From the definition of the dot product, we know that we can find the projection of a vector r onto a unit vector by computing the dot product of r and . The dot product is a projection operator for vectors that maps a vector r onto its component in the direction of . We ca...
Nonetheless, some objections have been raised against such a dynamic approach, especially against its practical complexity and the lack of a clear definition of the domain of its applicability. In this paper, an attempt to define more precisely the field of application for a dynamic approach is ...
A linear visco-elasticity ansatz for the multiphase-field method is introduced in the form of a Maxwell-Wiechert model. The implementation follows the idea of solving the mechanical jump conditions in the diffuse interface regions, hence the continuous traction condition and Hadamard’s compatibility c...
In the context of industrial design, the Quantities of Interest (QoI) are used to determine whether the chosen technological solution meets the functional requirements. A performance criterion generally referred to as an objective function\(\mathcal {J}(\varvec{\chi })\)can be evaluated at the...
A conditional performance measure for a stochastic system is, by definition, the mean of a sequence of stationary observations conditioned on the occurrence of a particular event or system state. (For example, the mean waiting times of customers in each priority class in a priority queueing ...
AI generated definition based on: Systems Biomedicine, 2010 About this pageSet alert Also in subject areas: Computer Science Materials ScienceDiscover other topics On this page Definition Chapters and Articles Related Terms Recommended Publications Chapters and Articles You might find these chapters and ...
In this section, we provide a general overview of the vortical structures that develop around the Flettner rotor. Although an unequivocal definition for the minimal turbulent unit as the vortex does not yet exist35, to identify organised and coherent flow structures, the λ2-criterion proposed by...
Also, due to the definition of the objective function, they exhibit low constraint violations. Consequently, these designs reside in the vicinity of the boundary Xb of the feasible region. Based on {xc(j)}, we will set up the domain of the surrogate model to be employed for global search...
‘simplex gradients’ is shown. The definition of when a problem is ‘solved’ may vary—when the true global optimum is known, the solutions found within a certain tolerance of this optimal value may be called solutions, but when this optimum is not known, the solvers that find the best ...
We give a new proof of the existence of $$O(n^{\epsilon })$$ -round public-coin concurrent zero-knowledge arguments for $$\mathcal {NP}$$ , where $$\epsilo