Pub Date : 2023-01-01DOI: 10.36120/2587-3644.v14i2.57-67
Natalia Neagu, M. Popa, V. Orlov
For the ternary differential system of Lyapunov-Darboux type with nonlinearities of degree four, using the Lie algebra admitted by this system, was obtained the analytic first integral, determined the Lyapunov function and the conditions of stability of the unperturbed motion.
{"title":"Stability of unperturbed motion governed by the ternary differential system of Lyapunov-Darboux type with nonlinearities of degree four","authors":"Natalia Neagu, M. Popa, V. Orlov","doi":"10.36120/2587-3644.v14i2.57-67","DOIUrl":"https://doi.org/10.36120/2587-3644.v14i2.57-67","url":null,"abstract":"For the ternary differential system of Lyapunov-Darboux type with nonlinearities of degree four, using the Lie algebra admitted by this system, was obtained the analytic first integral, determined the Lyapunov function and the conditions of stability of the unperturbed motion.","PeriodicalId":340784,"journal":{"name":"Acta et commentationes: Ştiinţe Exacte şi ale Naturii","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122992648","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 : 2023-01-01DOI: 10.36120/2587-3644.v14i2.47-52
V. Shcherbacov
We prolong research of Schroder quasigroups and Schroder T-quasigroups.
扩展了Schroder拟群和Schroder t -拟群的研究。
{"title":"Schroder T-quasigroups of generalized associativity","authors":"V. Shcherbacov","doi":"10.36120/2587-3644.v14i2.47-52","DOIUrl":"https://doi.org/10.36120/2587-3644.v14i2.47-52","url":null,"abstract":"We prolong research of Schroder quasigroups and Schroder T-quasigroups.","PeriodicalId":340784,"journal":{"name":"Acta et commentationes: Ştiinţe Exacte şi ale Naturii","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134359666","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 : 2023-01-01DOI: 10.36120/2587-3644.v14i2.7-14
I. Cherevko, A. Dorosh, Ivan Haiuk, A. Pertsov
Boundary value problems for nonlinear integro-differential equations of the neutral type are investigated. A scheme for approximating the boundary value problem solution using cubic splines of defect two is proposed and substantiated. A model example illustrating the proposed approximation scheme is considered.
{"title":"Approximation of solutions of boundary value problems for integro-differential equations of the neutral type using a spline function method","authors":"I. Cherevko, A. Dorosh, Ivan Haiuk, A. Pertsov","doi":"10.36120/2587-3644.v14i2.7-14","DOIUrl":"https://doi.org/10.36120/2587-3644.v14i2.7-14","url":null,"abstract":"Boundary value problems for nonlinear integro-differential equations of the neutral type are investigated. A scheme for approximating the boundary value problem solution using cubic splines of defect two is proposed and substantiated. A model example illustrating the proposed approximation scheme is considered.","PeriodicalId":340784,"journal":{"name":"Acta et commentationes: Ştiinţe Exacte şi ale Naturii","volume":"117 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124715420","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 : 2023-01-01DOI: 10.36120/2587-3644.v14i2.38-46
A. Suba
We classify all cubic differential systems with a center-focus critical point and the line at infinity of maximal multiplicity. It is proved that the critical point is of the center type if and only if the divergence of vector field associated to differential system vanishes.
{"title":"Centers of cubic differential systems with the line at infinity of maximal multiplicity","authors":"A. Suba","doi":"10.36120/2587-3644.v14i2.38-46","DOIUrl":"https://doi.org/10.36120/2587-3644.v14i2.38-46","url":null,"abstract":"We classify all cubic differential systems with a center-focus critical point and the line at infinity of maximal multiplicity. It is proved that the critical point is of the center type if and only if the divergence of vector field associated to differential system vanishes.","PeriodicalId":340784,"journal":{"name":"Acta et commentationes: Ştiinţe Exacte şi ale Naturii","volume":"332 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132301353","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 : 2023-01-01DOI: 10.36120/2587-3644.v14i2.81-87
A. Turcanu
It is demonstrated that any theory of relative torsion is defined by the left and the right products.
证明了任何相对扭转理论都是由左右乘积来定义的。
{"title":"The left product, the right product and the theories of relative torsion","authors":"A. Turcanu","doi":"10.36120/2587-3644.v14i2.81-87","DOIUrl":"https://doi.org/10.36120/2587-3644.v14i2.81-87","url":null,"abstract":"It is demonstrated that any theory of relative torsion is defined by the left and the right products.","PeriodicalId":340784,"journal":{"name":"Acta et commentationes: Ştiinţe Exacte şi ale Naturii","volume":"53 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131129331","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 : 2023-01-01DOI: 10.36120/2587-3644.v14i2.53-56
O. Gok
Let $E$ and $F$ be Banach lattices and $X$ and $Y$ be Banach spaces. A linear operator $T: E rightarrow F$ is called regular if it is the difference of two positive operators. $L_{r}(E,F)$ denotes the vector space of all regular operators from $E$ into $F$. A continuous linear operator $T: E rightarrow X$ is called $M$-weakly compact operator if for every disjoint bounded sequence $(x_{n})$ in $E$, we have $lim_{n rightarrowinfty} | Tx_{n} | =0$. $W^{r}_{M}(E,F)$ denotes the regular $M$-weakly compact operators from $E$ into $F$. This paper is devoted to the study of regular operators and $M$-weakly compact operators on Banach lattices. We show that $F$ has a b-property if and only if $L_{r}(E,F)$ has b-property. Also, $W^{r}_{M}(E,F)$ is a $KB$-space if and only if $F$ is a $KB$-space.
设$E$和$F$为巴拿赫格$X$和$Y$为巴拿赫空间。如果线性算子$T: E rightarrow F$是两个正算子的差，则称为正则算子。$L_{r}(E,F)$表示从$E$到$F$的所有正则算子的向量空间。连续线性算子$T: E rightarrow X$称为$M$ -弱紧算子，如果对于$E$中的每一个不相交有界序列$(x_{n})$，我们有$lim_{n rightarrowinfty} | Tx_{n} | =0$。$W^{r}_{M}(E,F)$表示从$E$到$F$的正则$M$ -弱紧化算子。本文研究了Banach格上的正则算子和$M$ -弱紧算子。我们证明$F$有b性质当且仅当$L_{r}(E,F)$有b性质。同样，$W^{r}_{M}(E,F)$是一个$KB$ -space当且仅当$F$是一个$KB$ -space。
{"title":"On regular operators on Banach lattices","authors":"O. Gok","doi":"10.36120/2587-3644.v14i2.53-56","DOIUrl":"https://doi.org/10.36120/2587-3644.v14i2.53-56","url":null,"abstract":"Let $E$ and $F$ be Banach lattices and $X$ and $Y$ be Banach spaces. A linear operator $T: E rightarrow F$ is called regular if it is the difference of two positive operators. $L_{r}(E,F)$ denotes the vector space of all regular operators from $E$ into $F$. A continuous linear operator $T: E rightarrow X$ is called $M$-weakly compact operator if for every disjoint bounded sequence $(x_{n})$ in $E$, we have $lim_{n rightarrowinfty} | Tx_{n} | =0$. $W^{r}_{M}(E,F)$ denotes the regular $M$-weakly compact operators from $E$ into $F$. This paper is devoted to the study of regular operators and $M$-weakly compact operators on Banach lattices. We show that $F$ has a b-property if and only if $L_{r}(E,F)$ has b-property. Also, $W^{r}_{M}(E,F)$ is a $KB$-space if and only if $F$ is a $KB$-space.","PeriodicalId":340784,"journal":{"name":"Acta et commentationes: Ştiinţe Exacte şi ale Naturii","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124188816","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 : 2023-01-01DOI: 10.36120/2587-3644.v14i2.68-80
Vadim Repesco
The present study delves into the investigation of phase portraits of polynomial differential systems, which are systems of differential equations of the form $frac{dx}{dt} = P(x,y), frac{dy}{dt} = Q(x,y)$, where $x$ and $y$ are the dependent variables and $t$ is the independent variable. The functions $P(x,y)$ and $Q(x,y)$ are polynomials in $x$ and $y$. The main objective of this research is to obtain the phase portraits of polynomial differential systems of degree $nin { 3, 4, 5}$ and having an invariant straight line at the infinity of maximal multiplicity.
{"title":"Phase portraits of some polynomial differential systems with maximal multiplicity of the line at the infinity","authors":"Vadim Repesco","doi":"10.36120/2587-3644.v14i2.68-80","DOIUrl":"https://doi.org/10.36120/2587-3644.v14i2.68-80","url":null,"abstract":"The present study delves into the investigation of phase portraits of polynomial differential systems, which are systems of differential equations of the form $frac{dx}{dt} = P(x,y), frac{dy}{dt} = Q(x,y)$, where $x$ and $y$ are the dependent variables and $t$ is the independent variable. The functions $P(x,y)$ and $Q(x,y)$ are polynomials in $x$ and $y$. The main objective of this research is to obtain the phase portraits of polynomial differential systems of degree $nin { 3, 4, 5}$ and having an invariant straight line at the infinity of maximal multiplicity.","PeriodicalId":340784,"journal":{"name":"Acta et commentationes: Ştiinţe Exacte şi ale Naturii","volume":"57 4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126073271","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 : 2023-01-01DOI: 10.36120/2587-3644.v14i2.24-37
V. Neagu, Diana Bîclea
The article presents a method for solving characteristic singular integral equations perturbed with compact operators. The method consists in reducing the solution of these equations to the solution of the systems of singular (unperturbed) equations, which are solved by factoring the coefficients of the obtained systems. The method presented concerns some results of Gohberg and Krupnik and can be used in solving other classes of functional equations with composite operators that fit into the scheme described by Theorem 1.1.
{"title":"Extension of linear operators with application","authors":"V. Neagu, Diana Bîclea","doi":"10.36120/2587-3644.v14i2.24-37","DOIUrl":"https://doi.org/10.36120/2587-3644.v14i2.24-37","url":null,"abstract":"The article presents a method for solving characteristic singular integral equations perturbed with compact operators. The method consists in reducing the solution of these equations to the solution of the systems of singular (unperturbed) equations, which are solved by factoring the coefficients of the obtained systems. The method presented concerns some results of Gohberg and Krupnik and can be used in solving other classes of functional equations with composite operators that fit into the scheme described by Theorem 1.1.","PeriodicalId":340784,"journal":{"name":"Acta et commentationes: Ştiinţe Exacte şi ale Naturii","volume":"145 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129441058","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 : 2023-01-01DOI: 10.36120/2587-3644.v14i2.15-23
M. Popa
In this work there were formulated 18 problems from the theory of invariant processes, Lie algebras, commutative graded algebras, generating functions and Hilbert series, orbit theory and Lyapunov stability theory that are important to be solved. There was substantiated the necessity of using the solutions of these problems in the qualitative theory of differential systems.
{"title":"Problems of the theory of invariants and Lie algebras applied in the qualitative theory of differential systems","authors":"M. Popa","doi":"10.36120/2587-3644.v14i2.15-23","DOIUrl":"https://doi.org/10.36120/2587-3644.v14i2.15-23","url":null,"abstract":"In this work there were formulated 18 problems from the theory of invariant processes, Lie algebras, commutative graded algebras, generating functions and Hilbert series, orbit theory and Lyapunov stability theory that are important to be solved. There was substantiated the necessity of using the solutions of these problems in the qualitative theory of differential systems.","PeriodicalId":340784,"journal":{"name":"Acta et commentationes: Ştiinţe Exacte şi ale Naturii","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116479658","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 : 2022-11-01DOI: 10.36120/2587-3644.v13i1.110-115
A. Trofim, Anastasia Verdes
The article reflects data on the use of cyanobacteria pigments in cosmetology. One of the sources of natural antioxidants are the pigments obtained from various algae and cyanobacteria. An essential source for extracting pigments and biologically active substances used in cosmetology, pharmaceuticals, etc. is represented by algae and cyanobacteria. Also, the extracts from cyanobacteria have an important role in the anti-wrinkle effect. Useful pigments include: carotenoids, xanthophylls, astaxanthin, fucoxanthin, chlorophyll, phycoerythrin.
{"title":"Use of natural pigments obtained from cyanobacteria and algae","authors":"A. Trofim, Anastasia Verdes","doi":"10.36120/2587-3644.v13i1.110-115","DOIUrl":"https://doi.org/10.36120/2587-3644.v13i1.110-115","url":null,"abstract":"The article reflects data on the use of cyanobacteria pigments in cosmetology. One of the sources of natural antioxidants are the pigments obtained from various algae and cyanobacteria. An essential source for extracting pigments and biologically active substances used in cosmetology, pharmaceuticals, etc. is represented by algae and cyanobacteria. Also, the extracts from cyanobacteria have an important role in the anti-wrinkle effect. Useful pigments include: carotenoids, xanthophylls, astaxanthin, fucoxanthin, chlorophyll, phycoerythrin.","PeriodicalId":340784,"journal":{"name":"Acta et commentationes: Ştiinţe Exacte şi ale Naturii","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126516480","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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