Bosonization, Singularity Analysis, Nonlocal Symmetry Reductions and Exact Solutions of Supersymmetric KdV Equation

Assuming that there exist at least two fermionic parameters, the classical N= 1 supersymmetric Korteweg-de Vries (SKdV) system can be transformed to some coupled bosonic systems. The boson fields in the bosonized SKdV (BSKdV) systems are defined on even Grassmann algebra. Due to the intrusion of other Grassmann parameters, the BSKdV systems are different from the usual non-supersymmetric integrable systems, and many more abundant solution structures can be unearthed. With the help of the singularity analysis, the Painlev\'e property of the BSKdV system is proved and a B\"acklund transformation (BT) is found. The BT related nonlocal symmetry, we call it as residual symmetry, is used to find symmetry reduction solutions of the BSKdV system. Hinted from the symmetry reduction solutions, a more generalized but much simpler method is established to find exact solutions of the BSKdV and then the SKdV systems, which actually can be applied to any fermionic systems.Comment: 21 pages; 0 figure

Second language user support

Computer users rarely experience entirely trouble-free interaction. The natural variety ofindividuals ensures that no software systems yield constantly fluent interaction for allusers. In consequence, software designers often strive to ameliorate this situation bybuilding 'user support' into their systems. User support can take different forms but,conventionally, each aims to assist the needy end-user by means of facilities directly supporting the performance of certain operations, or through supply of information thatadvises the user on available system functionality.The present paper briefly characterises a range of user support facilities before describingone requirement in greater detail. This aspect considers the needs of users whose mother-tongue is not English, but who are obliged to use English-based information systems. Inthis context, 'helping the user' must reasonably extend beyond mere advice on systemoperation to selective elucidation of information content. We regard this move as alogical extension of the user support concept, by seeking to address specific interactionneeds in a target user population. An example of this approach is described through aninformation system, in the domain of civil engineering, for native Chinese speakers ofEnglish

From fire whirls to blue whirls and combustion with reduced pollution.

Fire whirls are powerful, spinning disasters for people and surroundings when they occur in large urban and wildland fires. Whereas fire whirls have been studied for fire-safety applications, previous research has yet to harness their potential burning efficiency for enhanced combustion. This article presents laboratory studies of fire whirls initiated as pool fires, but where the fuel sits on a water surface, suggesting the idea of exploiting the high efficiency of fire whirls for oil-spill remediation. We show the transition from a pool fire, to a fire whirl, and then to a previously unobserved state, a "blue whirl." A blue whirl is smaller, very stable, and burns completely blue as a hydrocarbon flame, indicating soot-free burning. The combination of fast mixing, intense swirl, and the water-surface boundary creates the conditions leading to nearly soot-free combustion. With the worldwide need to reduce emissions from both wanted and unwanted combustion, discovery of this state points to possible new pathways for reduced-emission combustion and fuel-spill cleanup. Because current methods to generate a stable vortex are difficult, we also propose that the blue whirl may serve as a research platform for fundamental studies of vortices and vortex breakdown in fluid mechanics

Anomalous impurity effect on magnetization in frustrated one-dimensional ferro- and ferrimagnets

Significant decrease of spontaneous magnetization in frustrated one-dimensional ferro- and ferrimagnets due to non-magnetic impurities is predicted. Using the density-matrix renormalization group method and the exact diagonalization method, we confirm that the total spin can vanish due to a single impurity in finite chains. Introducing the picture of magnetic domain inversion, we numerically investigate the impurity-density dependence of magnetization. In particular, we show that even with an infinitesimal density of impurities the magnetization in the ground state is reduced by about 40% from that of the corresponding pure system. Conditions for the materials which may show this anomalous impurity effect are formulated.Comment: 4 pages, 6 figure