Let X be a smooth genus g curve equipped with a simple morphism f : X → C, where C is either the projective line or more generally any smooth curve whose gonality is computed by finitely many pencils. Here we apply a method developed by Aprodu to prove that if g is big enough then X satisfies both Green and Green-Lazarsfeld conjectures. We also partially address the case in which the gonality o...

We obtain some inequalities related to the powers of numerical radius inequalities of Hilbert space operators. Some results that employ the Hermite-Hadamard inequality for vectors in normed linear spaces are also obtained. We improve and generalize some inequalities with respect to Specht's ratio. Among them, we show that, if $A, Bin mathcal{B(mathcal{H})}$ satisfy in some conditions, it follow...

A canonical construction of a balanced big Cohen-Macaulay algebra for a domain of finite type over C is obtained by taking ultraproducts of absolute integral closures in positive characteristic. Among the applications are a new tight closure characterization of rational singularities in characteristic zero, and a necessary condition for Q-Gorenstein logterminal singularities. In particular, it ...

The introduction to this special issue on psychological research involving big data summarizes the highlights of 10 articles that address a number of important and inspiring perspectives, issues, and applications. Four common themes that emerge in the articles with respect to psychological research conducted in the area of big data are mentioned, including: (a) The benefits of collaboration acr...

Responds to G. J. Rich's comments on the current author's original article which presented evidence supporting the idea that multicultural experience can facilitate creativity. Rich has argued that our review, although timely and important, was somewhat limited in scope, focusing mostly on smaller forms of creativity ("little c": e.g., paper-and-pencil measures of creativity) as well as on larg...

Let V be a compact symplectic manifold and {γα | α = 1, · · ·N} be a basis for H(V ;C). We choose γ1 to be the identity of cohomology ring of V . Let γ α = ηγβ with (η) representing the inverse matrix of the Poincáre intersection pairing. As a convention, repeated Greek letter indices are summed up over their entire ranges from 1 to N . Recall that the big phase space for Gromov-Witten invarian...

We compute correlation functions of closed strings in Misner space, a big crunch big bang universe. We develop a general method for correlators with twist fields, which are relevant for the investigation on the condensation of winding tachyon. We propose to compute the correlation functions by performing an analytic continuation of the results in C/ZN Euclidean orbifold. In particular, we obtai...