upper and lower boundsperturbation theoryExtensive Hylleraas-CI calculations for the lowest P-o states of He-4 were performed. The dependence of the variational energy values E-kappa on the mass parameter kappa given by kappa = m(He2+)/m(e-) discussed. Furthermore, lower bounds to E-kappa...
Microsoft Excel is a powerful tool when it comes to handling data and performing statistical calculations. Creating a confidence interval in Excel is a key skill for statisticians, scientists and people in a range of professions. Excel can be used to find the upper and lower bounds in statistics...
It is shown that one can construct lower bounds using the reduced density matrix that corresponds to the upper bound. These lower bounds converge to an exact value with the expansion of the basis. We perform the calculations of both bounds with realistic nucleon-nucleon potential for ground ...
In this paper, we give some sharp lower and upper bounds for the Laplacian spectral radius of trees that depend on only the degree sequences, i.e., (1) Let T be a tree with n vertices and k pendant vertices. Then μ(T)⩽μ(Tn,k),where the equality holds if and only if T is...
When a shield tunnel is excavated in water-rich strata with soft upper and hard lower layers, the failure mode of the tunnel face may shift from an overall failure mode to a partial failure mode. To address this issue, three-dimensional discrete failure
We derive analytical lower and upper bounds for the entanglement Rényi-α entropy of arbitrary dimensional bipartite quantum systems. We also demonstrate the application our bound for some concrete examples. Moreover, we establish the relation between entanglement Rényi-α entropy and some other ...
lower bound for the price of an Asian option, while Feynman & Hibbs (1965) applied it to introduce a variational result for essentially the same quantity, c.q. the partition matrix, an important quantity in mathematical physics. Proposition 2 For any two rvs Y and Z, let L := E(Y |...
In the case 0<L≤2, a lower bound is also obtained: σk(M)≥(1−L2)n−1σk(CL,dr2+g0), However, this inequality does not appear to be sharp. In this paper, we will look for upper bounds for the Steklov eigenvalues of hypersurfaces of revolution. First, we recall that there...
Upper bounds on library dependencies can lead to breakage or installation problems in the future, so more curious if this can get changed to a lower bound to avoid breakage, or if there is a fundamental incompatibility with the lhapdf source code with cython v3 that would require a change in...
All of the known first-principles calculations obey the new bound. This bound can be sharpened by further constraining the ratios Cπ,CΠ from shear and bulk viscosity (and performing a similar analysis including effects from charge conductivity), especially in systems at finite baryon density. ...