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Wyniki wyszukiwania dla: MATHEMATICAL MORPHOLOGY
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Bondage number of grid graphs
PublikacjaThe bondage number b(G) of a nonempty graph G is the cardinality of a smallest set of edges whose removal from G results in a graph with domination number greater than the domination number of G. Here we study the bondage number of some grid-like graphs. In this sense, we obtain some bounds or exact values of the bondage number of some strong product and direct product of two paths.
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Reducing the number of periodic points in the smooth homotopy class of a self-map of a simply-connected manifold with periodic sequence of Lefschetz numbers
PublikacjaLet f be a smooth self-map of an m-dimensional (m >3) closed connected and simply-connected manifold such that the sequence of the Lefschetz num- bers of its iterations is periodic. For a fixed natural r we wish to minimize, in the smooth homotopy class, the number of periodic points with periods less than or equal to r. The resulting number is given by a topological invariant J[f] which is defned in combinatorial terms and is...
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Convergence of rational multistep methods of of Adams-Padé type
PublikacjaRational generalizations of multistep schemes, where the linear stiff part of a given problem is treated by an A-stable rational approximation, have been proposed by several authors, but a reasonable convergence analysis for stiff problems has not been provided so far. In this paper we directly relate this approach to exponential multistep methods, a subclass of the increasingly popular class of exponential integrators. This natural,...
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On bipartization of cubic graphs by removal of an independent set
PublikacjaWe study a new problem for cubic graphs: bipartization of a cubic graph Q by deleting sufficiently large independent set.
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On the partition dimension of trees
PublikacjaGiven an ordered partition Π={P1,P2,…,Pt} of the vertex set V of a connected graph G=(V,E), the partition representation of a vertex v∈V with respect to the partition Π is the vector r(v|Π)=(d(v,P1),d(v,P2),…,d(v,Pt)), where d(v,Pi) represents the distance between the vertex vv and the set Pi. A partition Π of V is a resolving partition of G if different vertices of G have different partition representations, i.e., for every...
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Existence of solutions with an exponential growth for nonlinear differential-functional parabolic equations
PublikacjaWe consider the Cauchy problem for nonlinear parabolic equations with functional dependence.We prove Schauder-type existence results for unbounded solutions. We also prove existence of maximal solutions for a wide class of differential functional equations.
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Fractional problems with advanced arguments
PublikacjaThis paper concerns boundary fractional differential problems with advanced arguments. We investigate the existence of initial value problems when the initial point is given at the end point of an interval. Nonhomogeneous linear fractional differential equations are also studied. The existence of solutions for fractional differential equations with advanced arguments and with boundary value problems has been investigated by using...
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Positive solutions to fractional differential equations involving Stieltjes integral conditions
PublikacjaIn this paper, we investigate nonlocal boundary value problems for fractional differential equations with dependence on the first-order derivatives and deviating arguments. Sufficient conditions which guarantee the existence of at least three positive solutions are new and obtained by using the Avery–Peterson theorem. We discuss problems (1) and (2) when argument b can change the character on [0, 1], so in some subinterval I of...
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Monotone iterative method for first-order differential equations at resonance
PublikacjaThis paper concerns the application of the monotone iterative technique for first-order differential equations involving Stieltjes integrals conditions. We discuss such problems at resonance when the measure in the Stieltjes integral is positive and also when this measure changes the sign. Sufficient conditions which guarantee the existence of extremal, unique and quasi-solutions are given. Three examples illustrate the results.
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The computational complexity of the backbone coloring problem for planar graphs with connected backbones
PublikacjaIn the paper we study the computational complexity of the backbone coloring problem for planar graphs with connected backbones. For every possible value of integer parameters λ≥2 and k≥1 we show that the following problem: Instance: A simple planar graph GG, its connected spanning subgraph (backbone) HH. Question: Is there a λ-backbone coloring c of G with backbone H such that maxc(V(G))≤k? is either NP-complete or polynomially...
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Boundary problems for fractional differential equations
PublikacjaIn this paper, the existence of solutions of fractional differential equations with nonlinear boundary conditions is investigated. The monotone iterative method combined with lower and upper solutions is applied. Fractional differential inequalities are also discussed. Two examples are added to illustrate the results.
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Elastoplastic law of Cosserat type in shell theory with drilling rotation
PublikacjaWithin the framework of six-parameter non-linear shell theory, with strain measures of the Cosserat type, we develop small-strain J2-type elastoplastic constitutive relations. The relations are obtained from the Cosserat plane stress relations assumed in each shell layer, by through-the-thickness integration employing the first-order shear theory. The formulation allows for unlimited translations and rotations. The constitutive...
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Interval incidence coloring of bipartite graphs
PublikacjaIn this paper we study the problem of interval incidence coloring of bipartite graphs. We show the upper bound for interval incidence coloring number (χii) for bipartite graphs χii≤2Δ, and we prove that χii=2Δ holds for regular bipartite graphs. We solve this problem for subcubic bipartite graphs, i.e. we fully characterize the subcubic graphs that admit 4, 5 or 6 coloring, and we construct a linear time exact algorithm for subcubic...
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Interval incidence graph coloring
PublikacjaIn this paper we introduce a concept of interval incidence coloring of graphs and survey its general properties including lower and upper bounds on the number of colors. Our main focus is to determine the exact value of the interval incidence coloring number χii for selected classes of graphs, i.e. paths, cycles, stars, wheels, fans, necklaces, complete graphs and complete k-partite graphs. We also study the complexity of the...
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On trees with double domination number equal to 2-domination number plus one
PublikacjaA vertex of a graph is said to dominate itself and all of its neighbors. A subset D subseteq V(G) is a 2-dominating set of G if every vertex of V(G)D is dominated by at least two vertices of D, while it is a double dominating set of G if every vertex of G is dominated by at least two vertices of D. The 2-domination (double domination, respectively) number of a graph G is the minimum cardinality of a 2-dominating (double dominating,...
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Hat problem on odd cycles
PublikacjaThe topic is the hat problem in which each of n players is randomly fitted with a blue or red hat. Then everybody can try to guess simultaneously his own hat color by looking at the hat colors of the other players. The team wins if at least one player guesses his hat color correctly, and no one guesses his hat color wrong; otherwise the team loses. The aim is to maximize the probability of a win. In this version every player can...
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Boundary vlue problems for difference equations with causal operators
PublikacjaPraca dotyczy problemów brzegowych dla równań różnicowych.Podano warunki dostateczne na istnienie ekstremalnych rozwiązań stosując metodę iteracji monotonicznych.
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On the size of identifying codes in triangle-free graphs
PublikacjaIn an undirected graph G, a subset C⊆V(G) such that C is a dominating set of G, and each vertex in V(G) is dominated by a distinct subset of vertices from C, is called an identifying code of G. The concept of identifying codes was introduced by Karpovsky, Chakrabarty and Levitin in 1998. For a given identifiable graph G, let gammaID(G) be the minimum cardinality of an identifying code in G. In this paper, we show that for any connected...
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Two almost homoclinic solutions for second-order perturbed Hamiltonian systems
PublikacjaW niniejszym artykule badamy problem istnienia rozwiązań prawie homoklinicznych (rozwiązań znikających w nieskończonościach) dla układów Hamiltonowskich drugiego rzędu (układów Newtonowskich) z zaburzeniem. Nasz wynik jest uogólnieniem twierdzenia Rabinowitza-Tanaki o istnieniu rozwiązania homoklinicznego dla układów bez zaburzenia [Math. Z. 206 (1991) 473-499]. O zaburzeniu zakładamy, że jest dostatecznie małe w przestrzeni funkcji...
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Dirichlet-to-Neumann and Neumann-to-Dirichlet methods for eigenvalues and eigenfunctions of the Laplace operator
PublikacjaPrzedstawiono dwie metody służące do znajdowania wartości własnych i funkcji własnych równania Helmholtza w ograniczonej dziedzinie. Punktem wyjścia była konstrukcja zasad wariacyjnych uwzględniających możliwość stosowania nieciągłych funkcji próbnych (lub funkcji próbnych o nieciągłych pochodnych normalnych). Następny etap to wykorzystanie powierzchniowych operatorów całkowych typu DtN i NtD. Efektywność metod przetestowano na...
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Scheduling of unit-length jobs with cubic incompatibility graphs on three uniform machines
PublikacjaWe consider the problem of scheduling n identical jobs on 3 uniform machines with speeds s1, s2, and s3 to minimize the schedule length. We assume that jobs are subject to some kind of mutual exclusion constraints, modeled by a cubic incompatibility graph. We how that if the graph is 2-chromatic then the problem can be solved in O(n^2) time. If the graph is 3-chromatic, the problem becomes NP-hard even if s1>s2=s3.
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Tight bounds on the complexity of semi-equitable coloring of cubic and subcubic graphs
PublikacjaWe consider the complexity of semi-equitable k-coloring, k>3, of the vertices of a cubic or subcubic graph G. In particular, we show that, given a n-vertex subcubic graph G, it is NP-complete to obtain a semi-equitable k-coloring of G whose non-equitable color class is of size s if s>n/3, and it is polynomially solvable if s, n/3.
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Method of lines for physiologically structured models with diffusion
PublikacjaWe deal with a size-structured model with diffusion. Partial differential equations are approximated by a large system of ordinary differential equations. Due to a maximum principle for this approximation method its solutions preserve positivity and boundedness. We formulate theorems on stability of the method of lines and provide suitable numerical experiments.
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Edge coloring of graphs of signed class 1 and 2
PublikacjaRecently, Behr (2020) introduced a notion of the chromatic index of signed graphs and proved that for every signed graph (G, σ) it holds that ∆(G) ≤ χ′(G,σ) ≤ ∆(G) + 1, where ∆(G) is the maximum degree of G and χ′ denotes its chromatic index. In general, the chromatic index of (G, σ) depends on both the underlying graph G and the signature σ. In the paper we study graphs G for which χ′(G, σ) does not depend on σ. To this aim we...
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A polynomial algorithm for finding T-span of generalized cacti.
PublikacjaW pracy opisano wielomianowy algorytm wyznaczający optymalne T-pokolorowania dla uogólnionych kaktusów.
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The complexity of the T-coloring problem for graphs with small degree.
PublikacjaW pracy ustalono złożoność obliczeniową problemu optymalnego kolorowania grafów o ustalonym stopniu.
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Numerical integration of a coupled Korteweg-deVries system
PublikacjaMetoda numeryczna została wprowadzona do rozwiązania ogólnych układów równańKorteweg´a- de Vries´a. Zastosowana do równania Hirota-Satsuma.
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Effect of adhesive compliance in the assessment of soft adhesives with the wedge test
PublikacjaWedge tests are usually analysed assuming that the free, unbonded members may be treated as encastré cantilever beams. However, if the adhesive layer is sufficiently flexible (e.g., due to low elastic modulus), then significant strain in the bonded region may occur and lead to modification of the behaviour outside this region. Using in conjunction a sensitive strain gauge method on asymmetric wedge tests and a mathematical analysis...
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Forced Vibrations in a Dynamic System That Is Damped By a Mechanism Which Trans-Pass Through Its Singular Position
PublikacjaThe paper focuses on forced vibrations of a mechanical system. The system is composed of two structurally different parts: multibody modelled and finite elements modelled. To improve its numerical behaviour, author-proposed technique of tuning of modal properties is proposed. To combine the two sub-models, constraint equations are introduced and dynamics equations are extended with appropriate Lagrange multipliers. A slightly modified...
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Space vector modulation in multilevel inverters of the servo drives of the trajectory measurements telescopes
PublikacjaUsing the MatLab/Simulink mathematical model of a three-phase three-level voltage inverter, the influence of the space-vector modulation (SVM) algorithm on the pulsations of the current (torque) of an AC motor in the range of low rotation speeds is considered. It is shown that the SVM of the second kind does not provide a pulsations level comparable to the pulsations of a sinusoidal pulse-width modulation (SPWM), both in the static...
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The Influence of Water and Mineral Oil on Pressure Losses in Hydraulic Motor
PublikacjaIn this paper, pressure losses in hydraulic motor supplied with water and mineral oil (two liquids that have significantly different viscosity and lubricating properties) are described and compared. The experimental tests were conducted using a hydraulic satellite motor that is dedicated to working with different liquids, including water. The methodology of measuring the pressure drop in internal channels of this motor is also...
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One-dimensional chaos in a system with dry friction: analytical approach
PublikacjaWe introduce a new analytical method, which allows to find chaotic regimes in non-smooth dynamical systems. A simple mechanical system consisting of a mass and a dry friction element is considered. The corresponding mathematical model is being studied. We show that the considered dynamical system is a skew product over a piecewise smooth mapping of a segment (the so-called base map). For this base map we demonstrate existence of...
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FPGA Based Real Time Simulations of the Face Milling Process
PublikacjaThe article presents a successful implementation of the milling process simulation at the Field-Programmable Gate Array (FPGA). By using FPGA, very rigorous Real-Time (RT) simulation requirements can be met. The response time of the FPGA simulations is significantly reduced, and the time synchronization is better than in a typical RT system implemented in software. The FPGA-based approach is characterized by enormous flexibility...
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Influence of Fluid Compressibility and Movements of the Swash Plate Axis of Rotation on the Volumetric Efficiency of Axial Piston Pumps
PublikacjaThis paper describes the design of a swash plate axial piston pump and the theoretical models describing the bulk modulus of aerated and non-aerated fluids. The dead space volume is defined and the influence of this volume and the fluid compressibility on the volumetric efficiency of the pump is considered. A displacement of the swash plate rotation axis is proposed to reduce the dead space volume for small swash plate swing angles....
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Estimation of fracture toughness and shear yield stress of orthotropic materials in cutting with rotating tools
PublikacjaThe cutting force is an energetic effect of splitting material, and might be considered from a point of view of modern fracture mechanics. Forecasting of the shear plane angle in cutting broaden possibilities for modelling of the cutting process even for thin uncut chips. Such mathematical model has been developed here for description of the orthotropic materials’ cutting on the base of fracture theory, and includes work of separation...
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Performance of microbial fuel cells operated under anoxic conditions
PublikacjaNowadays, microbial fuel cells (MFC) stand up as a promising renewable energy source. Due to the ability of the MFC to oxidize a wide spectrum of substrates, wastewater seems to be one of the most interesting fuels. Unfortunately, wastewater could contain electron acceptors such as nitrate, which could interfere with the electrical performance of the MFC. In this work, the influence of oxidised nitrogen forms on the electricity...
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Wpływ struktur wsparcia na efektywność nauczania języka pisanego w środowisku e-learningowym
PublikacjaThe process of knowledge and language skills development during an online course can be very effective if student engagement in learning is achieved. This can be attained by introducing general and specific support mechanisms prior to the commencement of the course and during it. The former relates to the technological aspect, that is to familiarizing students with the functionalities of the virtual learning environment they will...
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Mechatronics design, modelling and controlling of the Stewart-Gough platform
PublikacjaThis paper presents a mechatronics design of a low cost Stewart-Gough platform (SGP) with rotary actuators. The designed SGP is supposed to be applied in a ball & plate control system. The synthesis of the ball & plate control system is also within the subject of the paper. A mechatronics design process of the SGP was conducted with computer-aided design (CAD) software. Unique analytical solutions of an inverse kinematics problem...
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Verification of safety in low-voltage power systems without nuisance tripping of residual current devices
PublikacjaLow-voltage power systems require initial and periodical verification to check the effectiveness of protection against electric shock. As a protection in case of fault, automatic disconnection of supply is most often used. To verify such a protection measure, the earth fault loop impedance or resistance is measured. This measurement is easy to perform in circuits without residual current devices. When residual current devices are...
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Hybrid Finite Element Method Development for Offshore Structures’ Calculation with the Implementation of Industry Standards
PublikacjaIn the design process of offshore steel structures, it is typical to employ commercial calculation codes in which simulation and evaluation of results are performed on the basis of the available standards (e.g. API, DNV, Lloyds). The modeling and solution rely on finite element methods and cover the simulation of the structure’s properties along with the influence of the marine environment – sea currents, wave and wind loading,...
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A New Approach to Chemical Recycling of Polyamide 6.6 and Synthesis of Polyurethanes with Recovered Intermediates
PublikacjaA new efficient method for the chemical decomposition of polyamide 6.6 by the glycolysis and amino-glycolysis processes was proposed. The glycolysis was conducted using the mass excess of ethylene glycol (EG) as a decomposing agent in the presence of a catalyst. Also, a mixture of EG and triethylenetetramine was used as another decomposing agent in the amino- glycolysis process. The described process of decomposition did not...
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Identification of the Contamination Source Location in the Drinking Water Distribution System Based on the Neural Network Classifier
PublikacjaThe contamination ingression to the Water Distribution System (WDS) may have a major impact on the drinking water consumers health. In the case of the WDS contamination the data from the water quality sensors may be efficiently used for the appropriate disaster management. In this paper the methodology based on the Learning Vector Quantization (LVQ) neural network classifier for the identification of the contamination source location...
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Modelling the loss of time caused by traffic incidents on motorways
PublikacjaFor each road incident important factors like location, capacity reduction, traffic management, duration of road incidents and amount of traffic should be defined. All performer operations and effects of incidents affect the capacity of the road, average speed, time loss, vehicle queues and traffic jams. In the article road incidents were divided into planned and unexpected. Statistical analysis prepared using the database of traffic...
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Modeling of traffic safety indictors on Polish national road network
PublikacjaAlthough decreased from 2001 to 2013, Poland’s road deaths improved at a slower rate than the rest of the EU, leaving Poland as one of the worst road safety performing countries in the EU. The national road network in Poland, despite the dynamic transformation and development, still does not conform to the EU safety standards. Similar situation exists in other EU countries, particularly those in Central and Eastern Europe. Safety...
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The basics of design and experimental tests of the commutation unit of a hydraulic satellite motor
Publikacjahe article presents an analytical method to design the commutation unit in a hydraulic satellite motor. It is shown that the size of the holes feeding the working chambers and their location on the plates closing those chambers depends on the geometrical dimensions of the working mechanism. The overlap in the commutation unit depends on the rotational speed range. It is demonstrated that the geometrical dimensions of the commutation...
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Rheological characteristics of oligomeric semiproducts gained via chemical degradation of polyurethane foam using crude glycerin in the presence of different catalysts
PublikacjaPolyurethane (PU) recycling is a topic of growing interest due to the increasing amount of polyurethane waste. The main purpose of polyurethane chemical recycling is to recover the starting polyol. In this study, a method of polyurethane thermochemical recycling, glycerolysis by means of crude glycerin, is proposed. This work presents a comparative study of commercial catalysts used in order to accelerate the decomposition process,...
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Cross-Platform Real-Time Nuclear Reactor Basic Principle Simulator
PublikacjaAbstract—In the paper several approaches to building the real-time basic principle simulators of nuclear reactor processes are presented and their characteristics are analyzed. The characteristics of developed simulators for MATLAB/Simulink including their limitations, and the idea of a cross-platform simulator independent of specific hardware or software are presented. Mathematical models of selected nuclear reactor’s processes...
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Prediction of coking dynamics for wet coal charge
PublikacjaA one-dimensional transient mathematical model describing thermal and flow phenomena during coal coking in an oven chamber was studied in the paper. It also accounts for heat conduction in the ceramic oven wall when assuming a constant temperature at the heating channel side. The model was solved numerically using partly implicit methods for gas flow and heat transfer problems. The histories of temperature, gas evolution and internal...
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A Multi-Fidelity Surrogate-Model-Assisted Evolutionary Algorithm for Computationally Expensive Optimization Problems
PublikacjaIntegrating data-driven surrogate models and simulation models of different accuracies (or fideli-ties) in a single algorithm to address computationally expensive global optimization problems has recently attracted considerable attention. However, handling discrepancies between simulation models with multiple fidelities in global optimization is a major challenge. To address it, the two major contributions of this paper include:...
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Influence of water and mineral oil on the leaks in satellite motor commutation unit clearances
PublikacjaThe article describes the flow rates of mineral oil and water flowing, as working media, through the commutation unit of a hydraulic satellite motor. It is demonstrated that geometrical dimensions of commutation unit clearances change as a function of the machine shaft rotation angle. Methods for measuring the rate of this flow and the pressure in the working chamber are presented. The results of pressure measurements in the working...