Relaxation techniques for solving nonlinear systems and global optimisation problems require bounding from below the nonconvexities that occur in the constraints or in the objective function by affine or convex
In contrast to the waveguide QED bound states6, the presence of the cavity results in the second term, which removes the cusp such that the function is smooth at x = 0. The strong localisation within a time 1/Γ in the difference coordinate means that the two photons in the bound ...
AI代码解释 publicvoidsolveChildProblems(LinearProgram lp,double[]solution,int maxElement){searchDepth++;LinearProgram lp1=newLinearProgram(lp);LinearProgram lp2=newLinearProgram(lp);String constr_name="c"+(lp.getConstraints().size()+1);// Name of the new constraint double[] constr_val = new...
A function f is said to have a upper bound C if f(x)<=C for all x in its domain. The least upper bound is called the supremum. A set is said to be bounded from above if it has an upper bound.
D3DXSphereBoundProbe function (D3DX10math.h) - Determines if a ray intersects the volume of a sphere's bounding box.
Quantum key distribution (QKD)1,2 offers a long-term solution to secure key exchange. Due to photon loss in transmission, it was believed that the repeaterless key rate is bounded by a linear function of the transmittance, O(η) (refs. 3,4), limiting the
// FUNCTION TEMPLATE upper_bound template <class _FwdIt, class _Ty, class _Pr> _NODISCARD _CONSTEXPR20 _FwdIt upper_bound(_FwdIt _First, _FwdIt _Last, const _Ty& _Val, _Pr _Pred) { // find first element that _Val is before _Adl_verify_range(_First, _Last); auto _UFirst ...
The following pseudocode demonstrates the comparison operation of the function: Copy XMVECTOR Control; Control.x = (V.x <= Bounds.x && V.x >= -Bounds.x) ? 0xFFFFFFFF : 0; Control.y = (V.y <= Bounds.y && V.y >= -Bounds.y) ? 0xFFFFFFFF : 0; ...
In streamcipher, nonlinearity of a function f(x) from F2n to F2n is an important measure [1]. The nonlinearity of a function f(x) is defined as follows. The Walsh transfer Wf of f(x) is defined by(13)Wf:F2n×F2n→C;(a,b)↦∑x∈F2n(−1)Tr(af(x)+bx). Then the Wals...
The function f(ω) can be complex, and its modulus will determine the ultimate limit for scattering in this case. Namely, if ω|f(ω)|>1, the single-channel limit could be exceeded, since σ1 would then be larger than σMax. To derive an analytical expression for it, we investigate ...