Факультет математики і інформатики

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A 1000-tube model of human systemic arterial vasculature
(2010) Kizilova, N.
(A, φ) - метод суммирования рядов
(Харьков : Издательство Харьковского университета, 1983) Давыдов, Николай Алексеевич; Давидов, Микола Олексійович
About One Model of Consecutive Qubit Binary Testing
(V. Karazin Kharkiv National University, 2010) Thawi, M.; Zholtkevych, G.
Qubit binary tests models are considered in the paper. For each binary test the state of compound quantum-classical system is associated. Formulas for density matrices transformation under binary test are obtained. Method for computing probabilistic characteristics of testing outcomes is proposed. Class of probabilistic measures on testing outcome sequences space is described.
Analysis of stress distribution and leaf blade bending during
(2003) Kizilova, N.
Mechanical factors play an important role in plant tissues growth and development. Plant growth is tightly connected with cell divisions, new cell walls appearing and cell volumes increasing caused by turgor pressure and cell walls loosening and yielding. In biomechanics the plant tissue is considered as integral porous deformable skeleton of cell walls filled with viscous incompressible liquid (intracellular liquid and contents of plant vessels). Xylem sap moves through the xylem vessels, delivers mineral and regulatory components into cells and provides increasing of mass of the solid skeleton. The rate of cell growth is controlled by wall loosening caused by biochemical factors and wall yielding under the influence of the turgor pressure. The tissues consist of elements with different geometry and mechanical properties which are arranged in regular patterns.
Applied problems of microfluidics and nanofluidics : methodical recommendations for practical course and individual work
(Kharkiv : V.N. Karazin Kharkiv National University, 2023) Kizilova, Nataliya N.; Кізілова, Наталія Миколаївна
The basic knowledge of the micro/nanorheology and micro/nanofluidics are presented. The detailed solutions for the laminar flows of classical fluids between parallel plates and coaxial cylindrical tubes (both Poiseuille and Couette flows), laminar flow in an open inclined duct, Poiseuille flow in the channels with elliptic, circular, triangle and rectangle cross-sections and given. The corresponding solutions for the suspensions of microparticles (microfluids) and nanoparticles (nanofluids) of the Navier-Stokes equations with velocity slip boundary conditions of the first and second order, respectively, are presented for the most of the problems while the rest are proposed as individual tasks. For students of mathematical and physical faculties who study nanosciences, nanotechnologies and are interested in practical skills in solving applied problems of micro/nanofluidics.
Bio-Thermo-Hydro-Mechanics: problems and perspectives
(2011) Kizilova, N.; Samit, R.; Petrov, N.; Szekeres, A.
Biophysical mechanisms of long-distance transport of liquids and signaling in high plants
(2004) Kizilova, N.; Posdniak, L.O.
Wave phenomena have been observed in numerous experiments with whole plants. One of possible mechanisms of the long-distance high-speed signaling in high plants is connected with concentration waves that can propagate through the conducting systems of plants. One-dimensional axisymmetrical stationary flow of a viscous liquid with osmotically active dissolved component through a long thin rigid cylindrical tube is considered as a model of the conducting vessel of the plant. Constant concentrations of the component at the inlet and outlet of the vessel are maintained by the live cells of the vegetative organs of the plant. Nonlinear concentration distribution along the tube and the parabolic velocity profiles are obtained. Propagation of small excitations of concentrations and velocities along the tube is considered. Expression for the wave velocity U is presented. The range U=20-60 m/s is obtained by numerical estimations at wide variations of the parameters within the physiological limits. The time delay in signal transmission in the system root-leaves corresponds to the experimental data. In that way the concentration waves can mediate high-speed transferring of information between the organs of plants.
(C)-свойство (A, α)- и (A х(C, α))-методов суммирования рядов и теоремы тауберова типа
(Харьков : Издательство Харьковского университета, 1979) Тесленко, Леонид Степанович; Михалин, Геннадий Александрович; Тесленко, Леонід Степанович; Михалін, Генадій Олександрович
Common Constructal Principles in Design of Transportation Networks in Plants and Animals
(2008) Kizilova, N.
Common principles of design of long-distance liquid transport in the nature are discussed. Some results of measurements on the preparations and casts of the large systemic and small and medium intraorgan arteries are presented. The regularities between the diameters and the branching angles of the arteries in the bifurcations are revealed. The results of measurements on the conducting systems of plant leaves with different shape, size and type of the vasculature are also presented and compared to the arterial vasculatures. It is found the principles of construction are the same in the transportation networks of animals and higher plants and correspond to the model of optimal branching pipeline that provides liquid delivery at minimal total energy costs. A relationship between the length of the path along any subtree of the pipeline and the corresponding drainage area has been found for the leaf venation. The relationship corresponds to the Hack’s law revealed for the river basins. A model of the steady flow in the pipeline with permeable walls is proposed for the liquid delivery in the leaves. It was found, a balance between the inflow of the liquid into a subtree and its consumption by the cells in the corresponding area leads to the Hack’s law. A comparative study of the hydraulic conductivity of the leaves of different evolutionary age is carried out and validity of the constructal law is shown.
Common principles in construction of biological networks
(2004) Kizilova, N.
In the present paper the statistical data on network geometry of the venation system of Morus alba leaf are presented. The mathematical model of the sap motion in the conducting system of a leaf is proposed. On the base of the solution of an optimization problem the principle of optimal construction of a bifurcation in plant leaf venation that correspond to Murray’s law is obtained.
Computational Approach to Optimal Transport
(2004) Kizilova, N.
Long-distance liquid transport in biosystems is provided by special branching systems of tubes (arteries, veins, plant vessels). Geometry of the systems possesses similar patterns and can be investigated by computer methods of pattern recognition. Here some results on plant leaf venation investigation are presented. The lengths, diameters and branching angles are estimated for the leaves of different shape, size and venation type. The statistical distributions of the measured parameters are similar to the corresponding ones which have been obtained for arterial beds. The both correspond to the model of optimal branching pipeline which provide liquid delivering at minimum total energy consumptions. The biomechanical model of liquid motion in a system consisting of a long thin tube with permeable walls which is embedded into a biological porous medium is considered. The pressure distributions and velocity fields for different geometry of the system are obtained. The main result is when the delivering liquid is completely absorbed by the alive cells in the porous medium the relation between the diameter and the length of the tube and the total volume of the medium which correspond to the measured data is reached.
Computerized posturography for data analysis and mathematical
(2007) Kizilova, N.; Karpinsky, M.
Mechanisms of balance control are investigated on computerized posturography data on vertical two-legged and uncomfortable one-legged stance measured on healthy subjects. Oscillations of the centre of mass in the course of 30 s standing and the corresponding trajectories for a step forward off the force platform have been computed. Spectral analysis of the time series revealed three main harmonics for the studied postures. When a volunteer was balancing standing on one leg, all the harmonics were shifted towards the high frequencies and the sway amplitude was twice increased in comparison with comfortable two-legged vertical stance. Decomposition of the sway trajectories into the rambling and trembling components has been carried out. It was shown that in the course of the one-legged stance the balance control strategy includes ‘scanning’ of the larger area with bigger sway amplitudes in the vicinity of the stable state as compared to two-legged stance. A mathematical model of the body as a multi-link system is considered. Mass and inertia of each body segment and torques in joints are taken into consideration. The calculated own and forced frequencies of the model correspond to the spectral analysis of the posturography data. One-legged stance is proposed as an excellent tool for revealing the balance problems. It is shown that investigation of the oscillations and trajectories of the centre of mass for the step forward off the force platform is perspective for medical diagnostics to distinguish between the spine and joint pathologies.
Construction principles and control over transport systems organization in biological tissues
(2003) Kizilova, N.
The main common principles of the long-range transport systems construction in animal and plant tissues are summarized. The results of measurement of conducting system geometry in Cotinus obovatus leaf are analyzed. It is shown that the principles of design of the conducting systems in animals and higher plants are the same and correspond to the model of optimal pipeline. The mathematical model of fluid motion in the conducting system of the leaf as a mo tion in a branching pipeline with permeable walls is investigated. The cost of a bifurcation of the vessels is analyzed. The hypothesis of the control principle of optimal transport system formation in the growing leaf is discussed. As an example the self-similar conducting system with loops is investigated and compared with some venation systems in plant leaves.
A continual analogue of a theorem by M. Fekete and G. Polya
(2001) Katkova, O.; Vishnyakova, A.
A Detailed Digital Model of the Human Arterial System
(2005) Kizilova, N.
A detailed model of the human circulation is developed. The large systemic arteries are presented by the branching system of straight viscoelastic tubes which corresponds topology of the human circulation. Terminal elements at the outlets of the system are presented by tree-like systems with a given topology (with/without anastomoses) and certain geometrical relations between the lengths and diameters of the vessels of different branching orders and the relation between the maximal total length of the vasculature and diameter of the feeding artery. The relations have been obtained by analysis of the morphometric data. They allow correct calculations of the hydraulic resistance and wave impedance of the arterial beds of different organs. The proposed outflow boundary conditions are more preferable then the Windkessels and the regular tree-like systems because they describe both resonant properties of the intraorgan vasculatures and the distributed sources of the reflected waves. The model describes realistic pressure and flow waves and pressure-flow dependences either in the aorta or in the feeding arteries of the inner organs. The latter underlies possibility of the novel noninvasive diagnostics of the state (normal or pathological) of the intraorgan circulation by noninvasive measuring the wall oscillations and blood flow velocity in any cross-section of the feeding artery of the organ.
Evaluation of human postural balance in quiet standing by direct measurement of human body center of mass acceleration
(2009) Kizilova, N.; Jarmalienė, E.; Šešok, A.; Daunoravičienė, K.; Griškevičius, J.
Present article deals with the evaluation of human postural balance in quiet standing by the direct measuring of center of mass acceleration. Displacements of subjects’ center of mass were determined and trajectories in anterior-posterior-medial-lateral plane were obtained. Comparison of parameters between subjects with stroke and healthy subjects was performed and measurements revealed higher sway amplitudes of subjects with stroke.
Flow distribution and wave propagation in arterial systems with anastomoses
(2005) Kizilova, N.; Sechin, R.P.
Blood flow and wave propagation in the systems of compliant tubes filled with a fluid have been examined as a model of the systemic circulation and the intraorgan arterial networks have been modeled as Windkessel elements or regular treelike branching structures. Real intraorgan vasculatures possess some geometrical regularity and can be modeled as fractal-like trees. Nevertheless blood flow in the real beds and their self-similar models have some differences. Moreover real vasculatures often have anastomoses which provide additional pathways for blood flow and wave propagation and reflection. Arterial beds in the small and large intestine, in stomach and limbs have arterial anastomoses that influence input admittance spectra of the beds in comparison with the tree-like systems.
Hierarchic Decomposition of Pre-machines as Models of Software System Components
(Державне підприємство «Центральний науково-дослідний інститут навігації і управління», 2011-12) Zholtkevych, G.; Perepelytsya, I.
In this paper we consider a model of system interaction with the environment, which allows us to forget its full protocol from time to time. Mathematical models of such interactions are pre-machines. We showed that the machines can be completely described in terms of some special class of digraphs. An approach to analyzing the structure of pre-machines in terms of their derivatives series is offered.
The isomorphism problem for finitary incidence rings
(Kharkov: V. N. Karazin national university, 2009) Khripchenko, N.
У збірнику містяться матеріали Сьомої міжнародної алгебраїчної конференції в Україні, присвяченої 120-річчю від дня народження професора Харківського університету Антона Казиміровича Сушкевича. The collection contains the abstracts of talks of 7th International Algebraic Conference in Ukraine dedicated to the 120th anniversary of Professor of Kharkov University Anton Kazimirovich Sushkevich.
J-нерастягивающие операторы
(Харьков : Вища школа. Изд-во при Харьк. ун-те, 1986) Кужель, Сергей Александрович; Кужель, Сергій Олександрович