Let S be a set of states of a physical system and p(s) the probability of an occurrence of an event when the system is in state s∈S. The function p from S to [0,1] is called a numerical event, multidimensional probab...Let S be a set of states of a physical system and p(s) the probability of an occurrence of an event when the system is in state s∈S. The function p from S to [0,1] is called a numerical event, multidimensional probability or, more precisely, S-probability. If a set of numerical events is ordered by the order of real functions one obtains a partial ordered set P in which the sum and difference of S-probabilities are related to their order within P. According to the structure that arises, this further opens up the opportunity to decide whether one deals with a quantum mechanical situation or a classical one. In this paper we focus on the situation that P is generated by a given set of measurements, i.e. S-probabilities, without assuming that these S-probabilities can be complemented by further measurements or are embeddable into Boolean algebras, assumptions that were made in most of the preceding papers. In particular, we study the generation by S-probabilities that can only assume the values 0 and 1, thus dealing with so called concrete logics. We characterize these logics under several suppositions that might occur with measurements and generalize our findings to arbitrary S-probabilities, this way providing a possibility to distinguish between potential classical and quantum situations and the fact that an obtained structure might not be sufficient for an appropriate decision. Moreover, we provide some explanatory examples from physics.展开更多
Let(M,ω)be a symplectic manifold.In this paper,the authors consider the notions of musical(bemolle and diesis)isomorphisms ω~b:T M→T~*M and ω~?:T~*M→TM between tangent and cotangent bundles.The authors prove that...Let(M,ω)be a symplectic manifold.In this paper,the authors consider the notions of musical(bemolle and diesis)isomorphisms ω~b:T M→T~*M and ω~?:T~*M→TM between tangent and cotangent bundles.The authors prove that the complete lifts of symplectic vector field to tangent and cotangent bundles is ω~b-related.As consequence of analyze of connections between the complete lift ~cω_(T M )of symplectic 2-form ω to tangent bundle and the natural symplectic 2-form dp on cotangent bundle,the authors proved that dp is a pullback o f^cω_(TM)by ω~?.Also,the authors investigate the complete lift ~cφ_T~*_M )of almost complex structure φ to cotangent bundle and prove that it is a transform by ω~?of complete lift^cφ_(T M )to tangent bundle if the triple(M,ω,φ)is an almost holomorphic A-manifold.The transform of complete lifts of vector-valued 2-form is also studied.展开更多
In this paper the authors consider the bundle of affinor frames over a smooth manifold,define the Sasaki metric on this bundle,and investigate the Levi-Civita connection of Sasaki metric.Also the authors determine the...In this paper the authors consider the bundle of affinor frames over a smooth manifold,define the Sasaki metric on this bundle,and investigate the Levi-Civita connection of Sasaki metric.Also the authors determine the horizontal lifts of symmetric linear connection from a manifold to the bundle of affinor frames and study the geodesic curves corresponding to the horizontal lift of the linear connection.展开更多
The main purpose of this paper is to study the differential geometrical objects on tangent bundle corresponding to dual-holomorphic objects of dual-holomorphic manifold.As a result of this approach,the authors find a ...The main purpose of this paper is to study the differential geometrical objects on tangent bundle corresponding to dual-holomorphic objects of dual-holomorphic manifold.As a result of this approach,the authors find a new class of lifts(deformed complete lifts)in the tangent bundle.展开更多
Considering the bundle of 2-jets as a realization of the holomorphic manifold over 3-dimensional nilpotent algebra,the authors introduce a new class of lifts of connections in the bundle of 2-jets which is a generaliz...Considering the bundle of 2-jets as a realization of the holomorphic manifold over 3-dimensional nilpotent algebra,the authors introduce a new class of lifts of connections in the bundle of 2-jets which is a generalization of the complete lifts.展开更多
We propose a method for representing heteroge- neous concept lattices as classical concept lattices. Particu- larly, we describe a transformation of heterogeneous formal context into a binary one, such that correspond...We propose a method for representing heteroge- neous concept lattices as classical concept lattices. Particu- larly, we describe a transformation of heterogeneous formal context into a binary one, such that corresponding concept lattices will be isomorphic. We prove the correctness of this transformation by the basic theorem for heterogeneous as well as classical concept lattices.展开更多
文摘Let S be a set of states of a physical system and p(s) the probability of an occurrence of an event when the system is in state s∈S. The function p from S to [0,1] is called a numerical event, multidimensional probability or, more precisely, S-probability. If a set of numerical events is ordered by the order of real functions one obtains a partial ordered set P in which the sum and difference of S-probabilities are related to their order within P. According to the structure that arises, this further opens up the opportunity to decide whether one deals with a quantum mechanical situation or a classical one. In this paper we focus on the situation that P is generated by a given set of measurements, i.e. S-probabilities, without assuming that these S-probabilities can be complemented by further measurements or are embeddable into Boolean algebras, assumptions that were made in most of the preceding papers. In particular, we study the generation by S-probabilities that can only assume the values 0 and 1, thus dealing with so called concrete logics. We characterize these logics under several suppositions that might occur with measurements and generalize our findings to arbitrary S-probabilities, this way providing a possibility to distinguish between potential classical and quantum situations and the fact that an obtained structure might not be sufficient for an appropriate decision. Moreover, we provide some explanatory examples from physics.
文摘Let(M,ω)be a symplectic manifold.In this paper,the authors consider the notions of musical(bemolle and diesis)isomorphisms ω~b:T M→T~*M and ω~?:T~*M→TM between tangent and cotangent bundles.The authors prove that the complete lifts of symplectic vector field to tangent and cotangent bundles is ω~b-related.As consequence of analyze of connections between the complete lift ~cω_(T M )of symplectic 2-form ω to tangent bundle and the natural symplectic 2-form dp on cotangent bundle,the authors proved that dp is a pullback o f^cω_(TM)by ω~?.Also,the authors investigate the complete lift ~cφ_T~*_M )of almost complex structure φ to cotangent bundle and prove that it is a transform by ω~?of complete lift^cφ_(T M )to tangent bundle if the triple(M,ω,φ)is an almost holomorphic A-manifold.The transform of complete lifts of vector-valued 2-form is also studied.
文摘In this paper the authors consider the bundle of affinor frames over a smooth manifold,define the Sasaki metric on this bundle,and investigate the Levi-Civita connection of Sasaki metric.Also the authors determine the horizontal lifts of symmetric linear connection from a manifold to the bundle of affinor frames and study the geodesic curves corresponding to the horizontal lift of the linear connection.
文摘The main purpose of this paper is to study the differential geometrical objects on tangent bundle corresponding to dual-holomorphic objects of dual-holomorphic manifold.As a result of this approach,the authors find a new class of lifts(deformed complete lifts)in the tangent bundle.
文摘Considering the bundle of 2-jets as a realization of the holomorphic manifold over 3-dimensional nilpotent algebra,the authors introduce a new class of lifts of connections in the bundle of 2-jets which is a generalization of the complete lifts.
文摘We propose a method for representing heteroge- neous concept lattices as classical concept lattices. Particu- larly, we describe a transformation of heterogeneous formal context into a binary one, such that corresponding concept lattices will be isomorphic. We prove the correctness of this transformation by the basic theorem for heterogeneous as well as classical concept lattices.
