1,529 Result(s)
within
Qingfeng **g
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Chapter
The First Construction Theorem
Let (Ω,F,P) be a complete probability space, and E=(l,2,•••). σ(ω) is a random variable taking values in [0,∞). x(t,ω) is a function taking values in E and defined for all ω∈Ω,t∈[0, σ(ω))). For every t≥0, let ...
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Chapter
General Theory
The purpose of this chapter is to give an exposition of the general theory of minimal nonnegative solutions for systems of nonnegative linear equations.
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Chapter
Arbitrary Q-Processes
In this chapter, we shall investigate arbitrary Q-processes on the basis of the study of minimal Q-processes and Q-processes of order one.
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Chapter
Construction of Q-Processes
First we stipulate that all the Q-processes that occurred in §§13.1—13.3 possess the Property (D) introduced in §1.1, and their Q-matrices satisfy (9.1.1).
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Chapter
The Second Construction Theorem
Suppose(Ω,F,P)is a complete probability space, $${X^{(n)}}(\omega ) = \left\{ {{x^{(n)}}(t,\,\,\omega ),t\,\, < \,\,{\sigma ^{(n)}}(\omega )} \...
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Chapter
Calculation
Lemma 4.1.1 Let A = (aij) be a primitive matrix of order n, and let r be its maximal eigenvalue. If
(4.1.1) $$r \geqslant 1,$$ -
Chapter
Martin Entrance Boundary Theory
For simplicity, we shall identify the Markov chain X(ω)= {xn(ω),n <ζ(ω)+1} with its transition probability matrix P = (pij; i,j∈E), so P is also called a Markov chain.
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Chapter
Q-Processes of Order One
Part I of this book, indicates that the minimal Q -process and Q -processes of order one are the bases for the study of general Q-processes. In the preceding chapter we studied the minimal Q-process, and in this ...
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Chapter
Criteria for the Uniqueness of Q-Processes
Suppose X = {x(t,ω), t < σ (ω)} is a homogeneous denumerable Markov process defined on a complete probability space (Ω, F, P), with phase space E = {1, 2, ⋯}, and transition probabilities p ij ...
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Chapter
Qualitative Theory
As indicated in §12.1, with respect to any given Q-matrix, the following three fundamental problems should be answered: (A) Whether there exists a Q-process with Q as its density matrix. (B) If one does exist the...
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Chapter
Systems of 1-Bounded Equations
In the last chapter, we studied a method for calculating the minimal nonnegative solutions of systems of nonnegative linear equations. But most systems of nonnegative linear equations encountered are of a spec...
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Chapter
Martin Exit Boundary Theory
The theory of the Martin exit boundary for a Markov chain was first established by Doob [12] and then generalized by Hunt. Many works appeared thereafter, but in all those works there are always some restricti...
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Chapter
Minimal Q-Processes
Assume that X(ω) = {x{t, ω), t < σ(ω)} is a homogeneous denumerable Markov process defined on a complete probability space (Ω, F, P), with the denumerable set E = {1, 2, ⋯} as its minimal state space, (p ...
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Chapter
General Theory
Let (Ω, F, P) be a probability space; ξ(ω) is a random variable taking values in the set {0, 1, 2, ⋯}; x{ω) is a function taking values in the countable set E = {1, 2, ⋯} and defined for all
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Chapter
The Structure of Science and Technology in History: On the Factors Delaying the Development of Science and Technology in China in Comparison with the West since the 17th Century (Part One)
Based on statistical analysis of the scientific and technological achievements of China and the West during the past two thousand years, this paper compares the special features of the development of each as a...
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Chapter
Historical Changes in the Structure of Science and Technology (Part Two, A Commentary)
This article further describes the intrinsic relationship between the structure of science and the social structure, specifically the formation of a primitive scientific structure, its exemplary role in the es...
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Article
Parallel computation of fourier transform on distributed memory computer system
Multicomputer systems (distributed memory computer systems) are becoming more and more popular and will be wildly used in scientific researches. In this paper, we present a parallel algorithm of Fourier Transf...
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Article
Vitrificational cryopreservation and subsequently fertile plant regeneration from rice (Oryza sativa L.) embryogenic suspension cells
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Article
A Phenomenological Model of the LS2 Ion Channel
A molecular dynamics simulation has been performed on a synthetic membrane-spanning ion channel, consisting of four α-helical peptides, each of which is composed of the sequence Ac-(LSLLLSL)3-CONH2. In the presen...
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Article
Control of solidification structure of wear-resistant austenite-bainite polyphase steel with nodular eutectic
A new austenite-bainite polyphase steel with nodular carbides can be obtained by controlling the solidification structure of the steel melt, which only contains manganese and silicon, with modification of Si-C...
