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Journal of Applied Mathematics and Physics 2023年第3期11卷 721-736页

作者： Dan Liu Bill school of Physics Neijiang Normal University Neijiang China American Mathematical Physics studies Manchester USA

In quantum mechanics, there are two very famous formulas. One is the energy formula of the bose particle, called planck’s law. The other is the wavelength formula, which is called the de Broy wavelength. According to Einstein’s mass-energy equation, we have studied planck’s law and De Bloy’s wavelength, and generalized it to the De Bloy’s wavelength formula from low speed to light speed. Then, on this basis, the smallest particle is defined as mass quantum. The new wavelength formula is obtained from the mass quantum and converted into the frequency formula. The generalized planck’s law is obtained.

关键词： Quantum Mechanics planck’s law Einstein’s Mass and Energy Equation Debroy Wavelength Generalized planck’s law

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Zipf’s law, Benford’s law, and Pareto Rule

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Advances in Pure Mathematics 2023年第3期13卷 174-180页

作者： Oded Kafri Kafri Nihul Ltd. Tel Aviv Israel

From a basic probabilistic argumentation, the Zipfian distribution and Benford’s law are derived. It is argued that Zipf’s law fits to calculate the rank probabilities of identical indistinguishable objects and that Benford’s distribution fits to calculate the rank probabilities of distinguishable objects. i.e. in the distribution of words in long texts all the words in a given rank are identical, therefore, the rank distribution is Zipfian. In logarithmic tables, the objects with identical 1st digits are distinguishable as there are many different digits in the 2nd, 3rd… places, etc., and therefore the distribution is according to Benford’s law. Pareto 20 - 80 rule is shown to be an outcome of Benford’s distribution as when the number of ranks is about 10 the probability of 20% of the high probability ranks is equal to the probability of the rest of 80% low probability ranks. It is argued that all these distributions, including the central limit theorem, are outcomes of planck’s law and are the result of the quantization of energy. This argumentation may be considered a physical origin of probability.

关键词： Zipf’s law Benford’s law Pareto 20 - 80 Rule planck’s law Max Entropy

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A Novel Approach to Probability

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Advances in Pure Mathematics 2016年第4期6卷 201-211页

作者： Oded Kafri Kafri Nihul Ltd. Tel Aviv Israel

When P indistinguishable balls are randomly distributed among L distinguishable boxes, and considering the dense system , our natural intuition tells us that the box with the average number of balls P/L has the highest probability and that none of boxes are empty;however in reality, the probability of the empty box is always the highest. This fact is with contradistinction to sparse system (i.e. energy distribution in gas) in which the average value has the highest probability. Here we show that when we postulate the requirement that all possible configurations of balls in the boxes have equal probabilities, a realistic “long tail” distribution is obtained. This formalism when applied for sparse systems converges to distributions in which the average is preferred. We calculate some of the distributions resulted from this postulate and obtain most of the known distributions in nature, namely: Zipf’s law, Benford’s law, particles energy distributions, and more. Further generalization of this novel approach yields not only much better predictions for elections, polls, market share distribution among competing companies and so forth, but also a compelling probabilistic explanation for planck’s famous empirical finding that the energy of a photon is hv.

关键词： Probability statistics Benford’s law Zipf’s law planck’s law Configurational Entropy

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study the Performance and Analyze the Uncertainty of 1.6 m Irradiation Thermometer

Study the Performance and Analyze the Uncertainty of 1.6 m I...

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Measurement Touch the World——IEEE 2011 10th International Conference on Electronic Measurement & Instruments(ICEMI’2011)

作者： Ye Zikui 1 2 Hao Xiaopeng 2 Yuan Zundong 2 Yang Jian 1 1 College of Applied Nuclear Technology and Automation Engineering Chengdu University of Technology Chengdu610059 China Division of Thermometry and Materials Evaluation National Institute of Metrology P.R.China Beijing100013 China

An irradiation thermometer with 1.6 m center wavelength was established at National Institute of Metrology P.R.China,temperature range of which is from 420 to 1085.This paper introduces the measurement principle,structure and calibration method of irradiation thermometer,the stability of the irradiation thermometer,the noise equivalent temperature difference （NETD） of the thermometer at Zn fixed point and the expanded uncertainty at Zn,Al and Cu fixed points.The stability is 0.05,0.07 and 0.05 during four months at Zn,Al and Cu fixed points,respectively.The value of the NETD including 16 times measurement results is lower than 25 mk at freezing platform of Zn fixed point.The expanded uncertainty of the irradiation thermometer is 0.24,0.26,and 0.22 at Zn,Al and Cu fixed points,respectively.

关键词： Radiation thermometry planck’s law irradiation thermometer Calibration methods,NETD uncertainty

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spectral-based Inferential Measurement of Grey-body's Temperature

Spectral-based Inferential Measurement of Grey-body's Temper...

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国防光电子论坛第二届新型探测技术及其应用研讨会

作者： Feng Zheng Liying Liu Lingxi Zhu Kewei Huan Ye Li Xiaoguang,shi Faculty of science Changchun University of Science and Technology

Aiming at the problems of temperature measurement and the defects of radiance thermometry theory, one method of spectral-based inferential measurement is proposed, which adopts the Empirical Risk Minimization(ERM) functional model as the temperature measurement model. Then, the radiance thermometry theory and inferential measurement technology are discussed comparatively. Temperatures of some targets, such as tungsten lamp and solar surface, are measured by spectral-based inferential measurement.

关键词： Inferential measurement Temperature Grey-body planck’s law

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