In non-digital projection systems, the inaccuracy of phase shifts is one of the most important nonlinear errors. In this paper, an efficient and universal compensation algorithm is proposed, which does not need to fin...
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In non-digital projection systems, the inaccuracy of phase shifts is one of the most important nonlinear errors. In this paper, an efficient and universal compensation algorithm is proposed, which does not need to find the exact phase shift amounts, but to compensate the periodical errors by a universal two-coefficient error model. With this model, only two error coefficients should to be searched for any multi-step phase shift algorithm. To find the error coefficients, a correlation process and a tool known as the probability density function (PDF) are used. First, a set of pre-simulated PDF curves are generated with the different error coefficients. Second, a practical PDF curve from captured fringes is calculated. Finally, the correlation process is carried out to locate the most similar simulated PDF curve, whose error coefficients are the practical ones. In this paper, we demonstrate the compensation for three, four and five-step phase-shifting algorithms separately. Experimental results show that this method has high universality, and can meet the requirements of rapid and high accuracy measurement.
In this paper, we study a three-dimensional stochastic vegetation-water model in arid ecosystems, where the soil water and the surface water are considered. First, for the deterministic model, the possible equilibria ...
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In this paper, we study a three-dimensional stochastic vegetation-water model in arid ecosystems, where the soil water and the surface water are considered. First, for the deterministic model, the possible equilibria and the related local asymptotic stability are studied. Then, for the stochastic model, by constructing some suitable stochastic Lyapunov functions, we establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution (omega) over bar (.). In a biological interpretation, the existence of the distribution (omega) over bar (.) implies the long-term persistence of vegetation under certain conditions. Taking the stochasticity into account, a quasi-positive equilibrium (D) over bar* related to the vegetation-positive equilibrium of the deterministic model is defined. By solving the relevant Fokker-Planck equation, we obtain the approximate expression of the distribution (omega) over bar (.) around the equilibrium (D) over bar*. In addition, we obtain sufficient condition R-0(E)< 1 for vegetation extinction. For practical application, we further estimate the probability of vegetation extinction at a given time. Finally, based on some actual vegetation data from Wuwei in China and Sahel, some numerical simulations are provided to verify our theoretical results and study the impact of stochastic noise on vegetation dynamics.
Stochastic resetting is a rapidly developing topic in the field of stochastic processes and their applications. It denotes the occasional reset of a diffusing particle to its starting point and effects, inter alia, op...
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The probability density functions of proton, anti-proton, and net-proton multiplicity distributions are constructed from the Beam Energy Scan results of the STAR experiment using the Pearson curve method. The construc...
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The probability density functions of proton, anti-proton, and net-proton multiplicity distributions are constructed from the Beam Energy Scan results of the STAR experiment using the Pearson curve method. The constructed distributions of proton and anti-proton are compared with Poisson and Binomial distributions. The net-proton probability distributions are compared with Skellam distributions to study the O(4) criticality near the chiral crossover transition. The C-6/C-2 results estimated from the obtained PDFs are compared with Skellam and Binomial baselines for the Beam Energy Scan data. The current study shows some signatures of O(4) criticality, which can be further investigated by precision measurements of the cumulants and understanding the contribution of non-critical fluctuations to them. This study also provides a baseline for the higher order cumulant measurement in the upcoming RHIC BES II program and future LHC run.
This paper presents a research study focused on uncovering the hidden population distribution from the viewpoint of a variational non-Bayesian approach. It asserts that if the hidden probability density function (PDF)...
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In this study, an analytical method for fast spectral fatigue-life prediction under Broad-Band random loading is proposed. It is based on the power spectral density of stress in the structure and the Rice peak stress ...
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In this study, an analytical method for fast spectral fatigue-life prediction under Broad-Band random loading is proposed. It is based on the power spectral density of stress in the structure and the Rice peak stress distribution of a stationary Gaussian random process. The novel simple closed-form solution employs special HyperGeometric function which analytically describes the transcendent error weighting function between the Gaussian and Rayleigh distributions inherent in the Rice model. HyperGeometric-based solution outperforms other currently existing approximate methods based on the Rice peak distribution, e.g. Chaudhury, Kam, Dover, Chow and Lee, Lu et al. etc. Straightforward computational applicability and fast engineering implementation of obtained general closed-form results is accented throughout the investigation.
This work deals with a new version of the probabilistic transformation method (PTM). In particular, it aims to report a new version of the PTM able to treat those systems in which input and output variables are linked...
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This work deals with a new version of the probabilistic transformation method (PTM). In particular, it aims to report a new version of the PTM able to treat those systems in which input and output variables are linked with each other by means of non-bijective transformations. The formulation proposed allows to derive firstly the characteristic function (CF) of any response element in a very simple way without any kind of saturation;secondly, it allows to evaluate the probability density function (PDF) using the inverse Fourier transform. The work presents a brief overview of the classical version of the PTM and the new theoretical aspects are rigorously justified with extensive use of distributions;a numerical application is performed to verify the reliability of the proposed approach. (C) 2021 Elsevier B.V. All rights reserved.
Random processes play a crucial role in scientific research, often characterized by distribution functions or probability density functions (PDFs). These PDFs serve as essential approximations of the actual and freque...
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The probability density function of the arrival time of Čerenkov light on a photo-multiplier tube has been studied. This study covers light production, transmission and detection. The light production includes the lig...
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We propose that the square root of a probability density function can be represented as a linear combination of Gaussian kernels. It is shown that if the Gaussian kernel centres and kernel width are known, then the ma...
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