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Wyniki wyszukiwania dla: ASSOCIATED LEGENDRE FUNCTIONS
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Orthogonality relations for the associated Legendre functions of imaginary order
PublikacjaOrthogonality relations for the associated Legendre functions of imaginary order are derived. They are expressed in terms of the Dirac delta function. The method is based on some known properties of the associated Legendre functions and the Dirac delta distribution. A special case of one of the relations has appeared in some recent applications.
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A Dirac delta-type orthogonality relation for the on-the-cut generalized associated Legendre functions of the first kind with imaginary second upper indices
PublikacjaThe orthogonality relation for the on-the-cut generalized associated Legendre functions of the first kind with imaginary second upper indices is evaluated in a closed form. It is found to be proportional to a sum of two terms, both depending on the second upper indices and containing the Dirac delta distribution.
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On parameter derivatives of the associated Legendre function of the first kind (with applications to the construction of the associated Legendre function of the second kind of integer degree and order)
PublikacjaZnaleziono cztery nowe wyrażenia dla pochodnej stowarzyszonej funkcji Legendre'a pierwszego rodzaju względem jej stopnia w przypadku, gdy rząd i stopień są liczbami naturalnymi. Wyniki wykorzystano do podania nowych wyrażeń dla stowarzyszonych funkcji Legendre'a drugiego rodzaju z naturalnymi rzędem i stopniem.
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On the derivative of the associated Legendre function of the first kind of integer order with respect to its degree (with applications to the construction of the associated Legendre function of the second kind of integer degree and order).
PublikacjaWyprowadzono szereg zamkniętych wyrażeń dla pochodnych stowarzyszonej funkcji Legendre'a pierwszego rodzaju względem jej dolnego indeksu w przypadku, gdy górny indeks jest liczbą całkowitą. Wyniki zastosowano do znalezienia pewnych nowych reprezentacji (w tym typu Rodriguesa) stowarzyszonych funkcji Legendre'a drugiego rodzaju o indeksach całkowitych.
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Some integrals and series involving the Gegenbauer polynomials and the Legendre functions on the cut (-1,1)
PublikacjaZaprezentowano metode obliczenia dwóch całek oznaczonych zawierających wielomiany Gegenbauera. Wynik wykorzystano do znalezienia sum czterech szeregów o wyrazach zawierających wielomiany Gegenbauera oraz funkcje Legendre'a (pierwszego lub drugiego rodzaju) na odcinku (-1,1).
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How Can We Identify Electrophysiological iEEG Activities Associated with Cognitive Functions?
PublikacjaElectrophysiological activities of the brain are engaged in its various functions and give rise to a wide spectrum of low and high frequency oscillations in the intracranial EEG (iEEG) signals, commonly known as the brain waves. The iEEG spectral activities are distributed across networks of cortical and subcortical areas arranged into hierarchical processing streams. It remains a major challenge to identify these activities in...
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On the derivative of associated Le.gendre function of the first kind of integer degree with respect to its order (with applications to the construction of the associated Legendre function of the second kind of integer degree and order)
PublikacjaW pracy podano szereg zamkniętych wyrażeń dla pochodnej stowarzyszonej funkcji Legendre'a o stopniu (dolnym indeksie) całkowitym względem jej rzędu (górnego indeksu). Wyniki zastosowano do wyprowadzenia kilku nowych reprezentacji, w tym typu Rodriguesa, stowarzyszonych funkcji Legendre'a drugiego rodzaju z całkowityni indeksani.
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On the derivatives $\partial^{2}P_{\nu}(z)/\partial\nu^{2}$ and $\partial Q_{\nu}(z)/\partial\nu$ of the Legendre functions with respect to their degrees
PublikacjaWe provide closed-form expressions for the degree-derivatives $[\partial^{2}P_{\nu}(z)/\partial\nu^{2}]_{\nu=n}$ and $[\partial Q_{\nu}(z)/\partial\nu]_{\nu=n}$, with $z\in\mathbb{C}$ and $n\in\mathbb{N}_{0}$, where $P_{\nu}(z)$ and $Q_{\nu}(z)$ are the Legendre functions of the first and the second kind, respectively. For $[\partial^{2}P_{\nu}(z)/\partial\nu^{2}]_{\nu=n}$, we find that % \begin{displaymath} \frac{\partial^{2}P_{\nu}(z)}{\partial\nu^{2}}\bigg|_{\nu=n} =-2P_{n}(z)\Li_{2}\frac{1-z}{2}+B_{n}(z)\ln\frac{z+1}{2}+C_{n}(z), \end{displaymath} % where...
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A highly-efficient technique for evaluating bond-orientational order parameters
PublikacjaWe propose a novel, highly-efficient approach for the evaluation of bond-orientational order parameters (BOPs). Our approach exploits the properties of spherical harmonics and Wigner 3jj-symbols to reduce the number of terms in the expressions for BOPs, and employs simultaneous interpolation of normalised associated Legendre polynomials and trigonometric functions to dramatically reduce the total number of arithmetic operations....
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Analytical calculations of scattering lengths for a class of long-range potentials of interest for atomic physics
PublikacjaWe derive two equivalent analytical expressions for an $l$th partial-wave scattering length $a_{l}$ for central potentials with long-range tails of the form % \begin{math} \displaystyle V(r)=-\frac{\hbar^{2}}{2m}\frac{Br^{n-4}}{(r^{n-2}+R^{n-2})^{2}} -\frac{\hbar^{2}}{2m}\frac{C}{r^{2}(r^{n-2}+R^{n-2})}, \end{math} % ($r\geqslant r_{s}$, $R>0$). % For $C=0$, this family of potentials reduces to the Lenz potentials discussed in...
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Multilevel model order reduction with generalized compression of boundaries for 3-d FEM electromagnetic analysis
PublikacjaThis paper presents a multilevel Model Order Reduction technique for a 3-D electromagnetic Finite Element Method analysis. The reduction process is carried out in a hierarchical way and involves several steps which are repeated at each level. This approach brings about versatility and allows one to efficiently analyze complex electromagnetic structures. In the proposed multilevel reduction the entire computational domain is covered...
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GNIAZDA PRZEDSIĘBIORCZOŚCI W STREFIE PODMIEJSKIEJ METROPOLII
PublikacjaProblem suburbanizacji jest wciąż aktualny w analizach rozwoju miast. Przybiera często formy spontanicznego rozlewania się miast (urban sprawl). Badacze tego problemu skupiają się przeważnie na rozwoju funkcji mieszkaniowej w strefach podmiejskich. Specyficzny charakter polskiego procesu suburbanizacji polega na równoległym rozwoju klasycznej suburbanizacji osiedleńczej oraz rozwoju mikro- oraz małych i średnich przedsiębiorstw....
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On the dervative of the Legendre function of the first kind with respect to its degree [Corrigendum]
PublikacjaSkorygowano błąd matematyczny w pracy: R. Szmytkowski, On the derivative of the Legendre function of the first kind with respect to its degree, J. Phys. A: Math. Gen. Vol. 39(2006) s. 15147-15172 [744014]
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Improving the accuracy of subgridding scheme in finite differences method based on Legendre polynomials expansion
PublikacjaIn this article the Legendre polynomials have been used to interpolate the field at the boundary of the meshes of different densities. The numerical verification of the proposed technique has been carried out in frequency domain. It has been shown that the accuracy of the presented method is very high and stable - the error monotonically decreases as a function of the refinement factor.
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Macroeconomic functions of the Russian stock market
PublikacjaThe purpose of this article is to present the structure of the stock market in the Russian Federation and the significance of this part of national financial system for the whole economy, particularly the degree of main macroeconomic functions fulfillment. First part of the text includes an overview of the main theoretical concepts linked with the stock market roles as well as a brief description of results of selected studies...
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Integrity level verification for safety-related functions
PublikacjaThis article describes methods for safety integrity level (SIL) verification of safety-related functions with regard to probabilistic criteria given international standards IEC 61508 and IEC 61511. These functions are to be realized using the electrical, electronic and programmable electronic (E/E/PE) systems or safety instrumented systems (SIS). Some methods are proposed for quantitative probabilistic modelling taking into account...
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SELECTION OF DIAGNOSTIC FUNCTIONS IN A WHEELED TRACTOR
PublikacjaIn a classical approach to damage diagnosis, the technical condition of an analyzed machine is identified based on the measured symptoms, such as performance, thermal state or vibration parameters. In wheeled tractor the fundamental importance has monitoring and diagnostics during exploitation concerning technical inspection and fault element localizations. The main functions of a diagnostic system are: monitoring tractor components...
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An orthogonality relation for the Whittaker functions of the second kind of imaginary order
PublikacjaPrzeprowadzono dowód ortogonalności funkcji Whittakera drugiego rodzaju rzędu urojonego. Użyto metody analogicznej do tej, którą zaprezentowano we wcześniejszej pracy tych samych autorów [J. Math. Anal. Appl. 365 (2010) 195-197], poświęconej funkcjom Macdonalda rzędu urojonego.
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The problem of infections associated with implants – an overview
PublikacjaImplant-associated infections are serious and relatively common complication that leads to implant loss. The purpose of this paper is to gather knowledge about this issue. A literature review of the epidemiology, risk factors and pathogenesis of infections related to implants was carried out. This position collects data on commonly used implants and infections associated with them from various fields of medicine and contains classifications...
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On the derivative of the Legendre function of the first kind with respect to its degree
PublikacjaPokazano, że pochodna po indeksie funkcji Legendre'a pierwszego rodzaju, obliczona dla całkowitej wartości indeksu, może być wyrażona przez funkcje elementarne. Skonstruowano kilka jawnych reprezentacji tej pochodnej. Zaprezentowano przykłady zastosowań otrzymanych wzorów.
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Termination functions for evolutionary path planning algorithm
PublikacjaIn this paper a study of termination functions (stop criterion) for evolutionary path planning algorithm is presented. Tested algorithm is used to determine close to optimal ship paths in collision avoidance situation. For this purpose a path planning problem is defined. A specific structure of the individual path and fitness function is presented. For the simulation purposes a close to real tested environment is created. Five...
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Airfoil Design Under Uncertainty Using Non-Intrusive Polynomial Chaos Theory and Utility Functions
PublikacjaFast and accurate airfoil design under uncertainty using non-intrusive polynomial chaos (NIPC) expansions and utility functions is proposed. The NIPC expansions provide a means to efficiently and accurately compute statistical information for a given set of input variables with associated probability distribution. Utility functions provide a way to rigorously formulate the design problem. In this work, these two methods are integrated...
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Anisotropic Orlicz–Sobolev spaces of vector valued functions and Lagrange equations
PublikacjaIn this paper we study some properties of anisotropic Orlicz and Orlicz–Sobolev spaces of vector valued functions for a special class of G-functions. We introduce a variational setting for a class of Lagrangian Systems. We give conditions which ensure that the principal part of variational functional is finitely defined and continuously differentiable on Orlicz–Sobolev space.
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Addendum to ''On the derivative of the Legendre function of the first kind with respect to its degree''
PublikacjaPraca stanowi uzupełnienie wcześniejszej publikacji autora [J. Phys. A: Math. Gen. 39(2006) 15147-15172]. Przedstawiono w niej nowe wyrażenia dla pochodnej funkcji Legendre'a względem jej indeksu i zastosowano je do konstrukcji dwóch nowych reprezentacji funkcji Legendre'a drugiego rodzaju z całkowitym indeksem.
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The properties, functions and use of selenium compounds in living organisms
PublikacjaSelenium occurs in the environment in inorganic and organic compounds. For many years it was regarded as a toxic element, causing numerous illnesses and diseases. But research in the last 50 years has revealed a "bright side" to this element, especially as a component of selenoproteins, selenium makes a significant contribution to the health of humans and animals. The selenium content in an organism depends on its concentration...
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Safety integrity level verification for safety-related functions with security aspects
PublikacjaThe article is devoted some important issues of the functional safety analysis, in particular the safetyintegrity level (SIL) verification of safety functions to be implemented within the distributed controland protection systems with regard to cyber security aspects. The procedure for functional safety man-agement includes hazard identification, risk analysis and assessment, specification of overall safetyrequirements and definition...
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Technical Limitations in Merging Secular and Sacred Functions in Monumental Churches
PublikacjaThe abandonment of churches and their adaptation for secular purposes is a current subject in Europe and worldwide. Most cases involve objects that were desacralized and then rebuilt as a whole object for alternative functions. Thus far, the merging of secular and sacred functions in one monumental Catholic church has not raised any issues. The paper describes the case of St. Catherine’s Church in Gdansk, Poland, where sacred function...
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Wavelet filtering of signals without using model functions
PublikacjaThe effective wavelet filtering of real signals is impossible without determining their shape. The shape of a real signal is related to its wavelet spectrum. For shape analysis, a continuous color wavelet spectrogram of signal level is often used. The disadvantage of continuous wavelet spectrogram is the complexity of analyzing a blurry color image. A real signal with additive noise strongly distorts the spectrogram based on continuous...
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Performance Evaluation of Control Plane Functions in ASON/GMPLS Architecture
PublikacjaIt is assumed that demands of information society could be satisfied by architecture ASON/GMPLS comprehended as Automatically Switched Optical Network (ASON) with Generalized Multi-Protocol Label Switching (GMPLS) protocols. Introduction this solution must be preceded performance evaluation to guarantee society expectations. Practical realization is expensive and simulations models are necessary to examine standardized propositions....
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ANALYSIS OF POSSIBILITIES FOR THE USE OF VOLUME-DELAY FUNCTIONS IN THE PLANNING MODULE OF THE TRISTAR SYSTEM
PublikacjaTravel time is a measure commonly used for traffic flow modelling and traffic control. It also helps to evaluate the quality of traffic control systems in urban areas. Traffic control systems that use traffic models to predict changes and disruptions in vehicle flows have to use vehicle speed-prediction models. Travel time estimation studies the effects of traffic volumes on a street section at an average speed. The TRISTAR Integrated...
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CyberEye: New Eye-Tracking Interfaces for Assessment and Modulation of Cognitive Functions beyond the Brain
PublikacjaThe emergence of innovative neurotechnologies in global brain projects has accelerated research and clinical applications of BCIs beyond sensory and motor functions. Both invasive and noninvasive sensors are developed to interface with cognitive functions engaged in thinking, communication, or remembering. The detection of eye movements by a camera offers a particularly attractive external sensor for computer interfaces to monitor,...
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MESOSCALE FUNCTIONS OF GPS SLANT DELAY
PublikacjaThe paper presents a computer module for GPS slant delay determination using data from COAMPS (Coupled Ocean/Atmosphere Mesoscale Prediction System) mesoscale non-hydrostatic model of the atmosphere which is run on IA64 Feniks computer cluster in the Department of Civil Engineering and Geodesy of the Military University of Technology. The slant delay is the result of integrating the ray (eikonal) equation for the spatial function...
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Melatonin in the skin: synthesis, metabolism and functions
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Offsetting, relations, and blending with perturbation functions
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Single-phase power electronics transformer with active functions for smart grid
PublikacjaThis paper presents the control of one cell of a modular single-phase power electronics transformer with active functions for meeting the smart grid concept. In this way, the converter could be used not only as a conventional transformer but also for grid such as reactive power, harmonic elimination and energy storage. The topology of the cell is composed by a bidirectional converter with three stages: a half bridge in the input...
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THE CREATIVE AND SYMBOLIC FUNCTIONS OF DAYLIGHT IN THE ART MUSEUM BUILDINGS OF THE 21st CENTURY
PublikacjaThe paper presents the results of the study on the current extent of daylight use in contemporary buildings of art museums, focusing especially on the possibilities of aesthetic function. A case study and critical analysis were used as the research method. Selected, representative examples of museums of the 21st century are discussed with regard to the creative and functional use of daylight and the application of advanced technology....
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Automotive Validation Functions for On-line Test Evaluation of Hybrid Real-time Systems
PublikacjaThe aim of this paper is to present the means of black-box on-line test evaluation for hybrid real-time systems. The described procedures can be used for the model-based testing process so as to improve its effectiveness. In particular, intelligent automotive validation functions are considered, which are divided into different types depending on the nature of the evaluated issue. All provided definitions are specified on the meta-model...
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Entropy Production Associated with Aggregation into Granules in a Subdiffusive Environment
PublikacjaWe study the entropy production that is associated with the growing or shrinking of a small granule in, for instance, a colloidal suspension or in an aggregating polymer chain. A granule will fluctuate in size when the energy of binding is comparable to k_{B}T, which is the “quantum” of Brownian energy. Especially for polymers, the conformational energy landscape is often rough and has been commonly modeled as being self-similar...
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Psychosocial risks associated with the profession of train driver
PublikacjaExcellent competencies as well as a good physical and mental health are required in train drivers’ profession. Despite the changes in the structure of employment the train drivers above 46 years and job tenure longer than 30 years are the largest group. The generation gap is becoming more pronounced, and its fulfilment will not be easy. It is related not only to training of new personnel but also promotion of healthy work environment...
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Application of sliding switching functions in backstepping based speed observer of induction machine
PublikacjaThe paper presents an analysis of the speed observer which is based on the backstepping and sliding mode approach. The speed observer structure is based on the extended mathematical model of an induction machine. The observer structure is based on the measured phase stator currents and transformed to ( αβ ) coordinate system. The stator voltage vector components are treated as known values. Additionally, such an observer structure...
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URBAN MENTORING JAKO NOWA TECHNIKA WPRÓŁPRACY W PROCESIE PLANOWANIA PARTCYPACYJNEGO
PublikacjaW 25 lat od powrotu demokracji opierającej się o neoliberalny paradygmat rozwoju kraju, Polska przyjęła Krajową Politykę Miejską 2030. Wraz z ustawą o rewitalizacji w nowoczesny sposób określa ona pole współpracy władz samorządowych i administracji z mieszkańcami, przejście do drugiej fazy rozwoju społeczeństwa demokratycznego – mieszkańców współgospodarzy przestrzeni miast. Powolna ewolucja tej relacji, silnie obarczonej dziedzictwem...
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Variational principles for bound states of Schrödinger and Dirac equations allowing the use of discontinuous trial functions
PublikacjaWe present systematic constructions of variational principles for energies of bound states of the Schroedinger and Dirac equations. The principles allow the use of discontinuous trial functions. The method employed is based on a generalized Lagrange procedure. Relationships between our variational principles and those available in the literature are established.
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Modelling of residential sales price with kriging using different distance metrics in different correlation functions
PublikacjaThe modelling and estimation of sales prices based on economical conditions are important for housing sector especially in developing countries. Analysts are focused on the subject to analyze price movements and estimate the future trend of the sales prices for housing sector. In this study, we tried to generate a robust and efficient model related to the subject. Firstly, we investigated economic variables affecting housing sales...
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Separability Assessment of Selected Types of Vehicle-Associated Noise
PublikacjaMusic Information Retrieval (MIR) area as well as development of speech and environmental information recognition techniques brought various tools in-tended for recognizing low-level features of acoustic signals based on a set of calculated parameters. In this study, the MIRtoolbox MATLAB tool, designed for music parameter extraction, is used to obtain a vector of parameters to check whether they are suitable for separation of...
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New potential functions for greedy independence and coloring
PublikacjaA potential function $f_G$ of a finite, simple and undirected graph $G=(V,E)$ is an arbitrary function $f_G : V(G) \rightarrow \mathbb{N}_0$ that assigns a nonnegative integer to every vertex of a graph $G$. In this paper we define the iterative process of computing the step potential function $q_G$ such that $q_G(v)\leq d_G(v)$ for all $v\in V(G)$. We use this function in the development of new Caro-Wei-type and Brooks-type...
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Steroidogenesis in the skin: Implications for local immune functions
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CRH functions as a growth factor/cytokine in the skin
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Comment on the orthogonality of the Macdonald functions of imaginary order
PublikacjaPrzeprowadzono dowód ortogonalności funkcji Macdonalda z urojonym indeksem. Zastosowana metoda jest znacznie prostsza od innych prezentowanych do tej pory w literaturze.
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Erratum to "Formulas and Theorems for the Special Functions of Mathematical Physics" by W. Magnus, F. Oberhettinger, R. P. Soni
PublikacjaWe correct a number of misprints in the handbook "Formulas and theorems for the special functions of mathematial physics" (3rd edition) by Magnus, Oberhettinger and Soni.
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Automatic Clustering of EEG-Based Data Associated with Brain Activity
PublikacjaThe aim of this paper is to present a system for automatic assigning electroencephalographic (EEG) signals to appropriate classes associated with brain activity. The EEG signals are acquired from a headset consisting of 14 electrodes placed on skull. Data gathered are first processed by the Independent Component Analysis algorithm to obtain estimates of signals generated by primary sources reflecting the activity of the brain....