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Ground-0 Axioms *** Principles and Second Law:From the Geometry of Light and Logic of Photon to Mind-Light-Matter Unity-AI&QI

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IEEE/CAA Journal of Automatica Sinica 2021年第3期8卷 534-553页

作者： Wen-ran zhang Department of Computer Science Georgia Southern UniversityStatesboroGA 30460 USA

Without the geometry of light and logic of photon,observer-observability forms a paradox in modern science,truthequilibrium finds no unification,and mind-light-matter unity is unreachable in ***,quantum mechanics has been shrouded with mysteries preventing itself from reaching definable causality for a general purpose analytical quantum computing ***-0 Axioms are introduced as an equilibrium-based,dynamic,bipolar set-theoretic unification of the first principles of science and the second law of *** literatures are critically reviewed to justify the self-evident nature of Ground-0 Axioms.A historical misinterpretation by the founding fathers of quantum mechanics is identified and *** disproves spacetime geometries(including but not limited to Euclidean and Hilbert spaces)as the geometries of light and truth-based logics(including but not limited to bra-ket quantum logic)as the logics of *** with logically definable causality and Dirac 3-polarizer experiment,bipolar quantum geometry(BQG)and bipolar dynamic logic(BDL)are identified as the geometry of light and the logic of photon,respectively,and wave-particle complementarity is shown less fundamental than bipolar *** a result,Ground-0 Axioms lead to a geometrical and logical illumination of the quantum and classical worlds as well as the physical and mental *** logical resolutions to the EPR and Schr?dinger’s cat paradoxes,an analytical quantum computing paradigm named quantum intelligence(QI)is *** is shown that QI makes mind-light-matter unity and quantum-digital compatibility logically reachable for quantumneuro-fuzzy AI-machinery with groundbreaking *** is contended that Ground-0 Axioms open a new era of science and philosophy—the era of mind-light-matter unity in which humanlevel white-box AI&QI is logically prompted to join Einstein’s grand unification to foster major scientific advances.

关键词： Analytical quantum computing bipolar fuzzy sets bipolar quantum agents business intelligence cognitive neuroscience dynamic equilibrium Einstein-Bohr debate information conservational computing/cryptography computational psychiatry international relations logically definable causality quantum intelligence quantum-neuro-fuzzy AI human level AI&QI quantum superposition/entanglement white-box brain model

A WEAK GALERKIN MIXED FINITE ELEMENT METHOD FOR SECOND-ORDER ELLIPTIC EQUATIONS WITH ROBIN BOUNDARY CONDITIONS

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Journal of Computational Mathematics 2016年第5期34卷 532-548页

作者： Qian zhang ran zhang Department of Mathematics Jilin University Changchun China Applied and Computational Mathematics Division Beijing Computational Science Research Center Beijing China

In this paper, we present a weak Galerkin （WG） mixed finite element method for solving the second-order elliptic equations with Robin boundary conditions. Stability and a priori error estimates for the coupled method are derived. We present the optimal order error estimate for the WG-MFEM approximations in a norm that is related to the L^2 for the flux and H1 for the scalar function. Also an optimal order error estimate in L^2 is derived for the scalar approximation by using a duality argument. A series of numerical experiments is presented that verify our theoretical results.

关键词： Second-order elliptic equations Robin boundary conditions Weak Galerkin,Weak divergence.

FINITE ELEMENT AND DISCONTINUOUS GALERKIN METHOD FOR STOCHASTIC HELMHOLTZ EQUATION IN TWO-AND THREE-DIMENSIONS

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Journal of Computational Mathematics 2008年第5期26卷 702-715页

作者： Yanzhao Cao ran zhang Kai zhang Department of Mathematics Florida A&M University TaUahassee FL32307 USA Department of Mathematics Jilin University Changchun 130023 China

In this paper, we consider the finite element method and discontinuous Galerkin method for the stochastic Helmholtz equation in R^d （d = 2, 3）. Convergence analysis and error estimates are presented for the numerical solutions. The effects of the noises on the accuracy of the approximations are illustrated. Numerical experiments are carried out to verify our theoretical results.

关键词： Stochastic partial differential equation Finite element method Discontinuous Galerkin method Stochastic Helmholtz equation.

Temperature-dependent Raman spectroscopic study of ferroelastic K_2Sr(MoO_4)

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Chinese Physics B 2018年第11期27卷 591-595页

作者： Ji zhang De-Ming zhang ran-ran zhang An Hui Xin Hua University Hefei 230088 China Anhui Institute of Optics and Fine Mechanics Chinese Academy of Sciences Hefei 230031 China High Magnetic Field Laboratory of the Chinese Academy of Sciences Hefei 230031 China

Raman scattering measurements of K_2 Sr（MoO_4）2 were performed in the temperature range of 25–750？C. The Raman spectrum of the low-temperature phase α-K_2 Sr（MoO_4）2 that was obtained by first-principle calculations indicated that the Raman bands in the wavenumber region of 250–500 cm-1 are related to Mo–O bending vibrations in MoO4 tetrahedra,while the Raman bands in the wavenumber region of 650–950 cm-1 are attributed to stretching vibrations of Mo–O *** temperature-dependent Raman spectra reveal that K_2 Sr（MoO_4）2 exhibits two sets of modifications in the Raman spectra at ～ 150？C and ～ 475？C, attributed to structural phase transitions. The large change of the Raman spectra in the temperature range of 150？C to 475？C suggests structural instability of the medium-temperature phase β-K_2 Sr（MoO_4）2.

关键词： ferroelastics K2Sr(MoO4)2 crystal Raman spectroscopy phase transition

Fixed Points of Meromorphic Functions and of Their Differences,Divided Differences and Shifts

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Acta Mathematica Sinica,English Series 2016年第10期32卷 1189-1202页

作者： ran ran zhang Zong Xuan CHEN Department of Mathematics Guangdong University of Education School of Mathematical Sciences South China Normal University

Let f（z） be a finite order meromorphic function and let c ∈ C ／ {0} be a constant. If f（z） has a Borel exceptional value α∈ C, it is proved that max{τ（f（z））, τ（ △cf（z）） } = max{τ（f（z））, τ（f（z ＋ c））} = max{T（ τ（△cf（z））, τ（f（z ＋ c））} = σ（f（z））. If f（z） has a Borel exceptional value b ∈ （C ／ {0}） ∪ {∞}, it is proved that max{τ（f（z））,τ（△cf（z）/f（z）}=max（τ（△cf（z）/f（z））,τ（f（z＋c））}=σ（f（z））unless f（z） takes a special form. Here T（g（z）） denotes the exponent of convergence of fixed points of the meromorphic function g（z）, and a（g（z）） denotes the order of growth of g（z）.

关键词： Fixed point meromorphic function complex difference shift

Neighboring optimal guidance using higher-order dynamics approximation with application to orbital injection problem

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Chinese Journal of Aeronautics 2024年第5期37卷 426-440页

作者： Xinglun CHEN ran zhang Huifeng LI School of Astronautics Beihang UniversityBeijing 100191China

Neighboring optimal guidance,a method to obtain a suboptimal guidance law by approximately solving the first-order necessary conditions based on a nominal trajectory,is widely used in the aerospace field due to its high computational efficiency and low resource *** more advanced scenarios,the existing methods still have a problem that the guidance accuracy and optimality will seriously degrade when the actual state largely deviates from the nominal *** is mainly caused by the approximate description of the first-order conditions in terms of total flight time and nonlinear *** address this problem,a higher-order neighboring optimal guidance method is ***,a novel total flight time updating strategy,together with a normalized time scale,is presented that transforms the optimal problem with free total flight time into a more tractable optimal problem with fixed total flight ***,using the vector partial derivative method,a higher-order approximation is adopted,instead of the first-order approximation,to accurately describe the nonlinear dynamical and terminal constraints,thus obtaining a polynomially constrained quadratic optimal ***,to numerically solve the polynomially constrained quadratic optimal problem,a Newton-type iterative algorithm based on the orthogonal decomposition is *** the iterative solution within each guidance period,the corrections to control quantities and total flight time are *** proposed method is applied to a launch vehicle orbital injection problem,and simulation results show that it achieves high accuracy of orbital injection and optimality of performance index.

关键词： Optimal control Neighboring optimal guidance Launch vehicles Orbital injection Higher-order approximation

Model-free adaptive optimal design for trajectory tracking control of rocket-powered vehicle

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Chinese Journal of Aeronautics 2020年第6期33卷 1703-1716页

作者： Wenming NIE Huifeng LI ran zhang School of Astronautics Beihang UniversityBeijing 100083China Key Laboratory of Spacecraft Design Optimization and Dynamic Simulation Technologies Ministry of EducationBeijing 100083China

An adaptive optimal trajectory tracking controller is presented for the Solid-RocketPowered Vehicle(SRPV)with uncertain nonlinear non-affine dynamics in the framework of adaptive dynamic ***,considering that the ascent model of the SRPV is non-affine,a model-free Single Network Adaptive Critic(SNAC)method is developed based on the dynamic neural network and the traditional SNAC *** developed model-free SNAC method overcomes the limitation of the traditional SNAC method that can only be applied to affine ***,a closed-form adaptive optimal controller is designed for the non-affine dynamics of *** controller can adjust its parameters under different flight conditions and converge to the approximate optimal controller through online ***,the convergence to the approximate optimal controller is *** theoretical analysis of the uniformly ultimate boundedness of the tracking error is also *** results demonstrate the effectiveness of the proposed controller.

关键词： Adaptive dynamic programming Dynamic neural network Model-free Solid-rocket-powered vehicle Trajectory tracking

Dy_(2-x)Y_xTi_2O_7: phonon vibration and magnetization with dilution

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Rare Metals 2015年第2期34卷 81-88页

作者： Hui Liu You-Ming Zou Shi-Le zhang ran-ran zhang Chang-Jin zhang Yu-Heng zhang High Magnetic Field Laboratory Chinese Academy of Sciences and University of Science and Technology of China

In this paper, the dilution effects of non-magnetic Y ions on spin-ice compound Dy_2Ti_2O_7 by infrared and Raman spectra and magnetization measurements were investigated. An anomalous phonon softening with temperature decreasing is found in both the parent and diluted compounds, and Y doping can relax the softening of phonons except that of the IR mode near 233 cm^-1, indicating a strong phonon–phonon coupling in the spin-ice *** magnetization measurements reveal that the nonmagnetic impurities do not severely influence the spin-ice rules in the ground state when the level of dilution is not very high. However, a large amount of dilution enhance the disorder and break the spin-ice state because the collective spin-flip clusters are no longer available.

关键词： Dilution effect Spin ice Pyrochlore Frustration

A WEAK GALERKIN FINITE ELEMENT METHOD FOR THE LINEAR ELASTICITY PROBLEM IN MIXED FORM

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Journal of Computational Mathematics 2018年第4期36卷 469-491页

作者： Ruishu Wang ran zhang Department of Mathematics Jilin University Changchun 130012 China

In this paper, we use the weak Galerkin （WG） finite element method to solve the mixed form linear elasticity problem. In the mixed form, we get the discrete of proximation of the stress tensor and the displacement field. For the WG methods, we define the weak function and the weak differential operator in an optimal polynomial approximation spaces. The optimal error estimates are given and numerical results are presented to demonstrate the efficiency and the accuracy of the weak Galerkin finite element method.

关键词： Linear elasticity Mixed form Korn's inequality Weak Galerkin finite element method