Integration of the hyperbolic telegraph equation in (1+1) dimensions via the generalized differential quadrature method

AbstractThe 2D generalized differential quadrature method (hereafter called ((1+1)-GDQ) is introduced within the context of dynamical system for solving the hyperbolic telegraph equation in (1+1) dimensions. Best efficiency is obtained with a low-degree polynomial (n⩽8) for both time variable and x-direction. From realistic examples, some models are presented to illustrate an excellent performance of the proposed method, compared with the exact results

THE BOUND STATES FOR THE NON POLYNOMIAL POTENTIAL VIA THE GENERALIZED DIFFERENTIAL QUADRATIC METHOD

In a previous work, we have introduced the generalized differential quadratic method (called GDQ) to handle the Schrödingerequation. This paper deals with a particular situation in which an application to the non polynomial potential is considered. Theresults are compared with some numerical examples for the same potential of interest. Dans un récent travail nous avons introduit la méthode quadratique différentielle généralisée pour manipuler l’équation deSchrödinger. Cet article traite une situation particulière dans laquelle une application à un potentiel non polynomial estconsidérée. Les résultats sont confrontés avec des exemples numériques pour le même potentiel d’intérêt

Functional imaging studies of cognition using 99mTc-HMPAO SPECT: empirical validation using the n-back working memory paradigm

{Purpose} Functional activation protocols are widely applied for the study of brain-cognition relations. Only few take advantage of the intrinsic characteristics of SPECT, particularly those allowing cognitive assessment outside of the camera, in settings close to the standard clinical or laboratory ones. The purpose of the study was to assess the feasibility of a split-dose activation protocol with 99mTc-HMPAO using low irradiation dose. {Materials and methods} A two-scans protocol was applied to 12 healthy young volunteers using 270 MBq of 99mTc-HMPAO per scan, with each image associated to a particular experimental condition of the verbal {n}-back working memory task (0-back, 2-back). Subtraction method was used to identify regional brain activity related to the task. {Results} Voxel-wise statistical analysis showed left lateralized activity associated with the 2-back task, compared to the 0-back task. Activated regions, mainly prefrontal and parietal, were similar to those observed in previous fMRI and 15O-PET studies. {Conclusion} The results support the use of 99mTc-HMPAO SPECT for the investigation of brain-cognition relations and demonstrate the feasibility of optimal quality images despite low radiopharmaceutical doses. The findings also acknowledge the use of HMPAO as a radioligand to capture neuro-energetic modulations linked to cognitive activity. They encourage extending the application of the described activation protocol to clinical populations

Exact solutions for the KdV–mKdV equation with time-dependent coefficients using the modified functional variable method

In this article, the functional variable method (fvm for short) is introduced to establish new exact travelling solutions of the combined KdV–mKdV equation. The technique of the homogeneous balance method is used in second stage to handle the appropriated solutions. We show that, the method is straightforward and concise for several kinds of nonlinear problems. Many new exact travelling wave solutions are successfully obtained