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During a constant sensing time duration, we model the detection problem on the sub-band k as one choosing between a hypothesis ( {H}_{0, k} ), which represents the absence of the primary signals, and an alternative hypothesis ( {H}_{1, k} ), which represents the presence of the primary signals, k ∈ {1, 2, …, K}.

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We're a nation that guarantees the freedom to worship as one chooses.

But for the early dwellers there, "winter would normally have been a relaxed and enjoyable season largely spent visiting, feasting, singing, making tools and clothing, making love and sleeping as long as one chose.

As long as one chooses the constants according to the relations listed in Table 1 and substitutes the appropriate (F xi)) into Eq. (37), one obtains the exact periodic traveling wave solutions to the generalized ((3+1))-dimensional NLSE.

Our first claim is that on finite time intervals [ 0, T ], w ˜ ϵ, β is a good approximation of w ϵ inside ℰ as long as one chooses β sufficiently small.

On the contrary, to the extent that religion enters into the equation, the country was obviously founded on the principle that everyone has a fundamental right to act in accordance with one's religious beliefs, or not, as one chooses.

This year, as America celebrates Religious Freedom Day, it is important to remember that this freedom is the right to believe and behave as one chooses without fear, because church and state are separated, but it is not a license to discriminate or to impose one's religious beliefs on others.

Then for disjoint clusters we can write, We propose for (possibly) non-disjoint clusters the measure, which represents the probability that a cluster chosen randomly from the set A i is the same as one chosen randomly from A j.

In ancient Israel and in various Christian cultures, the king was anointed in the rite of coronation as the one chosen by God to rule over the people.

Choose one ball at random, look at its color, replace the ball in the box, and add to the box another ball of the same color as the one chosen.

"Neil came up with a well-realized smorgasbord of potential identities and good allegories for how one chooses the identity one chooses as an adult".

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