In the following we deal with the case b≠0 in (1). Substituting y=f(x) as in (3) in the equation of Nq,r, and exploiting the linearity of the trace function, we get N(x)=T(akxk)+…+T(a2x2)+T(a1x)+T(a0). (4) No
A Derivation of the Poisson structure A.1 Lax matrix and its Poisson structure Consider the following matrix function on the Heisenberg double L = T −1BT , (A.1) where T is the Frobenius solution of the factorisation problem (2.12). On the reduced space L turns into the Lax matrix ...
To study the performance of this CFC protocol we measure the average bit error, as a function of the number of photons in which the bit is encoded, M, for five different values of N number of BSs. For the logic 0, we configure the MZIs in Bob’s laboratory as mirrors (see Fig. ...
As before we study another property of the trace function. The proof of the following lemma is similar to Proposition 1, so we omit it here. Lemma 15 If for all a∈R, we have Tr(ax)=0, then x=0. Armed with Lemma 15 and the sphere-packing bound, we can prove Theorem 6 as ...
An efficient contact tracing rapidly depletes the hidden poolHand populates the traced poolT, and thus stabilizes the total number of infectionsT + H(Fig.2a). The system relaxes to its equilibrium, which is a function of TTI and epidemiological parameters (Supplementary Eqs. (3)–(5))...
ℏ and compute the leading coefficient. We will consider new Weyl-type estimates for the counting function:NEc, ρ(ℏ)=#{k∈N/|Ek(ℏ)−E|⩽ρℏ}. Previous article in issue Next article in issueReferences REFERENCES 1 V.I. Arnold, S.M. Gusein-Zade, A.N. Varchenko ...
The study keystones of pseudo-random sequence are its construction methods and randomness analysis. As the property of pseudo-random sequences, the linear complexity is defined as the length of the shortest linear shift register, which can generate the sequences [1]. By the Berlekamp–Massey ...
In a case study, we first divide taxi drivers into top drivers and ordinary drivers, according to their performance as calculated from their GPS traces over a week, and analyze the space-time distribution and operating patterns of the top drivers. Then, we compare the space-time distribution ...
Remark 1 . The proof of the trace identity makes use of the notion of 'rank' as used in the continuous case [lo]. The rank is an integer-valued function which is defined on U, A, e E G and E such that d a b )= p ( a ) + p ( b ) when ab makes sense, where p ( ...
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