Pub Date : 2021-12-28DOI: 10.46991/pysu:a/2021.55.3.169
K. K. Grigoryan
In the problem of electron diffraction by a standing light wave (the Kapitza–Dirac effect), an electronic refractive index can be defined as the ratio of electron momenta in the wave field and outside it. Moreover, both kinetic and canonical electron momenta can be used for this purpose, which corresponds to the Abraham–Minkowski controversy in photonic optics. It is shown that in both cases the same expression for the electronic refractive index is obtained. This is consistent with Barnett's resolution of the Abraham–Minkowski dilemma.
{"title":"ANALOGUE OF THE ABRAHAM–MINKOWSKI CONTROVERSY IN ELECTRONIC OPTICS","authors":"K. K. Grigoryan","doi":"10.46991/pysu:a/2021.55.3.169","DOIUrl":"https://doi.org/10.46991/pysu:a/2021.55.3.169","url":null,"abstract":"In the problem of electron diffraction by a standing light wave (the Kapitza–Dirac effect), an electronic refractive index can be defined as the ratio of electron momenta in the wave field and outside it. Moreover, both kinetic and canonical electron momenta can be used for this purpose, which corresponds to the Abraham–Minkowski controversy in photonic optics. It is shown that in both cases the same expression for the electronic refractive index is obtained. This is consistent with Barnett's resolution of the Abraham–Minkowski dilemma.","PeriodicalId":21146,"journal":{"name":"Proceedings of the YSU A: Physical and Mathematical Sciences","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79589016","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 : 2021-11-05DOI: 10.46991/pysu:a/2021.55.3.160
Albert Kh. Sahakyan, Rafayel R. Kamalian
An interval vertex-coloring of a graph $G$ is a coloring of the vertices of the graph with intervals of integers such that the intervals of any two adjacent vertices do not intersect. In this paper we consider the case, where for each vertex $v$ there is a length $l(v)$ and a set of colors $S(v),$ from which the colors should be and it is required to find an interval vertex-coloring $gamma$ such that for each vertex $v$ the restrictions are met, i.e. $|gamma(v)|=l(v),gamma(v) subseteq S(v) $. We will provide a pseudo-polynomial algorithm for cactus graphs. If it is impossible to have an interval vertex-coloring that satisfies all the restrictions, then the algorithm will tell that as well.
{"title":"INTERVAL VERTEX-COLORINGS OF CACTUS GRAPHS WITH RESTRICTIONS ON VERTICES","authors":"Albert Kh. Sahakyan, Rafayel R. Kamalian","doi":"10.46991/pysu:a/2021.55.3.160","DOIUrl":"https://doi.org/10.46991/pysu:a/2021.55.3.160","url":null,"abstract":"An interval vertex-coloring of a graph $G$ is a coloring of the vertices of the graph with intervals of integers such that the intervals of any two adjacent vertices do not intersect. In this paper we consider the case, where for each vertex $v$ there is a length $l(v)$ and a set of colors $S(v),$ from which the colors should be and it is required to find an interval vertex-coloring $gamma$ such that for each vertex $v$ the restrictions are met, i.e. $|gamma(v)|=l(v),gamma(v) subseteq S(v) $. We will provide a pseudo-polynomial algorithm for cactus graphs. If it is impossible to have an interval vertex-coloring that satisfies all the restrictions, then the algorithm will tell that as well.","PeriodicalId":21146,"journal":{"name":"Proceedings of the YSU A: Physical and Mathematical Sciences","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80786335","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 : 2021-11-05DOI: 10.46991/pysu:a/2021.55.3.153
Arman A. Bayramyan
We construct systems of independent defining relations for free Burnside groups $B(m,3)$ of ranks $m=2, 3$. The proof for the case $m=2$ is established using the matrix representation of $B(2,3)$. For the case $m=3$ the approach is based on the natural embedding of $B(2,3)$ into $B(3,3)$.
{"title":"ON INDEPENDENT SYSTEMS OF DEFINING RELATIONS FOR FREE BURNSIDE GROUPS OF PERIOD 3","authors":"Arman A. Bayramyan","doi":"10.46991/pysu:a/2021.55.3.153","DOIUrl":"https://doi.org/10.46991/pysu:a/2021.55.3.153","url":null,"abstract":"We construct systems of independent defining relations for free Burnside groups $B(m,3)$ of ranks $m=2, 3$. The proof for the case $m=2$ is established using the matrix representation of $B(2,3)$. For the case $m=3$ the approach is based on the natural embedding of $B(2,3)$ into $B(3,3)$.","PeriodicalId":21146,"journal":{"name":"Proceedings of the YSU A: Physical and Mathematical Sciences","volume":"3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82077232","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 : 2021-08-30DOI: 10.46991/pysu:a/2021.55.2.131
A. A. Matevosyan, A. G. Matevosyan
Simple harmonic motion was investigated of a rotational oscillating system. The effect of dumping and forcing on motion of the system was examined and measurements were taken. Resonance in a oscillating system was investigated and quality factor of the dumping system was measured at different damping forces using three different methods. Resonance curves were constructed at two different damping forces. A probabilistic model was built and system parameters were estimated from the resonance curves using Stan sampling platform. The quality factor of the oscillating system when the additional dumping was turned off was estimated to be $Q = num{71 pm 1}$ and natural frequency $omega_0 = num{3.105 pm 0.008}, si{persecond}$.
{"title":"PARAMETER ESTIMATION FOR OSCILLATORY SYSTEMS","authors":"A. A. Matevosyan, A. G. Matevosyan","doi":"10.46991/pysu:a/2021.55.2.131","DOIUrl":"https://doi.org/10.46991/pysu:a/2021.55.2.131","url":null,"abstract":"Simple harmonic motion was investigated of a rotational oscillating system. The effect of dumping and forcing on motion of the system was examined and measurements were taken. Resonance in a oscillating system was investigated and quality factor of the dumping system was measured at different damping forces using three different methods. Resonance curves were constructed at two different damping forces. A probabilistic model was built and system parameters were estimated from the resonance curves using Stan sampling platform. The quality factor of the oscillating system when the additional dumping was turned off was estimated to be $Q = num{71 pm 1}$ and natural frequency $omega_0 = num{3.105 pm 0.008}, si{persecond}$.","PeriodicalId":21146,"journal":{"name":"Proceedings of the YSU A: Physical and Mathematical Sciences","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79863877","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 : 2021-08-30DOI: 10.46991/pysu:a/2021.55.2.123
S. Jilavyan, A. Khurshudyan
The concept of averaged controllability has been introduced relatively recently aiming to analyse the controllability of systems or processes containing some important parameters that may affect the controllability in usual sense. The averaged controllability of various specific and abstract equations has been studied so far. Relatively little attention has been paid to averaged controllability of coupled systems. The averaged state of a thermoelastic rectangular plate is studied in this paper using the well-known Green's function approach. The aim of the paper is to provide a theoretical background for further exact and approximate controllability analysis of fully coupled thermoelasticity equations which will appear elsewhere.
{"title":"AVERAGED CONTROLLABILITY OF THERMOELASTICITY EQUATIONS. AVERAGE STATE OF A RECTANGULAR PLATE","authors":"S. Jilavyan, A. Khurshudyan","doi":"10.46991/pysu:a/2021.55.2.123","DOIUrl":"https://doi.org/10.46991/pysu:a/2021.55.2.123","url":null,"abstract":"The concept of averaged controllability has been introduced relatively recently aiming to analyse the controllability of systems or processes containing some important parameters that may affect the controllability in usual sense. The averaged controllability of various specific and abstract equations has been studied so far. Relatively little attention has been paid to averaged controllability of coupled systems. The averaged state of a thermoelastic rectangular plate is studied in this paper using the well-known Green's function approach. The aim of the paper is to provide a theoretical background for further exact and approximate controllability analysis of fully coupled thermoelasticity equations which will appear elsewhere.","PeriodicalId":21146,"journal":{"name":"Proceedings of the YSU A: Physical and Mathematical Sciences","volume":"77 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90970287","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 : 2021-07-26DOI: 10.46991/pysu:a/2021.55.2.113
Albert Kh. Sahakyan, Rafayel R. Kamalian
An edge-coloring of a graph $G$ with consecutive integers $c_1,ldots,c_t$ is called an interval t-coloring, if all colors are used, and the colors of edges incident to any vertex of $G$ are distinct and form an interval of integers. A graph $G$ is interval colorable, if it has an interval t-coloring for some positive integer $t$. In this paper, we consider the case, where there are restrictions on the edges of the tree and provide a polynomial algorithm for checking interval colorability that satisfies those restrictions.
{"title":"INTERVAL EDGE-COLORINGS OF TREES WITH RESTRICTIONS ON THE EDGES","authors":"Albert Kh. Sahakyan, Rafayel R. Kamalian","doi":"10.46991/pysu:a/2021.55.2.113","DOIUrl":"https://doi.org/10.46991/pysu:a/2021.55.2.113","url":null,"abstract":"An edge-coloring of a graph $G$ with consecutive integers $c_1,ldots,c_t$ is called an interval t-coloring, if all colors are used, and the colors of edges incident to any vertex of $G$ are distinct and form an interval of integers. A graph $G$ is interval colorable, if it has an interval t-coloring for some positive integer $t$. In this paper, we consider the case, where there are restrictions on the edges of the tree and provide a polynomial algorithm for checking interval colorability that satisfies those restrictions.","PeriodicalId":21146,"journal":{"name":"Proceedings of the YSU A: Physical and Mathematical Sciences","volume":"109 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81643944","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 : 2021-01-01DOI: 10.46991/pysu:a/2021.55.2.148
K. K. Grigoryan
In the context of the Abraham–Minkowski controversy, the problem of the propagation of electromagnetic waves in a linear dielectric medium with a time-varying dielectric constant is considered. It is shown that the momentum of an electromagnetic wave in the form of Minkowski is preserved with an instantaneous change in the dielectric permittivity of the medium. At the same time, the Abraham momentum is not conserved, despite the spatial homogeneity of the problem. This circumstance is interpreted as a manifestation of the Abraham force.
{"title":"MOMENTUM OF AN ELECTROMAGNETIC WAVE IN TIME-VARYING DIELECTRIC MEDIA","authors":"K. K. Grigoryan","doi":"10.46991/pysu:a/2021.55.2.148","DOIUrl":"https://doi.org/10.46991/pysu:a/2021.55.2.148","url":null,"abstract":"In the context of the Abraham–Minkowski controversy, the problem of the propagation of electromagnetic waves in a linear dielectric medium with a time-varying dielectric constant is considered. It is shown that the momentum of an electromagnetic wave in the form of Minkowski is preserved with an instantaneous change in the dielectric permittivity of the medium. At the same time, the Abraham momentum is not conserved, despite the spatial homogeneity of the problem. This circumstance is interpreted as a manifestation of the Abraham force.","PeriodicalId":21146,"journal":{"name":"Proceedings of the YSU A: Physical and Mathematical Sciences","volume":"30 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84133029","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 : 2021-01-01DOI: 10.46991/pysu:a/2021.55.2.141
D. A. Martiryan
The use of the method developed in the CLAS collaboration (Jefferson Lab, USA) of improving leptons momentum for more correct studies of final state selection of quasi-real photoproduction resulting from the reaction to near threshold photoproduction of the $J/psi$ meson is described. The radiation photons that were detected in electromagnetic calorimeter were studied with electrons and positrons accompanied them in very narrow angles. The method of radiated photon selection of $e^+ e^- p^{prime}(e^{prime})$ reaction is given, where $e^+ e^-$ lepton pair is formed during the decay of $J/psi$ meson.
{"title":"THE RADIATIVE CORRECTIONS ACCOUNTING IN THE REACTION NEAR-THRESHOLD OF $J/psi$ PHOTOPRODUCTION","authors":"D. A. Martiryan","doi":"10.46991/pysu:a/2021.55.2.141","DOIUrl":"https://doi.org/10.46991/pysu:a/2021.55.2.141","url":null,"abstract":"The use of the method developed in the CLAS collaboration (Jefferson Lab, USA) of improving leptons momentum for more correct studies of final state selection of quasi-real photoproduction resulting from the reaction to near threshold photoproduction of the $J/psi$ meson is described. The radiation photons that were detected in electromagnetic calorimeter were studied with electrons and positrons accompanied them in very narrow angles. The method of radiated photon selection of $e^+ e^- p^{prime}(e^{prime})$ reaction is given, where $e^+ e^-$ lepton pair is formed during the decay of $J/psi$ meson.","PeriodicalId":21146,"journal":{"name":"Proceedings of the YSU A: Physical and Mathematical Sciences","volume":"41 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76180208","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 : 2020-12-18DOI: 10.46991/pysu:a/2017.51.2.187
R. S. Ghazaryan, S. Hakobyan, M. Shahinyan
Central moments of function of the differential melting curve (DMC) of DNA have been calculated through expansion of block DNA DMC to Gaussian components. Calculations showed that the first moment of DNA DMC characterizes the melting temperature, the second is DNA melting interval. Central moments of the third and fourth orders characterize distribution of nucleotides along DNA chain. It was shown that the distribution of nucleotides along DNA chain differs from quasi-arbitrary distribution.
{"title":"CALCULATION OF CENTRAL MOMENTS OF DIFFERENTIAL MELTING CURVE OF DNA MOLECULE","authors":"R. S. Ghazaryan, S. Hakobyan, M. Shahinyan","doi":"10.46991/pysu:a/2017.51.2.187","DOIUrl":"https://doi.org/10.46991/pysu:a/2017.51.2.187","url":null,"abstract":"Central moments of function of the differential melting curve (DMC) of DNA have been calculated through expansion of block DNA DMC to Gaussian components. Calculations showed that the first moment of DNA DMC characterizes the melting temperature, the second is DNA melting interval. Central moments of the third and fourth orders characterize distribution of nucleotides along DNA chain. It was shown that the distribution of nucleotides along DNA chain differs from quasi-arbitrary distribution.","PeriodicalId":21146,"journal":{"name":"Proceedings of the YSU A: Physical and Mathematical Sciences","volume":"27 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73370636","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 : 2020-12-15DOI: 10.46991/pysu:a/2020.54.3.127
A. Chubaryan, A. Hambardzumyan
We investigate the relations between the proof lines of non-minimal tautologies and its minimal tautologies for the Frege systems, the sequent systems with cut rule and the systems of natural deductions of classical and nonclassical logics. We show that for these systems there are sequences of tautologies ψn, every one of which has unique minimal tautologies φn such that for each n the minimal proof lines of φn are an order more than the minimal proof lines of ψn.
{"title":"ON NON-MONOTONOUS PROPERTIES OF SOME CLASSICAL AND NONCLASSICAL PROPOSITIONAL PROOF SYSTEMS","authors":"A. Chubaryan, A. Hambardzumyan","doi":"10.46991/pysu:a/2020.54.3.127","DOIUrl":"https://doi.org/10.46991/pysu:a/2020.54.3.127","url":null,"abstract":"We investigate the relations between the proof lines of non-minimal tautologies and its minimal tautologies for the Frege systems, the sequent systems with cut rule and the systems of natural deductions of classical and nonclassical logics. We show that for these systems there are sequences of tautologies ψn, every one of which has unique minimal tautologies φn such that for each n the minimal proof lines of φn are an order more than the minimal proof lines of ψn.","PeriodicalId":21146,"journal":{"name":"Proceedings of the YSU A: Physical and Mathematical Sciences","volume":"161 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75979089","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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