Weak formulations are important tools for the analysis of mathematical equations that permit the transfer of concepts of linear algebra to solve problems...

equation show up (the new form is called the weak formulation, and the solutions to it are called weak solutions). Somewhat surprisingly, a differential...

continuous operator problem, such as a differential equation, commonly in a weak formulation, to a discrete problem by applying linear constraints determined by...

computer. The first step is to convert P1 and P2 into their equivalent weak formulations. If u {\displaystyle u} solves P1, then for any smooth function v...

In number theory, Goldbach's weak conjecture, also known as the odd Goldbach conjecture, the ternary Goldbach problem, or the 3-primes problem, is the...

streamline upwind Petrov–Galerkin pressure-stabilizing Petrov–Galerkin formulation for incompressible Navier–Stokes equations can be used for finite element...

methods, where the so-called weakened weak (W2) formulation based on the G space theory were developed. The W2 formulation offers possibilities for formulate...

functional. The functional Φ {\displaystyle \Phi } is said to satisfy the weak Palais–Smale condition if for each sequence { x n } ⊂ X {\displaystyle \{x_{n}\}\subset...

Weak form and strong form may refer to: Weaker and stronger versions of a hypothesis, theorem or physical law Weak formulations and strong formulations...

condition of extremum (functional derivative equal zero) appears in a weak formulation (variational form) integrated with an arbitrary function δf. The fundamental...

u ∈ U such that Λ u = f . {\displaystyle \Lambda u=f.} However, in the weak formulation, this equation is only required to hold when "tested" against all other...

consider a generalized solution (known as a weak solution) by enlarging the class of functions. Many weak formulations involve the class of Sobolev functions...

introduced as follows. Let us consider an abstract problem posed as a weak formulation on a pair of Hilbert spaces V {\displaystyle V} and W {\displaystyle...

Helmholtz theorem. However, the compactness restriction in the usual formulation of the Hodge decomposition can be replaced by suitable decay assumptions...

optimization, the fundamental theorem of linear programming states, in a weak formulation, that the maxima and minima of a linear function over a convex polygonal...

based primarily on the judicious choice of test functions in the weak formulation of partial differential equations, is in strong contrast to Nash's...

{\displaystyle X} and X ∗ {\displaystyle X^{*}} are endowed with strong topology and weak* topology respectively. There exists r > 0 {\displaystyle r>0} such that...

plausible: weak formulations (which hold that precaution in the face of uncertain harms is permissible) are trivial, while strong formulations (which hold...

_{\Gamma _{N}}\mathbf {h} \cdot \mathbf {v} .} Having this in mind, the weak formulation of the Navier–Stokes equations is expressed as: find  u ∈ L 2 ( R +...

law, which had previously been proved in weaker formulations by many other authors. In Tao and Vu's formulation, the circular law becomes an immediate consequence...

{W}}=[L^{2}(\Omega )]^{3}} be two generic test functions. To obtain the weak formulation: multiply by p ∈ U {\displaystyle p\in U} the first equation of the...

The path integral formulation is a description in quantum mechanics that generalizes the stationary action principle of classical mechanics. It replaces...

the resulting Z0 and γ0 likewise have zero weak isospin. Weak hypercharge Weak charge Mathematical formulation of the Standard Model Glashow, Sheldon L...

applying a greedy algorithm, usually the fixed point algorithm, to the weak formulation of the problem. For each iteration i of the algorithm, a mode of the...

equation Helmholtz equation Uniqueness theorem for Poisson's equation Weak formulation Harmonic function Heat equation Potential theory Jackson, Julia A.;...

least 21 formulations of Mach's principle are possible, some being considered more strongly Machian than others.: 530  A relatively weak formulation is the...

mathematical problem (the partial differential equation) to be cast in a weak formulation. This is typically done by multiplying the differential equation by...

a non-Lipschitz surface. One (advanced) technique is to pass to a weak formulation and then apply the machinery of geometric measure theory; for that...

both lepton number and baryon number. Standard Model (mathematical formulation) Weak charge Donoghue, J.F.; Golowich, E.; Holstein, B.R. (1994). Dynamics...

recursive majority gate formulation), and Yoav Freund (boost by majority), were not adaptive and could not take full advantage of the weak learners. Schapire...