Trudna droga do Europy przez program Sokrates-Erasmus

The article presents the assumptions and one of the preconditions of the reform of teaching connected with the introduction of a point system for awarding credits for courses: the basic requirement laid down for colleges and universities applying for participation in the European Union Socrates-Erasmus Programme is adherence to the instructions of the European Credit Transfer System. The authoress also discusses the advancement of the work of individual types of higher education institutions and specialisations on the introduction of a system of conversion points. The source of information are data gathered by the Tempus Office on the basis of a questionnaire sent out at the beginning of 1997 to all higher education institutions.W artykule przedstawiono założenia oraz jedną z przesłanek reformy dydaktyki, związanej z wprowadzaniem punktowego systemu zaliczania zajęć: podstawowym wymaganiem stawianym uczelniom ubiegającym się o uczestnictwo w programie Unii Europejskiej Sokrates-Erasmus jest podporządkowanie zaliczeń Europejskiemu Systemowi Transferu Punktów. Autorka omawia ponadto stan zaawansowania prac nad wprowadzeniem systemu punktów przeliczeniowych w poszczególnych typach uczelni oraz na różnych kierunkach studiów. Źródło informacji stanowią dane zgromadzone przez Biuro Programu Tempus na podstawie ankiety wysłanej do wszystkich uczelni na początku 1997 r

Günther Schulz, Gisela-A. Schröder & Timm C. Richter, Bolschewistische Herrschaft und Orthodoxe Kirche in Russland. Das Landeskonzil 1917/1918. Quellen und Analysen. Wydawnictwo: Lit Verlag, Münster, 2005, 802 strony.

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Chrześcijaństwo pozakonfesjonalne i Søren Kierkegaard

According to Søren Kierkegaard, the development of Christianity is a history of going away from it, or at least of mitigating the criteria of belonging to it. Dane proposes two models of the trans confessional faith: (1) The recognition of the earthly life of Jesus Christ, of his death and resurrection, and nothing more. (2) The recognition of the faith as that which was defi ned above in the fi rst point and, additionally, on this basis of the choice of the Bible, which is possible as the secondary act related to the faith but not as its starting point. Moreover, all the interpretations of the beyond-confessional faith should be subjectively considered by a single individual. Kierkegaard mentions here some mystical elements. All the religious relationships should be personal in character. As far as the questions of faith and reason are concerned, the standpoint of Paulinism – either/or – is binding. Kierkegaard demands that the existing churches recognise themselves as representing the mitigated forms of Christianity; otherwise they have to undergo criticism. For him, the fi rst two centuries of the existence of Christianity are the ideal ones, and the personal model is the „witness of the truth”, of which he gives the detailed description. The increasing phenomenon of the trans-confessional faith has its roots in the civilisational changes (the secularization) as well as in the intensive manifestation, in the history of Christianity, of the practices which are inconsistent with the biblical background

The group of isometries of a Banach space and duality

We construct an example of a real Banach space whose group of surjective isometries has no uniformly continuous one-parameter semigroups, but the group of surjective isometries of its dual contains infinitely many of them. Other examples concerning numerical index, hermitian operators and dissipative operators are also shown.Comment: To appear in J. Funct. Ana

Numerical Measure of a Complex Matrix

International audienceWe introduce a natural probability measure over the numerical range of a complex matrix A ∈ M n (C). This numerical measure µ A can be defined as the law of the random variable X ∈ C when the vector X ∈ C n is uniformly distributed on the unit sphere. If the matrix A is normal, we show that µ A has a piecewise polynomial density f A , which can be identified with a multivariate B-spline. In the general (nonnormal) case, we relate the Radon transform of µ A to the spectrum of a family of Hermitian matrices, and we deduce an explicit representation formula for the numerical density which is appropriate for theoretical and computational purposes. As an application, we show that the density f A is polynomial in some regions of the complex plane which can be characterized geometrically, and we recover some known results about lacunas of symmetric hyperbolic systems in 2 + 1 dimensions. Finally, we prove under general assumptions that the numerical measure of a matrix A ∈ M n (C) concentrates to a Dirac mass as the size n goes to infinity

On the C-determinantal range for special classes of matrices

Let A and C be square complex matrices of sizen, the C-determinantal range of A is the subset of the complex plane{det(A−UCU^∗): UU^∗=In}. If A, C are both Hermitian matrices, then by a result of Fiedler (1971)[11] this set is a real line segment. In our paper we study this set for the case when C is a Hermitian matrix. Our purpose is to revisit and improve two well-known results on this topic. The first result is due to Li concerning theC-numerical range of a Hermitian matrix, see Condition 5.1 (a) in Li, (1994)[20]. The second one is due to C.-K. Li, Y.-T. Poon and N.-S. Sze about necessary and sufficient conditions for the C-determinantal range of A to be a subset of the line, (see Li et al. (2008)[21], Theorem 3.3)

The Exodus (Escape?) from Egypt

Autor Artykułu skupia się na zaprezentowaniu sprzecznych danych liczbowych dotyczących exodusu narodu wybranego z Egiptu. Liczby te oscylują w granicach od 6 tysięcy do ponad 600 tysięcy osób; niektórzy autorzy szacują łączną liczbę uciekinierów, wraz z rodzinami, nawet do 3 milinów osób (!). Niestety, nie ma możliwości adekwatnego przeliczenia danych zawartych w tekście Pisma św., w celu uniknięcia błędnych i przesadnych interpretacji. Jednocześnie dokonano krytyki dowolności związanych z uzupełnianiem tekstu wyjściowego. Całość artykułu oparta jest na analizie poglądów autorów polskich i zagranicznych. Tekst prezentuje szereg trudności z różnych dziedzin. Dotyczą one „Wyjścia”, bądź „ucieczki” ludu wybranego z niewoli egipskiej; sygnalizuje krytycznie problemy, nie pretendując do ich rozstrzygnięcia.The author focuses on the presentation of controversial numerical data relating to the Exodus of the Chosen People from Egypt. These figures range from 6 thousand to over 600 thousand people; some authors estimate the total number of refugee, along with families, even on 3 millions of persons (!). Unfortunately, it is not possible to adequately convert the data contained in the text of the Holy Scriptures, in order to avoid incorrect and over-interpretation. Simultaneously it has been proved the rlatitude of complementing the original text. Th e whole is based on analysis of the opinions of Polish and foreign authors. Th e text presents a number of diffi culties from diff erent areas. They relate to the „Exit” or „escape” of the Chosen People from slavery in Egypt, but do not to solve these problems