Dipole Polarizability of C28 and its Counterparts Nb4B18 and Ta4B18. Insights from a Density Functional Theory (DFT) Endeavour

We report on a preliminary investigation of the non linear optical (NLO) properties and in particular dipole polarizability. The target species are two perfect tetrahedral nanoclusters Nb4B18 and Ta4B18, along with their nanofullerene counterpart that is C28. Our study based on density functionals (DFs) that have gained popularity among the scientific community. In addition we performed Hartree-Fock calculations known for not including dynamic electron correlation. The DF obtained values are characterized by some dispersion, with maximal differences to be around 5 %, in all three cases. Given that the DFT introduces a fuzzy percentage of electron correlation sets the observed convergence of HF values to DFT ones is at least surprising. Furthermore, it should be said that though the values can be characterized as accurate their reliability should not be taken for granted. Last, we note the smooth convergence of LC-BLYP, LC-BP86, LC-BPW91 to LC-whPBE.

A Survey of the Elastic Flow of Curves and Networks

We collect and present in a unified way several results in recent years about the elastic flow of curves and networks, trying to draw the state of the art of the subject. In particular, we give a complete proof of global existence and smooth convergence to critical points of the solution of the elastic flow of closed curves in $${\mathbb {R}}^2$$ R 2 . In the last section of the paper we also discuss a list of open problems.

Minkowski inequalities and constrained inverse curvature flows in warped spaces

This paper deals with locally constrained inverse curvature flows in a broad class of Riemannian warped spaces. For a certain class of such flows, we prove long-time existence and smooth convergence to a radial coordinate slice. In the case of two-dimensional surfaces and a suitable speed, these flows enjoy two monotone quantities. In such cases, new Minkowski type inequalities are the consequence. In higher dimensions, we use the inverse mean curvature flow to obtain new Minkowski inequalities when the ambient radial Ricci curvature is constantly negative.

WHAT A DIFFERENCE ONE PROBABILITY MAKES IN THE CONVERGENCE OF BINOMIAL TREES

In the [Formula: see text]-period Cox, Ross, and Rubinstein (CRR) model, we achieve smooth convergence of European vanilla options to their Black–Scholes limits simply by altering the probability at one node, in fact, at the preterminal node between the closest neighbors of the strike in the terminal layer. For barrier options, we do even better, obtaining order [Formula: see text] convergence by altering the probability just at the node nearest the barrier, but only the first time it is hit. First-order smooth convergence for vanilla options was already achieved in Tian’s flexible model but here we show how second order smooth convergence can be achieved by changing one probability, leading to convergence of order [Formula: see text] with Richardson extrapolation. We illustrate our results with examples and provide numerical evidence of our results.

Ricci Iteration for Coupled Kähler–Einstein Metrics

In this paper, we introduce the “coupled Ricci iteration”, a dynamical system related to the Ricci operator and twisted Kähler–Einstein metrics as an approach to the study of coupled Kähler–Einstein (CKE) metrics. For negative 1st Chern class, we prove the smooth convergence of the iteration. For positive 1st Chern class, we also provide a notion of coercivity of the Ding functional and show its equivalence to the existence of CKE metrics. As an application, we prove the smooth convergence of the iteration on CKE Fano manifolds assuming that the automorphism group is discrete.

Kähler–Einstein metrics and the Kähler–Ricci flow on log Fano varieties

We prove the existence and uniqueness of Kähler–Einstein metrics on {{\mathbb{Q}}}-Fano varieties with log terminal singularities (and more generally on log Fano pairs) whose Mabuchi functional is proper. We study analogues of the works of Perelman on the convergence of the normalized Kähler–Ricci flow, and of Keller, Rubinstein on its discrete version, Ricci iteration. In the special case of (non-singular) Fano manifolds, our results on Ricci iteration yield smooth convergence without any additional condition, improving on previous results. Our result for the Kähler–Ricci flow provides weak convergence independently of Perelman’s celebrated estimates.

Visualization of oil spill at sea surface based on texture projection

In view of the merits and demerits of current oil spill visualization methods, the paper involves a study on a new type of visualization approach targeting oil spill at sea. To be specific, the visualization of sea oil spill is implemented with the adoption of texture projection method. The texture projection-induced jaggedly edge is displayed in the performance test results. Under the circumstance, Gauss smoothing filter is introduced to secure the smooth convergence of texture edge and thus bring forth satisfactory dynamic visualization effect. Already, this means has already been successfully applied to the Oil Spill Emergency 3D Drilling System, which evidenced the validity and reliability of the new method.