Sentence examples for this theorem states from inspiring English sources

This theorem states that if is a zonoid in, then.

This theorem states that the adaptive group bridge performs as well as the oracle [16].

This theorem states that when the locations and orientations of a seismic source and observation point are swapped, the same elastic response is observed.

This theorem states that relative to a partition of the vocabulary of an axiomatizable theory T into two classes, t and o (theoretical and observational, say) there exists an axiomatizable theory T* in the language whose only non-logical vocabulary is o, of all and only the consequences of T that are expressible in o alone.

This theorem states that a continuous signal with a limited spectrum can be accurately reconstructed (interpolated) by its values at the different frequency intervals, with the condition that there is an upper frequency spectrum signal.

This Theorem states that if there exists a scalar function W Y k ) satisfying the conditions, W Y k ) is posistive definite and ΔW Y k ) is negative definite, then the equilibrium state at the origin is uniformly asymptotically stable.

Informally, the theorem states the following: selecting the optimal experiment might be hard, and yet it is possible to easily select experiments that are provably near-optimal.

Specifically, in this case, Bayes' theorem states that our prior knowledge is updated by the current data to yield updated knowledge in the form of the posterior distribution.

In this case our main theorem states that the solution of (1) is of the type u t,x =varepsilon vbigl varepsilon^{4}t,xbigr) and v(T,x =b(T cos(x)+mathcal{O}bigl varepsilon^{1-32kappa}bigr), where b is the solution of the amplitude equation of Itô type db=biggl[biggl(nu-frac{11}{18}rho_{0}^{2} biggr b-C_{0}biggr b-C_{,dT+rho_{0}b^{5}biggr]eta}_{0},dT+rho_{ere (rho_{0}bsqrt{frac{27}{38pi}}alpha_{0}).

The Riesz representation theorem states that this mapping is an antilinear isomorphism.

Hence, if the consistency of Principia were provable by the methods used in Ackermann's proofs, it should be possible to formalize this proof in Principia; but this is what the second incompleteness theorem states is impossible.