Search results
Results from the WOW.Com Content Network
As Valtr (1998) showed, the set system derived from an art gallery problem has bounded VC dimension, allowing the application of set cover algorithms based on ε-nets whose approximation ratio is the logarithm of the optimal number of guards rather than of the number of polygon vertices. [12]
A particular problem in the area of liquid-state thermodynamics is the sourcing of reliable thermodynamic constants. These constants are necessary for the successful prediction of the free energy state of the system; without this information it is impossible to model the equilibrium phases of the system.
The primary difference between a computer algebra system and a traditional calculator is the ability to deal with equations symbolically rather than numerically. The precise uses and capabilities of these systems differ greatly from one system to another, yet their purpose remains the same: manipulation of symbolic equations.
An adjoint state equation is introduced, including a new unknown variable. The adjoint method formulates the gradient of a function towards its parameters in a constraint optimization form. By using the dual form of this constraint optimization problem, it can be used to calculate the gradient very fast.
If an equation can be put into the form f(x) = x, and a solution x is an attractive fixed point of the function f, then one may begin with a point x 1 in the basin of attraction of x, and let x n+1 = f(x n) for n ≥ 1, and the sequence {x n} n ≥ 1 will converge to the solution x.
Rouquerol et al. [6] suggested a procedure that is based on two criteria: C must be positive implying that any negative intercept on the BET plot indicates that one is outside the valid range of the BET equation. Application of the BET equation must be limited to the range where the term V(1-P/P 0) continuously increases with P/P 0.
In statistics, efficiency is a measure of quality of an estimator, of an experimental design, [1] or of a hypothesis testing procedure. [2] Essentially, a more efficient estimator needs fewer input data or observations than a less efficient one to achieve the Cramér–Rao bound.
Hydraulic jump in a rectangular channel, also known as classical jump, is a natural phenomenon that occurs whenever flow changes from supercritical to subcritical flow. In this transition, the water surface rises abruptly, surface rollers are formed, intense mixing occurs, air is entrained, and often a large amount of energy is dissipated.