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EN
The continued development of microprocessor-based knee prostheses has improved the independence of people with a femoral amputation in many environments. This study aimed to describe the effect of slopes on kinematic joint variables and segmental asymmetry.
EN
We study the relationship between the solutions of stationary integrable partial and ordinary differential equations and coefficients of the second-order ordinary differen¬tial equations invariant with respect to one-parameter Lie group. The classical symmetry method is applied. We prove that if the coefficients of ordinary differential equation satisfy the stationary integrable partial differential equation with two independent variables then the ordinary differential equation is integrable by quadratures. If special solutions of integrable partial differential equations are chosen, then the coefficients satisfy the stationary KdV equations. It was shown that the Ermakov equation belong to a class of these equations. In the framework of the approach we obtained the similar results for generalized Riccati equations. By using operator of invariant differentiation we describe a class of higher order ordinary differential equations for which the group-theoretical method enables us to reduce the order of ordinary differential equation.
3
Content available A novel method for invariant image reconstruction
EN
In this paper we propose a novel method for invariant image reconstruction with the properly selected degree of symmetry. We make use of Zernike radial moments to represent an image due to their invariance properties to isometry transformations and the ability to uniquely represent the salient features of the image. The regularized ridge regression estimation strategy under symmetry constraints for estimating Zernike moments is proposed. This extended regularization problem allows us to enforces the bilateral symmetry in the reconstructed object. This is achieved by the proper choice of two regularization parameters controlling the level of reconstruction accuracy and the acceptable degree of symmetry. As a byproduct of our studies we propose an algorithm for estimating an angle of the symmetry axis which in turn is used to determine the possible asymmetry present in the image. The proposed image recovery under the symmetry constraints model is tested in a number of experiments involving image reconstruction and symmetry estimation.
EN
Thanks to the transfer matrix method, we perform a theoretical investigation of the optical properties of the symmetrical photonic crystal designed as Bg5/Cu1/Bg5, where Cu1 is the first generation of the copper mean sequence and Bg5 is the fifth generation of the Bragg sequence. We design a developed polychromatic filter which allows the transmission of all the telecommunication wavelengths 0.85, 1.3, and 1.55 µm at oblique incidence for both of TE and TM polarization with a high transmission rate and high quality factor. This photonic crystal can be employed in the fabrication of telecommunication devices.
EN
In this paper, we consider a hybrid photonic crystal symmetrically deformed (Bg5/Cu3/Bg5) consisting of the third generation of the copper mean sequence (Cu3), sandwiched between two Bragg mirrors at the fifth generation (Bg5). Our system realizes a polychromatic filter that transmits five wavelengths in the visible spectrum independently of the polarization of the light transverse electric or transverse magnetic. Secondly, the photonic crystal (Bg5/Cu3/Bg5) undergoes the deformation y = xk + 1 (where k is the degree of deformation, x and y are respectively the coordinates of the system before and after the deformation). With a proper choice of the degree of deformation k, this photonic crystal maintains its property of polychromatic filter whose transmission wavelength is independent of the polarization’s state. Thanks to this deformation, we can disperse the optical windows in different spectra of visible light and exactly in the violet, blue, green, and orange light. This system can be used in the fabrication of color filter devices and the white light emitting diodes.
EN
Purpose: Subjects with post-stroke hemiparesis frequently present with asymmetric gait patterns. Symmetry, reflecting similarities in temporospatial, kinematic parameters, is an important measure of gait assessment. The study was designed to examine the relationships between asymmetry of temporal, spatial and kinematic gait parameters and walking velocity and distance. Methods: Temporospatial and kinematic gait parameters were examined in a group of 50 chronic post-stroke subjects and in a group of 25 healthy controls. Symmetry ratio was calculated for all the parameters. Gait velocity was measured during 10-metre test, the walking distance during 2-Minute Walk Test, and balance during Up&Go Test. Results: The relationship between stance phase duration symmetry and gait speed was at a moderate level (r = –0.43, p = 0.0173). There was a moderate relationship between swing phase symmetry and walking velocity and distance. The findings did not show a significant correlation between step length symmetry versus gait speed and distance. Conclusions: There is a mild relationship between self-selected gait velocity and walking distance versus temporal parameters symmetry. The findings do not confirm a relationship between self-selected gait velocity and walking distance versus spatial and kinematic parameters as well as balance. Likewise, no evidence confirms that asymmetry of temporal, spatial, kinematic gait parameters changes with the age of post-stroke subjects or is related to the length of time from stroke onset. Given the above, gait symmetry may be recognized as an important indicator of the level of gait control in post-stroke patients because it enables unique gait assessment, independent from other parameters.
7
Content available Rytm i symetria w sztuce Kerali
PL
Dalekie, archaiczne cywilizacje mają swoją symboliczną moc. W hinduskiej sztuce stanu Kerala zachwyca bogactwo drewnianej, tradycyjnej architektury powstałej na tle niezwykłego nadmorskiego krajobrazu. Tam przez wieki rozwinęło się wielokulturowe społeczeństwo Indian, tworząc mozaikę kulturową o  nigdzie niespotykanym bogactwie. Poniższa próba syntezy naturalnych i kulturowych zasobów architektonicznych i krajobrazowych oparta została na dwu pojęciach: rytmu i symetrii. Rytm w sztuce Kerali łączy tak pozornie dalekie: taniec i zdobnictwo, codzienną pracę i następstwo świąt, zdobienie ciała i podziały ogrodzenia. Z kolei symetria osi kompozycyjnych dominuje w architekturze budynków, sprowadza się do równowagi planu i sylwet. Ponad tym rytm boskich i ludzkich postaci. Tak więc studiując poniższe rozważania, na chwilę zapamiętajmy się w porządku, który od tysiąca lat cechuje Indie.
EN
The power of distant, ancient civilizations is often expressed symbolically. In the art of Kerala, the state in South India, the variety of wooden architecture and the landscape is enchanting. Against this background was developed the multicultural Indian society. There are two terms which describe in synthetic way the nature and kulture of Kerala. The rhythm is what joins the dance and ornamentation, everyday life and hardships, but also feasts, decoration of the neck and the fence of the building. The symmetry of composition in architecture is visible in the form of god or human in Indian art. So let us become absorbed in order which is typical for India since ages.
EN
Introduction and aims: The study shows the interpretation of Fibonacci numbers in botany. In particular, it is shown the interpretation of symmetry in the cross-sections of selected vegetables. Also have been presented some definitions of Fibonacci numbers and discuss their interpretation in certain cross-sections of selected vegetables. Therefore, the main aim of this work is to show the interpretation of Fibonacci numbers in the analysis of cross-sections of selected vegetables. Material and methods: Material consists some pictures of vegetables and their cross-sections which were made by the Authors of this paper. The method of visual and theoretical analysis has been performed in this paper. Results: In this paper, has been considered a series of interesting images of selected plants vegetables. Presented graphical interpretation of dual, triangular, tetragonal, pentagonal, hexagonal and decagonal symmetry, which shows the occurrence of Fibonacci numbers. Conclusions: Fibonacci numbers in botany are interpreted in the cross-sections of various vegetables. In some cross-sections of vegetables can be observed some dual, triangular, tetragonal, pentagonal, hexagonal and even decagonal symmetry. The interpretation of Fibonacci numbers may be used to supplement the classification of vegetables plants.
PL
Wstęp i cele: W pracy pokazano interpretację liczb Fibonacciego w botanice. W szczególności pokazano interpretację symetrii występującej przekrojach poprzecznych wybranych warzyw. Podano definicje liczb Fibonacciego oraz omówiono ich interpretację w określonych przekrojach poprzecznych wybranych warzyw. Zatem głównym celem pracy jest pokazanie interpretacji liczb Fibonacciego w analizie przekrojów poprzecznych wybranych warzyw. Materiał o metody: Materiałem są zdjęcia warzyw i ich przekrojów poprzecznych wykonane przez autorów pracy. Zastosowano metodę analizy wizualno-teoretycznej. Wyniki: W pracy otrzymano szereg interesujących zdjęć wybranych warzyw. Przedstawiono interpretację graficzną symetrii dualnej, trójkątnej, czworokątnej, pięciokątnej, sześciokątnej i dziesięciokątnej, w których pokazano występowanie liczb Fibonacciego. Wnioski: Interpretację liczb Fibonacciego można znaleźć w różnych przekrojach wybranych warzyw. W niektórych przekrojach warzyw można zaobserwować symetrię dualną, trójkątną, czworokątną, pięciokątną, sześciokątna a nawet dziesięciokątną. Interpretacja liczb Fibonacciego może być użyteczna w uzupełnieniu klasyfikacji warzyw.
EN
A compact Riemann surface X of genus g > 1 which has a conformal automorphism ρ of prime order p such that the orbit space X/(ρ) is the Riemann sphere is called cyclic p-gonal. Exceptional points in the moduli space Mg of compact Riemann surfaces of genus g are unique surface classes whose full group of conformal automorphisms acts with a triangular signature. We study symmetries of exceptional points in the cyclic p-gonal locus in Mg for which Aut(X)/(ρ is a dihedral group Dn.
EN
Important basic transformations, implemented in CAD systems, are congruence transformations, so-called isometries, which preserve the distance of points. Logic of CAD software bases on the reflection, translation, rotation, and similarity. This fact is the important desideratum in the teaching of Descriptive Geometry. The paper includes a proposal for a teaching from the scope of isometries on the plane and in three-dimensional space.
PL
Ważnymi przekształceniami zaimplementowanymi w oprogramowaniu CAD, są izometrie, czyli przekształcenia zachowujące odległość punktów. Logika tych systemów opiera się gównie na pojęciu symetrii, translacji i obrotu. Ważną jeszcze rolę odgrywa podobieństwo. Uwzględnienie tego faktu w nauczaniu geometrii wykreślnej jest ważnym dezyderatem dydaktycznym. Praca zawiera propozycję dydaktyczną z zakresu zastosowania izometrii na płaszczyźnie i w przestrzeni.
EN
Automated retinal vessel segmentation plays an important role in computer-aided diagnosis of serious diseases such as glaucoma and diabetic retinopathy. This paper contributes, (1) new Binary Hausdorff Symmetry (BHS) measure based automatic seed selection, and (2) new edge distance seeded region growing (EDSRG) algorithm for retinal vessel segmentation. The proposed BHS measure directly provides a binary symmetry decision at each pixel without the computation of continuous symmetry map and image thresholding. In a multiscale mask, the BHS measure is computed using the distance sets of opposite direction angle bins with sub-pixel resolution. The computation of the BHS measure from the Hausdorff distance sets involves point set matching based geometrical interpretation of symmetry. Then, we design a new edge distance seeded region growing (EDSRG) algorithm with the acquired seeds. The performance evaluation in terms of sensitivity, specificity and accuracy is done on the publicly available DRIVE, STARE and HRF databases. The proposed method is found to achieve state-of-the-art vessel segmentation accuracy in three retinal databases; DRIVE- sensitivity (0.7337), specificity (0.9752), accuracy (0.9539); STARE-sensitivity (0.8403), specificity (0.9547), accuracy (0.9424); and HRF-sensitivity (0.8159), specificity (0.9525), accuracy (0.9420).
PL
W artykule przedstawiono konwencjonalne kryterium symetrii dla modelu przekształtnikowego układu napędowego. Sformułowano koncepcję oraz scharakteryzowano etapy strojenia regulatora rozmytego. Zaprezentowano uzyskane charakterystyki sterowania dla wybranych wyjściowych funkcji przynależności.
EN
The paper presents the conventional symmetry criterion for the model of the converter drive system. The concept of the fuzzy controller was formulated and the tuning stages were characterized. The obtained control characteristics for the selected output membership function were presented.
PL
Starożytni symetrią nazywali harmonijny układ, określali nią proporcje i kanony piękna. Symetria była najbardziej podstawowym pojęciem ich estetyki ponieważ chodziło w niej właśnie o piękno. Symetria odgrywa zasadniczą rolę w sztuce porządkując płaszczyznę malarską i nadając jej określony rytm. Odzwierciedla także intelektualne znaczenia i symbole, przenikające się w twórczym działaniu artysty.
EN
The ancients used the term symmetry to call a harmony, it determines the proportion and canons of beauty. Symmetry was the most fundamental concept of aesthetics because it was just about beauty. Symmetry plays an essential role in the art of ordering a painting space and giving it a certain rhythm. It also reflects the intellectual meanings and symbols interwoven in the creative activity of the artist.
14
Content available Niedoskonałość symetrii
PL
W artykule przedstawiono rozważania na temat symetrii, percepcji symetrii oraz jej atrakcyjności (czy też nieatrakcyjności) jako zasady kompozycji w sztuce i architekturze. Symetryczność świata, potwierdzona przez uczonych i przez potoczne doświadczenie, może wyjaśniać nasze do niej upodobanie. Jako jeden z przykładów przekonujących nas o – jak się okazuje złudnej – symetryczności podano lustro, z którym nierozerwalnie związany jest problem zróżnicowania skali. Autor odwołuje się do Hermanna Weyla omawiającego rozmaite rodzaje symetrii i wiążącego z nią kategorię piękna. Następnie cytuje przykłady symetrii w architekturze (np. budowle Palladia, mozaiki geometryczne na posadzkach kościołów z intrygującym wzrok sześcianem Neckera). Mozaiki wprowadzają wątek iluzji optycznych i zależności percepcji od oczekiwań, co może otwierać drzwi do świata złudzeń. Dlatego czysto geometryczna symetria – dowodzi autor – nie jest atrakcyjna dla sztuki. Znacznie bardziej płodna jest dwuznaczność. Siatka z kilkuosiowią symetrycznością, tak użyteczna dla dużego obszaru sztuki, jest antynarracyjna, antyewolucyjna i ahistoryczna i choć znakomicie porządkuje formalnie, może nużyć monotonią. Jako przykład na odejście od tego toku myślenia autor daje przykład Asymetrii Zbigniewa Dłubaka, budynku muzeum w Bilbao (Frank Gehry), dworca kolejowego w Kioto (Hiroshi Hara) czy centrum sztuki w Stockton­on­Tees (Richard Wilson). Europejskie przywiązanie do symetrii autor kontrastuje z jej odrzuceniem w filozofii zen i będącej pod jej wpływem kulturą Japonii, Korei i Chin.
EN
The article presents considerations on symmetry, its perception and attractiveness (or conversely, unattractiveness) as a principle of composition in art and architecture. The symmetry of the world, confirmed both by science and everyday experience, can explain our preference for it. The mirror, given as an example of false visual symmetry, introduces the question of the scale. The author refers to Hermann Weyl who differentiates between various types of symmetry and associates symmetry with the category of beauty. Then the author goes on to discuss symmetry in architecture (e.g. Palladio’s buildings, mosaic floor patterns in churches with the intriguing Necker cube). Mosaics introduce the problem of optical illusions and the dependence of perception upon expectation – a relationship which can open the door to the world of illusion. That is why, argues the author, simple geometric symmetry is not attractive to art. Ambiguity is much more fruitful. The grid with its multiple symmetry axes, widely used in art, is anti­narrative, anti­developmental and anti­historical, and though it introduces perfect formal order, its monotony may be boring. The author gives examples of modern works departing from the principle of symmetry, like Asymetries by Zbigniew Dłubak, the museum in Bilbao (Frank Gehry), railway station in Kyoto (Hiroshi Hara) or art centre at Stockton­on­Tees (Richard Wilson). Finally, European attachment to symmetry is contrasted with the preference for asymmetry in Zen and in cultures under its influence, i.e. Japanese, Korean and Chinese.
EN
Purpose: The purpose of the study was to assess the symmetry of proprioceptive sense among female soccer players when trying to reproduce isometric knee extensions (right and left) and to analyze the impact of a given level of muscle force on proprioception. Methods: The study involved 12 soccer players aged 19.5 ± 2.65 years. Soccer players performed a control measurement of a maximum 3s (knee at the 90°) position in the joint. Subsequently, 70%, 50%, and 30% of the maximum voluntary contraction (MVC) were all calculated and then reproduced by each subject with feedback. Next, the players reproduced the predefined muscle contraction values in three sequences: A – 50%, 70%, 30%; B – 50%, 30%, 70%; C – 70%, 30%, 50% of MVC without visual control. Results: In every sequence, the participants found obtaining the value of 30% of MVC the most difficult. The value they reproduced most accurately was 70% of MVC. Both trial II and trial III demonstrated that the symmetry index SI significantly differed from values considered acceptable (SIRa). In each successive sequence the largest asymmetry occurred while reproducing the lowest values of MVC (30%) (p < 0.05). Conclusion: High level of prioprioceptive sense is important to soccer players due to the extensive overload associated with dynamics stops or changes in direction while running. Special attention should be paid to develop skills in sensing force of varying levels. It was much harder to reproduce the predefined values if there was no feedback.
16
EN
Practical expediency of application of genetic and geometric modeling methods for automated synthesis of magnetic separator multi-unit (multi-inductor) cylindrical structures is shown. Genetic model of structure formation of cylindrical multi-unit structures of magnetic separators is proposed. «Isomer maker» software enabling spatial arrangements of cylindrical inductors on the basis of the data introduced by the user is developed.
PL
W artykule pokazano praktyczną celowość aplikacji metody genetycznej I metody modelowania geometrycznego dla automatycznej syntezy separatora magnetycznego wieloinduktorowego o cylindrycznej budowie. Model genetyczny formowania konstrukcji o cylindrycznej wielojednostkowej budowie separatora magnetycznego został zaproponowany. Oprogramowanie ISOMER MAKER umożliwia przestrzenny układ induktorów ma podstawie danych wprowadzonych przez użytkownika.
PL
Rozwój technologiczny akceleratorówmedycznych oraz ekspansja technik dynamicznych: VMAT (Volumetric Modulated Arc Therapy), dMLC (dynamicMLC IMRT =sliding window IMRT) i innych spowodowały, że ich szerokie stosowanie w napromienianiu praktycznie wszystkich lokalizacji guzów stało się możliwe. Stosunkowo kontrowersyjnym zagadnieniem było stosowanie technik radioterapii wiązkami dynamicznymi w napromienianiu obszarów, w których ruchomość pacjenta oraz jego organów wewnętrznych wydają się mieć znaczący wpływ na jakość realizowanej terapii dynamicznymi wiązkami łukowymi. W celu wprowadzenia techniki łuków dynamicznych VMAT w napromienianiu piersi oraz ściany klatki piersiowej rozważono temat ruchomości oddechowej w sposób analogiczny jak w tzw. radioterapii bramkowanej, tj. poprzez zastosowanie tomografii 4D do przygotowania planu leczenia pacjenta i określenia obszaru tarczowego. Opracowana i wdrożona do realizacji została metoda stanowiąca kompilację dynamicznych łuków tangencjalnych (t-VMAT) oraz częściowego łuku dynamicznego (c-VMAT), zwykle o mieszanych energiach wiązek fotonowych (6 MV i 10 MV). W szczególnych przypadkach przygotowany został silikonowy bolus indywidualny, który wykorzystano w napromienianiu. Konturowanie obszaru przeznaczonego do radioterapii (tzw. obszaru tarczowego) wykonano na skanach w rekonstrukcji MIP (Maximum Intensity Projection), natomiast struktur krytycznych – na skanach uśrednionych z 10 różnych faz oddechowych (Avg10). Plany leczenia na warstwach Avg10 przygotowano w systemie planowania leczenia Monaco v5.00.002 (Elekta). Zaaprobowane przez lekarza prowadzącego plany leczenia przed realizacją na pacjencie poddano weryfikacji zarówno w fantomie MultiCube (IBA-Dosimetry GmbH) w konfiguracji z matrycą MatriXXEvolution (IBA-DosimetryGmbH), w fantomie płytowym RW3 oraz w matrycy MatriXXEvolution (IBA-DosimetryGmbH) sprzężonej z programem Compass (IBA-DosimetryGmbH), służącym do niezależnego pomiaru dawki na akceleratorze, jak również do przeliczania rozkładu dawki w pacjencie odrębnym algorytmem obliczeniowym.
EN
The technological development of medical linacs as well as the expansion of dynamic techniques, i.e. VMAT (Volumetric Modulated Arc Therapy), dMLC (dynamic MLC IMRT = sliding window IMRT), etc. have made the usage of dynamic delivery of radiation treatment (RT) possible regardless the tumor location inside the human body. However, the application of dynamic RT with arched beams to the regions, inside which the organs’ movement seems to have a large impact on the quality and success of radiotherapy, has been perceived as controversial. For the purpose of the implementation of dynamic arch technique VMAT in breast cancer RT and chest wall irradiation, the 4D computed tomography (the approach known from so called gated RT), has been implemented to prepare the RT plan as well as to determine the target volume motion. Radiotherapy method as a combination of tangential arches (tVMAT) and partial c-shape arch (cVMAT), generally using the mixed photon beams (6MV and 10MV) has been developed and implemented in clinical practice. The particular cases require the preparation of personal bolus made of silicone to be used in RT process. The target delineation has been made on the MIP (Maximum Intensity Projection) reconstructed CT scans, whereas organs at risk (OARs) were contoured on the scans averaged over 10 different breathing phases (Avg10). Radiotherapeutic plans were prepared on the Agv10 scans with the use of Monaco v5.00.002 (Elekta) treatment planning system. The plans approved by the physician for the realization were beforehand verified with the use of MultiCube phantom (IBA-Dosimetry GmbH) in conjunction with the MatriXXEvolution dosimetry device (IBA-Dosimetry GmbH), RW3 plate phantom, as well as MatriXXEvolution device coupled with the Compass software (IBA-Dosimetry GmbH). This latter configuration enables to perform the stand-alone measurement of the dose distribution realized by the linac as well as the independent calculation of the patient-specific dose distribution with the use of a separate algorithm.
EN
The objective of the research was to assess the effect of a 4-week-long training program on selected parameters: electromechanical delay (EMD) and amplitude of electromyographic signal (EMG). Fourteen female students of the University School of Physical Education participated in the study. Torques and surface electromyography were evaluated under static conditions. Surface electrodes were glued to both sides of the rectus abdominis (RA), external oblique (EO), and erector spinae (ES) muscles. The 4-week-long program was aimed at strengthening the abdominal muscles and resulted in increased EMD during maximum torque production by flexors of the trunk, increased amplitudes of the signals of the erector spinae (p = 0.005), and increased EMG amplitude asymmetry of the lower (p = 0.013) and upper part (p = 0.006) of the rectus abdominis muscle. In a training program composed of a large number of repetitions of strength exercises, in which the training person uses their own weight as the load (like in exercises such as curl-ups), the process of recruitment of motor units is similar to that found during fatiguing exercises and plyometric training.
EN
Although gait symmetry is being evaluated and reported in the literature with increasing frequency, there is still no generally accepted standard for assessing symmetry, making it difficult to compare studies and establish criteria to guide clinical decision-making. The purpose of this study was to ascertain whether gait symmetry in healthy subjects is consistent when assessed using various coefficients (RI, SI, GA, and SA), and if possible to identify a gait symmetry coefficient with the highest diagnostic utility. The study involved a group of 58 healthy university-level students of physical education and secondary school students aged 20.03 ± 0.97. Measurements of spatial-temporal gait parameters were conducted using the ZEBRIS platform. Our analysis supports existing recommendations that the symmetry index (SI) should be used as the most sensitive assessment of gait symmetry on the basis of spatial-temporal parameters in healthy subjects. Moreover, we developed normative values of individual features for diagnostic purposes.
EN
The formal models of physical systems are typically written in terms of differential equations. A transformation of the variables in a differential equation forms a symmetry group if it leaves the differential equation invariant. Symmetries of differential equations are very important for understanding of their properties. It can be said that the theory of Lie group symmetries of differential equations is general systematic method for finding solutions of differential equations. Despite of this fact, the Lie group theory is relatively unknown in engineering community. The paper is devoted to some important questions concerning this theory and for several equations resulting from the theory of elasticity their Lie group infinitesimal generators are given.
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