A geometric interpretation of Hamilton’s Harnack inequality for the Ricci flow

Analytical and computer models of false failure and undetected failure (error functions) were developed with tolerance control of the parameters of the components of the measuring technique. A geometric interpretation of the error functions as two-dimensional surfaces is given, which depend on the tolerance on the controlled parameter and the measurement error. The developed models are applicable both to theoretical laws of distribution, and to arbitrary laws of distribution of the measured quantity and measurement error. The results can be used in the development of metrological support of measuring equipment, the verification of measuring instruments, the metrological examination of technical documentation and the certification of measurement methods.

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Canonical smoothing of compact Aleksandrov surfaces via Ricci flow

Annales Scientifiques de l École Normale Supérieure ◽

10.24033/asens.2356 ◽

2018 ◽

Vol 51 (2) ◽

pp. 263-279

Author(s):

Thomas Richard

Keyword(s):

Ricci Flow

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Ricci Flow on Quasi Einstein Manifold

Annals of the Alexandru Ioan Cuza University - Mathematics ◽

10.2478/v10157-010-0032-6 ◽

2010 ◽

Vol 0 (-1) ◽

pp. 447-454

Author(s):

A. Bhattacharyya ◽

T. De

Keyword(s):

Ricci Flow ◽

Einstein Manifold

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GEOMETRIC THEORY OF MULTIDIMENSIONAL INTERPOLATION

Automation and modeling in design and management of ◽

10.30987/2658-6436-2020-1-9-16 ◽

2020 ◽

Vol 2020 (1) ◽

pp. 9-16

Author(s):

Evgeniy Konopatskiy

Keyword(s):

Response Function ◽

Algebraic Curves ◽

Geometric Theory ◽

Analytical Description ◽

Geometric Interpretation ◽

Affine Geometry ◽

Mathematical Apparatus ◽

Multidimensional Interpolation ◽

Pass Through

The paper presents a geometric theory of multidimensional interpolation based on invariants of affine geometry. The analytical description of geometric interpolants is performed within the framework of the mathematical apparatus BN-calculation using algebraic curves that pass through preset points. A geometric interpretation of the interaction of parameters, factors, and the response function is presented, which makes it possible to generalize the geometric theory of multidimensional interpolation in the direction of increasing the dimension of space. The conceptual principles of forming the tree of the geometric interpolant model as a geometric basis for modeling multi-factor processes and phenomena are described.

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