Pub Date : 2023-07-12DOI: 10.46991/pysu:a/2023.57.2.051
Smbat G. Shahinyan
An optimal stabilization problem for part of variables of rotary movement of a rigid body with one fixed point in the Sophia Kovalevskaya's case is discussed in this work. The differential equations of motion of the system are given and it is shown that the system may rotate around Ox with a constant angular velocity. Taking this motion as unexcited, the differential equations for the corresponding excited motion were drawn up. Then the system was linearized and a control action was introduced along one of the generalized coordinates. The optimal stabilization problem for part of the variables was posed and solved. The graphs of optimal trajectories and optimal control were constructed.
{"title":"ON OPTIMAL STABILIZATION OF PART OF VARIABLES OF ROTARY MOVEMENT OF A RIGID BODY WITH ONE FIXED POINT IN THE CASE OF SOPHIA KOVALEVSKAYA","authors":"Smbat G. Shahinyan","doi":"10.46991/pysu:a/2023.57.2.051","DOIUrl":"https://doi.org/10.46991/pysu:a/2023.57.2.051","url":null,"abstract":"An optimal stabilization problem for part of variables of rotary movement of a rigid body with one fixed point in the Sophia Kovalevskaya's case is discussed in this work. The differential equations of motion of the system are given and it is shown that the system may rotate around Ox with a constant angular velocity. Taking this motion as unexcited, the differential equations for the corresponding excited motion were drawn up. Then the system was linearized and a control action was introduced along one of the generalized coordinates. The optimal stabilization problem for part of the variables was posed and solved. The graphs of optimal trajectories and optimal control were constructed.","PeriodicalId":21146,"journal":{"name":"Proceedings of the YSU A: Physical and Mathematical Sciences","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139360164","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 : 2023-05-15DOI: 10.46991/pysu:a/2023.57.1.009
D. N. Harutyunyan
In this paper n-ary regular division associative algebras are discussed. It is shown that every operation in n-ary regular division associative algebra will be endo-linearly represented over the same binary group. Schauffler like theorem will be proved for those algebras.
{"title":"LINEARITY OF $n$-ARY ASSOCIATIVE ALGEBRAS","authors":"D. N. Harutyunyan","doi":"10.46991/pysu:a/2023.57.1.009","DOIUrl":"https://doi.org/10.46991/pysu:a/2023.57.1.009","url":null,"abstract":"In this paper n-ary regular division associative algebras are discussed. It is shown that every operation in n-ary regular division associative algebra will be endo-linearly represented over the same binary group. Schauffler like theorem will be proved for those algebras.","PeriodicalId":21146,"journal":{"name":"Proceedings of the YSU A: Physical and Mathematical Sciences","volume":"82 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77131584","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 : 2023-04-25DOI: 10.46991/pysu:a/2023.57.1.001
Y. Hakopian, Avetik H. Manukyan, Hamlet V. Mikaelyan
The present work is devoted to deriving closed form expressions for the elements of the Moore-Penrose inverse of tridiagonal real skew-symmetric matrices. In the first part of the work we obtain results, concerning matrices of even order. A calculation approach for the generalized inverses of odd order matrices is provided.
{"title":"THE MOORE-PENROSE INVERSE OF TRIDIAGONAL SKEW-SYMMETRIC MATRICES. I","authors":"Y. Hakopian, Avetik H. Manukyan, Hamlet V. Mikaelyan","doi":"10.46991/pysu:a/2023.57.1.001","DOIUrl":"https://doi.org/10.46991/pysu:a/2023.57.1.001","url":null,"abstract":"The present work is devoted to deriving closed form expressions for the elements of the Moore-Penrose inverse of tridiagonal real skew-symmetric matrices. In the first part of the work we obtain results, concerning matrices of even order. A calculation approach for the generalized inverses of odd order matrices is provided.","PeriodicalId":21146,"journal":{"name":"Proceedings of the YSU A: Physical and Mathematical Sciences","volume":"12 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77058269","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 : 2023-03-25DOI: 10.46991/pysu:a/2023.57.1.023
Tsovinar M. Jomardyan, G. Ananyan, V. Arakelyan
The effect of aluminum oxide nanoparticles (Al2O3) on the stability and conductivity of BLM (the bilayer lipid membrane) in solution was studied. It has been shown that Al2O3 nanoparticles increase the stability of BLM in an electric field, and BLM becomes more stable with increasing their concentration. The experimental data are analyzed in terms of the well-known theory of BLM stability, which is based on the concept of spontaneous formation of microscopic pores on the BLM, the development of which leads to the loss of BLM stability. It is shown that aluminum oxide nanoparticles increase the value of the coefficient of linear tension of the pore edge, and with an increase in the concentration of nanoparticles, the linear tension also increases. It has been shown that the presence of nanoparticles in the solution leads to a decrease in BLM conductivity.
{"title":"STABILITY AND CONDUCTIVITY OF BILAYER LIPID MEMBRANE IN PRESENCE $mathrm{Al_2O_3}$ NANOPARTICLES","authors":"Tsovinar M. Jomardyan, G. Ananyan, V. Arakelyan","doi":"10.46991/pysu:a/2023.57.1.023","DOIUrl":"https://doi.org/10.46991/pysu:a/2023.57.1.023","url":null,"abstract":"The effect of aluminum oxide nanoparticles (Al2O3) on the stability and conductivity of BLM (the bilayer lipid membrane) in solution was studied. It has been shown that Al2O3 nanoparticles increase the stability of BLM in an electric field, and BLM becomes more stable with increasing their concentration. The experimental data are analyzed in terms of the well-known theory of BLM stability, which is based on the concept of spontaneous formation of microscopic pores on the BLM, the development of which leads to the loss of BLM stability. It is shown that aluminum oxide nanoparticles increase the value of the coefficient of linear tension of the pore edge, and with an increase in the concentration of nanoparticles, the linear tension also increases. It has been shown that the presence of nanoparticles in the solution leads to a decrease in BLM conductivity.","PeriodicalId":21146,"journal":{"name":"Proceedings of the YSU A: Physical and Mathematical Sciences","volume":"33 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73164425","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 : 2022-10-21DOI: 10.46991/pysu:a/2022.56.3.107
D. N. Harutyunyan
In this paper $n$-ary regular division algebras are discussed, which are satisfying the hyperidentity of paramediality. It is shown that every operation in $n$-ary regular paramedial division algebra will be linearly represented over the same Abelian group. Similar results already obtained for regular medial division algebras in [1].
{"title":"ON REGULAR PARAMEDIAL DIVISION ALGEBRAS","authors":"D. N. Harutyunyan","doi":"10.46991/pysu:a/2022.56.3.107","DOIUrl":"https://doi.org/10.46991/pysu:a/2022.56.3.107","url":null,"abstract":"In this paper $n$-ary regular division algebras are discussed, which are satisfying the hyperidentity of paramediality. It is shown that every operation in $n$-ary regular paramedial division algebra will be linearly represented over the same Abelian group. Similar results already obtained for regular medial division algebras in [1].","PeriodicalId":21146,"journal":{"name":"Proceedings of the YSU A: Physical and Mathematical Sciences","volume":"54 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87761388","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 : 2022-10-21DOI: 10.46991/pysu:a/2022.56.3.116
T. K. Ghukasyan
The intrasubband and intersubband absorption of light by free charge carriers in a semiconductor nanowire upon scattering by polar optical phonons mediated by Rashba and Dresselhaus spin-orbit interactions has been studied. The dependence of the absorption coefficient on the energy of the incident photon is investigated by counting the transitions between different conduction subbands. It is shown that the spin-orbit interaction leads to an increase in the coefficient of intrasubband and intersubband absorption of light, with the peaks of the absorption coefficient being determined by the energies of the absorbed photon and the absorbed or emitted phonon. In this case, the difference between the values of the absorption coefficients with or without spin-orbit interaction has maximum in the range of the local minimum of the absorption coefficient obtained by ignoring the spin-orbit coupling.
{"title":"OPTICAL ABSORPTION IN SEMICONDUCTOR NANOWIRE MEDIATED BY ELECTRON-POLAR OPTICAL PHONON AND SPIN-ORBIT INTERACTIONS","authors":"T. K. Ghukasyan","doi":"10.46991/pysu:a/2022.56.3.116","DOIUrl":"https://doi.org/10.46991/pysu:a/2022.56.3.116","url":null,"abstract":"The intrasubband and intersubband absorption of light by free charge carriers in a semiconductor nanowire upon scattering by polar optical phonons mediated by Rashba and Dresselhaus spin-orbit interactions has been studied. The dependence of the absorption coefficient on the energy of the incident photon is investigated by counting the transitions between different conduction subbands. It is shown that the spin-orbit interaction leads to an increase in the coefficient of intrasubband and intersubband absorption of light, with the peaks of the absorption coefficient being determined by the energies of the absorbed photon and the absorbed or emitted phonon. In this case, the difference between the values of the absorption coefficients with or without spin-orbit interaction has maximum in the range of the local minimum of the absorption coefficient obtained by ignoring the spin-orbit coupling.","PeriodicalId":21146,"journal":{"name":"Proceedings of the YSU A: Physical and Mathematical Sciences","volume":"42 3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74579129","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 : 2022-10-17DOI: 10.46991/pysu:a/2022.56.3.085
Aghasi B. Ghazaryan, P. Petrosyan
A proper edge coloring of a graph $G$ is a mapping $alpha:E(G)longrightarrow mathbb{N}$ such that $alpha(e)not=alpha(e')$ for every pair of adjacent edges $e$ and $e'$ in $G$. In a proper edge coloring of a graph $G$, the palette of a vertex $v in V(G)$ is the set of colors assigned to the edges incident to $v$. The palette index of $G$ is the minimum number of distinct palettes occurring in $G$ among all proper edge colorings of $G$. A graph $G$ has a spanning star, if it has a spanning subgraph which is a star. In this paper, we consider the palette index of graphs having a spanning star. In particular, we give sharp upper and lower bounds on the palette index of these graphs. We also provide some upper and lower bounds on the palette index of the complete split and threshold graphs.
图$G$的适当边着色是$alpha:E(G) longightarrow mathbb{N}$的映射，使得$alpha(E)not=alpha(E ')$对于$G$中的每一对相邻边$ E $和$ E '$。在图$G$的适当边着色中，顶点$v 在v (G)$中的调色板是分配给与$v$相关的边的颜色集合。$G$的调色板指数是在$G$的所有适当的边着色中，在$G$中出现的不同调色板的最小数量。一个图G有一个生成星，如果它有一个生成子图是星形的。本文考虑了具有生成星的图的调色板索引。特别地，我们给出了这些图的调色板指数的上界和下界。我们还提供了完整分割图和阈值图的调色板索引的上界和下界。
{"title":"ON THE PALETTE INDEX OF GRAPHS HAVING A SPANNING STAR","authors":"Aghasi B. Ghazaryan, P. Petrosyan","doi":"10.46991/pysu:a/2022.56.3.085","DOIUrl":"https://doi.org/10.46991/pysu:a/2022.56.3.085","url":null,"abstract":"A proper edge coloring of a graph $G$ is a mapping $alpha:E(G)longrightarrow mathbb{N}$ such that $alpha(e)not=alpha(e')$ for every pair of adjacent edges $e$ and $e'$ in $G$. In a proper edge coloring of a graph $G$, the palette of a vertex $v in V(G)$ is the set of colors assigned to the edges incident to $v$. The palette index of $G$ is the minimum number of distinct palettes occurring in $G$ among all proper edge colorings of $G$. A graph $G$ has a spanning star, if it has a spanning subgraph which is a star. In this paper, we consider the palette index of graphs having a spanning star. In particular, we give sharp upper and lower bounds on the palette index of these graphs. We also provide some upper and lower bounds on the palette index of the complete split and threshold graphs.","PeriodicalId":21146,"journal":{"name":"Proceedings of the YSU A: Physical and Mathematical Sciences","volume":"20 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79010577","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 : 2022-09-18DOI: 10.46991/pysu:a/2022.56.3.097
H. Hakopian
Let a set of nodes $mathcal X$ in the plane be $n$-independent, i.e. each node has a fundamental polynomial of degree $n.$ Assume that $#mathcal X=d(n,n-3)+3= (n+1)+n+cdots+5+3.$ In this paper we prove that there are at most three linearly independent curves of degree less than or equal to $n-1$ that pass through all the nodes of $mathcal X.$ We provide a characterization of the case when there are exactly three such curves. Namely, we prove that then the set $mathcal X$ has a very special construction: either all its nodes belong to a curve of degree $n-2,$ or all its nodes but three belong to a (maximal) curve of degree $n-3.$ This result complements a result established recently by H. Kloyan, D. Voskanyan, and H. Hakopian. Note that the proofs of the two results are completely different.
设平面上的一组节点$mathcal X$是$n$独立的，即每个节点有一个阶为$n的基本多项式。假设美元 # mathcal X = d (n, n - 3) + 3 = (n + 1) + n + cdots + 5 + 3。本文证明了至多有三条小于或等于n-1次的线性无关曲线通过数学x的所有节点，并给出了恰好有三条这样的曲线的一个刻画。也就是说，我们证明了集合$mathcal X$有一个非常特殊的构造:它的所有节点都属于$n-2次曲线，$或者它的所有节点都属于$n-3次(最大)曲线。这一结果补充了最近由H. Kloyan, D. Voskanyan和H. Hakopian建立的结果。注意，这两个结果的证明是完全不同的。
{"title":"ON A RESULT CONCERNING ALGEBRAIC CURVES PASSING THROUGH $n$-INDEPENDENT NODES","authors":"H. Hakopian","doi":"10.46991/pysu:a/2022.56.3.097","DOIUrl":"https://doi.org/10.46991/pysu:a/2022.56.3.097","url":null,"abstract":"Let a set of nodes $mathcal X$ in the plane be $n$-independent, i.e. each node has a fundamental polynomial of degree $n.$ Assume that $#mathcal X=d(n,n-3)+3= (n+1)+n+cdots+5+3.$ In this paper we prove that there are at most three linearly independent curves of degree less than or equal to $n-1$ that pass through all the nodes of $mathcal X.$ We provide a characterization of the case when there are exactly three such curves. Namely, we prove that then the set $mathcal X$ has a very special construction: either all its nodes belong to a curve of degree $n-2,$ or all its nodes but three belong to a (maximal) curve of degree $n-3.$ This result complements a result established recently by H. Kloyan, D. Voskanyan, and H. Hakopian. Note that the proofs of the two results are completely different.","PeriodicalId":21146,"journal":{"name":"Proceedings of the YSU A: Physical and Mathematical Sciences","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81325954","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 : 2022-07-13DOI: 10.46991/pysu:a/2022.56.2.058
A. Chubaryan
In this paper four proof complexity characteristics for some class of balanced tautologies are investigated in two proof systems of propositional logic. One of the considered systems is based on determinative disjunctive normal form, the other on the generalization of splitting method. The optimal upper and lower bounds by logarithmic scale for all main proof complexity characteristics of considered tautologies are obtained in both systems.
{"title":"PROOF COMPLEXITIES ON A CLASS OF BALANCED FORMULAS IN SOME PROPOSITIONAL SYSTEMS","authors":"A. Chubaryan","doi":"10.46991/pysu:a/2022.56.2.058","DOIUrl":"https://doi.org/10.46991/pysu:a/2022.56.2.058","url":null,"abstract":"In this paper four proof complexity characteristics for some class of balanced tautologies are investigated in two proof systems of propositional logic. One of the considered systems is based on determinative disjunctive normal form, the other on the generalization of splitting method. The optimal upper and lower bounds by logarithmic scale for all main proof complexity characteristics of considered tautologies are obtained in both systems.","PeriodicalId":21146,"journal":{"name":"Proceedings of the YSU A: Physical and Mathematical Sciences","volume":"16 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77933350","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 : 2022-07-13DOI: 10.46991/pysu:a/2022.56.2.066
Zhirayr A. Baghdasaryan
Microwave near-field distribution of the GPS patch antenna was visualized by a thermo-elastic optical indicator microscopy (TEOIM) technique at $1.575~GHz$. Visualization of the antenna radiation is realized to describe the electromagnetic field intensity and distribution depending on the distance from the antenna surface and optical indicator. Experimental data was compared and confirmed with simulation results, which are in good agreement. Possible applications of the TEOIM system were discussed.
{"title":"IMAGING OF MICROWAVE NEAR-FIELD DISTRIBUTION OF GPS PATCH ANTENNA","authors":"Zhirayr A. Baghdasaryan","doi":"10.46991/pysu:a/2022.56.2.066","DOIUrl":"https://doi.org/10.46991/pysu:a/2022.56.2.066","url":null,"abstract":"Microwave near-field distribution of the GPS patch antenna was visualized by a thermo-elastic optical indicator microscopy (TEOIM) technique at $1.575~GHz$. Visualization of the antenna radiation is realized to describe the electromagnetic field intensity and distribution depending on the distance from the antenna surface and optical indicator. Experimental data was compared and confirmed with simulation results, which are in good agreement. Possible applications of the TEOIM system were discussed.","PeriodicalId":21146,"journal":{"name":"Proceedings of the YSU A: Physical and Mathematical Sciences","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83909156","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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