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Search Results: 1 - 10 of 966 matches for " Zbigniew Szafraniec "
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On the number of branches of real curve singularities
Aleksandra Nowel,Zbigniew Szafraniec
Mathematics , 2010, DOI: 10.1112/blms/bdr040
Abstract: There is presented a method for computing the number of branches of a real analytic curve germ from $R^n$ to $R^m$, where m is greater or equal to n, having a singular point at the origin, and the number of half--branches of the set of double points of an analytic germ from $R^2$ to $R^3$.
Algebraically Constructible Functions and Signs of Polynomials
Adam Parusinski,Zbigniew Szafraniec
Mathematics , 1996,
Abstract: We show that on real algebraic sets algebraically constructible functions coincide with the finite sums of signs of polynomials. Then we give some applications.
Mappings from R^3 to R^3 and signs of swallowtails
Justyna Bobowik,Zbigniew Szafraniec
Mathematics , 2014,
Abstract: Let M be an oriented 3-manifold. For a generic f \in C^ \infty(M,R^3), there is a discrete set of swallowtail critical points. In that case, at any swallowtail point p there exists a well-oriented coordinate system centered at p, and a coordinate system centered at f(p), such that locally f has the form f_\pm(x,y,z)=(\pm xy+x^2 z+x^4,y,z), so one may associate with p a sign I(f,p)\in \{\pm 1\}. A geometric definition of the sign associated with a swallowtail was recently introduced by Goryunov. We shall show how to compute the number of swallowtail points having the positive/negative sign, in the case where f : R^n \rightarrow R^n is a polynomial mapping, in terms of signatures of quadratic forms.
Nowe trendy w elektroterapii niewydolno ci serca
Zbigniew Szafraniec,Jerzy Krzysztof Wranicz
Polish Journal of Cardiology , 2012,
Abstract: Niewydolno serca to donios y problem populacyjny, który corocznie dotyka miliony ludzi na wiecie i generuje wielomilionowe obci enie dla systemów zdrowotnych krajów rozwini tych. Ogromny post p w leczeniu farmakologicznym tej jednostki chorobowej, jaki dokona si w ci gu minionych 20 lat, spowodowa , e wyd u y si czas prze ycia chorych, jednak rokowanie nadal jest z e. Rozwój elektroterapii sprawi , e cz pacjentów mo e by skutecznie leczona przy pomocy urz dzeń wszczepialnych, co wyd u a prze ycie i, co równie wa ne, cz sto poprawia jako ycia. W zwi zku z ci g ym post pem wspó cze nie stajemy przed wieloma wyzwaniami, z którymi przyjdzie nam si zmierzy w trakcie kwalifikowania do zabiegów, wszczepiania urz dzeń ró nego typu i opieki poimplantacyjnej chorych z niewydolno ci serca. Artyku ten przedstawia w zarysie najwa niejsze zagadnienia dotycz ce elektroterapii niewydolno ci serca poruszane w ostatnim roku, w szczególno ci za przewidywania odpowiedzi na resynchronizacj , rozszerzenia wskazań do implantacji kardiostymulatorów resynchronizuj cych, selekcji pacjentów do pierwotnej prewencji nag ego zgonu sercowego przy u yciu wszczepialnych kardiowerterów- defibrylatorów oraz tzw. optymalizacji ustawień.
On polynomial mappings from the plane to the plane
Iwona Krzy?anowska,Zbigniew Szafraniec
Mathematics , 2012,
Abstract: Let f be a generic polynomial mapping mapping from the plane to the plane. There are constructed quadratic forms whose signatures determine the number of positive and negative cusps of f.
Polynomial mappings into a Stiefel manifold and immersions
Iwona Krzy?anowska,Zbigniew Szafraniec
Mathematics , 2011,
Abstract: For a polynomial mapping from S^{n-k} to the Stiefel manifold \widetilde{V}_k(\R^{n}), where n-k is even, there is presented an effective method of expressing the corresponding element of the homotopy group \pi_{n-k}\widetilde{V}_k(\R^{n})\simeq\Z in terms of signatures of quadratic forms. There is also given a method of computing the intersection number for a polynomial immersion from S^m to \R^{2m}.
Immersions of spheres and algebraically constructible functions
Iwona Karolkiewicz,Aleksandra Nowel,Zbigniew Szafraniec
Mathematics , 2007,
Abstract: Let L be an algebraic set and let g : R^(n+1) \times L --> R^(2n) (n is even) be a polynomial mapping such that for each l in L there is r(l)>0 such that the mapping g_l = g(.,l) restricted to the sphere S^n(r) is an immersion for every 0
An algebraic formula for the intersection number of a polynomial immersion
Iwona Karolkiewicz,Aleksandra Nowel,Zbigniew Szafraniec
Mathematics , 2008,
Abstract: There is presented an algorithm for computing the topological degree for a large class of polynomial mappings. As an application there is given an effective algebraic formula for the intersection number of a polynomial immersion M --> R^2m, where M is an m-dimensional algebraic manifold.
Rural Social Capital versus European and Global Challenges (About "good" and "bad" Social Capital)
Piotr Mikiewicz, Krystyna Szafraniec
Eastern European Countryside , 2009, DOI: 10.2478/v10130-009-0007-3
Abstract: This text has two aims - to relate the results of research carried out in IRWiR PAN (Institute for Rural and Agricultural Development Polish Academy of Sciences) on rural social capital and achieve a useful social interpretation of those results referring to the theory of social capital. Social capital is nowadays becoming a very important element in academic and political discourse. It is seen as having the potential for greater efficiency in levelling social differences, improving the opportunities of rural inhabitants. No matter how popular and positive, social capital can be understood in various ways due to its various theoretical sources, it is also possible to point out its negative aspects. This text is an attempt at showing the nuances of how social capital works. The first part presents the basic understanding of the category discussed here. The second part is a presentation of the results of empirical research where interpretation was carried out in the light of earlier outlined concepts.
Moments from their very truncations
F. H. Szafraniec
Mathematics , 2007,
Abstract: It is known that positive definiteness is not enough for the multidimensional moment problem to be solved. We would like throw in to the garden of existing in this matter so far results one more, a result which takes into considerations the utmost possible truncations.
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