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Content available remote Witruwiańska harmonia form
Od niezliczonych pokoleń ludzkie reakcje na bodźce z otoczenia powtarzają się. Przekazywane genetycznie w więźbie aksonów są stale weryfikowane. Miara piękna, odbicie harmonii świata codziennie wdrukowuje się w strukturę mózgu. Przyjemność estetyczna jest zakorzeniona w najstarszych ewolucyjnie częściach mózgu i wyrasta z poczucia zadowolenia, z braku zagrożeń. W naszym umyśle tkwi wzorzec kompozycji idealnej - witruwiańskie venustas.
Experiences, which have been concentrated and layered by thousands of generations in the inner being of man subsequently formed an ideal image of amicable environment, good composition and form. Human mind is a resonator of good form. The work of art built according to rules of such resonance contains visual truth about nature: venustas.
Content available remote Jordan structure on prime rings with centralizers
Our object in this paper is to study the generalization of Borut Zalar result in [1] on Jordan centralizer of semiprime rings by prove the following result: Let R be a prime of characteristic different from 2, and U be a Jordan ideal of R. If T is an additive mapping from R to itself satisfying the following condition T(ur + ru) = uT(r) + T(r)u, then T(ur) = uT(r), for all r is an element of R, u is an element of U.
Content available remote On some subsemigroups of the groups L1/s and L1/nieskończoność
The problem of determination of some class of geometric objects has been reduced about forty years ago to consideration of some subsemigroups of the differential group L1/s (cf. [1] and [6]). Over the last years many papers has been devoted the problem of determining of subsemigroups and subgroups of the group L/s (see among others (2], (3] and (5]-[15]). In this paper we are going to generalize the results from [5], [9] and (13] concerning determination of some form subsemigroups of the group L1/s.
Content available remote Weil homomorphism in non-commutative differential spaces
In this paper we construct Weil homomorphism in locally free module over a non-commutative differential space, which is a generalization of Sikorski differential space [6]. We consider real case, but the complex case can be done analogusly.
Content available remote A note on homomorphisms of inner product spaces
Recently, Buhagiar and Chetcuti [1] have shown that if V1 and V2 are two separable, real inner product spaces such that the modular ortholattices of their finite and cofmite subspaces are algebraically isomorphic, then V1 and V2 are isomorphic as inner product spaces. Their proof is based on the properties of inner product spaces, in particular it makes use of Gleason's theorem. In this note we show, using techniques of projective geometry, that their result holds for any inner product spaces, real, complex or quaternionic, of dimension at least three, not necessarily separable. We also consider the case when the algebraic isomorphism is replaced by a homomorphism, and the case when the underlying fields of V1 and V2 are not the same.
Content available remote Boolean carried homomorphisms in orthomodular lattices
Let L, L1 be orthomodular lattices. Let us say that a surjective homomorphism f : L - L1 is Boolean carried if for any maximal Boolean subalgebra B1 of L1 there is a maximal Boolean subalgebra B of L such that f(B) = B1. In this note we investigate the class HOMC all L's such that all surjective homomorphisms from L to orthomodular lattices are Boolean carried. We prove as a main result that if L possesses at most countably many infinite maximal Boolean subalgebras then L L HOMC- We also relate the class HOMCto the classes previously studied and provide some model-theoretic propertiesHOMC.
Content available remote A categorial characterization of the mixed extension of a noncooperative game
Some variants of the notion of a homomorphism between noncooperative games are discussed and the respective categories of noncooperative games are introduced. It is shown that the mixed extension of a noncooperative game can be viewed as a value of the functor which is a left adjoint to the forgetful functor from some category of convex games to suitable category of noncooperative games.
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