Pub Date : 2021-09-05DOI: 10.33581/1561-4085-2021-24-4-311-316
S. Sakovich
The integrability of a four-dimensional sixth-order bilinear equation associated with the exceptional affine Lie algebra D(1)4 is studied by means of the singularity analysis. This equation is shown to pass the Painlevé test in three distinct cases of its coefficients, exactly when the equation is effectively a three-dimensional one, equivalent to the BKP equation.
{"title":"Integrability of One Bilinear Equation: Singularity Analysis and Dimension","authors":"S. Sakovich","doi":"10.33581/1561-4085-2021-24-4-311-316","DOIUrl":"https://doi.org/10.33581/1561-4085-2021-24-4-311-316","url":null,"abstract":"The integrability of a four-dimensional sixth-order bilinear equation associated with the exceptional affine Lie algebra D(1)4 is studied by means of the singularity analysis. This equation is shown to pass the Painlevé test in three distinct cases of its coefficients, exactly when the equation is effectively a three-dimensional one, equivalent to the BKP equation.","PeriodicalId":43601,"journal":{"name":"Nonlinear Phenomena in Complex Systems","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46772088","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 : 2021-06-25DOI: 10.33581/1561-4085-2021-24-2-133-144
Y. Chernichenko
New form factor components of two relativistic with equal masses fermions bound state in the case of a vector current are obtained. Consideration is performed within the framework of the relativistic quasipotential approach on the basis of covariant Hamiltonian formulation of quantum field theory by transition to three-dimensional relativistic configurational representation in the case of two relativistic particles with equal masses and spin 1/2.
{"title":"Form Factor of the Two Fermions Bound State: The Case of Equal Masses and Vector Currentl","authors":"Y. Chernichenko","doi":"10.33581/1561-4085-2021-24-2-133-144","DOIUrl":"https://doi.org/10.33581/1561-4085-2021-24-2-133-144","url":null,"abstract":"New form factor components of two relativistic with equal masses fermions bound state in the case of a vector current are obtained. Consideration is performed within the framework of the relativistic quasipotential approach on the basis of covariant Hamiltonian formulation of quantum field theory by transition to three-dimensional relativistic configurational representation in the case of two relativistic particles with equal masses and spin 1/2.","PeriodicalId":43601,"journal":{"name":"Nonlinear Phenomena in Complex Systems","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46248670","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 : 2021-06-25DOI: 10.33581/1561-4085-2021-24-2-145-155
G. Omel'yanov
The general Degasperis-Prosesi equation (gDP) describes the evolution of the water surface in a unidirectional shallow water approximation. We consider essentially non-integrable versions of this model and analyze their cuspon-type solutions, that is continuous traveling waves with the unbounded first derivative.
{"title":"Cuspon-type Waves and Their Properties","authors":"G. Omel'yanov","doi":"10.33581/1561-4085-2021-24-2-145-155","DOIUrl":"https://doi.org/10.33581/1561-4085-2021-24-2-145-155","url":null,"abstract":"The general Degasperis-Prosesi equation (gDP) describes the evolution of the water surface in a unidirectional shallow water approximation. We consider essentially non-integrable versions of this model and analyze their cuspon-type solutions, that is continuous traveling waves with the unbounded first derivative.","PeriodicalId":43601,"journal":{"name":"Nonlinear Phenomena in Complex Systems","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45489965","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 : 2021-06-25DOI: 10.33581/1561-4085-2021-24-2-156-165
M. Makarova, Ivan A. Kovalew, D. W. Serow
A symmetric m-tilings model on the plane is assembled to be a phase portrait for a structurally stable Hamiltonian system. Integral of the system is the quasi-periodic function with m-fold rotational symmetry being result of the semi-dynamic system action on the unit interval. Some examples for pentagonal and heptagonal tilings has been built in detail. Some properties of an additive measure and order for tilings have been discussed.
{"title":"Structurally Stable Symmetric Tilings on the Plane","authors":"M. Makarova, Ivan A. Kovalew, D. W. Serow","doi":"10.33581/1561-4085-2021-24-2-156-165","DOIUrl":"https://doi.org/10.33581/1561-4085-2021-24-2-156-165","url":null,"abstract":"A symmetric m-tilings model on the plane is assembled to be a phase portrait for a structurally stable Hamiltonian system. Integral of the system is the quasi-periodic function with m-fold rotational symmetry being result of the semi-dynamic system action on the unit interval. Some examples for pentagonal and heptagonal tilings has been built in detail. Some properties of an additive measure and order for tilings have been discussed.","PeriodicalId":43601,"journal":{"name":"Nonlinear Phenomena in Complex Systems","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46624458","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 : 2021-06-25DOI: 10.33581/1561-4085-2021-24-2-104-111
E. Melnikova, D. Gorbach, I. I. Rushnova, O. S. Kabanova, S. S. Slusarenko, A. Tolstik, C. Losmanschi, A. Meshalkin, E. Achimova
The energy and spectral conditions for single-stage holographic recording of a diffraction optical element based on the carbazole-containing azo polymer, that forms singular light beams (optical vortices), have been established. With the atomic-force microscopy (AFM), the surface morphology of the recorded relief holograms was studying, and their diffraction efficiency has been estimated. The topology of the generated optical phase singularities has been studied and the stability range of an optical vortex having the topological charge l = 2 has been found. The possibility of using the developed diffractive optical element in the scheme of optical tweezers for manipulating micro-objects is demonstrated.
{"title":"Optical Vortices Generation by Azopolymeric Relief Gratings","authors":"E. Melnikova, D. Gorbach, I. I. Rushnova, O. S. Kabanova, S. S. Slusarenko, A. Tolstik, C. Losmanschi, A. Meshalkin, E. Achimova","doi":"10.33581/1561-4085-2021-24-2-104-111","DOIUrl":"https://doi.org/10.33581/1561-4085-2021-24-2-104-111","url":null,"abstract":"The energy and spectral conditions for single-stage holographic recording of a diffraction optical element based on the carbazole-containing azo polymer, that forms singular light beams (optical vortices), have been established. With the atomic-force microscopy (AFM), the surface morphology of the recorded relief holograms was studying, and their diffraction efficiency has been estimated. The topology of the generated optical phase singularities has been studied and the stability range of an optical vortex having the topological charge l = 2 has been found. The possibility of using the developed diffractive optical element in the scheme of optical tweezers for manipulating micro-objects is demonstrated.","PeriodicalId":43601,"journal":{"name":"Nonlinear Phenomena in Complex Systems","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44193509","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 : 2021-06-25DOI: 10.33581/1561-4085-2021-24-2-166-174
A. A. Khrushchinsky, S. Kuten, K. Verenich, L. F. Babichev, Thi Dieu Hien Le
The paper is devoted to the analysis and optimization of the composition of the fission ionization chamber radiator, consisting of a mixture of two and three nuclides, to ensure the constant sensitivity of the chamber over a long period of time.
{"title":"Optimization of the Radiator Composition of a \"Non-Burning\" Fission Ionization Chamber","authors":"A. A. Khrushchinsky, S. Kuten, K. Verenich, L. F. Babichev, Thi Dieu Hien Le","doi":"10.33581/1561-4085-2021-24-2-166-174","DOIUrl":"https://doi.org/10.33581/1561-4085-2021-24-2-166-174","url":null,"abstract":"The paper is devoted to the analysis and optimization of the composition of the fission ionization chamber radiator, consisting of a mixture of two and three nuclides, to ensure the constant sensitivity of the chamber over a long period of time.","PeriodicalId":43601,"journal":{"name":"Nonlinear Phenomena in Complex Systems","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45967891","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 : 2021-06-25DOI: 10.33581/1561-4085-2021-24-2-175-183
S. Khryashchev
Control systems with a finite number of control settings are considered. It is assumed that any polysystem operates in continuous time and control switchings occur at some certain discrete time instants. A control goal is to transfer a polysystem from an initial state to a final state. Controllability of systems switched in discrete time is studied. Controls are constructed by using the theory of generalized multicomponent continued fractions and the congruences theory. Applications of the proposed control method to specific systems are discussed.
{"title":"A Method of Finding Discrete Controls for Switched Dynamical Systems by Applying Continued Fractions","authors":"S. Khryashchev","doi":"10.33581/1561-4085-2021-24-2-175-183","DOIUrl":"https://doi.org/10.33581/1561-4085-2021-24-2-175-183","url":null,"abstract":"Control systems with a finite number of control settings are considered. It is assumed that any polysystem operates in continuous time and control switchings occur at some certain discrete time instants. A control goal is to transfer a polysystem from an initial state to a final state. Controllability of systems switched in discrete time is studied. Controls are constructed by using the theory of generalized multicomponent continued fractions and the congruences theory. Applications of the proposed control method to specific systems are discussed.","PeriodicalId":43601,"journal":{"name":"Nonlinear Phenomena in Complex Systems","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46208047","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 : 2021-06-25DOI: 10.33581/1561-4085-2021-24-2-112-132
Tuyet Dao Van, M. Ablameyko, S. Ablameyko, H. Hoang, Dzung Pham Thi Kim, Quy Hoang Van, Huy Tran Van
The paper describes e-Health system based on telemedicine platform and GRID layer model. We identify the currently isolated hospital subsystems that should be integrated. Telemedicine platform was proposed that was designed to enable secure management and analysis of patient data and DICOM images in a grid environment. The platform provides doctors the capacity to upload and query medical information stored over distributed servers. It was built also for sharing data between remote hospitals to help doctors in diagnosis. We propose the software components and Grid infrastructure for implementation of the Telemedicine platform and show some results of our implementation in the hospitals.
{"title":"E-Health System Based on Telemedicine Platform and GRID Layer Model","authors":"Tuyet Dao Van, M. Ablameyko, S. Ablameyko, H. Hoang, Dzung Pham Thi Kim, Quy Hoang Van, Huy Tran Van","doi":"10.33581/1561-4085-2021-24-2-112-132","DOIUrl":"https://doi.org/10.33581/1561-4085-2021-24-2-112-132","url":null,"abstract":"The paper describes e-Health system based on telemedicine platform and GRID layer model. We identify the currently isolated hospital subsystems that should be integrated. Telemedicine platform was proposed that was designed to enable secure management and analysis of patient data and DICOM images in a grid environment. The platform provides doctors the capacity to upload and query medical information stored over distributed servers. It was built also for sharing data between remote hospitals to help doctors in diagnosis. We propose the software components and Grid infrastructure for implementation of the Telemedicine platform and show some results of our implementation in the hospitals.","PeriodicalId":43601,"journal":{"name":"Nonlinear Phenomena in Complex Systems","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43328488","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 : 2021-06-25DOI: 10.33581/1561-4085-2021-24-2-184-191
I. A. Shershan, T. Shishkina
The problem of the bremsstrahlung contribution calculation as a part of the radiative corrections in the case of single gauge boson production was discussed. It was shown that the hard photon bremsstrahlung contribution can be divided into the finite and divergent terms. The exact calculation of soft photon bremsstrahlung and infrared part of hard photon bremsstrahlung was presented in frame of the dimensional regularization scheme. Numerical analysis of radiative corrections to the cross sections of single gauge boson production was performed.
{"title":"Modern Technique for Real Photon Radiative Correction Calculations","authors":"I. A. Shershan, T. Shishkina","doi":"10.33581/1561-4085-2021-24-2-184-191","DOIUrl":"https://doi.org/10.33581/1561-4085-2021-24-2-184-191","url":null,"abstract":"The problem of the bremsstrahlung contribution calculation as a part of the radiative corrections in the case of single gauge boson production was discussed. It was shown that the hard photon bremsstrahlung contribution can be divided into the finite and divergent terms. The exact calculation of soft photon bremsstrahlung and infrared part of hard photon bremsstrahlung was presented in frame of the dimensional regularization scheme. Numerical analysis of radiative corrections to the cross sections of single gauge boson production was performed.","PeriodicalId":43601,"journal":{"name":"Nonlinear Phenomena in Complex Systems","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49207319","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 : 2021-06-25DOI: 10.33581/1561-4085-2021-24-2-198-202
S. Zdravković, ladimir Sivčević
In this work, we study nonlinear dynamics of microtubules. An important interaction among constitutive particles is modeled using W-potential. We compare a symmetric potential with two kinds of non-symmetric ones. An advantage of the latter ones is demonstrated.
{"title":"Non-Symmetrical W-potential in Nonlinear Biophysics of Microtubules","authors":"S. Zdravković, ladimir Sivčević","doi":"10.33581/1561-4085-2021-24-2-198-202","DOIUrl":"https://doi.org/10.33581/1561-4085-2021-24-2-198-202","url":null,"abstract":"In this work, we study nonlinear dynamics of microtubules. An important interaction among constitutive particles is modeled using W-potential. We compare a symmetric potential with two kinds of non-symmetric ones. An advantage of the latter ones is demonstrated.","PeriodicalId":43601,"journal":{"name":"Nonlinear Phenomena in Complex Systems","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41597933","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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