Erratum: Decay of passive scalars under the action of single scale smooth velocity fields in bounded two-dimensional domains: From non-self-similar probability distribution functions to self-similar eigenmodes [Phys. Rev. E66, 056302 (2002)]

2003 ◽  
Vol 68 (1) ◽  
Author(s):  
Jai Sukhatme ◽  
Raymond T. Pierrehumbert
Keyword(s):  
Probability Distribution ◽  
Velocity Fields ◽  
Distribution Functions ◽  
Two Dimensional ◽  
Passive Scalars ◽  
Probability Distribution Functions ◽  
Single Scale ◽  
Self Similar

Probabilistic Nodes Combination

2012 ◽  
Vol 3 (3) ◽  
pp. 22-35
Author(s):  
Dariusz Jakóbczak
Keyword(s):  
Probability Distribution ◽  
Orthogonal Matrix ◽  
Distribution Functions ◽  
Two Dimensional ◽  
Curve Reconstruction ◽  
Probability Distribution Functions ◽  
Key Points ◽  
The Family ◽  
Curve Interpolation ◽  
Inverse Functions

Mathematics and computer science are interested in methods of 2D curve interpolation and extrapolation using the set of key points (knots or nodes). Proposed method, called by author Probabilistic Nodes Combination (PNC), is such a method. This novel PNC method is introduced in the case of Hurwitz- Radon Matrices (MHR). MHR method is based on the family of Hurwitz-Radon (HR) matrices which possess columns composed of orthogonal vectors. Two-dimensional curve is modeled and interpolated via different functions as probability distribution functions: polynomial, sinus, cosine, tangent, cotangent, logarithm, exponent, arcsin, arccos, arctan, arcctg or power function, also inverse functions. It is shown how to build the orthogonal matrix operator and how to use it in a process of curve reconstruction.

Extended two-dimensional belief function based on divergence measurement

2020 ◽  
pp. 1-8
Author(s):  
Jianping Fan ◽  
Jing Wang ◽  
Meiqin Wu
Keyword(s):  
Belief Function ◽  
Distribution Functions ◽  
Divergence Measure ◽  
Uncertain Information ◽  
Belief Functions ◽  
Two Dimensional ◽  
Probability Distribution Functions ◽  
Basic Probability ◽  
The Difference ◽  
Supporting Degree

The two-dimensional belief function (TDBF = (mA, mB)) uses a pair of ordered basic probability distribution functions to describe and process uncertain information. Among them, mB includes support degree, non-support degree and reliability unmeasured degree of mA. So it is more abundant and reasonable than the traditional discount coefficient and expresses the evaluation value of experts. However, only considering that the expert’s assessment is single and one-sided, we also need to consider the influence between the belief function itself. The difference in belief function can measure the difference between two belief functions, based on which the supporting degree, non-supporting degree and unmeasured degree of reliability of the evidence are calculated. Based on the divergence measure of belief function, this paper proposes an extended two-dimensional belief function, which can solve some evidence conflict problems and is more objective and better solve a class of problems that TDBF cannot handle. Finally, numerical examples illustrate its effectiveness and rationality.

Probability Distribution Functions for the Random Forced Burgers Equation

1997 ◽  
Vol 78 (10) ◽  
pp. 1904-1907 ◽  
Author(s):  
Weinan E ◽  
Konstantin Khanin ◽  
Alexandre Mazel ◽  
Yakov Sinai
Keyword(s):  
Probability Distribution ◽  
Burgers Equation ◽  
Distribution Functions ◽  
Probability Distribution Functions
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