Pub Date : 2017-12-15DOI: 10.46991/pysu:a/2017.51.3.250
V. G. Petrosyan
The Dirichlet boundary value problem in the weighted spaces $L^{1}(rho)$ on the unit circle $T={z: |z|=1}$ is investigated, where $rho(t)={|t-t_{k}|}^{alpha_{k}}$,~~$k=1,dots,m$, lb $t_{k}in T$ and $alpha_{k}$ are arbitrary real numbers. The problem is to determine a function $Phi(z)$ analytic in unit disc such that: $ lim_{rrightarrow 1-0}|RePhi(rt)-f(t)|_{L^{1}(rho_{r})}=0, $ where $fin L^{1}(rho)$. In the paper necessary and sufficient conditions for solvability of the problem are given and the general solution is written in the explicit form.
{"title":"DIRICHLET BOUNDARY VALUE PROBLEM IN THE WEIGHTED SPACES $L^{1}(rho)$","authors":"V. G. Petrosyan","doi":"10.46991/pysu:a/2017.51.3.250","DOIUrl":"https://doi.org/10.46991/pysu:a/2017.51.3.250","url":null,"abstract":"The Dirichlet boundary value problem in the weighted spaces $L^{1}(rho)$ on the unit circle $T={z: |z|=1}$ is investigated, where $rho(t)={|t-t_{k}|}^{alpha_{k}}$,~~$k=1,dots,m$, lb $t_{k}in T$ and $alpha_{k}$ are arbitrary real numbers. The problem is to determine a function $Phi(z)$ analytic in unit disc such that: $ lim_{rrightarrow 1-0}|RePhi(rt)-f(t)|_{L^{1}(rho_{r})}=0, $ where $fin L^{1}(rho)$. In the paper necessary and sufficient conditions for solvability of the problem are given and the general solution is written in the explicit form.","PeriodicalId":21146,"journal":{"name":"Proceedings of the YSU A: Physical and Mathematical Sciences","volume":"24 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2017-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80116338","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 : 2017-12-15DOI: 10.46991/pysu:a/2017.51.3.269
Shant Arakelyan
Electromagnetic field localization in a subwavelength metallic slit by a thermo-elastic optical indicator microscope (TEOIM) was investigated. As an indicator for the TEOIM system a slide glass with sizes of $20times 20times0.5~(mm)$ was used, on the surface of which an $mathrm{Al}$ film of $20~nm$ thickness was vaporized using the vacuum evaporation technique, with various slit width $(10-50~mu m).$ Strongly localized electromagnetic field has been exited in the slits by $50~ GHz$ generator and was visualized by a TEOIM. The waveguide properties of the system were characterized by COMSOL Multiphysics$^{circledR}$ additionally. The simulation results are in good agreement with the visualization data set.
{"title":"INVESTIGATION OF LOCALIZED ELECTROMAGNETIC FIELD IN A SUBWAVELENGTH METALLIC SLIT","authors":"Shant Arakelyan","doi":"10.46991/pysu:a/2017.51.3.269","DOIUrl":"https://doi.org/10.46991/pysu:a/2017.51.3.269","url":null,"abstract":"Electromagnetic field localization in a subwavelength metallic slit by a thermo-elastic optical indicator microscope (TEOIM) was investigated. As an indicator for the TEOIM system a slide glass with sizes of $20times 20times0.5~(mm)$ was used, on the surface of which an $mathrm{Al}$ film of $20~nm$ thickness was vaporized using the vacuum evaporation technique, with various slit width $(10-50~mu m).$ Strongly localized electromagnetic field has been exited in the slits by $50~ GHz$ generator and was visualized by a TEOIM. The waveguide properties of the system were characterized by COMSOL Multiphysics$^{circledR}$ additionally. The simulation results are in good agreement with the visualization data set.","PeriodicalId":21146,"journal":{"name":"Proceedings of the YSU A: Physical and Mathematical Sciences","volume":"37 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2017-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74618223","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 : 2017-12-15DOI: 10.46991/pysu:a/2017.51.3.211
N. Aharonyan, H. O. Harutyunyan
In the paper, using a relationship between probability $P(L(omega)subset mathbf {D}) $ that a random segment of length $l$ in $R^{n}$ having a common point with body $D$ entirely lying in $D$ and the covariogram of $D$, we obtain the explicit form of $P(L(omega)subset mathbf {D}) $ for any triangle on the plane.
本文利用R^{n}$中长度为$ L $的随机线段有一个公点且体$D$完全在$D$上的概率$P(L(omega)子集mathbf {D}) $与$D$的协变函数之间的关系，得到了平面上任意三角形的$P(L(omega)子集mathbf {D}) $的显式形式。
{"title":"GEOMETRIC PROBABILITY CALCULATION FOR A TRIANGLE","authors":"N. Aharonyan, H. O. Harutyunyan","doi":"10.46991/pysu:a/2017.51.3.211","DOIUrl":"https://doi.org/10.46991/pysu:a/2017.51.3.211","url":null,"abstract":"In the paper, using a relationship between probability $P(L(omega)subset mathbf {D}) $ that a random segment of length $l$ in $R^{n}$ having a common point with body $D$ entirely lying in $D$ and the covariogram of $D$, we obtain the explicit form of $P(L(omega)subset mathbf {D}) $ for any triangle on the plane.","PeriodicalId":21146,"journal":{"name":"Proceedings of the YSU A: Physical and Mathematical Sciences","volume":"26 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2017-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86981692","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 : 2017-12-15DOI: 10.46991/pysu:a/2017.51.3.262
Rezaei Masoud
The present work considers the optimal stabilization problem in rotational motion of a rigid body around its center of gravity. The case of the Euler rotational motion of a rigid body around a fixed point is considered. The optimal stabilization problem of the considered motion is assumed and solved. Input controls are introduced in the direction of the generalized coordinates, full controllability of linear approximation of the system is checked. Besides the optimal stabilization problem of the system on classical sense is solved, optimal Lyapunov function, optimal controls and value of functional are obtained.
{"title":"OPTIMAL STABILIZATION OF ROTATIONAL MOTION OF A RIGID BODY AROUND ITS CENTER OF GRAVITY","authors":"Rezaei Masoud","doi":"10.46991/pysu:a/2017.51.3.262","DOIUrl":"https://doi.org/10.46991/pysu:a/2017.51.3.262","url":null,"abstract":"The present work considers the optimal stabilization problem in rotational motion of a rigid body around its center of gravity. The case of the Euler rotational motion of a rigid body around a fixed point is considered. The optimal stabilization problem of the considered motion is assumed and solved. Input controls are introduced in the direction of the generalized coordinates, full controllability of linear approximation of the system is checked. Besides the optimal stabilization problem of the system on classical sense is solved, optimal Lyapunov function, optimal controls and value of functional are obtained.","PeriodicalId":21146,"journal":{"name":"Proceedings of the YSU A: Physical and Mathematical Sciences","volume":"2 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2017-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87163150","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 : 2017-12-15DOI: 10.46991/pysu:a/2017.51.3.217
V. S. Atabekyan, H. T. Aslanyan, H. Grigoryan, A. Grigoryan
We prove that the free Burnside groups $B(m,3)$ of period 3 and rank $mgeq1$ have Magnus's property, that is if in $B(m,3)$ the normal closures of $r$ and $s$ coincide, then $r$ is conjugate to $s$ or $s^{-1}$. We also prove that any automorphism of $B(m,3)$ induced by a Nielsen automorphism of the free group $F_m$ of rank $m$. We show that the kernel of the natural homomorphism $text{Aut}(B(2,3)) rightarrow GL_2(mathbb{Z}_3)$ is the group of inner automorphisms of $B(2,3)$.
{"title":"ANALOGUES OF NIELSEN'S AND MAGNUS'S THEOREMS FOR FREE BURNSIDE GROUPS OF PERIOD 3","authors":"V. S. Atabekyan, H. T. Aslanyan, H. Grigoryan, A. Grigoryan","doi":"10.46991/pysu:a/2017.51.3.217","DOIUrl":"https://doi.org/10.46991/pysu:a/2017.51.3.217","url":null,"abstract":"We prove that the free Burnside groups $B(m,3)$ of period 3 and rank $mgeq1$ have Magnus's property, that is if in $B(m,3)$ the normal closures of $r$ and $s$ coincide, then $r$ is conjugate to $s$ or $s^{-1}$. We also prove that any automorphism of $B(m,3)$ induced by a Nielsen automorphism of the free group $F_m$ of rank $m$. We show that the kernel of the natural homomorphism $text{Aut}(B(2,3)) rightarrow GL_2(mathbb{Z}_3)$ is the group of inner automorphisms of $B(2,3)$.","PeriodicalId":21146,"journal":{"name":"Proceedings of the YSU A: Physical and Mathematical Sciences","volume":"112 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2017-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88454842","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 : 2017-12-15DOI: 10.46991/pysu:a/2017.51.3.255
A. Grishko
The equations of oscillations of a two-layer plate are obtained on the basis of the assumption of Kirchhoff's hypothesis concerning the packet as a whole when the contact surfaces of the plate can slide freely relative to each other. It is assumed that the tangential stresses in the boundary conditions on the contact surface of the plates are zero. The dependence of bending and planar vibrations is obtained. The conditions for the appearance of a resonance are obtained.
{"title":"VIBRATIONS OF TWO-LAYERED PLATES IN CASE OF SLIDING CONTACT BETWEEN CONTACT SURFACES OF THE PLATE","authors":"A. Grishko","doi":"10.46991/pysu:a/2017.51.3.255","DOIUrl":"https://doi.org/10.46991/pysu:a/2017.51.3.255","url":null,"abstract":"The equations of oscillations of a two-layer plate are obtained on the basis of the assumption of Kirchhoff's hypothesis concerning the packet as a whole when the contact surfaces of the plate can slide freely relative to each other. It is assumed that the tangential stresses in the boundary conditions on the contact surface of the plates are zero. The dependence of bending and planar vibrations is obtained. The conditions for the appearance of a resonance are obtained.","PeriodicalId":21146,"journal":{"name":"Proceedings of the YSU A: Physical and Mathematical Sciences","volume":"48 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2017-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87020620","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 : 2017-12-15DOI: 10.46991/pysu:a/2017.51.3.231
M. I. Karakhanyan
Some aspects on strict topology in algebras of continuous and bounded functions on completely regular spaces are discussed in this work. Also some properties of their dual spaces are investigated.
本文讨论了完全正则空间上连续有界函数代数中严格拓扑的若干问题。研究了它们的对偶空间的一些性质。
{"title":"ON ALGEBRAS OF BOUNDED FUNCTIONS ON COMPLETELY REGULAR SPACES","authors":"M. I. Karakhanyan","doi":"10.46991/pysu:a/2017.51.3.231","DOIUrl":"https://doi.org/10.46991/pysu:a/2017.51.3.231","url":null,"abstract":"Some aspects on strict topology in algebras of continuous and bounded functions on completely regular spaces are discussed in this work. Also some properties of their dual spaces are investigated.","PeriodicalId":21146,"journal":{"name":"Proceedings of the YSU A: Physical and Mathematical Sciences","volume":"6 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2017-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72568032","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 : 2017-12-15DOI: 10.46991/pysu:a/2017.51.3.241
K. Navasardyan
It is proved, that if the square partial sums $sigma_{q_n}(textbf{x})$ of a multiple Franklin series converge in measure to a function $f$, the ratio $dfrac{q_{n+1}}{q_n}$ is bounded and the majorant of partial sums satisfies to a necessary condition, then the coefficients of the series are restored by the function $f$.
{"title":"UNIQUENESS THEOREMS FOR MULTIPLE FRANKLIN SERIES","authors":"K. Navasardyan","doi":"10.46991/pysu:a/2017.51.3.241","DOIUrl":"https://doi.org/10.46991/pysu:a/2017.51.3.241","url":null,"abstract":"It is proved, that if the square partial sums $sigma_{q_n}(textbf{x})$ of a multiple Franklin series converge in measure to a function $f$, the ratio $dfrac{q_{n+1}}{q_n}$ is bounded and the majorant of partial sums satisfies to a necessary condition, then the coefficients of the series are restored by the function $f$.","PeriodicalId":21146,"journal":{"name":"Proceedings of the YSU A: Physical and Mathematical Sciences","volume":"57 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2017-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74213659","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 : 2017-08-15DOI: 10.46991/pysu:a/2017.51.2.139
A. Harutyunyan, W. Lusky
In the present paper we consider the Toeplitz-$T_{bar{h}}^{ alpha}$ and differentiation-$D^delta $ operators on the Besov spaces $B_p(beta)$ for all $0< p
在本文中，我们考虑了所有$0< p
{"title":"OPERATORS ON THE BESOV SPACES OF HOLOMORPHIC FUNCTIONS ON THE UNIT BALL IN $mathbb{C}^n$","authors":"A. Harutyunyan, W. Lusky","doi":"10.46991/pysu:a/2017.51.2.139","DOIUrl":"https://doi.org/10.46991/pysu:a/2017.51.2.139","url":null,"abstract":"In the present paper we consider the Toeplitz-$T_{bar{h}}^{ alpha}$ and differentiation-$D^delta $ operators on the Besov spaces $B_p(beta)$ for all $0< p<infty.$ We show that $T_{bar{h}}^{ alpha}: B_p(beta)rightarrow B_p(beta)$ for $bar hin H^infty(B^n)$ and $D^delta :B_p(beta)rightarrow B_p(widetildebeta)$, where $widetildebeta=beta +pdelta .$","PeriodicalId":21146,"journal":{"name":"Proceedings of the YSU A: Physical and Mathematical Sciences","volume":"39 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2017-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77684565","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 : 2017-06-15DOI: 10.46991/pysu:a/2017.51.2.146
A. Gulyan
In this article the “bonus hunger” behavior for the Alternative bonus–malus system (BMS) is discussed. The Alternative BMS is a model, where the next premium is the combination of the previous premium and the aggregate claim amount. The key characteristics for the comparison are the discounted premium reduction for some time horizon and the entire claim amount. Existence of the steady state for the BMS discussed in this paper was proved and the probability of claiming for the general model and for its steady state was found out.
{"title":"“BONUS HUNGER” BEHAVIOR IN THE ALTERNATIVE BONUS–MALUS SYSTEM","authors":"A. Gulyan","doi":"10.46991/pysu:a/2017.51.2.146","DOIUrl":"https://doi.org/10.46991/pysu:a/2017.51.2.146","url":null,"abstract":"In this article the “bonus hunger” behavior for the Alternative bonus–malus system (BMS) is discussed. The Alternative BMS is a model, where the next premium is the combination of the previous premium and the aggregate claim amount. The key characteristics for the comparison are the discounted premium reduction for some time horizon and the entire claim amount. Existence of the steady state for the BMS discussed in this paper was proved and the probability of claiming for the general model and for its steady state was found out.","PeriodicalId":21146,"journal":{"name":"Proceedings of the YSU A: Physical and Mathematical Sciences","volume":"236 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2017-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80357404","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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