis degree was determined according to the Ishak semi-quantitative scale. Toxic liver fibrosis before the start of its transformation into cirrhosis (9 weeks) was accompanied by an increase in the number of CD68+ cells compared with the control. At all subsequent experiment stages, no differences were found in comparison to the control. In the liver of control rats, CD206+ cells were practically absent. Throughout the experiment, their number remained above the control point – 3 weeks. With the progression of liver cirrhosis, a decrease in the number of CD206+ cells was noted, but it did not reach a level of 3 weeks. Morphologically, two different groups of CD68+ cells were identified. One group of cells had a pterygoid shape and they were located mainly in the liver sinusoids. The second group of CD68+ cells had a round shape and different localization. They were detected around the vessels of portal zones, surrounded brown pigment accumulations in connective tissue septa, were observed near single lying groups or groups of giant hepatocytes and liver cells containing brown pigment in the cytoplasm, and were also noted in the foci of necrosis of hepatocytes. Cells, expressing the CD206 marker, are round in shape and are elongated and located in the liver sinusoids. Presumably, round-shaped CD68+ cells perform a phagocytic function, and pterygoid-shaped CD68+ cells transdifferentiate into CD206+ cells that have anti-inflammatory properties.
{"title":"Role of CD68+ and CD206+ cells in the progression of toxic liver fibrosis in rats","authors":"E. I. Lebedeva, A. T. Shchastniy, A. S. Babenka","doi":"10.29235/1561-8323-2023-67-5-417-424","DOIUrl":"https://doi.org/10.29235/1561-8323-2023-67-5-417-424","url":null,"abstract":"The aim of the work was to evaluate the role of stellate macrophages in a large number of points of toxic liver fibrosis in rats. Liver fibrosis and cirrhosis in male Wistar rats were induced with thioacetamide at a dose of 200 mg/kg animal weight for 17 weeks. Histological preparations of the liver were stained with hematoxylin and eosin according to the Mallory method. Immunohistochemical examination was performed on paraffin sections using monoclonal mouse antibodies CD68 and polyclonal rabbit antibodies CD206. The fibrosis degree was determined according to the Ishak semi-quantitative scale. Toxic liver fibrosis before the start of its transformation into cirrhosis (9 weeks) was accompanied by an increase in the number of CD68+ cells compared with the control. At all subsequent experiment stages, no differences were found in comparison to the control. In the liver of control rats, CD206+ cells were practically absent. Throughout the experiment, their number remained above the control point – 3 weeks. With the progression of liver cirrhosis, a decrease in the number of CD206+ cells was noted, but it did not reach a level of 3 weeks. Morphologically, two different groups of CD68+ cells were identified. One group of cells had a pterygoid shape and they were located mainly in the liver sinusoids. The second group of CD68+ cells had a round shape and different localization. They were detected around the vessels of portal zones, surrounded brown pigment accumulations in connective tissue septa, were observed near single lying groups or groups of giant hepatocytes and liver cells containing brown pigment in the cytoplasm, and were also noted in the foci of necrosis of hepatocytes. Cells, expressing the CD206 marker, are round in shape and are elongated and located in the liver sinusoids. Presumably, round-shaped CD68+ cells perform a phagocytic function, and pterygoid-shaped CD68+ cells transdifferentiate into CD206+ cells that have anti-inflammatory properties.","PeriodicalId":41825,"journal":{"name":"DOKLADY NATSIONALNOI AKADEMII NAUK BELARUSI","volume":"61 ","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135869929","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-30DOI: 10.29235/1561-8323-2023-67-5-366-372
D. A. Schadinskii
In this paper, blow-up sufficient conditions and upper bound of blow-up time for solution of Neumann and Dirichlet problems for reaction diffusion equations with non-linear gradient have been obtained. These equations have been found from the comparison of theorems, Jensen’s inequality and conservations laws. By using a similar proof approach for the finite-difference case, the finite-difference scheme was constructed, approximating the above-mentioned Neumann problem, for which sufficient conditions and upper bound of blow-up time, consistent with appropriate conditions and bound for the appropriate differential problem, have been obtained.
{"title":"Comparison theorem in blow-up problems for reaction diffusion equations and for their approximations","authors":"D. A. Schadinskii","doi":"10.29235/1561-8323-2023-67-5-366-372","DOIUrl":"https://doi.org/10.29235/1561-8323-2023-67-5-366-372","url":null,"abstract":"In this paper, blow-up sufficient conditions and upper bound of blow-up time for solution of Neumann and Dirichlet problems for reaction diffusion equations with non-linear gradient have been obtained. These equations have been found from the comparison of theorems, Jensen’s inequality and conservations laws. By using a similar proof approach for the finite-difference case, the finite-difference scheme was constructed, approximating the above-mentioned Neumann problem, for which sufficient conditions and upper bound of blow-up time, consistent with appropriate conditions and bound for the appropriate differential problem, have been obtained.","PeriodicalId":41825,"journal":{"name":"DOKLADY NATSIONALNOI AKADEMII NAUK BELARUSI","volume":"130 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136069513","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-30DOI: 10.29235/1561-8323-2023-67-359-365
A. V. Lebedev, Yu. V. Trubnikov, M. M. Chernyavsky
The article presents a development of the Euler–Lagrange method for calculation of all roots of an arbitrary polynomial P(z) with complex coefficients based on the calculation of the limits of ratios of determinants (as in the Bernoulli–Aitken–Nikiporets methods) built by means of the Taylor and Laurent series coefficients for the function P′(z) / P(z).
{"title":"On the Bernoulli–Euler–Lagrange–Aitken numerical method for roots of polynomials","authors":"A. V. Lebedev, Yu. V. Trubnikov, M. M. Chernyavsky","doi":"10.29235/1561-8323-2023-67-359-365","DOIUrl":"https://doi.org/10.29235/1561-8323-2023-67-359-365","url":null,"abstract":"The article presents a development of the Euler–Lagrange method for calculation of all roots of an arbitrary polynomial P(z) with complex coefficients based on the calculation of the limits of ratios of determinants (as in the Bernoulli–Aitken–Nikiporets methods) built by means of the Taylor and Laurent series coefficients for the function P′(z) / P(z).","PeriodicalId":41825,"journal":{"name":"DOKLADY NATSIONALNOI AKADEMII NAUK BELARUSI","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136068935","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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