Pub Date : 2022-07-13DOI: 10.46991/pysu:a/2022.56.2.043
V. S. Atabekyan, H. T. Aslanyan, Satenik T. Aslanyan
It is proved that for every odd $n ge 1039$ there are two words $u(x, y), v(x,y)$ of length $le 658n^2$ over the group alphabet ${x,y}$ of the free Burnside group $B(2 ,n),$ which generate a free Burnside subgroup of the group $B(2,n)$. This implies that for any finite subset $S$ of the group $B(m,n)$ the inequality $|S^t|>4cdot 2.9^{[frac{t}{658s^2}]}$ holds, where $s$ is the smallest odd divisor of $n$ that satisfies the inequality $sge1039$.
证明了对于每一个奇数$n ge 1039$，在自由Burnside群$B(2 ,n),$的群字母表${x,y}$上有两个长度为$le 658n^2$的单词$u(x, y), v(x,y)$，它们产生了自由Burnside群$B(2,n)$的子群。这意味着对于群$B(m,n)$的任意有限子集$S$，不等式$|S^t|>4cdot 2.9^{[frac{t}{658s^2}]}$成立，其中$s$是满足不等式$sge1039$的$n$的最小奇约数。
{"title":"POWERS OF SUBSETS IN FREE PERIODIC GROUPS","authors":"V. S. Atabekyan, H. T. Aslanyan, Satenik T. Aslanyan","doi":"10.46991/pysu:a/2022.56.2.043","DOIUrl":"https://doi.org/10.46991/pysu:a/2022.56.2.043","url":null,"abstract":"It is proved that for every odd $n ge 1039$ there are two words $u(x, y), v(x,y)$ of length $le 658n^2$ over the group alphabet ${x,y}$ of the free Burnside group $B(2 ,n),$ which generate a free Burnside subgroup of the group $B(2,n)$. This implies that for any finite subset $S$ of the group $B(m,n)$ the inequality $|S^t|>4cdot 2.9^{[frac{t}{658s^2}]}$ holds, where $s$ is the smallest odd divisor of $n$ that satisfies the inequality $sge1039$.","PeriodicalId":21146,"journal":{"name":"Proceedings of the YSU A: Physical and Mathematical Sciences","volume":"65 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76978131","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/2022.56.2.049
Arman A. Bayramyan
In this article, we explore the automorphisms of endomorphism semigroups and automorphism groups of the finite elementary Abelian groups. In particular, we prove that $mathrm{Aut}(mathrm{End}(Z_poplusZ_popluscdotsoplusZ_p))$ can be canonically embedded into $mathrm{Aut}(mathrm{Aut}(Z_poplusZ_popluscdotsoplusZ_p))$ using an elementary approach based on matrix operations. We also show that all automorphisms of $mathrm{End}(Z_poplusZ_popluscdotsoplusZ_p)$ are inner.
{"title":"ON AUTOMORPHISM GROUPS OF ENDOMORPHISM SEMIGROUPS OF FINITE ELEMENTARY ABELIAN GROUPS","authors":"Arman A. Bayramyan","doi":"10.46991/pysu:a/2022.56.2.049","DOIUrl":"https://doi.org/10.46991/pysu:a/2022.56.2.049","url":null,"abstract":"In this article, we explore the automorphisms of endomorphism semigroups and automorphism groups of the finite elementary Abelian groups. In particular, we prove that $mathrm{Aut}(mathrm{End}(Z_poplusZ_popluscdotsoplusZ_p))$ can be canonically embedded into $mathrm{Aut}(mathrm{Aut}(Z_poplusZ_popluscdotsoplusZ_p))$ using an elementary approach based on matrix operations. We also show that all automorphisms of $mathrm{End}(Z_poplusZ_popluscdotsoplusZ_p)$ are inner.","PeriodicalId":21146,"journal":{"name":"Proceedings of the YSU A: Physical and Mathematical Sciences","volume":"10 5 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79562998","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 : 2022-06-13DOI: 10.46991/pysu:a/2022.56.2.074
Ararat H. Stepanyan, H. Haroyan
Miniaturization of antipodal Vivaldi antenna (AVA) based on high dielectric constant and magnetodielectric ferrite materials is studied. The basic parameters of antipodal Vivaldi antenna based on high dielectric and magnetodielectric materials (MDM) are compared. To miniaturize the size of the antenna by a higher factor, MDM ferrite with paremeters $varepsilon_r=mu_r=8$ is used. The analysis shows that MDM based Vivaldi antenna surface is minimized by a factor of 4 compared to that of air-based Vivaldi antenna. The sizes of AVA are $120 times 120 times 1~(mm).$
研究了基于高介电常数和磁介电铁氧体材料的对映维瓦尔第天线(AVA)小型化。比较了高介电材料和磁介电材料对映维瓦尔第天线的基本参数。为了使天线的尺寸更小，使用了参数为$varepsilon_r=mu_r=8$的MDM铁氧体。分析表明，与基于空气的Vivaldi天线相比，基于MDM的Vivaldi天线表面减少了4倍。AVA的大小为 $120 times 120 times 1~(mm).$
{"title":"MINIATURIZED ANTIPODAL VIVALDI ANTENNA BASED ON MAGNETODIELECTRIC MATERIALS","authors":"Ararat H. Stepanyan, H. Haroyan","doi":"10.46991/pysu:a/2022.56.2.074","DOIUrl":"https://doi.org/10.46991/pysu:a/2022.56.2.074","url":null,"abstract":"Miniaturization of antipodal Vivaldi antenna (AVA) based on high dielectric constant and magnetodielectric ferrite materials is studied. The basic parameters of antipodal Vivaldi antenna based on high dielectric and magnetodielectric materials (MDM) are compared. To miniaturize the size of the antenna by a higher factor, MDM ferrite with paremeters $varepsilon_r=mu_r=8$ is used. The analysis shows that MDM based Vivaldi antenna surface is minimized by a factor of 4 compared to that of air-based Vivaldi antenna. The sizes of AVA are $120 times 120 times 1~(mm).$","PeriodicalId":21146,"journal":{"name":"Proceedings of the YSU A: Physical and Mathematical Sciences","volume":"16 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73009284","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 : 2022-04-04DOI: 10.46991/pysu:a/2022.56.1.027
Sh. Navasardyan
The equivalence between the concepts of normal and perfectly stable subgroups is shown. The proof of the main theorem is based on a novel concept of hypergroups over a group.
给出了正规子群与完全稳定子群概念之间的等价性。主要定理的证明是基于群上超群的新概念。
{"title":"PERFECTLY STABLE AND NORMAL SUBGROUPS","authors":"Sh. Navasardyan","doi":"10.46991/pysu:a/2022.56.1.027","DOIUrl":"https://doi.org/10.46991/pysu:a/2022.56.1.027","url":null,"abstract":"The equivalence between the concepts of normal and perfectly stable subgroups is shown. The proof of the main theorem is based on a novel concept of hypergroups over a group.","PeriodicalId":21146,"journal":{"name":"Proceedings of the YSU A: Physical and Mathematical Sciences","volume":"12 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87995030","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 : 2022-03-25DOI: 10.46991/pysu:a/2022.56.1.001
Grigor Gevorgyan
In this paper central extensions of free groups of infinitely based varieties of S.I. Adian are constructed. Using this extensions we prove that the Schur multipliers of mentioned relatively free groups are free Abelian groups of infinite rank. It is well-known that these varieties are given by identities in two variables. For a fixed rank $m$, the set of free groups of rank $m$ of these varieties has the cardinality of continuum.
{"title":"ON SCHUR MULTIPLIERS OF SOME RELATIVELY FREE GROUPS","authors":"Grigor Gevorgyan","doi":"10.46991/pysu:a/2022.56.1.001","DOIUrl":"https://doi.org/10.46991/pysu:a/2022.56.1.001","url":null,"abstract":"In this paper central extensions of free groups of infinitely based varieties of S.I. Adian are constructed. Using this extensions we prove that the Schur multipliers of mentioned relatively free groups are free Abelian groups of infinite rank. It is well-known that these varieties are given by identities in two variables. For a fixed rank $m$, the set of free groups of rank $m$ of these varieties has the cardinality of continuum.","PeriodicalId":21146,"journal":{"name":"Proceedings of the YSU A: Physical and Mathematical Sciences","volume":"2 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83031704","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 : 2022-03-25DOI: 10.46991/pysu:a/2022.56.1.033
V. Ohanyan, Vigen H. Khalatyan
In the present paper we obtain a relationship between the covariogram and distribution function of the distance between two uniformly and independently distributed points. Additionally, we calculate the distribution function of the distance between these two points in a disk, a ball and a triangle.
{"title":"RELATION BETWEEN THE COVARIOGRAM AND DISTRIBUTION FUNCTION OF THE DISTANCE BETWEEN TWO UNIFORM AND INDEPENDENT POINTS","authors":"V. Ohanyan, Vigen H. Khalatyan","doi":"10.46991/pysu:a/2022.56.1.033","DOIUrl":"https://doi.org/10.46991/pysu:a/2022.56.1.033","url":null,"abstract":"In the present paper we obtain a relationship between the covariogram and distribution function of the distance between two uniformly and independently distributed points. Additionally, we calculate the distribution function of the distance between these two points in a disk, a ball and a triangle.","PeriodicalId":21146,"journal":{"name":"Proceedings of the YSU A: Physical and Mathematical Sciences","volume":"87 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80846196","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 : 2022-03-25DOI: 10.46991/pysu:a/2022.56.1.007
K. Khachatryan, A. Hakobyan
The work is devoted to a special class of nonlinear integral equations on the positive semi-axis with conservative kernel that corresponds to a nonlinear operator, for which the property of complete continuity in the space of bounded functions fails. In different special cases this class of equations has applications in particular branches of mathematical physics. In particular, this kind of equations can be met in the radiative transfer theory, kinetic theory of gases, kinetic theory of plasma and in the $p$-adic open-closed string theory. Using a combination of special iterations with the monotonic operator theory methods, that work in defined conical segments it is possible to prove a constructive existence theorem of nonnegative nontrivial bounded solution that has finite limit at infinity. The asymptotics of the constructed solution will also be studied. It is also given an example of nonlinear equation, for which the uniqueness of the solution in the space of bounded functions fails. At the end of the paper will consider some classes of equations both applied and pure theoretical character.
{"title":"ON NONTRIVIAL SOLVABILITY OF ONE CLASS OF NONLINEAR INTEGRAL EQUATIONS WITH CONSERVATIVE KERNEL ON THE POSITIVE SEMI-AXIS","authors":"K. Khachatryan, A. Hakobyan","doi":"10.46991/pysu:a/2022.56.1.007","DOIUrl":"https://doi.org/10.46991/pysu:a/2022.56.1.007","url":null,"abstract":"The work is devoted to a special class of nonlinear integral equations on the positive semi-axis with conservative kernel that corresponds to a nonlinear operator, for which the property of complete continuity in the space of bounded functions fails. In different special cases this class of equations has applications in particular branches of mathematical physics. In particular, this kind of equations can be met in the radiative transfer theory, kinetic theory of gases, kinetic theory of plasma and in the $p$-adic open-closed string theory. Using a combination of special iterations with the monotonic operator theory methods, that work in defined conical segments it is possible to prove a constructive existence theorem of nonnegative nontrivial bounded solution that has finite limit at infinity. The asymptotics of the constructed solution will also be studied. It is also given an example of nonlinear equation, for which the uniqueness of the solution in the space of bounded functions fails. At the end of the paper will consider some classes of equations both applied and pure theoretical character.","PeriodicalId":21146,"journal":{"name":"Proceedings of the YSU A: Physical and Mathematical Sciences","volume":"64 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80185323","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 : 2022-03-25DOI: 10.46991/pysu:a/2022.56.1.019
Levon N. Muradyan
A graph $G$ is called a complete $r$-partite $(rgeq 2)$ graph, if its vertices can be divided into $r$ non-empty independent sets $V_1,ldots,V_r$ in a way that each vertex in $V_i$ is adjacent to all the other vertices in $V_j$ for $1leq i
图$G$被称为完全$r$ -部$(rgeq 2)$图，如果它的顶点可以被分成$r$非空独立集$V_1,ldots,V_r$，并且$V_i$中的每个顶点与$V_j$中的所有其他顶点相邻，对于$1leq i
{"title":"ON INTERVAL EDGE-COLORINGS OF COMPLETE MULTIPARTITE GRAPHS","authors":"Levon N. Muradyan","doi":"10.46991/pysu:a/2022.56.1.019","DOIUrl":"https://doi.org/10.46991/pysu:a/2022.56.1.019","url":null,"abstract":"A graph $G$ is called a complete $r$-partite $(rgeq 2)$ graph, if its vertices can be divided into $r$ non-empty independent sets $V_1,ldots,V_r$ in a way that each vertex in $V_i$ is adjacent to all the other vertices in $V_j$ for $1leq i<jleq r$. Let $K_{n_{1},n_{2},ldots,n_{r}}$ denote a complete $r$-partite graph with independent sets $V_1,V_2,ldots,V_r$ of sizes $n_{1},n_{2},ldots,n_{r}$. An edge-coloring of a graph $G$ with colors $1,2,ldots,t$ is called an emph{interval $t$-coloring}, if all colors are used and the colors of edges incident to each vertex of $G$ are distinct and form an interval of integers. In this paper we have obtained some results on the existence and construction of interval edge-colorings of complete $r$-partite graphs. Moreover, we have also derived an upper bound on the number of colors in interval colorings of complete multipartite graphs.","PeriodicalId":21146,"journal":{"name":"Proceedings of the YSU A: Physical and Mathematical Sciences","volume":"12 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84314106","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 : 2022-01-12DOI: 10.46991/pysu:a/2012.46.3.014
Yu. M. Movsisyan
It is well known that free Boolean algebra on n free generators is isomorphic to the Boolean algebra of Boolean functions of n variables. The free distributive lattice on n free generators is isomorphic to the lattice of monotone Boolean functions of n variables. In this paper we introduce the concept of De Morgan function and prove that the free De Morgan algebra on n free generators is isomorphic to the De Morgan algebra of De Morgan functions of n variables. Keywords: Antichain, monotone Boolean function, De Morgan function, free De Morgan algebra.
{"title":"A FUNCTIONAL REPRESENTATION OF FREE DE MORGAN ALGEBRAS","authors":"Yu. M. Movsisyan","doi":"10.46991/pysu:a/2012.46.3.014","DOIUrl":"https://doi.org/10.46991/pysu:a/2012.46.3.014","url":null,"abstract":"It is well known that free Boolean algebra on n free generators is isomorphic to the Boolean algebra of Boolean functions of n variables. The free distributive lattice on n free generators is isomorphic to the lattice of monotone Boolean functions of n variables. In this paper we introduce the concept of De Morgan function and prove that the free De Morgan algebra on n free generators is isomorphic to the De Morgan algebra of De Morgan functions of n variables. Keywords: Antichain, monotone Boolean function, De Morgan function, free De Morgan algebra.","PeriodicalId":21146,"journal":{"name":"Proceedings of the YSU A: Physical and Mathematical Sciences","volume":"91 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74664584","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 : 2021-12-28DOI: 10.46991/pysu:a/2021.55.3.174
B. Minasyan
In the article we observed the microwave absorption of sodium chloride (NaCl) and glucose aqueous solution with different concentrations by using a thermoelastic optical indicator microscope (TEOIM). The non-invasive sensing technology of TEOIM is giving a big advantage compared to other detection technologies. By a TEOIM were visualized the change in distribution of microwave field depending on concentration of NaCl and glucose in $8-14~GHz$ range. This article is shown the investigation results for different concentrations of NaCl $(0-2.5%)$ and represented the behavior of averaged microwave near-field intensity for glucose (varied of $0-10%$ range) and NaCl (fixed at $0.9%$) complex aqueous solutions.
{"title":"SENSING OF SODIUM CHLORIDE AND GLUCOSE MIXED AQUEOUS SOLUTION BY USING A THERMOELASTIC OPTICAL INDICATOR MICROSCOPE","authors":"B. Minasyan","doi":"10.46991/pysu:a/2021.55.3.174","DOIUrl":"https://doi.org/10.46991/pysu:a/2021.55.3.174","url":null,"abstract":"In the article we observed the microwave absorption of sodium chloride (NaCl) and glucose aqueous solution with different concentrations by using a thermoelastic optical indicator microscope (TEOIM). The non-invasive sensing technology of TEOIM is giving a big advantage compared to other detection technologies. By a TEOIM were visualized the change in distribution of microwave field depending on concentration of NaCl and glucose in $8-14~GHz$ range. This article is shown the investigation results for different concentrations of NaCl $(0-2.5%)$ and represented the behavior of averaged microwave near-field intensity for glucose (varied of $0-10%$ range) and NaCl (fixed at $0.9%$) complex aqueous solutions.","PeriodicalId":21146,"journal":{"name":"Proceedings of the YSU A: Physical and Mathematical Sciences","volume":"62 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82866055","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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