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Search results for: ASSOCIATED LEGENDRE FUNCTIONS
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Orthogonality relations for the associated Legendre functions of imaginary order
PublicationOrthogonality 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
PublicationThe 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)
PublicationZnaleziono 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).
PublicationWyprowadzono 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)
PublicationZaprezentowano 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?
PublicationElectrophysiological 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)
PublicationW 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
PublicationWe 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
PublicationWe 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
PublicationWe 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
PublicationThis 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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Robert Jankowski prof. dr hab. inż.
PeopleHe was born on December 26, 1968 in Gdynia. A graduate of the High School at the Consulate of Poland in Benghazi, Libya (1987), a student at the Gdańsk University of Technology (MSc studies, 1987-1991 and 1992-1993), University of Sheffield, England (BSc studies, 1991-1992), University of Roskilde, Denmark (MSc course, 1993) and University of Tokyo, Japan (PhD studies, 1994-1997). From the beginning of his professional career associated...
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Tomasz Krolikowski dr hab. inż.
PeopleIn 1996, I have graduated from the Faculty of Marine Science of Szczecin University and obtained a master's degree - ocean engineering engineer " - Control and Ocean Engineering Measurements". In 1994 I was hired as an assistant trainee at the Institute of Computer Science Technical University of Szczecin, and after graduating in 1996, I was employed as academic and teaching at the Institute of Computer Science in the Department...
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Piotr Marczak dr inż. arch.
PeoplePiotr Marczak is an Assistant Professor at the Faculty of Architecture, Gdańsk University of Technology and since 2016 a Vice-Dean for Education and Promotion. He is also is also a member of the Pomeranian District Chamber of Architects (POIA RP). His research and publications focus on the theory of architecture, revitalization and transformation within the ports areas and the Baltic coast. These studies are associated with the...
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GNIAZDA PRZEDSIĘBIORCZOŚCI W STREFIE PODMIEJSKIEJ METROPOLII
PublicationProblem 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]
PublicationSkorygowano 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
PublicationIn 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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Functions of Language
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INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS
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Macroeconomic functions of the Russian stock market
PublicationThe 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
PublicationThis 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
PublicationIn 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
PublicationPrzeprowadzono 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
PublicationImplant-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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Behavioral and Brain Functions
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On the derivative of the Legendre function of the first kind with respect to its degree
PublicationPokazano, 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
PublicationIn 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
PublicationFast 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
PublicationIn 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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Breast implant-associated anaplastic large cell lymphoma - Female, 40 - Tissue image [10040729541212901]
Open Research DataThis is the histopathological image of BREAST tissue sample obtained in Medical University Gdańsk and deposited in ZMDL-GUMED. The sample image was taken using: Pannoramic 250 3DHistech slide scanner (20x magnification) and saved to DICOM format.
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Breast implant-associated anaplastic large cell lymphoma - Female, 40 - Tissue image [10040729541214921]
Open Research DataThis is the histopathological image of BREAST tissue sample obtained in Medical University Gdańsk and deposited in ZMDL-GUMED. The sample image was taken using: Pannoramic 250 3DHistech slide scanner (20x magnification) and saved to DICOM format.
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Breast implant-associated anaplastic large cell lymphoma - Female, 40 - Tissue image [10040729541212331]
Open Research DataThis is the histopathological image of BREAST tissue sample obtained in Medical University Gdańsk and deposited in ZMDL-GUMED. The sample image was taken using: Pannoramic 250 3DHistech slide scanner (20x magnification) and saved to DICOM format.
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Breast implant-associated anaplastic large cell lymphoma - Female, 40 - Tissue image [3300730069445181]
Open Research DataThis is the histopathological image of BREAST tissue sample obtained in Medical University Gdańsk and deposited in ZMDL-GUMED. The sample image was taken using: Pannoramic 250 3DHistech slide scanner (20x magnification) and saved to DICOM format.
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Breast implant-associated anaplastic large cell lymphoma - Female, 40 - Tissue image [10040729541212601]
Open Research DataThis is the histopathological image of BREAST tissue sample obtained in Medical University Gdańsk and deposited in ZMDL-GUMED. The sample image was taken using: Pannoramic 250 3DHistech slide scanner (20x magnification) and saved to DICOM format.
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Breast implant-associated anaplastic large cell lymphoma - Female, 40 - Tissue image [10040729541214991]
Open Research DataThis is the histopathological image of BREAST tissue sample obtained in Medical University Gdańsk and deposited in ZMDL-GUMED. The sample image was taken using: Pannoramic 250 3DHistech slide scanner (20x magnification) and saved to DICOM format.
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Breast implant-associated anaplastic large cell lymphoma - Female, 40 - Tissue image [10040729541219801]
Open Research DataThis is the histopathological image of BREAST tissue sample obtained in Medical University Gdańsk and deposited in ZMDL-GUMED. The sample image was taken using: Pannoramic 250 3DHistech slide scanner (20x magnification) and saved to DICOM format.
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Breast implant-associated anaplastic large cell lymphoma - Female, 40 - Tissue image [10040729541211191]
Open Research DataThis is the histopathological image of BREAST tissue sample obtained in Medical University Gdańsk and deposited in ZMDL-GUMED. The sample image was taken using: Pannoramic 250 3DHistech slide scanner (20x magnification) and saved to DICOM format.
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Breast implant-associated anaplastic large cell lymphoma - Female, 42 - Tissue image [10040729541217341]
Open Research DataThis is the histopathological image of BREAST tissue sample obtained in Medical University Gdańsk and deposited in ZMDL-GUMED. The sample image was taken using: Pannoramic 250 3DHistech slide scanner (20x magnification) and saved to DICOM format.
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Breast implant-associated anaplastic large cell lymphoma - Female, 42 - Tissue image [10040729541212031]
Open Research DataThis is the histopathological image of BREAST tissue sample obtained in Medical University Gdańsk and deposited in ZMDL-GUMED. The sample image was taken using: Pannoramic 250 3DHistech slide scanner (20x magnification) and saved to DICOM format.
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Breast implant-associated anaplastic large cell lymphoma - Female, 42 - Tissue image [10040729541216851]
Open Research DataThis is the histopathological image of BREAST tissue sample obtained in Medical University Gdańsk and deposited in ZMDL-GUMED. The sample image was taken using: Pannoramic 250 3DHistech slide scanner (20x magnification) and saved to DICOM format.
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Breast implant-associated anaplastic large cell lymphoma - Female, 42 - Tissue image [10040729541219141]
Open Research DataThis is the histopathological image of BREAST tissue sample obtained in Medical University Gdańsk and deposited in ZMDL-GUMED. The sample image was taken using: Pannoramic 250 3DHistech slide scanner (20x magnification) and saved to DICOM format.
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Addendum to ''On the derivative of the Legendre function of the first kind with respect to its degree''
PublicationPraca 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
PublicationSelenium 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
PublicationThe 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
PublicationThe 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
PublicationThe 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
PublicationIt 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
PublicationTravel 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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Journal of Inequalities and Special Functions
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CyberEye: New Eye-Tracking Interfaces for Assessment and Modulation of Cognitive Functions beyond the Brain
PublicationThe 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,...