On the theory of divergence-measure fields and its applications

2001 ◽  
Vol 32 (3) ◽  
pp. 401-433 ◽  
Author(s):  
Gui-Qiang Chen ◽  
Hermano Frid
Keyword(s):  
Divergence Measure

Information content of the determinations of the amount of an analyte

1988 ◽  
Vol 53 (12) ◽  
pp. 3021-3028 ◽  
Author(s):  
Karel Eckschlager ◽  
Jiří Fusek
Keyword(s):  
Reference Material ◽  
Information Content ◽  
Analytical Method ◽  
Analytical Signal ◽  
Divergence Measure ◽  
Analytical Results

It is shown how the information content expressed in terms of the extended divergence measure I(r; p, p0) depends on the amount of the component to be determined when homoscedastic and heteroscedastic dependences of the analytical signal on the amount of the analyte are distinguished. The importance of the accuracy is pointed out, with which the amount of the analyte is known in a reference material employed for testing a particular analytical method. Rules are set, the maintaining of which is aimed at avoiding the origin of null information content of analytical results.

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.

scholarly journals Pairings between bounded divergence-measure vector fields and BV functions

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Graziano Crasta ◽  
Virginia De Cicco ◽  
Annalisa Malusa
Keyword(s):  
Vector Field ◽  
Conservation Laws ◽  
Bounded Variation ◽  
Vector Fields ◽  
Hyperbolic Conservation Laws ◽  
Divergence Measure ◽  
Compensated Compactness ◽  
Hyperbolic Conservation ◽  
Bv Functions ◽  
Bounded Functions

AbstractWe introduce a family of pairings between a bounded divergence-measure vector field and a function u of bounded variation, depending on the choice of the pointwise representative of u. We prove that these pairings inherit from the standard one, introduced in [G. Anzellotti, Pairings between measures and bounded functions and compensated compactness, Ann. Mat. Pura Appl. (4) 135 1983, 293–318], [G.-Q. Chen and H. Frid, Divergence-measure fields and hyperbolic conservation laws, Arch. Ration. Mech. Anal. 147 1999, 2, 89–118], all the main properties and features (e.g. coarea, Leibniz, and Gauss–Green formulas). We also characterize the pairings making the corresponding functionals semicontinuous with respect to the strict convergence in \mathrm{BV}. We remark that the standard pairing in general does not share this property.

scholarly journals Rigidity and trace properties of divergence-measure vector fields

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Gian Paolo Leonardi ◽  
Giorgio Saracco
Keyword(s):  
Vector Fields ◽  
Extremal Solution ◽  
Divergence Measure ◽  
Higher Dimension ◽  
Regular Domain ◽  
Curvature Equation ◽  
Mean Curvature Equation ◽  
Divergence Free Vector ◽  
Prescribed Mean Curvature Equation ◽  
Rigidity Property

AbstractWe consider a φ-rigidity property for divergence-free vector fields in the Euclidean n-space, where {\varphi(t)} is a non-negative convex function vanishing only at {t=0}. We show that this property is always satisfied in dimension {n=2}, while in higher dimension it requires some further restriction on φ. In particular, we exhibit counterexamples to quadratic rigidity (i.e. when {\varphi(t)=ct^{2}}) in dimension {n\geq 4}. The validity of the quadratic rigidity, which we prove in dimension {n=2}, implies the existence of the trace of a divergence-measure vector field ξ on an {\mathcal{H}^{1}}-rectifiable set S, as soon as its weak normal trace {[\xi\cdot\nu_{S}]} is maximal on S. As an application, we deduce that the graph of an extremal solution to the prescribed mean curvature equation in a weakly-regular domain becomes vertical near the boundary in a pointwise sense.

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