Chemical stabilities of six low-energy isomers of C24 derived from global-minimum search are investigated. The six isomers include one classical fullerene (isomer 1) whose cage is composed of only five- and six-membered rings (56-MRs), three nonclassical fullerene structures whose cages contain at least one four-membered ring (4-MR), one plate, and one monocyclic ring. Chemical and electronic p...

In this paper we make a full analysis of the symmetry reductions beam equation by using classical Lie method infinitesimals and nonclassical method. We consider travelling wave depending on form an arbitrary function. have found several new classes solutions that not been considered before: expressed in terms Jacobi elliptic functions, Wadati solitons compactons. Several coherent structures are...

Quasi-permanent light-induced second-order susceptibility x s2d of octupolar molecules is demonstrated. The octupolar molecule Ethyl Violet was oriented in a solgel matrix by a purely optical poling technique. The method consists of a seeding process based on a nonclassical holographic process with coherent two-frequency mixing. The growth of the induced x s2d is monitored in real time by frequ...

Classical and nonclassical symmetries of the nonlinear heat equation ut = uxx + f(u), (1) are considered. The method of differential Gröbner bases is used both to find the conditions on f(u) under which symmetries other than the trivial spatial and temporal translational symmetries exist, and to solve the determining equations for the infinitesimals. A catalogue of symmetry reductions is given ...

Second order matrix equations arise in the description of real dynamical systems. Traditional modal control approaches utilise the eigenvectors of the undamped system to diagonalise the system matrices. A regrettable consequence of this approach is the discarding of residual off-diagonal terms in the modal damping matrix. This has particular importance for systems containing skew-symmetry in th...

This paper is essentially a presentation of a unifying and comprehensive scheme, where several different notions of symmetry for differential problems may be considered and compared. In particular, this approach will permit the introduction of “subtler” notions of conditional symmetries (or “nonclassical symmetries ”) [1–5], with a clear distinction and characterization of these symmetries and ...

In this paper we make a full analysis of the symmetry reductions of a beam equation by using the classical Lie method of infinitesimals and the nonclassical method. We consider travelling wave reductions depending on the form of an arbitrary function. We have found several new classes of solutions that have not been considered before: solutions expressed in terms of Jacobi elliptic functions, W...

introduction nonclassical congenital adrenal hyperplasia (cah) is characterized by sufficient cortisol and aldosterone production at the cost of androgen overproduction. hydrocortisone or dexamethasone in supraphysiological doses are current treatment; however, their downside is suppression of endogenous cortisol production resulting in corticosteroid dependency. we aimed to treat children with...