The Effect of Orbital Angular Momentum on Nondiffracting Ultrashort Optical Pulses

We introduce a new class of nondiffracting optical pulses possessing orbital angular momentum. By generalizing the X-waves solution of the Maxwell equation, we discover the coupling between angular momentum and the temporal degrees of freedom of ultra-short pulses. The spatial twist of propagation invariant light pulse turns out to be directly related to the number of optical cycles. Our results may trigger the development on novel multi-level classical and quantum transmission channels free of dispersion and diffraction, may also find application in the manipulation of nano-structured objects by ultra-short pulses, and for novel approaches to the spatio-temporal measurements in ultrafast photonics

Automorphisms of the UHF algebra that do not extend to the Cuntz algebra

Automorphisms of the canonical core UHF-subalgebra F_n of the Cuntz algebra O_n do not necessarily extend to automorphisms of O_n. Simple examples are discussed within the family of infinite tensor products of (inner) automorphisms of the matrix algebras M_n. In that case, necessary and sufficient conditions for the extension property are presented. It is also addressed the problem of extending to O_n the automorphisms of the diagonal D_n, which is a regular MASA with Cantor spectrum. In particular, it is shown the existence of product-type automorphisms of D_n that are not extensible to (possibly proper) endomorphisms of O_n

Solitonization of the Anderson Localization

We study the affinities between the shape of the bright soliton of the one-dimensional nonlinear Schroedinger equation and that of the disorder induced localization in the presence of a Gaussian random potential. With emphasis on the focusing nonlinearity, we consider the bound states of the nonlinear Schroedinger equation with a random potential; for the state exhibiting the highest degree of localization, we derive explicit expressions for the nonlinear eigenvalue and for the localization length by using perturbation theory and a variational approach following the methods of statistical mechanics of disordered systems. We numerically investigate the linear stability and "superlocalizations". The profile of the disorder averaged Anderson localization is found to obey a nonlocal nonlinear Schroedinger equationComment: 5 pages, 3 figure

Chengyu in Chinese Language Teaching: A preliminary analysis of Italian learners’ data

Chengyu, also known as Chinese four-character idioms, are a type of traditional Chinese idiom, mostly consisting of four characters. They commonly derive from classic Chinese literary sources, including those of the three great philosophical and religious traditions that influenced the entire East Asia cultural sphere: Confucianism, Daoism and Buddhism. Chengyu, therefore, possess a wide range of cultural references, and, from Chinese, spread to the languages of the other countries of the sinosphere, such as Japan and Korea. Although many scholars have emphasized the importance of the acquisition of chengyu, not much attention has been paid to chengyu learning in Chinese Language Teaching research so far. As a preliminary attempt to address this gap, this paper reports the results of two small-scale, exploratory experiments, aimed at investigating Italian learners’ general knowledge of chengyu and their main interpretation strategies, as well as comparing the effectiveness of direct and indirect instruction in chengyu teaching. The experiments involved participants from Bachelor and Master programs of Roma Tre University. The results show a predominant effect of negative transfer from Italian, as well as a better performance of the participants who received indirect instruction

Half-flat nilmanifolds

We introduce a double complex that can be associated to certain Lie algebras, and show that its cohomology determines an obstruction to the existence of a half-flat SU(3)-structure. We obtain a classification of the 6-dimensional nilmanifolds carrying an invariant half-flat structure.Comment: 14 pages; v2: corrected equation in introduction; added solvable example; rearranged contents of Proposition 3 and Lemma 4; v3: corrected typos, added remark about unimodular cas