Table 2. Comparisons the influences on the convergence rate λ2 under different upper limits of delays with the same other data. Empty CellCase 1Case 3 Diffusion coefficient τ=3.5 τ=3 Convergence rate 19% 29% Example 4.1 shows the feasibility of our [Theorem 3.1–3.2], whose unique existe...
Using the convolution theorem of Fourier integrals where ϕ0(r) varies slowly compared to the lattice constant, the q-dependent dielectric function becomes (8.30)ε(q)=1−4πq2χ(q). The reason we go through the usual procedures elaborated by Ehrenreich and Cohen (1959), and discussed in...
L − 1, …, 1. LetK(l)andN(l)denote the numbers of logical and physical qubits of\({{{\mathcal{Q}}}^{(l)}\), respectively, which turn out to be\({K}^{(l)}=\mathop{\prod }\nolimits_{{l}^{{\prime} } = 1}^{...
provide more confidence in the latter, we first introduced a weaker variant, calledN-\mathsf {MXDH}, that holds (as we prove it in the full version [22]) in the generic bilinear group model for Type-3 pairings and next prove that both variants are actually related as stated in Theorem...
A resistance in series to the power source limits the maximum power due to the Maximum power transfer theorem according to the formula Pmax = v^2 / (4*Ri) (unfortunately the English wiki article is not that great. See also here or refer to the equivalent wiki article in German) Multipl...
(by the prime number theorem) we expect\(\alpha \approx \kappa \). We shall denote the pseudorandom function by\(F_k(x)\), where the key and output will be interpreted as elements of\({\mathbb {F}}_p\)in much of our MPC protocol. In practice the function\(F_k(x)\)we ...
Theorem 1.2 LetΩ be an open bounded set of class C2. Then there exists a linear continuous operatorγv∈ L(E(Ω), H-1/2(Γ)) such that (1.18)γvu= the restriction of u·v to ⌈, for every u∈D(Ω¯). The following generalize...
By the mean value theorem of elementary calculus, if ϕ(t) is differentiable, there exists a time instant t between t1 and t2 such that (1.3.7)ϕ(t2)−ϕ(t1)=(t2−t1)ϕ′(t). Let pi be the period of one particular oscillation of s(t), and let fi = 1/pi. If we...
prove its correctness and state our main security theorem. The proof of security will appear in the full version. In Sect.4, we show how to instantiate our general paradigm based on the DDH problem: In Sect.4.1, we review the DDH and DLSE problems and prove a few statements. In Sect....
{eq}(x \frac{d}{dx} - \alpha)^n {/eq}, y(x) = 0 where {eq}\alpha {/eq} = constant and n = positive integer Differential Equation : The differential equation may be categorized into several types based on its order. The differential equation...