Various properties of the characteristic functions of random variables in a non-commutative C*-probability space are studied in this paper. It turns out that the distributions of random variables are uniquely determin...Various properties of the characteristic functions of random variables in a non-commutative C*-probability space are studied in this paper. It turns out that the distributions of random variables are uniquely determined by their characteristic functions. By using the properties of characteristic functions, a central limit theorem for a sequence of independent identically distributed random variables in a C*-probability space is established as well.展开更多
For a probability space (X, B, μ) a subfamily F of the σ-algebra B is said to be a regular base if every B ∈ B can be arbitrarily approached by some member of F which contains B in the sense of the measure theory. ...For a probability space (X, B, μ) a subfamily F of the σ-algebra B is said to be a regular base if every B ∈ B can be arbitrarily approached by some member of F which contains B in the sense of the measure theory. Assume that {R γ } γ∈Γ is a countable family of relations of the full measure on a probability space (X, B, μ), i.e. for every γ ∈ Γ there is a positive integer s γ such that R γ ? $X^{s_\gamma } $ with $\mu ^{s_\gamma } $ (R γ ) = 1. In the present paper we show that if (X, B, μ) has a regular base, the cardinality of which is not greater than the cardinality of the continuum, then there exists a set K ? X with μ*(K) = 1 such that (x 1, …, $x_{^{s_\gamma } } $ ) ∈ R γ for any γ ∈ Γ and for any s γ distinct elements x 1, …, $x_{^{s_\gamma } } $ of K, where μ* is the outer measure induced by the measure μ. Moreover, an application of the result mentioned above is given to the dynamical systems determined by the iterates of measure-preserving transformations.展开更多
This paper presents the Advanced Observer Model (AOM), a groundbreaking conceptual framework designed to clarify the complex and often enigmatic nature of quantum mechanics. The AOM serves as a metaphorical lens, brin...This paper presents the Advanced Observer Model (AOM), a groundbreaking conceptual framework designed to clarify the complex and often enigmatic nature of quantum mechanics. The AOM serves as a metaphorical lens, bringing the elusive quantum realm into sharper focus by transforming its inherent uncertainty into a coherent, structured ‘Frame Stream’ that aids in the understanding of quantum phenomena. While the AOM offers conceptual simplicity and clarity, it recognizes the necessity of a rigorous theoretical foundation to address the fundamental uncertainties that lie at the core of quantum mechanics. This paper seeks to illuminate those theoretical ambiguities, bridging the gap between the abstract insights of the AOM and the intricate mathematical foundations of quantum theory. By integrating the conceptual clarity of the AOM with the theoretical intricacies of quantum mechanics, this work aspires to deepen our understanding of this fascinating and elusive field.展开更多
In this paper we discuss a step further some convergence and continuity problems of distribution function on R^i. We give the following results: (1)distribution function F(x_1,…,x_k) on R^k is continuous if and only ...In this paper we discuss a step further some convergence and continuity problems of distribution function on R^i. We give the following results: (1)distribution function F(x_1,…,x_k) on R^k is continuous if and only if all marginal distribution functions of F is continuous on R^1. (2)If limF_n(x_1,……,x_k)=F(x_1,…,x_k) and limF_n(x_1—0,…,x_k—0)=F(x_1—0,…,x_k—0) at all non-continuity points of F, then展开更多
We introduce the concept of T-fuzzy subhypermodules of hypermodules with respect to triangular norms and obtain some results. In particular, we define a probabilistic version of hypermodules using random sets and show...We introduce the concept of T-fuzzy subhypermodules of hypermodules with respect to triangular norms and obtain some results. In particular, we define a probabilistic version of hypermodules using random sets and show that fuzzy hypermodules defined in triangular norms are consequences of probabilistic hypermodules under certain conditions.展开更多
A lot of forms and applications have been found in Poincar6 inequality, but the optimum constants satisfying Poincar6 inequality have not been estimated. This paper estimates the optimum constants λ0 and λ1 satisfyi...A lot of forms and applications have been found in Poincar6 inequality, but the optimum constants satisfying Poincar6 inequality have not been estimated. This paper estimates the optimum constants λ0 and λ1 satisfying Poincaré inequality by using isoperimetric constants. It is λ0≥k0^2/（2R） and λ1 ≥k1^2/（2R）.展开更多
We examine 14 plates of the globular cluster M3 (NGC 5272) taken with the 40 cm refractor at the Sheshan station of Shanghai Astronomical Observatory. The plates span over a period of about 77 years. The positions and...We examine 14 plates of the globular cluster M3 (NGC 5272) taken with the 40 cm refractor at the Sheshan station of Shanghai Astronomical Observatory. The plates span over a period of about 77 years. The positions and absolute proper motions of eight stars in the Hipparcos Catalogue and of 49 stars in the Tycho-2 Catalogue are used as the reference frame. The astrometric reduction is made with the central overlapping principle. The absolute proper motions of 534 stars in a region of about 100' × 100' around the cluster are measured. With the new proper motion data the membership probabilities of the stars are determined. The average absolute proper motion obtained for the cluster is -0.06±0.30 mas yr-1 in R.A. and -2.6±0.30 mas yr-1 in Decl. By combining this result with the known distance and radial velocity of the cluster, we also obtained the Galactic orbit of M3 for a chosen three-component Galactic potential.展开更多
In our paper we will mainly construct a stochastic model from uncertainty and establish some properties on it.we will next show that the existence of supporting prices and optimal paths,and obtain some results similar...In our paper we will mainly construct a stochastic model from uncertainty and establish some properties on it.we will next show that the existence of supporting prices and optimal paths,and obtain some results similar to Optimal Growth in which there are the some methods展开更多
基金the Shanghai Science and Technology Commission, No. 01ZA14003.
文摘Various properties of the characteristic functions of random variables in a non-commutative C*-probability space are studied in this paper. It turns out that the distributions of random variables are uniquely determined by their characteristic functions. By using the properties of characteristic functions, a central limit theorem for a sequence of independent identically distributed random variables in a C*-probability space is established as well.
基金This work was supported by the National Science Fbundation of China (Grant No. 10471049)
文摘For a probability space (X, B, μ) a subfamily F of the σ-algebra B is said to be a regular base if every B ∈ B can be arbitrarily approached by some member of F which contains B in the sense of the measure theory. Assume that {R γ } γ∈Γ is a countable family of relations of the full measure on a probability space (X, B, μ), i.e. for every γ ∈ Γ there is a positive integer s γ such that R γ ? $X^{s_\gamma } $ with $\mu ^{s_\gamma } $ (R γ ) = 1. In the present paper we show that if (X, B, μ) has a regular base, the cardinality of which is not greater than the cardinality of the continuum, then there exists a set K ? X with μ*(K) = 1 such that (x 1, …, $x_{^{s_\gamma } } $ ) ∈ R γ for any γ ∈ Γ and for any s γ distinct elements x 1, …, $x_{^{s_\gamma } } $ of K, where μ* is the outer measure induced by the measure μ. Moreover, an application of the result mentioned above is given to the dynamical systems determined by the iterates of measure-preserving transformations.
文摘This paper presents the Advanced Observer Model (AOM), a groundbreaking conceptual framework designed to clarify the complex and often enigmatic nature of quantum mechanics. The AOM serves as a metaphorical lens, bringing the elusive quantum realm into sharper focus by transforming its inherent uncertainty into a coherent, structured ‘Frame Stream’ that aids in the understanding of quantum phenomena. While the AOM offers conceptual simplicity and clarity, it recognizes the necessity of a rigorous theoretical foundation to address the fundamental uncertainties that lie at the core of quantum mechanics. This paper seeks to illuminate those theoretical ambiguities, bridging the gap between the abstract insights of the AOM and the intricate mathematical foundations of quantum theory. By integrating the conceptual clarity of the AOM with the theoretical intricacies of quantum mechanics, this work aspires to deepen our understanding of this fascinating and elusive field.
文摘In this paper we discuss a step further some convergence and continuity problems of distribution function on R^i. We give the following results: (1)distribution function F(x_1,…,x_k) on R^k is continuous if and only if all marginal distribution functions of F is continuous on R^1. (2)If limF_n(x_1,……,x_k)=F(x_1,…,x_k) and limF_n(x_1—0,…,x_k—0)=F(x_1—0,…,x_k—0) at all non-continuity points of F, then
基金Supported by the National Natural Science Foundation of China ( No.60474022)the Key Science Foundation of Education Committee of Hubei Province,China (No.2004Z002 D200529001)
文摘We introduce the concept of T-fuzzy subhypermodules of hypermodules with respect to triangular norms and obtain some results. In particular, we define a probabilistic version of hypermodules using random sets and show that fuzzy hypermodules defined in triangular norms are consequences of probabilistic hypermodules under certain conditions.
基金The Science and Technology Foundation of Chongqing Municipal Education Commission (No.KJ071106)
文摘A lot of forms and applications have been found in Poincar6 inequality, but the optimum constants satisfying Poincar6 inequality have not been estimated. This paper estimates the optimum constants λ0 and λ1 satisfying Poincaré inequality by using isoperimetric constants. It is λ0≥k0^2/（2R） and λ1 ≥k1^2/（2R）.
基金NKBRSF19990754 and National Natural Sciences Foundation under grant 19833010．
文摘We examine 14 plates of the globular cluster M3 (NGC 5272) taken with the 40 cm refractor at the Sheshan station of Shanghai Astronomical Observatory. The plates span over a period of about 77 years. The positions and absolute proper motions of eight stars in the Hipparcos Catalogue and of 49 stars in the Tycho-2 Catalogue are used as the reference frame. The astrometric reduction is made with the central overlapping principle. The absolute proper motions of 534 stars in a region of about 100' × 100' around the cluster are measured. With the new proper motion data the membership probabilities of the stars are determined. The average absolute proper motion obtained for the cluster is -0.06±0.30 mas yr-1 in R.A. and -2.6±0.30 mas yr-1 in Decl. By combining this result with the known distance and radial velocity of the cluster, we also obtained the Galactic orbit of M3 for a chosen three-component Galactic potential.
文摘In our paper we will mainly construct a stochastic model from uncertainty and establish some properties on it.we will next show that the existence of supporting prices and optimal paths,and obtain some results similar to Optimal Growth in which there are the some methods
