The original frequency-amplitude formulation reads ω 2 = ω 1 2 R 2 t − ω 2 2 R 1 t R 2 − R 1. Open image in new window (19).
A better formulation reads as follows: Maximize the number of multiply covered proteins in a valid covering of all proteins, by using a fixed number of epitopes.
With the Hilbert space H ≔ { τ ∈ H (div, Ω ; R d × d ) : ∫ Ω tr d x = 0 } for the stresses, the mixed weak formulation reads ∫ Ω (σ : dev τ + u ⋅ div τ ) d x = 0 for all τ ∈ H, ∫ Ω v ⋅ div σ d x = − ∫ Ω v ⋅ f d x for all v ∈ L 2 (Ω ; R d ).
Stated in terms of choice functions, Zermelo's first formulation of AC reads: AC1: Any collection of nonempty sets has a choice function.
The weak formulation of (3) reads ∫ Ω ( div u ¯ ) q − ∫ Ω 1 λ p q = 0 for every q ∈ Q. (4).
Then the weak formulation of (1) reads as follows: find (uin H_{0}^{1}(Omega)) such that B u,v):=int_{Omega}a x,y nabla ucdotnabla v,dx,dy=int_{Omega}fv,dx,dy= f,v), quad forall vin H_{0}^{1}(Omega).
(2) A classical variational formulation of (1) reads as follows: find (lambda, psi inmathbb{R}times V) such that int_{varOmega }varDelta psi varDelta chi dvarOmega =lambda int_{varOmega } (boldsymbol{sigma} nablapsi) cdotnablachi, d varOmega, quad forall chiin V. (3) It is immediate to prove that the eigenvalues of the above problem are real and positive whenever σ is positive definite.
Introducing the bilinear form a and the linear form f as (15) a (u, v ) = ∫ Ω A ∇ u · ∇ vdx, f (v ) = ∫ Ω fvdx, the Galerkin formulation of this problem reads: Find u h ∈ V h 0 such that (16) a (u h, v h ) = f (v h ) for all v h ∈ V h 0. It is well known that (16) is a well-posed problem and has a unique solution.
The mathematical formulation of the CLE reads as (1) [ K ∼ T + (λ j ∗ - λ ) K ∼ ˙ T ] · v j ∗ = 0, j = 1, 2, 3, …, N, where K ∼ T denotes the tangent stiffness matrix of a structure in the frame of FEM, evaluated along the primary path; (2) K ∼ ˙ T ≔ d K ∼ T d λ, where λ stands for a dimensionless load factor; (λ j ∗ - λ, v j ∗ ) is the j-th eigenpair, with (3) v j ∗ · v j ∗ = 1.
Note that without the i = 0 term, this formulation denotes the distribution for reads with at least one error.
In a similar, but easier way, one can show that the SEM formulation of the monodomain problem reads (13) χ C M ∂ V ∂ t + K V = M I stim − χ M I ion w, c, V = F along with given cell model, boundary and initial conditions.
