The not-so-peculiar case of calcium oxide: a weakness in atomic natural orbital basis sets for calcium

Atomic natural orbital (ANO) basis sets for calcium may produce surprisingly poor atomic and molecular properties and energetics. The weaknesses in these basis sets may be traced primarily to deficiencies within the sets of d functions which are incapable of effectively correlating the 3s and 3p electrons. Examples are given which show that addition of tight d functions to the ANO basis is required to achieve qualitatively correct energetics and structures for conventionally bonded calcium compounds.     

A Lax type operator for quantum finite W-algebras

Selecta Mathematica - For a reductive Lie algebra $$\mathfrak {g}$$ , its nilpotent element f and its faithful finite dimensional representation, we construct a Lax operator L(z) with coefficients...     

Convex Entire Noncommutative Functions are Polynomials of Degree Two or Less

We establish several new relations between the discrete transition operator, the continuous Laplacian and the averaging operator associated with combinatorial and metric graphs. It is shown that these operators can be expressed through each other in a very explicit way. In particular, the averaging operator appears to be closely related to the solutions of the associated wave equation. The machinery used allows one to study a class of infinite graphs without assumption on the local finiteness.     

Monitoring nanotechnology using patent classifications: an overview and comparison of nanotechnology classification schemes

Patents are an essential information source used to monitor, track, and analyze nanotechnology. When it comes to search nanotechnology-related patents, a keyword search is often incomplete and struggles to cover such an interdisciplinary discipline. Patent classification schemes can reveal far better results since they are assigned by experts who classify the patent documents according to their technology. In this paper, we present the most important classifications to search nanotechnology patents and analyze how nanotechnology is covered in the main patent classification systems used in search systems nowadays: the International Patent Classification (IPC), the United States Patent Classification (USPC), and the Cooperative Patent Classification (CPC). We conclude that nanotechnology has a significantly better patent coverage in the CPC since considerable more nanotechnology documents were retrieved than by using other classifications, and thus, recommend its use for all professionals involved in nanotechnology patent searches.     

Linear extension sums as valuations on cones

The geometric and algebraic theory of valuations on cones is applied to understand identities involving summing certain rational functions over the set of linear extensions of a poset.