Open Access e-Journal Cardiometry - No.14 May 2019

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and the obtained computation data are supported bythe known experimental studies of the motion of theblood formed elements in the blood vessels.Statement on ethical issuesResearch involving people and/or animals is in fullcompliance with current national and internationalethical standards.Conflict of interestNone declared.Author contributionsAll the authors read the ICMJE criteria for authorshipand approved the final manuscript.References1. Rudenko MY. Problems and prospects for the studyof hemodynamics based on electrocardiograms. Scientificand study guide. Moscow: RosNOU, 2006. 12p. [in Russian]2. Voronova OK. Development of models and algorithmsof the automated estimation of transport functionin cardiovascular system: Dissertation. Voronezh:VorSTU; 1995 [in Russian]3. Shiller N, Osipov MA. Clinical echocardiography.Moscow: Practice, 2005. 344 p. [in Russian]4. Landau LD, Lifshitz EM. Mechanics of continuousmedia. M.-L., 1944. 244 p. [in Russian]5. Fuks NA. The mechanics of aerosols. Moscow: PublishingHouse of the Academy of Sciences, 1955. 351p. [in Russian]6. Hydroacoustic encyclopedia. Ed. by TimoshenkoVI. Taganrog: Publishing house of TRTU. 2000. p.456. [in Russian]7. Timoshenko VI, Chernov NN. Interaction and diffusionof particles in a sound field. Monograph. Rostov-on-Don:Rostizdat LLC, 2003. 304p. [in Russian]8. Chernov NN, Zagray NP, Laguta, MV, VarenikovaAY. Method for determining size of inhomogeneity localizationregion based on analysis of secondary wavefield of second harmonic. Journal of Physics: ConferenceSeries. 22 May 2018;1015(3). Article No. 032081.9. Gong X, Liu X, Zhang D. Study of third-order nonlinearparameter C/A for biological specimens. NonlinearAcoustics – Fundamental and Applications. 2008;Proceedings of 18th International Symposium on NonlinearAcoustics ed B.O. Enflo, C.M. Hedberg, L Kariand Melville (New York: American Institute of Physics).10. Borisov AV, Kuznetsov SP, Mamaev IS, TenenevVA. Describing the motion of a body with an ellipticalcross section in a viscous uncompressible fluidby model equations reconstructed from data processing.Technical Physics Letters. 2016;42(9):886-90. doi:10.1134/S1063785016090042.11. Vetchanin EV, Mamaev IS, Tenenev VA. The self-propulsionof a body with moving internal masses in a viscousfluid. Regular and Chaotic Dynamics. 2013;18(1-2):100-17. doi: 10.1134/S1560354713010073.12. Aul'chenko SM, Kaledin VO, Shpakova YV. Forcedoscillations of shells of revolution in a viscous fluidflow. Technical Physics Letters. 2009;35(2):114-6. doi:10.1134/S1063785009020059.13. Chernov NN, Laguta MV, Varenikova AY. Researchof appearance and propagation of higher harmonicsof acoustic signals in the nonlinear media.Journal of Pharmaceutical Sciences and Research.November 2017;9(11):2241-6.14. Bur'Kov DV, Starchenko IB, Timoshenko VI. Scatteringof parametric array signals by spherical unregularities.4th International Conference on Actual Problems ofElectronic Instrument Engineering, APEIE 1998 – Proceedings,Volume 1998, September, 1998, Pages 263-264.15. Voronin VA, Kotlyarov VV, Kuznetsov VP, et al. Investigationof a receiving parametric array with extendedbase. Akusticheskii Zurnal. March 1992;38(2):353-6.20 | Cardiometry | Issue 14. May 2019
ORIGINAL RESEARCH Submitted: 22.3.2017, Accepted: 7.4.2017, Published: 25.5.2017DOI: 10.12710/cardiometry.2017.10.1833Preprinted at www.arXiv.org: 1703.07239 [physics.gen-ph] [physics.flu-dyn] 22 Mar 2017https://arxiv.org/ftp/arxiv/papers/1703/1703.07239.pdfThe new analytical solution of the 3D Navier-Stokesequation for compressible medium clarifies thesixth Millennium Prize problemSergey G. Chefranov 1* , Artem S. Chefranov 11A.M. Obukhov Institute of Atmospheric Physics Russian Academy of SciencesRussia, 119017, Moscow, Pyzhevsky lane 3*Corresponding author:e-mail: schefranov@mail.ru, a.chef@bk.ruAbstractThe limitations of capabilities of the existing mathematical weather prediction (includingforecasting for weather-sensitive individuals) cannot be duly realized nowadaysdue to the fact that till now there is no proof of the existence and uniquenessof smooth solutions of the three-dimensional (3D) Navier-Stokes equation (in anyfinite period of time).We have obtained a new analytical solution of the Cauchy problem of this equationin an unbounded space, which has finite energy for any values of time.KeywordsHydrodynamics, Compressibility, Viscosity, Turbulence, Vortex wavesImprintSergey G. Chefranov, Artem S. Chefranov. The new analytical solution of the 3DNavier-Stokes equation for compressible medium clarifies the sixth MillenniumPrize problem; Cardiometry; No.10 May 2017; p. 18–33; DOI:10.12710/cardiometry.2017.10.1833; Available online: www.cardiometry.net/issues/no10-may-2017/analytical-solution-of-the-navier-stokes-equationIntroduction1. The proper understanding of manyprocesses in nature and engineeringsystems is closely connected with theexistence of the fundamental and appliedproblem of turbulence, whichremains unsolved for more than a centurydue to the absence of exact analyticalnonstationary smooth vortexsolutions of the Navier – Stokes (NS)equation. The development of the statisticalapproach to its solution gavea lot of interesting results, but at thesame time led to a new, still unsolved,problem of the closure in the descriptionof different moments of the vortexfield, an approximated solution ofwhich was proposed by KolmogorovA.N., Geizenberg V. et al. [1].In order to solve the problem of turbulency,in its turn, it is required toproperly understand the mechanismof the appearance of randomnessdue to instability of a deterministiccontinual dynamic system describedby the NS equation. In this case, theproblem of the appearance and developmentof turbulence is linked tothe problem of self-organization ofcoherent structures emerging fromchaos and to the associated issues ofnonrandom randomness in an individuallife of a human and in lifespans of living species treated in thecontext of the Sinai billiards [2].However, till the present, an analyticallysmooth on the whole time axisnonstationary solution of the three-dimensional(3D) NS equation has notbeen found and even the correspondingtheorem of the existence and uniquenessof such solution has not yet beenproven [1].Actually, up to date in hydrodynamicsonly a few exact solutions arewell known, but, however, none ofthem is nonstationary and at the sametime is defined in an unbounded (orwith periodic boundary conditions)space [1–4]. Only weak nonstationarysolutions describing, for example,dynamics and interactions betweensingular vortex objects in thetwo-dimensional (2D) and three-dimensional(3D) ideal incompressiblemedium are known [3, 5, 6]. At thesame time, for the 3D ideal mediumflows there are some conceptual ideason a possibility of the existence ofnonstationary solutions of the Euler –Helmholtz (EH) equation only on anunbounded interval of time 0 ≤ t < t 0(see [1, 3, 6, 7] and the references giventherein). This time value for incompressiblemedium is determinedexclusively by the 3D effect of vortexfilament stretching, which may lead toan explosive unbounded growth of theenstrophy (the integral of the squaredIssue 14. May 2019 | Cardiometry | 21
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Page 5 and 6: 64 Prospects for the application of
Page 7 and 8: Prof. Mohammad AleemCairo Universit
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Page 11 and 12: Dear Reader!The present issue of ou
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Page 39 and 40: REPORT Submitted: 15.1.2019; Accept
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Page 51 and 52: LECTURESCardiometry laws and axioms
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ORIGINAL RESEARCH Submitted: 11.12.
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RMSE =N'∑( xn ( ) − x ( n))n=1N
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а)а)b)Figure 4. Histogram of quan
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Conflict of interestNone declared.A
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ORIGINAL RESEARCH Submitted: 12.2.2
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Figure 1. Cardiographic examination
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Table 1. Main statistical data upon
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During an alternate demonstration o
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inee’s reaction or response has b
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all the paired answers, with one of
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Table 1. Distribution of the gaze f
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psychophysical methods. Moscow: Eks
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IntroductionSuccessful applications
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Table 1 herein, upon the completion
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Table 1. Main statistical parameter
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ANALYTICAL NOTECardio-oculometric(c
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Open Access e-Journal Cardiometry - No.14 May 2019

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