Arithmetic Fujita approximation

On volumes of arithmetic line bundles

We show an arithmetic generalization of the recent work of Lazarsfeld–Mustaţǎ which uses Okounkov bodies to study linear series of line bundles. As applications, we derive a log-concavity inequality on volumes of arithmetic line bundles and an arithmetic Fujita approximation theorem for big line bundles.

SOCIÉTÉ MATHÉMATIQUE DE FRANCE quatrième série - tome 43 fascicule 4 juillet - août 2010 Huayi CHEN Arithmetic Fujita approximation

Self-similar fractals and arithmetic dynamics

‎The concept of self-similarity on subsets of algebraic varieties‎ ‎is defined by considering algebraic endomorphisms of the variety‎ ‎as `similarity' maps‎. ‎Self-similar fractals are subsets of algebraic varieties‎ ‎which can be written as a finite and disjoint union of‎ ‎`similar' copies‎. ‎Fractals provide a framework in which‎, ‎one can‎ ‎unite some results and conjectures in Diophantine g...

Automated classification of pulmonary nodules through a retrospective analysis of conventional CT and two-phase PET images in patients undergoing biopsy

Objective(s): Positron emission tomography/computed tomography (PET/CT) examination is commonly used for the evaluation of pulmonary nodules since it provides both anatomical and functional information. However, given the dependence of this evaluation on physician’s subjective judgment, the results could be variable. The purpose of this study was to develop an automated scheme for the classific...

Close interval approximation of piecewise quadratic fuzzy numbers for fuzzy fractional program

  The fuzzy approach has undergone a profound structural transformation in the past few decades. Numerous studies have been undertaken to explain fuzzy approach for linear and nonlinear programs. While, the findings in earlier studies have been conflicting, recent studies of competitive situations indicate that fractional programming problem has a positive impact on comparative scenario. We pro...