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Search results for: critical points
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Deterministic rendezvous of asynchronous bounded-memory agents in polygonal terrains
PublicationWe consider two versions of the rendezvous problem: exact RV, when the points representing agents have to coincide at some time, and e-RV, when these points have to get at distance less than e in the terrain. In any terrain, each agent chooses its trajectory, but the movements of the agent on this trajectory are controlled by an adversary that may, e.g. speed up or slow down the agent.
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Homoclinic orbits for a class of singular second order Hamiltonian systems in ℝ3
PublicationWe consider a conservative second order Hamiltonian system \ddot{q}+ ∇V(q)=0 in R3 with a potential V having a global maximum at the origin and a line l ∩ {0} = ∅ as a set of singular points. Under a certain compactness condition on V at infinity and a strong force condition at singular points we study, by the use of variational methods and geometrical arguments, the existence of homoclinic solutions of the system.
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Digital Processing of Frequency–Pulse Signal in Measurement System
PublicationThe work presents the issue of the use of multichannel measurement systems of sensors processing input value to impulse signal frequency. The frequency impulse signal obtained from such sensors is often required to be processed at the same time with a voltage signal which is obtained from other sensors used in the same measurement system. In such case, it is usually necessary to sample the output signals from all sensors in the...
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Identification of Kinematic Excitation Function by the Modal Coordinates Estimation of the System's Dynamics
PublicationThe paper presents a method of the kinematic excitation courses’ identification in excitation points, based on the car road test acceleration at different measurement points. For the purpose of the laboratory fatigue life investigation of contemporary complex structures (e.g. cars bodies) and components of these structures (i.e. cars roofs), only a few first vibration modes are usually taken into account. During real life tests...
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Estimation and Prediction of Vertical Deformations of Random Surfaces, Applying the Total Least Squares Collocation Method
PublicationThis paper proposes a method for determining the vertical deformations treated as random fields. It is assumed that the monitored surfaces are subject not only to deterministic deformations, but also to random fluctuations. Furthermore, the existence of random noise coming from surface’s vibrations is also assumed. Such noise disturbs the deformation’s functional models. Surface monitoring with the use of the geodetic levelling...
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Novel Vision Monitoring Method Based on Multi Light Points for Space-Time Analysis of Overhead Contact Line Displacements
PublicationThe article presents an innovative vision monitoring method of overhead contact line (OCL) displacement, which utilizes a set of LED light points installed along it. A light point is an, LED fed from a battery. Displacements of the LED points, recorded by a camera, are interpreted as a change of OCL shape in time and space. The vision system comprises a camera, properly situated with respect to the OCL, which is capable of capturing...
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Galerkin formulations with Greville quadrature rules for isogeometric shell analysis: Higher order elements and locking
PublicationWe propose new Greville quadrature schemes that asymptotically require only four in-plane points for Reissner-Mindlin (RM) shell elements and nine in-plane points for Kirchhoff-Love (KL) shell elements in B-spline and NURBS-based isogeometric shell analysis, independent of the polynomial degree of the elements. For polynomial degrees 5 and 6, the approach delivers high accuracy, low computational cost, and alleviates membrane and...
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Accuracy analysis of 3D model obtained by photogrammetric method on the example of historic room from Wisłoujście Fortress
PublicationThe article presents a comparison of obtained models of a test object. Close range photogrammetry was used to obtain 3D models. As test object was used one of the rooms located in Wisłoujście Fortress in Gdańsk, Poland. Different models were obtained by using different distribution and number of reference points. Article contains analysis of differences between coordinates of control points obtained from total station measurements...
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High Speed Milling vibration surveillance with optimal spindle speed based on optimal speeds map
PublicationThe paper presents the method of the surveillance of the self-excited chatter vibration. At first, the workpiece modal parameters are estimated based on experimental data which leads to verification of computational model. Then, for selected surface points optimal spindle speeds are calculated. By considering sufficient amount of points it is possible to build a map of optimal spindle speeds. Experimental results show that this...
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On Computing Curlicues Generated by Circle Homeomorphisms
PublicationThe dataset entitled Computing dynamical curlicues contains values of consecutive points on a curlicue generated, respectively, by rotation on the circle by different angles, the Arnold circle map (with various parameter values) and an exemplary sequence as well as corresponding diameters and Birkhoff averages of these curves. We additionally provide source codes of the Matlab programs which can be used to generate and plot the...
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Solving Boundary Value Problems for Second Order Singularly Perturbed Delay Differential Equations by ε-Approximate Fixed-Point Method
PublicationIn this paper, the boundary value problem for second order singularly perturbed delay differential equation is reduced to a fixed-point problem v = Av with a properly chosen (generally nonlinear) operator A. The unknown fixed-point v is approximated by cubic spline vh defined by its values vi = vh(ti) at grid points ti, i = 0, 1, ... ,N. The necessary for construction the cubic spline and missing the first derivatives at the boundary...
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Navigational decision support system during approach manoeuvre in emergency STS transfer operation
PublicationThe paper is concerned with the problem of safe trajectory planning for approaching during emergency STS (Ship to Ship) transfer operation with oil spill. The safe trajectory means that the way points does not cross in the area of the environment with the static and dynamic obstacles and at the same time satisfies ship's stopping and speed deceleration performance. The evolutionary path planning algorithm is used to determine trajectory...
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The analysis of the determination of points positions using photogrammetric methods
PublicationThis article was created as a result of research conducted within the master thesis. The purpose of the research was to analyze the accuracy of determining the actual position of the photographed points according to the calculated parameters. The accuracy of photos alignment was determined as parameters, which determine their external and internal orientation. In order to determine the location of the determined points, it was...
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Periodic Points for Sphere Maps Preserving MonopoleFoliations
PublicationLet S^2 be a two-dimensional sphere. We consider two types of its foliations with one singularity and maps f:S^2→S^2 preserving these foliations, more and less regular. We prove that in both cases f has at least |deg(f)| fixed points, where deg(f) is a topological degree of f. In particular, the lower growth rate of the number of fixed points of the iterations of f is at least log|deg(f)|. This confirms the Shub’s conjecture in...
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Discrete and continuous fractional persistence problems – the positivity property and applications
PublicationIn this article, we study the continuous and discrete fractional persistence problem which looks for the persistence of properties of a given classical (α=1) differential equation in the fractional case (here using fractional Caputo’s derivatives) and the numerical scheme which are associated (here with discrete Grünwald–Letnikov derivatives). Our main concerns are positivity, order preserving ,equilibrium points and stability...
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Have you heard about ALAN? Now, there is also ROLAN!
PublicationThis article examines the new ROLAN movement and points out why this might be the next big thing for lighting professionals.
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A new method of presosns identification based on comparative analysis of 3D face models
PublicationThe article presents the use of modern close range photogrammetry for possessing highly accurate 3D models of the human face (including the ears). Modern methods used to obtain precise data describing the construction of a human face, and even the whole human body, should allow to get finished measurement material in a very short time. Those features belong to the optical scanning technology. Comparative analysis of models of the...
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Photogrammetric and total station's measurement of compressed column's model
PublicationModelling studies continue to play an important role. One of such study is stress determination in the reinforcement bars of reinforced columns and determine column's axis deformation. The article presents measurements results of control points located on the model of reinforced concrete column. The column was compressed in few series till it's destruction. In this studies, photogrammetric method and total station measurements...
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Assessment of the Current Potential of Hydropower for Water Damming in Poland in the Context of Energy Transformation
PublicationThe present paper indicates that hydropower, including small hydropower plants (SHPs), may play a very important role in Poland’s energy transformation in the near future. The development of SHPs may also increase water resources in the steppe Poland. Additionally, the aim of the present research is to conduct the PEST analysis of SHPs in Poland, taking into account the SHP potential. For the first time, maps showing the power...
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Biodegradable Polymer Packaging Materials in Seawater Environment
PublicationIn this chapter, our interest is directed into dea/ocean/lakes biodegradable environment for polymer packaging materials from two different points of view.
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Distribution of volatile organohalogen compounds in petrochemical plant water streams
PublicationThe study assesses halogenated volatile organic compound concentrations in the water and wastewaterstreams of a petrochemical plant. Water samples were collected at 11 sampling points during 5 samplingcampaigns. The samples were collected from the oil dewaxing unit and in the wastewater treatmentplant. Dichloromethane and 1,2-dichloroethane were the most frequently determined compounds. Tetrachloroethenewas also detected at the...
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Minimal number of periodic points of smooth boundary-preserving self-maps of simply-connected manifolds
PublicationLet M be a smooth compact and simply-connected manifold with simply-connected boundary ∂M, r be a fixed odd natural number. We consider f, a C1 self-map of M, preserving ∂M . Under the assumption that the dimension of M is at least 4, we define an invariant Dr(f;M,∂M) that is equal to the minimal number of r-periodic points for all maps preserving ∂M and C1-homotopic to f. As an application, we give necessary and sufficient...
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Algorithms for Ship Movement Prediction for Location Data Compression
PublicationDue to safety reasons, the movement of ships on the sea, especially near the coast should be tracked, recorded and stored. However, the amount of vessels which trajectories should be tracked by authorized institutions, often in real time, is usually huge. What is more, many sources of vessels position data (radars, AIS) produces thousands of records describing route of each tracked object, but lots of that records are correlated...
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Deterministic rendezvous of asynchronous bounded-memory agents in polygonal terrains
PublicationTwo mobile agents, modeled as points starting at differentlocations of an unknown terrain, have to meet. The terrain is a polygon with polygonal holes. We consider two versions of this rendezvous problem: exact RV, when the points representing the agents have to coincide at some time, and epsilon-RV, when these points have to get at distance less than epsilon in the terrain. In any terrain, each agent chooses its trajectory, but...
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Minimization of the number of periodic points for smooth self-maps of simply-connected manifolds with periodic sequence of Lefschetz numbers
PublicationLet f be a smooth self-map of m-dimensional, m ≥ 4, smooth closed connected and simply-connected manifold, r a fixed natural number. For the class of maps with periodic sequence of Lefschetz numbers of iterations the authors introduced in [Graff G., Kaczkowska A., Reducing the number of periodic points in smooth homotopy class of self-maps of simply-connected manifolds with periodic sequence of Lefschetz numbers, Ann. Polon. Math....
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System of monitoring of the Forest Opera in Sopot structure and roofing
PublicationThe authors present a solution realized in Forest Opera (name in Polish: Opera Leśna) in Sopot (Poland) in connection with the modernization and construction of a new roof. The complicated structure of the roof of the facility and the used covering in form of membrane made of technical fabric required (for security reasons) to install the unit of devices allowing for the continuous geodetic monitoring of the facility. Monitoring...
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Microencapsulation of fish oil – determination of optimal wall material and encapsulation methodology
PublicationFor the first time, we present a meta-analysis of experimental and literature data to determine which microencapsulation methodology, and which wall material are best suited to protect fish oil. Our analysis covered a period of several decades of research (1984–2018). The analysis was conducted on 196 literature data-points, and 16 data-points determined experimentally for this publication. PLS regression was used to determine...
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Estimation of the minimal number of periodic points for smooth self-maps of odd dimensional real projective spaces
PublicationLet f be a smooth self-map of a closed connected manifold of dimension m⩾3. The authors introduced in [G. Graff, J. Jezierski, Minimizing the number of periodic points for smooth maps. Non-simply connected case, Topology Appl. 158 (3) (2011) 276-290] the topological invariant NJD_r[f], where r is a fixed natural number, which is equal to the minimal number of r-periodic points in the smooth homotopy class of f. In this paper smooth...
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Complex Root Finding Algorithm Based on Delaunay Triangulation
PublicationA simple and flexible algorithm for finding zeros of a complex function is presented. An arbitrary-shaped search region can be considered and a very wide class of functions can be analyzed, including those containing singular points or even branch cuts. The proposed technique is based on sampling the function at nodes of a regular or a self-adaptive mesh and on the analysis of the function sign changes. As a result, a set of candidate points...
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On root finding algorithms for complex functions with branch cuts
PublicationA simple and versatile method is presented, which enhances the complex root finding process by eliminating branch cuts and branch points in the analyzed domain. For any complex function defined by a finite number of Riemann sheets, a pointwise product of all the surfaces can be obtained. Such single-valued function is free of discontinuity caused by branch cuts and branch points. The roots of the new function are the same as the...
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Galerkin formulations of isogeometric shell analysis: Alleviating locking with Greville quadratures and higher-order elements
PublicationWe propose new quadrature schemes that asymptotically require only four in-plane points for Reissner–Mindlin shell elements and nine in-plane points for Kirchhoff–Love shell elements in B-spline and NURBS-based isogeometric shell analysis, independent of the polynomial degree p of the elements. The quadrature points are Greville abscissae associated with pth-order B-spline basis functions whose continuities depend on the specific...
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Expedited simulation-driven design optimization of UWB antennas by means of response features
PublicationIn this work, a method for fast design optimization of broadband antennas is considered. The approach is based on a feature-based optimization (FBO) concept where reflection characteristics of the structure at hand are formulated in terms of suitably defined feature points. Redefinition of the design problem allows for reducing the design optimization cost, because the dependence of feature point coordinates on antenna dimensions...
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Application of Doubly Connected Dominating Sets to Safe Rectangular Smart Grids
PublicationSmart grids, together with the Internet of Things, are considered to be the future of the electric energy world. This is possible through a two-way communication between nodes of the grids and computer processing. It is necessary that the communication is easy and safe, and the distance between a point of demand and supply is short, to reduce the electricity loss. All these requirements should be met at the lowest possible cost....
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Resolving Conflicts in Object Tracking in Video Stream Employing Key Point Matching
PublicationA novel approach to resolving ambiguous situations in object tracking in video streams is presented. The proposed method combines standard tracking technique employing Kalman filters with global feature matching method. Object detection is performed using a background subtraction algorithm, then Kalman filters are used for object tracking. At the same time, SURF key points are detected only in image sections identified as moving...
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Gaze tracking in multi-display environment
PublicationThis paper presents the basic ideas of eye and gaze tracking in multiple-display environment. The algorithm for display detection and identification is described as well as the rules for gaze interaction in multi display environment. The core of the method is to use special LED markers and eye and scene tracking glasses. Scene tracking camera registers markers position which is then represented as a cloud of points. Analyzing the...
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Method of determining the residual fluxes in transformer core
PublicationThe article presents the method of calculating the residual induction in transformer columns. The method is based on measurement of the magnetic induction in selected points around the transformer core. The values of residual induction are calculated as linear combination of the results of measurement.
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Rotating rod and ball
PublicationWe consider a mechanical system consisting of an infinite rod (a straight line) and a ball (a massless point) on the plane. The rod rotates uniformly around one of its points. The ball is reflected elastically when colliding with the rod and moves freely between consecutive hits. A sliding motion along the rod is also allowed. We prove the existence and uniqueness of the motion with a given position and velocity at a certain time...
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Weak forms of shadowing in topological dynamics
PublicationWe consider continuous maps of compact metric spaces. It is proved that every pseudotrajectory with sufficiently small errors contains a subsequence of positive density that is point-wise close to a subsequence of an exact trajectory with the same indices. Also, we study homeomor- phisms such that any pseudotrajectory can be shadowed by a finite number of exact orbits. In terms of numerical methods this property (we call it multishadowing)...
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Dynamic Analysis of the Turnout Diverging Track for HSR with Variable Curvature Sections
PublicationThe paper presents an analytical method of identifying the curvature of the turnout diverging track consisting of sections of varying curvature. Both linear and nonlinear (polynomial) curvatures of the turnout diverging track are identified and evaluated in the paper. The presented method is a universal one, it enables to assume curvature values at the beginning and end point of the geometrical layout of the turnout. The results...
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Outlier detection method by using deep neural networks
PublicationDetecting outliers in the data set is quite important for building effective predictive models. Consistent prediction can not be made through models created with data sets containing outliers, or robust models can not be created. In such cases, it may be possible to exclude observations that are determined to be outlier from the data set, or to assign less weight to these points of observation than to other points of observation....
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Analysis of antibiotic resistance in Escherichia coli isolated from the Reda River and the Oliwski Stream using basic statistical methods = Zastosowanie metod ststystycznych do analizy antybiotykoodporności bakterii wskaźnikowych pochodzących z rzeki Redy i Potoku Oliwskiego
PublicationIn this study distribution of antimicrobial resistance patterns among fecal indicator bacteria (Escherichia coli and Enterococcus spp.) was examined in two watercourses. The susceptibility analyses were carried out against the antimicrobial agents, important in treating human E. coli and enterococcal infection. Water samples were obtained from the Oliwski Stream and from the Reda River. On each watercourse the five representative...
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The Arnold conjecture in $ \mathbb C\mathbb P^n $ and the Conley index
Publicationn this paper we give an alternative, purely Conley index based proof of the Arnold conjecture in CP^n asserting that a Hamiltonian diffeomorphism of CP^n endowed with the Fubini-Study metric has at least (n+1) fixed points.
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Accuracy of marine gravimetric measurements in terms of geodetic coordinates of land reference benchmark
PublicationThe article presents how the values of (3D) coordinates of land reference points affect the results of gravimetric measurements made from the ship in sea areas. These measurements are the basis for 3D maritime inertial navigation, improving ships' operational safety. The campaign verifying the network absolute point coordinates used as a reference point for relative marine gravity measurements was described. The obtained values...
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Rapid Yield Estimation and Optimization of Microwave Structures Exploiting Feature-Based Statistical Analysis
PublicationIn this paper, we propose a simple, yet reliable methodology to expediteyield estimation and optimization of microwave structures. In our approach,the analysis of the entire response of the structure at hand (e.g., $S$-parameters asa function of frequency) is replaced by response surface modeling of suitablyselected feature points. On the one hand, this is sufficient to determinewhether a design satisfies given performance specifications....
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Trajectory planning for Service Ship during emergency STS transfer operation
PublicationIn this paper trajectory for approaching during emergency STS transfer operation with oil spill is considered as a sequence of navigation manoeuvres in specific navigational environment. The designed way points - ship positions and speed are determined as reference values to support navigator in decision making during steering and to mitigate the risk of collision which mostly results from exceeding the speed limit of approaching....
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Application of Regression Line to Obtain Specified Number of Points in Reduced Large Datasets
PublicationModern measurement techniques like scanning technology or sonar measurements, provide large datasets, which are a reliable source of information about measured object, however such datasets are sometimes difficult to develop. Therefore, the algorithms for reducing the number of such sets are incorporated into their processing. In the reduction algorithms based on the...
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Impact of optimization of ALS point cloud on classification
PublicationAirborne laser scanning (ALS) is one of the LIDAR technologies (Light Detection and Ranging). It provides information about the terrain in form of a point cloud. During measurement is acquired: spatial data (object’s coordinates X, Y, Z) and collateral data such as intensity of reflected signal. The obtained point cloud is typically applied for generating a digital terrain model (DTM) and a digital surface model (DSM). For DTM...
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Multi Parameter Sliding Test Result Evaluation for The Selection of Material Pair for Wear Resistant Components of a Hydraulic motor Dedicated for Use With Environmentally Friendly Working Fluids
PublicationIn the paper the method and results are presented of the testing of tribological performance of a number of hard materials available commercially. The tests consisted in unidirectional sliding with liquid lubrication. The load and velocity regime chosen were similar to a standard four-ball lubricity test with constant velocity and load increasing over time. The regime was modified in such a way that over the initial part of the...
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Fast Multi-Objective Aerodynamic Optimization Using Sequential Domain Patching and Multifidelity Models
PublicationExploration of design tradeoffs for aerodynamic surfaces requires solving of multi-objective optimization (MOO) problems. The major bottleneck here is the time-consuming evaluations of the computational fluid dynamics (CFD) model used to capture the nonlinear physics involved in designing aerodynamic surfaces. This, in conjunction with a large number of simulations necessary to yield a set of designs representing the best possible...
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Seven Different Lighting Conditions in Photogrammetric Studies of a 3D Urban Mock-Up
PublicationOne of the most important elements during photogrammetric studies is the appropriate lighting of the object or area under investigation. Nevertheless, the concept of “adequate lighting” is relative. Therefore, we have attempted, based on experimental proof of concept (technology readiness level—TRL3), to verify the impact of various types of lighting emitted by LED light sources for scene illumination and their direct influence...