Sentence examples for by the theory there from inspiring English sources

Because without the Higgs mechanism and the Higgs boson predicted by the theory, there would be no way to explain why fundamental particles have a mass, and without that there's no way to explain why these particles stick together to form atoms, molecules and hence all the structure of the universe.

By this theory, there is always a question of who is going to tend to the nest, defend against predators, forage for the next meal.

By the abstract Hodge theory, there is a self-adjoint operator G N ∈ L ( L N ) Open image in new window mapping into the orthogonal complement of kerΔ N such that 1 L N = H N + Δ N G N Open image in new window on L N, where H N is the orthogonal projection onto the finite-dimensional space kerΔ N =kerDN−1∗.

By the abstract Hodge theory, there is a self-adjoint operator G N − 1 ∈ L ( L N − 1 ) Open image in new window which maps into the orthogonal complement of kerΔN−1and fulfills 1 L N − 1 = H N − 1 + Δ N − 1 G N − 1 Open image in new window.

Hence by the theory of multipliers, there exists a (thetainmathbb {R}) such that I'_{f,g}bigl omega^{0}_{1}, omega^{0}_{2}bigr)=thetapsi'_{f,g} bigl omega ^{0}_{1},omega^{0}_{2} bigr).

By Wiman-Valiron theory, there is a subset E 5 ⊂ ( 1, ∞ ) with finite logarithmic measure.

According to the cardiac lipotoxicity theory, there are potential mechanisms by which lipid accumulation may interact directly with excitation-contraction coupling.

Although [4] shows that Algorithm 1.1 can get a longer stepsize, and hence is a better algorithm than the extragradient method proposed by Korpelevich [5] in theory, there is still the need to calculate two projections onto the feasible set C and onto a related set C ∩ H k at each iteration.

Hence, by some basic set theory, there is no set containing all the objects.

Hence, by the theory of Lagrange multipliers, there exists θ ∈ R such that I λ ′ ( u 0 ) = θ ψ λ ′ ( u 0 ), in X − 1.

Proof If u 0 is a local minimizer for J λ on M λ , then u 0 is a solution of the optimization problem minimize J λ ( u ) subject to ψ λ ( u ) = 0. Hence, by the theory of Lagrange multipliers, there exists θ ∈ R such that J λ ′ ( u 0 ) = θ ψ λ ′ ( u 0 ) in  [ H ] ∗. (2.6).