We use the auxiliary principle technique to suggest and analyze an implicit method for solving the equilibrium problems on Hadamard manifolds. The convergence of this new implicit method requires only the speudomonotonicity, which is a weaker condition than monotonicity. Some special cases are also considered.

The prevalence of implicit intergroup bias in adults underscores the importance of knowing when during development such biases are most amenable to change. Although research suggests that implicit intergroup bias undergoes little change across development, no studies have directly examined whether developmental differences exist in the capacity for novel implicit associations to form or change....

In this article an explicit method (relying on representation theory) to construct packings in Grassmannian space is presented. Infinite families of configurations having only one non-trivial set of principal angles are found using 2-transitive groups. These packings are proved to reach the simplex bound and are therefore optimal w.r.t. the chordal distance. The construction is illustrated by a...

A machine learning approach for modeling the influence of external environments and fields on molecules has been developed, which allows prediction various types molecular spectra in vacuum under implicit explicit solvation.

We present an explicit method to produce upper bounds for the dimension of the moduli spaces of complete integral Gorenstein curves with prescribed symmetric Weierstrass semigroups.

Among various models that incorporate solvation effects into first-principles-based electronic structure theory such as density functional theory (DFT), the average solvent electrostatic potential/molecular dynamics (ASEP/MD) method is particularly advantageous. This method explicitly includes the nature of complicated solvent structures that is absent in implicit solvation methods. Because the...

The treatment of hydration effects in protein dynamics simulations varies in model complexity and spans the range from the computationally intensive microscopic evaluation to simple dielectric screening of charge-charge interactions. This paper compares different solvent models applied to the problem of estimating the free-energy differencebetween two loop conformations in acetylcholinesterase....

Many studies have examined the effect of different approaches to teaching grammar including explicit and implicit instruction. However, research in this area is limited in a number of respects. One such limitation pertains to the issue of construct validity of the measures, i.e. the knowledge developed through implicit instruction has been measured through instruments which favor th...