Each angle Δ θ i from a sample of angles is equivalent to a vector of length unity on a circle:.
Vector d JD [ n JD × 1] consists of elements indicating the direct environmental burden per unit production of the Japanese commodities, and i JD (i 1 = α )[ n JD × 1] is a vector with an element of unity solely for Japanese commodity i1 = α and an element of zero for other commodities.
where A =(α n,k ) n,k, 1 K is the unity vector of size K and ||·||0 is the l 0 norm, e.g., the number of non-zero elements of the considered vector.
where e k is a column vector of length N with unity for the kth element and zero for the others.
This dot product of two vectors is a measure of the angular distance between them; a dot product of zero means that the vectors are orthogonal (i.e., the documents are totally different), and a dot product of unity indicates that the vectors are exactly parallel (or that the documents are similar).
In mDC, the feature vector is augmented by a regularization constant of unity to acquire the property of Euclidean distance and maintain the computational efficiency of direction cosine [ 12].
with p being the row vector of the equilibrium state probabilities, the unity matrix I, and the zero vector 0. Figure 2 Single-satellite state models assuming two states.
i G [ n G × 1] is vector of which all of the elements are unity.
where L and M denote the numbers of range and Doppler bin CSR measures, N is the length of transmit waveform vector, ω M = e − 1 2 π / M is the M th root of unity.
where y 0 is the initial vector of final demand, Δy, column vector of change in final demand, Δ p ˆ diagonal matrix (a matrix with the elements of the vector in the main diagonal and zeros in outside the main diagonal) of price changes (in % or share of unity) and ε ˆ diagonal matrix of elasticities.
"This is a sign of unity".
