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The combinatorics of green＇s functions in planar field theories

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Frontiers of physics 2016年第6期11卷 1-23页

作者： Kurusch Ebrahimi-Fard Frederic Patras ICMAT C/Nicolds Cabrera no. 13-15 28049 Madrid Spain. On leave from UHA Mulhouse France Univ. de Nice Labo. J-A. Dieudonnd UMR 7351 CNRS Parc Valrose 06108 Nice Cedex 02 France

The aim of this exposition is to provide a detailed description of the use of combinatorial algebra in quantum field theory in the planar setting. Particular emphasis is placed on the relations between different types of planar green’s functions. The primary object is a Hopf algebra that is naturally defined on variables representing non-commuting sources, and whose coproduct splits into two half-coproducts. The latter give rise to the notion of an unshuffle bialgebra. This setting allows a description of the relation between full and connected planar green’s functions to be given by solving a simple linear fixed point equation. We also include a brief outline of the consequences of our approach in the framework of ordinary quantum field theory.

关键词： planar field theory green’s functions free probability Hopf algebra shuffle algebra partitions

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ON sEVERAL ANALYTICAL THEORETICAL PROBLEMs OF THE sTRUCTURE AND DYNAMICs OF THE UPPER ATMOsPHERE (Ⅰ)——green’s functions, DIFFERENTIAL OPERATOR OF TIDEs, THREE-DIMENsIONAL sTRATIFIED MODEL AND DIFFUsION WAVEs OF THE THERMOsPHERE

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science in China,ser.A 1978年第5期 645-662页

作者：陈哲明

In this paper we have derived for the first time a new differential operator (differential operator of thermospheric tides), a set of new functions (green’s functions of the thermosphere, eigenfunctions of the differential operator of thermospheric tides) and a new type of atmospheric waves (the diffusion waves).By transforming the continuity and energy equations into two self-adjoint nonhomogeneous second-order differential equations, a new analytical solution of the thermospheric concentration and temperature variations and green’s functions of the thermosphere are *** the three dimensional problem, using the stratified model and the finite integral transform, we have obtained green’s functions for the vertically stratified thermosphere, and the differential operator of the thermospheric tides and its eigenfunctions. This new operator is a generalization of the well-known classical operator of spherical harmonic waves and the so-called Laplace differential operator of the atmospheric tides, wh

关键词： DIFFERENTIAL OPERATOR OF TIDEs green’s functions ON sEVERAL ANALYTICAL THEORETICAL PROBLEMs OF THE sTRUCTURE AND DYNAMICs OF THE UPPER ATMOsPHERE THREE-DIMENsIONAL sTRATIFIED MODEL AND DIFFUsION WAVEs OF THE THERMOsPHERE

Inverse Differential Operators in Time and space

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Journal of Applied Mathematics and Physics 2023年第12期11卷 3789-3799页

作者： Edwin Eugene Klingman Cybernetic Micro systems Inc. San Gregorio USA

When one function is defined as a differential operation on another function, it’s often desirable to invert the definition, to effectively “undo” the differentiation. A green’s function approach is often used to accomplish this, but variations on this theme exist, and we examine a few such variations. The mathematical analysis of is sought in the form if such an inverse operator exists, but physics is defined by both mathematical formula and ontological formalism, as I show for an example based on the Dirac equation. Finally, I contrast these “standard” approaches with a novel exact inverse operator for field equations.

关键词： Matrix-Inverse Differential Operators green’s functions Dirac’s Equation Wave Equations Inverse Curl Operator

A two-stage algorithm of adaptive model-based parameter estimation and its application in the fast calculation of green’s function in multi-layer soils

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Progress in Natural science:Materials International 2004年第10期 87-93页

作者： LEE Jae-bok Changwon641-600 Korea Electrotechnology Research Institute

A two-stage algorithm is presented to determine an analytical model-based rational function by adaptively selecting sam-pling *** the first stage,the rational interpolation function is created by using stoer-Bulirsch algorithm and comparing the fitted model with the different *** the second stage,the fitted model is validated by comparing with the first-principle model at a set of checking *** checking points will be added to the sampling series determined in the first stage to improve the fitted *** new proposed algorithm is more accurate and effective than that using stoer-Bulirsch interpolation only due to the fact that it appends the validation *** a highly oscillating curve is approximated,the validation ensures the fitting *** the two-stage MBPE algorithm,some time-consuming electromagnetic computations can be replaced by the interpolation from the fitting functions,which can increase the computational efficiency *** method is used to calculate the samplings of the green’s functions in a multi-layer horizontal soil to demonstrate its *** number of samples used to accurately model such green’s functions is less than20for the typical soil *** computational time can be reduced by more than two orders of magnitude compared with that using the conventional uniform sampling technology.

关键词： model-based parameter estimation adaptive sampling multi-layer soil green’s functions

Modeling of Atmospheric Gravity Effects for High-Precision Observations

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International Journal of Geosciences 2013年第4期4卷 663-671页

作者： Olga Gitlein Ludger Timmen Jürgen Müller Institut für Erdmessung Leibniz Universitat HannoverHannoverGermany

Temporal variations of atmospheric density distribution induce changes in the gravitational air mass attraction at a specific observation site. Additionally, the load of the atmospheric masses deforms the Earth’s crust and the sea surface. Variations in the local gravity acceleration and atmospheric pressure are known to be corrected with an admittance of about 3 nm/s2 per hPa as a standard factor, which is in accordance with the IAG Resolution No. 9, 1983. A more accurate admittance factor for a gravity station is varying with time and depends on the total global mass distribution within the atmosphere. The Institut für Erdmessung (IfE) performed absolute gravity observations in the Fennoscandian land uplift area nearly every year from 2003 to 2008. The objective is to ensure a reduction with 3 nm/s2 accuracy. Therefore, atmospheric gravity changes are modeled using globally distributed ECMWF data. The attraction effect from the local zone around the gravity station is calculated with ECMWF 3D weather data describing different pressure levels up to a height of 50 km. To model the regional and global attraction, and all deformation components the green’s functions method and surface ECMWF 2D weather data are used. For the annually performed absolute gravimetry determinations, this approach improved the reductions by 8 nm/s2 (-19 nm/s2 to +4 nm/s2). The gravity modeling was verified using superconducting gravimeter data at station Membach inBelgiumimproving the residuals by about 15%.

关键词： Atmospheric Reduction green’s functions ECMWF Absolute Gravimetry superconducting Gravimeter