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Aronszajn and Sikorski subcartesian differential spaces

100%

Cushman R. , Śniatycki J.

Bulletin of the Polish Academy of Sciences. Mathematics

2021

tom Vol. 69, no. 2

171--180

We construct a natural transformation between the category of Aronszajn subcartesian spaces and the category of subcartesian differential spaces, which is a subcategory of Sikorski differential spaces.

Integration on differential spaces

51%

Dziewa-Dawidczyk D. , Pasternak-Winiarski Z.

Demonstratio Mathematica

2014

tom Vol. 47, nr 3

748--762

The generalization of the n-dimensional cube, an n-dimensional chain, the exterior derivative and the integral of a differential n-form on it are introduced and investigated. The analogue of Stokes theorem for the differential space is given.

On the leaves of a prefoliation of a K-differential space

44%

Piątkowski A.

Demonstratio Mathematica

2004

tom Vol. 37, nr 3

689--696

The definition of a prefoliation (M,F) of a K-differential space and the theorem about regularity of the inclusion of a leaf of a prefoliation are reminded. An example of a pair (M, F) of SC-differential spaces with the same set of points, which shows that even if the identity of .M is an immersion F -> M and (top M, top F) is a topological foliation in the sense of Ehresmann then (M, F) has not to be a prefoliation, is given. In the end, we show that if L is a proper leaf of a prefoliation (M, F) then the both structures of a K-differential spaces coincide on L.

Slice theorem for differential spaces and reduction by stages

38%

Lusala T. , Śniatycki J.

Demonstratio Mathematica

2014

tom Vol. 47, nr 1

192--210

We show that the space P/G of orbits of a proper action of a Lie group G on a locally compact differential space P is a locally compact differential space with quotient topology. Applying this result to reduction of symmetries of Hamiltonian systems, we prove the reduction by stages theorem.

K-differential spaces as sheaves. Induced and coinduced structure

38%

Piątkowski A.

Demonstratio Mathematica

2005

tom Vol. 38, nr 2

495--506

Any K-differential space determines the sheaf of germs of its elements. We consider the K-differential space induced and coinduced by a single mapping. In this special case, we compare the sheaf of germs of the induced K-differential space with the inverse image of the sheaf of germs of a given K-differential space, and the sheaf of germs of the coinduced K-differential space with the image of the sheaf of germs of a given K-differential space.

Differential geometry approach in optimization of the business production process

38%

Falkiewicz E.

Central European Review of Economics & Finance

2023

tom 43

nr 2

5-16

In this work we show a new approach to the optimization of the production process – from a differential geometry point of view. It is known ([2]) analytical conditions of profit maximization and minimization of the cost in an enterprise. In the first part of this work, we show such a classical approach. In the second part of the work, we use geometrical methods to obtain a new geometrical approach to the production process.

On linear operators consistent with a subspace in differential spaces

32%

Multarzyński P.

Demonstratio Mathematica

2006

tom Vol. 39, nr 1

233-244

Linear operators on function and abstract algebras are considered and their consistency with an arbitrary subset or an ideal is studied. Then the consistency concept is formulated for general Poisson brackets in commutative algebras.

On some right invertible operators in differential spaces

32%

Multarzyński P.

Demonstratio Mathematica

2004

tom Vol. 37, nr 4

905--920

In this paper we consider the right invertibility problem of some linear operators defined on the algebra of smooth function on a differential space.

Weil homomorphism in non-commutative differential spaces

26%

Jagodziński T. , Sasin W.

Demonstratio Mathematica

2005

tom Vol. 38, nr 2

507--516

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.