Sentence examples for equal to the function from inspiring English sources

Only from the result of 3rd treatment, acupoints herbal patching seemed to be equal to the function of placebo, while rethinking its concept of acupoints herbal patching in Sanfu Days which means pasting herbal patch on some special acupoints in Sanfu Days.

In addition, since the full minimum for the first of (24) may be not available, we relax the result by assuming that a local minimum is achieved and that the target function in this local minimum x t+1 is smaller than or equal to the function value in x t.

Let B = { e 1, …, e n } be an orthonormal basis of R n with inner product 〈 ⋅, ⋅ 〉 and let p > 0. Define X p = { [ f ] | f : [ 0, 1 ] → R n, ∫ 0 1 | 〈 f ( t ), e k 〉 | p d t < + ∞, k = 1, …, n }, where [ f ] is the class of functions being equal to the function f a.e.

Suppose that ∑ i = 1 s t i ( l (., ȳ i ) + T D w - k ̄ ( m (., ȳ i ) - T E v ) ) is strictly B- p, r)-invex at a on S ∪ S1 with respect to η and B- ptisfying b(x, a) > 0 for -invex∈ S. Fur -invexe, atsume that ∑ h = 1 p μ h g h is B g -(p, r)-invex at a on S ∪ S1 with respect to the same function η and with respect to the function b g, but not necesatisfyingqual to the function b x

The above relation implies that the Mellin transform of the last integral is equal to the function e λ n s n, that is, e λ n s n = 1 π M { ∫ 0 ∞ e λ n r n cos ( n π 2 ) cos ( r ln ( t ) − λ n r n sin ( n π 2 ) ) d r ; s } = 1 π ∫ 0 ∞ t s − 1 ∫ 0 ∞ e λ n r n cos ( n π 2 ) cos ( r ln ( t ) − λ n r n sin ( n π 2 ) ) d r d t.

The adjustable parameter is chosen in such a way that the marginalised microcanonical partition function is equal to the partition function of interest (for instance, the canonical (constant volume) partition function) (57) Ω r N, p N, q M, p q M l → → ∫ d q M d p q M ∫ d q M d p q M Ω ′ r N, p N l l.

Lemma 2. Let {u ij } and {v ij } be two grid functions defined at the mesh points (x i, y j ) of the grid R h ∪ ∂R h, i = 0,..., N + 1, j = 0,..., M + 1 such that, at the point (x i, y j ) of ∂R h and t > 0, the grid function {u ij } is equal to the prescribed function U1(x i, y j, t) and the grid function {v ij } is equal to the null function, respectively.

Each individual has a parameter vector associated with it,, as given in equation 4. We define a fitness function Φ: I → ℝ, which is equal to the objective function E as defined in equation 3, and use the penalty function Π: I → ℝ defined in equation 5. Selection is performed to produce a set of μ offspring (here, we take μ = λ/5), according to a selection operator : I λ → I μ.

It is stated clearly in [9] that the function f ∗ is not equal to the gain function f in the proposed limiting Wilson Cowan equation (1.3), but rather connected to f such that E f ∗ ( ∑ j = 1 P W ˜ k j Θ t j ) = f ( ∑ j = 1 P W ˜ k j E Θ t j ) + higher order terms.

This provides an upper limit on extinction because this generating function will be greater than or equal to the generating function for all other random variables with the same m1 and n, on q∈ [ 0,1].

Approximately, we have (23) E r g, g ^ ≈ E s g, g ^ E s g 2 E s g ^ 2. Note that the correlation involves a function of three correlated random variables (s g ^, g, s g 2, s g ^ 2 ) and we must acknowledge that the expected value of a function of random variables is not usually exactly equal to the same function evaluated at the expected values of the random variables [ 19].