This article is not inspired by any religion or quantum many-worlds interpretation. The mathematics of multiverse is presented here. The mass operator was introduced earlier by Alnobani. This operator is used here to ...This article is not inspired by any religion or quantum many-worlds interpretation. The mathematics of multiverse is presented here. The mass operator was introduced earlier by Alnobani. This operator is used here to deduce the time state. It is found that time has four states and those four states are orthogonal. Time is the constitution of any verse. Time has direction. Every orthogonal direction of time belongs to a verse. Past and future belong to opposite directions of time and they are arbitrary. Other verses are there by their own and not a probabilities of any other verse and if any similarity it is only a coincidence. Among applications of this thesis is travelling through groups of galaxies, or more or less.展开更多
The generalized Virial theorem for mixed state, derived from the generalized Hellmann Feynman theorem, only applies to Hamiltonians in which potential of coordinates is separate from momentum energy term. In this pape...The generalized Virial theorem for mixed state, derived from the generalized Hellmann Feynman theorem, only applies to Hamiltonians in which potential of coordinates is separate from momentum energy term. In this paper we discuss Virial theorem for mixed state for some Hamiltonians with coordinate-momentum couplings in order to know their contributions to internal energy.展开更多
It is known that certain one parameter families of unimodal maps of the interval have a topological universality with regard to their dynamic behavior [ 1, 2]. As a parameter is smoothly increased, a fascinating varie...It is known that certain one parameter families of unimodal maps of the interval have a topological universality with regard to their dynamic behavior [ 1, 2]. As a parameter is smoothly increased, a fascinating variety of dynamic behaviors are produced. For some families the behaviors are monotonic in the parameter, while in others they are not [3]. The question is what sort of conditions on a one parameter family will ensure this monotonicity of the behavior with the parameter？ The answer is unknown and will not be given here. What we do instead is to investigate certain geometric-dynamic-combinatorial consequences of assuming that the family has this monotonicity. Specifically, using tools of symbolic dynamics, state space is ＂course grained＂ with a finite alphabet. We decompose a non-invertible map into nonlinear but invertible pieces. From these invertible pieces, we form inverse maps via composition along words. Equations of motion are developed for both forward and inverse orbits （in both the variables of state space and the parameter）, and an equation relating forward and inverse motions at fix-points is exhibited. Finally, we deduce a list of conditions, each of which is equivalent to monotone behavior. One of these conditions states that simple parity characteristics of words correspond to definite dynamics near fixed-points and vice versa.展开更多
In this paper, a quasi-Newton method fbr semi-blind estimation is derived for channel estimation in uplink cloud radio access networks （C-RANs）. Different from traditional pilot-aided estimation, semiblind estimatio...In this paper, a quasi-Newton method fbr semi-blind estimation is derived for channel estimation in uplink cloud radio access networks （C-RANs）. Different from traditional pilot-aided estimation, semiblind estimation utilizes the unknown data symbols in addition to the known pilot symbols to estimate the channel. An initial channel state information （CSI） obtained by least-squared （LS） estimation is needed in semi-blind estimation. BFGS （Brayben, Fletcher, Goldfarb and Shanno） algorithm, which employs data as well as pilot symbols, estimates the CSI though solving the problem provided by maximum-likelihood （ML） principle. In addition, mean-square-error （MSE） used to evaluate the estimation performance can be further minimized with an optimal pilot design. Simulation results show that the semi-blind estimation achieves a significant improvement in terms of MSE performance over the conventional LS estimation by utilizing data symbols instead of increasing the number of pilot symbols, which demonstrates the estimation accuracy and spectral efficiency are both improved by semiblind estimation for C-RANs.展开更多
This paper discusses the asymptotic stability and Riesz basis generation for a general tree-shaped network of vibrating strings. All exterior vertices are assumed to be fixed and interior vertices are imposed linear d...This paper discusses the asymptotic stability and Riesz basis generation for a general tree-shaped network of vibrating strings. All exterior vertices are assumed to be fixed and interior vertices are imposed linear damping feedbacks. This paper shows that the system is well-posed and asymptotically stable by C0-semigroup theory. With some additional conditions, the spectrum of the system is shown to be located in a strip that is parallel to the imaginary axis and the set of all generalized eigenfunctions is completed in the state space. These lead to the conclusion that there is a sequence of generalized eigenfunctions of the system, which forms a Riesz basis with parenthesis for the state space.展开更多
文摘This article is not inspired by any religion or quantum many-worlds interpretation. The mathematics of multiverse is presented here. The mass operator was introduced earlier by Alnobani. This operator is used here to deduce the time state. It is found that time has four states and those four states are orthogonal. Time is the constitution of any verse. Time has direction. Every orthogonal direction of time belongs to a verse. Past and future belong to opposite directions of time and they are arbitrary. Other verses are there by their own and not a probabilities of any other verse and if any similarity it is only a coincidence. Among applications of this thesis is travelling through groups of galaxies, or more or less.
文摘The generalized Virial theorem for mixed state, derived from the generalized Hellmann Feynman theorem, only applies to Hamiltonians in which potential of coordinates is separate from momentum energy term. In this paper we discuss Virial theorem for mixed state for some Hamiltonians with coordinate-momentum couplings in order to know their contributions to internal energy.
文摘It is known that certain one parameter families of unimodal maps of the interval have a topological universality with regard to their dynamic behavior [ 1, 2]. As a parameter is smoothly increased, a fascinating variety of dynamic behaviors are produced. For some families the behaviors are monotonic in the parameter, while in others they are not [3]. The question is what sort of conditions on a one parameter family will ensure this monotonicity of the behavior with the parameter？ The answer is unknown and will not be given here. What we do instead is to investigate certain geometric-dynamic-combinatorial consequences of assuming that the family has this monotonicity. Specifically, using tools of symbolic dynamics, state space is ＂course grained＂ with a finite alphabet. We decompose a non-invertible map into nonlinear but invertible pieces. From these invertible pieces, we form inverse maps via composition along words. Equations of motion are developed for both forward and inverse orbits （in both the variables of state space and the parameter）, and an equation relating forward and inverse motions at fix-points is exhibited. Finally, we deduce a list of conditions, each of which is equivalent to monotone behavior. One of these conditions states that simple parity characteristics of words correspond to definite dynamics near fixed-points and vice versa.
基金supported in part by the the National High Technology Research and Devel-opment Program of China(Grant No.2014AA01A701)National Natural Science Foundation of China(Grant No.61361166005)+2 种基金the State Major Science and Technology Special Projects(Grant No.2016ZX03001020006)the National Program for Support of Top-notch Young Pro-fessionalsthe Science and Technology Development Project of Beijing Municipal Education Commission of China(Grant No.KZ201511232036)
文摘In this paper, a quasi-Newton method fbr semi-blind estimation is derived for channel estimation in uplink cloud radio access networks （C-RANs）. Different from traditional pilot-aided estimation, semiblind estimation utilizes the unknown data symbols in addition to the known pilot symbols to estimate the channel. An initial channel state information （CSI） obtained by least-squared （LS） estimation is needed in semi-blind estimation. BFGS （Brayben, Fletcher, Goldfarb and Shanno） algorithm, which employs data as well as pilot symbols, estimates the CSI though solving the problem provided by maximum-likelihood （ML） principle. In addition, mean-square-error （MSE） used to evaluate the estimation performance can be further minimized with an optimal pilot design. Simulation results show that the semi-blind estimation achieves a significant improvement in terms of MSE performance over the conventional LS estimation by utilizing data symbols instead of increasing the number of pilot symbols, which demonstrates the estimation accuracy and spectral efficiency are both improved by semiblind estimation for C-RANs.
基金This research is supported in part by the Natural Science Foundation of China under Grant No. 60874035 and by the Scientific Research Initiation Foundation of Civil Aviation University of China （08QD09X）.
文摘This paper discusses the asymptotic stability and Riesz basis generation for a general tree-shaped network of vibrating strings. All exterior vertices are assumed to be fixed and interior vertices are imposed linear damping feedbacks. This paper shows that the system is well-posed and asymptotically stable by C0-semigroup theory. With some additional conditions, the spectrum of the system is shown to be located in a strip that is parallel to the imaginary axis and the set of all generalized eigenfunctions is completed in the state space. These lead to the conclusion that there is a sequence of generalized eigenfunctions of the system, which forms a Riesz basis with parenthesis for the state space.
