50 research outputs found
Regularity properties of multistage integration methods
No full textThe numerical method for ordinary differential equations is regular if it has the same set of finite asymptotic values as the underlying differential system. This paper examines the regularity and strong regularity properties of diagonally implicit multistage integration methods (DIMSIMs) introduced recently by J.C. Butcher. A sufficient condition for regularity and strong regularity of such methods of any order is given and it is proved that this condition is also necessary for two-step two-stage DIMSIMs of order greater than or equal to two. It is also demonstrated that there exist regular schemes in the class of explicit DIMSIMs. This is in contrast to explicit Runge-Kutta methods with more than one stage, which are always irregular
Nonlinear Optimization Approach to Construction of General Linear Methods of High Order
No full text. We describe the construction of diagonally implicit multistage integration methods of order and stage order p = q = 7 and p = q = 8 for ordinary differential equations. These methods were obtained using state-ofthe -art optimization methods, particularly variable-model trust-region leastsquares algorithms. Key Words. General linear method, ordinary differential equation, Astability, L-stability, least-squares minimization. AMS Subject Classification. 65L05, 65L20. Department of Mathematics and Statistics, The University of Auckland, Private Bag 92019, Auckland, New Zealand. The work of this author was assisted by the Marsden Fund of New Zealand. y Department of Mathematics, Arizona State University, Tempe, Arizona 85287. The work of this author was partially supported by the National Science Foundation under grant NSF DMS--9208048. z Department of Mathematics, Arizona State University, Tempe, Arizona 85287. The work of this author was partially supported by the National Scien..
A note on existence and uniqueness of solutions of neutral functional-differential equations with state-dependent delays
No full textsummary:Existence and uniqueness theorem for state-dependent delay-differential equations of neutral type is given. This theorem generalizes previous results by Grimm and the author
Construction of high order DIMSIMs for ordinary differential equations
No full text. The identification of high order DIMSIMs with appropriate stability properties requires the solution of high dimensional nonlinear equation systems. The approach to the solution of these equations, and hence the construction of suitable methods, that we will describe in this paper, is based on computation of the coefficients of the stability polynomial by a variant of the Fourier series method and solving the resulting systems of polynomial equations by least squares minimization. Examples of explicit and implicit methods of order 5 and 6 are given which are appropriate for nonstiff or stiff differential systems in a sequential computing environment. The coefficients of these methods were obtained numerically with the aid of lmdif.f and lmder.f from MINPACK. These programs minimize the sum of the squares of nonlinear functions by a modification of the Levenberg-Marquardt algorithm. The derived explicit and implicit methods have the same stability properties as explicit Runge-Kutta a..
Faust’s Wanderings
No full textPostać Fausta, wraz z motywem pragnienia wiedzy, samowiedzy i wiecznej młodości, wreszcie konfrontacji ze złem uosabianym przez szatana, należy do archetypów kultury europejskiej. Autor śledzi wędrówkę Fausta począwszy od przełomu XV i XVI w., kiedy to zaistniał jako postać historyczna i stał się bohaterem ludowej legendy, po współczesność. W końcu XVI w. frankfurcki drukarz Johann Spiess poświęcił mu książkę, która zyskała ogromną popularność. Potem pisali o nim Christopher Marlowe i Johann Wolfgang Goethe, wreszcie Tomasz Mann. Jackiewicz opisuje przeobrażenia tej postaci w kontekście warunków historycznych i kulturowych. Interesuje go też, jak Fausta przyswoiła sztuka filmowa, najpierw w epoce niemej (u Louisa Lumiére’a, Georges’a Mélièsa i Friedricha Wilhelma Murnaua), po czasy współczesne. Sporo miejsca poświęca analizie filmu René Claira Urok szatana (La beauté du diable, 1950). Porównuje wizję Claira z pierwowzorami literackimi, ale przede wszystkim sytuuje ją w polu francuskiej tradycji humanistycznej, a także wobec noweli Jeana Marcenaka. (Materiał nierecenzowany; pierwodruk: „Kwartalnik Filmowy” 1953, nr 10, s. 40-65).The figure of Faust, along with the motif of the desire for knowledge, self-knowledge and eternal youth, and finally confrontation with evil personified by Satan, belongs to the archetypes of European culture. The author traces Faust’s journey from the turn of the 15th and 16th centuries, when he emerged as a historical figure and became the hero of folk legend, to the present day. At the end of the 16th century, the Frankfurt printer Johann Spiess dedicated a book to him, which became extremely popular. Then Christopher Marlowe and Johann Wolfgang Goethe wrote about him, and finally Thomas Mann. Jackiewicz describes the transformations of this figure in the context of historical and cultural conditions. He is also interested in how Faust was adapted in film art, first in the silent era (by Louis Lumiére, Georges Méliès and Friedrich Wilhelm Murnau), and to the researcher’s contemporary times. He devotes a lot of space to the analysis of René Clair’s film Beauty and the Devil (La beauté du diable, 1950). He compares Clair’s vision with literary prototypes, but above all, he places him in the field of the French humanistic tradition, as well as in relation to Jean Marcenac’s novella. (Non-reviewed material; originally published in Kwartalnik Filmowy 1953, no. 10, pp. 40-65)
Remarks about influence of the territorial organization of a state on the executive branch of the government
No full textIn the article, the author strives to answer the question of how the territorial organization of a state infl uences the organization and the scope of tasks and competences of the executive branch of the government. Therefore, for the purpose of the article, the author defines the term ”executive branch of government” and then describes how the principles of unitarism and federalism infl uence the model of the executive branch of the government, in particular with regard to the horizontal division of power. The author limits his discussion to theoretical aspects, which he illustrates by giving examples of constitutional solutions from two selected countries: the Republic of Poland and the Swiss Confederation. In both cases, the tasks related to the executive power are performed not only by the central government and its administration but also by local and regional government bodies, which enables describing the executive branch of the government in a contemporary democratic state as ”distributed.” However, the structure of federal state determines the extent of the ”distribution” of tasks and competences of the executive branch of the government, in particular with regard to adoption of implementing regulations to statutes (federal and cantonal).Uniwersytet w BiałymstokuAleksandrowicz Maciej. 2009. System prawny Szwajcarii. Historia i współczesność, Białystok: Temida2.Banaszak Bogusław. 2007. Porównawcze prawo konstytucyjne współczesnych państw demokratycznych, Kraków: Wolters Kluwer Polska.Bożyk Stanisław. 2014. System organów państwowych. W Prawo konstytucyjne, Białystok: Temida2.Jackiewicz Andrzej. 2011. Territorial Organization of European States . Federalism, Regionalism, Unitarism, Białystok: Temida2.Jaskiernia Jerzy. 2009. Wprowadzenie do systemu państw federalnych. W Problemy rozwoju federalizmu we współczesnym świecie, Kielce: Wydawnictwo Uniwersytetu Humanistyczno-Przyrodniczego Jana Kochanowskiego.Sarnecki Paweł. 2008. Ogólna charakterystyka państwowości w Rzeczypospolitej Polskiej. W Prawo konstytucyjne RP, Warszawa: Wydawnictwo C.H.Beck.Czeszejko-Sochacki Zdzisław. 2002. System konstytucyjny Szwajcarii, Warszawa: Wydawnictwo Sejmowe.Matyja Mirosław. 2010. Swiss made. Jak funkcjonuje wielokulturowa Szwajcaria?, Brzezia Łąka: Wydawnictwo Poligraf.Rycerska Izabela. 2010. Tendencje reform samorządu terytorialnego w Szwajcarii. W Samorząd terytorialny w Europie Zachodniej, Warszawa: Dom Wydawniczy Elipsa.Rycerska Izabela. 2009. Kierunki rozwoju federacji szwajcarskiej. W Problemy rozwoju federalizmu we współczesnym świecie, Kielce: Wydawnictwo Uniwersytetu Humanistyczno-Przyrodniczego Jana Kochanowskiego.Suchecki Wiktor. 1968. Teoria federalizmu, Warszawa: Państwowe Wydawnictwo Naukowe.Winczorek Piotr. 2008. Komentarz do Konstytucji Rzeczypospolitej Polskiej z dnia 2 kwietnia 1997 roku, Warszawa: Liber.455-46320/B45546
Professional sports management. The case of Polish volleyball clubs.
No full textW pracy doktorskiej przedstawiona została problematyka zarządzania profesjonalnymi klubami sportowymi. Głównym celem pracy było zbadanie istoty, specyfiki i uwarunkowań profesjonalnego zarządzania klubami sportowymi w Polsce na przykładzie klubów siatkarskich. Zgromadzony materiał pozwolił na wypracowanie modelu zarządzania profesjonalnym klubem sportowym w Polsce oraz wniosków i rekomendacji dla kadry zarządzającej klubami.The dissertation presents the problem of the professional management in sports clubs. The author describes the characteristics and conditions of the professional management in Polish volleyball clubs. The author conducted a study in 11 professional volleyball clubs and expert surveys. The results of the analysis confirm the assumption that clubs focused on their stakeholders, creating value for the community and trying to maintain competitive balance
A nonlinear optimization approach to the construction of general linear methods of high order
No full textAbstractWe describe the construction of diagonally implicit multistage integration methods of order and stage order p = q = 7 and p = q = 8 for ordinary differential equations. These methods were obtained using state-of-the-art optimization methods, particularly variable-model trust-region least-squares algorithms
Immunitet parlamentarny we współczesnym świecie – ujęcie prawnoporównawcze
No full textThe purpose of the article is to determine the current form of parliamentary immunity in various countries. The author uses the comparative-law method to analyse constitutions that represent the most common solutions, taking into account the geographic criterion, used in countries located on different continents and having different legal cultures. The author analyses the subjective scope of non-accountability and non-violability and focuses on the time and place in which the protection is provided, and trace the objective scope of the protection and the solutions related to the possibility to lift the parliamentary immunities. The analysis leads to the conclusion that non-accountability is similar in different countries, has undergone few modifications over the years, and it is permanently formed. In the case of non-violability, there are more extensive differences, in particular in the objective scope and the degree of protection. However, various solutions prove that there is not a single universally accepted model of immunity and that the scope of the guaranteed protection can be more diverse, it can be subject to change, and be adapted to the changes in political systems and the political and social expectations
Error propagation of general linear methods for ordinary differential equations
No full textAbstractWe discuss error propagation for general linear methods for ordinary differential equations up to terms of order p+2, where p is the order of the method. These results are then applied to the estimation of local discretization errors for methods of order p and for the adjacent order p+1. The results of numerical experiments confirm the reliability of these estimates. This research has applications in the design of robust stepsize and order changing strategies for algorithms based on general linear methods
