Toward infinite‐dimensional Clifford analysis

Bernstein, Swanhild

doi:10.1002/mma.8291

Cited by 2 publications

(3 citation statements)

References 25 publications

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“…Air parameters: initial pressure 𝑝 , initial density 𝜌 ; 3. Soil parameters: soil density 𝜌 , soil elastic modulus 𝐸, sound velocity 𝑐; Geometric parameters: distance between explosion center 𝑅, height 𝐻 from explosion center to seismic measuring point [24,25].…”

Section: Particle Vibration Acceleration Functional Relationship Modelmentioning

confidence: 99%

Analysis of the ammunition explosion seismic wave propagation law

Shang,

Wang

2023

J. vibroeng.

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The seismic wave generated in the ammunition explosion process is one of the important technical indicators to evaluate the ammunition damage power. It is of great significance to evaluate the ammunition damage power and study the targets damage characteristics. In this study, experimental studies were carried out with TNT explosive mass of 1.25 kg, 5.25 kg, 10.5 kg and 30.75 kg, and the ground vibration velocity time-history curves at different measuring points were obtained. The functional relationship between ground particle vibration acceleration and TNT explosive mass was established by dimensional analysis method, and the functional relationship calculation accuracy was verified by the measured test data. The results show that the particle vibration acceleration peak value is positively correlated with the TNT explosive mass, and negatively correlated with the measuring point distance; The particle vibration acceleration calculation function established by the dimensional analysis method has high fitting accuracy for the existing test data, and can be used to calculate the ammunition explosion ground vibration acceleration peak value. The research results provide a high-precision calculation method for the peak value of explosion seismic wave ground vibration acceleration.

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Section: Particle Vibration Acceleration Functional Relationship Modelmentioning

confidence: 99%

Analysis of the ammunition explosion seismic wave propagation law

Shang,

Wang

2023

J. vibroeng.

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“…Especially, a probability space, random variables, and stochastic process will be introduced. Some of the results presented in this section are built upon extending the work [7], where first steps towards stochastic Clifford analysis have been made. The final goal of this section is to introduce martingales in the Clifford setting.…”

Section: Random Variables Stochastic Processes and Martingales In The...mentioning

confidence: 99%

“…Further ideas on generalising stochastic calculus to Clifford analysis have been presented in [7], where, among other results, Clifford random variables, Clifford white noise, and Clifford chaos expansion with the help of Hermite polynomials have been introduced. In this paper, we further extend and refine the results from [7] by discussing martingales, Brownian motion, and Itô formula in the Clifford setting. This way, we broaden ideas from [13,14,24] on complex Brownian motion and the Itô formula to the hypercomplex setting.…”

Section: Introductionmentioning

confidence: 99%

Brownian Motion, Martingales and Itô Formula in Clifford Analysis

Bernstein

Legatiuk

2022

Adv. Appl. Clifford Algebras

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Clifford analysis has been the field of active research for several decades resulting in various methods to solve problems in pure and applied mathematics. However, the area of stochastic analysis has not been addressed in its full generality in the Clifford setting, since only a few contributions have been presented so far. Considering that the tools of stochastic analysis play an important role in the study of objects, such as positive definite functions, reproducing kernels and partial differential equations, it is important to develop tools for the study of these objects in the context of Clifford analysis. Therefore, in this work-in-progress paper, we present further steps towards stochastic Clifford analysis by studying random variables, martingales, Brownian motion, and Itô formula in the Clifford setting, as well as their applications in Clifford analysis.

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Toward infinite‐dimensional Clifford analysis

Cited by 2 publications

References 25 publications

Analysis of the ammunition explosion seismic wave propagation law

Analysis of the ammunition explosion seismic wave propagation law

Brownian Motion, Martingales and Itô Formula in Clifford Analysis

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