Sentence examples for vector on which from inspiring English sources

Through trading, agents find a price vector on which everyone agrees, i.e., (mathbf {p}=E[m_{i}mathbf {X}]) for (i=1,ldots,I), and which maximizes utility.

For further considerations, we suppose that has smooth boundary (e.g., ), and the crack (smooth) can be extended to an arbitrary smooth, simply connected, closed curve enclosing a bounded domain such that the normal vector on coincides with the outward normal vector on which we again denote by.

This measure computes the 2-class Fisher criterion, given by (11) where (mathbf {d} = bar{varSigma}^{-1}varDelta ) is the directional vector on which data are projected, Δ=μ1−μ2, (bar{varSigma}^{-1}) is the pseudo-inverse of (bar{varSigma}), μ i is the mean vector for class i, (bar{varSigma} = avarSigma_{1} + 1-a varSigma_{2}}), 1-a varSigma_{2}e scatter matrix of instances for class c i.

whereS j andS k are the slopes of the vectors on which ends of the angle arc straddled, and ∥s j ∥ and ∥s k ∥ are their respective lengths.

In terms of these hallmarks, the dynamics of RBNs tends to become, on average, more chaotic as r is increased or if the average bias of the regulatory functions, defined as the difference between 0.5 and the proportion of input vectors on which it takes the Boolean value 1, decreases.

A vector space is a set of vectors closed under addition, and multiplication by constants, an inner product space is a vector space on which the operation of vector multiplication has been defined, and the dimension of such a space is the maximum number of nonzero, mutually orthogonal vectors it contains.

A Hilbert space, finally, is a vector space on which an inner product is defined, and which is complete, i.e., which is such that any Cauchy sequence of vectors in the space converges to a vector in the space.

Then, there exists a local tangent vector field on which is admissibly homotopic to in and such that is a nondegenerate pair.

The only case we are interested in here is the case (E otimes Lambda ^{0,q}(V^*)), where (E) is a vector space on which ({fancyscript{H}}) acts trivially, and begin{aligned} Lambda ^{0,q}(V^*) := underbrace{bar{V}^* wedge dots wedge bar{V}^*}_{qtext { times}}, end{aligned}where (V^*) is the dual vector space of (V).

We will show that there exists at most one function that, to any admissible pair, assigns a real number called the degree (or characteristic or rotation) of the tangent vector field on, which satisfies the following three properties that will be regarded as axioms.

The narrow-band signal model and the conventional MUSIC algorithm are introduced in Section 2. In Section 3, the steering vector of a ULA that used in the standard MUSIC is firstly reconstructed as two other steering vectors, based on which the proposed low-complexity cost function with spatial aliasing is addressed.