New variable separation approach: application to nonlinear diffusion equations

The concept of the derivative-dependent functional separable solution, as a generalization to the functional separable solution, is proposed. As an application, it is used to discuss the generalized nonlinear diffusion equations based on the generalized conditional symmetry approach. As a consequence, a complete list of canonical forms for such equations which admit the derivative-dependent functional separable solutions is obtained and some exact solutions to the resulting equations are described.Comment: 19 pages, 2 fig

A Model for the Moving `Wisps' in the Crab Nebula

I propose that the moving `wisps' near the center of the Crab Nebula result from nonlinear Kelvin-Helmholtz instabilities in the equatorial plane of the shocked pulsar wind. Recent observations suggest that the wisps trace out circular wavefronts in this plane, expanding radially at speeds approximately less than c/3. Instabilities could develop if there is sufficient velocity shear between a faster-moving equatorial zone and a slower moving shocked pulsar wind at higher latitudes. The development of shear could be related to the existence of a neutral sheet -- with weak magnetic field -- in the equatorial zone, and could also be related to a recent suggestion by Begelman that the magnetic field in the Crab pulsar wind is much stronger than had been thought. I show that plausible conditions could lead to the growth of instabilities at the radii and speeds observed, and that their nonlinear development could lead to the appearance of sharp wisplike features.Comment: 7 pages; 3 postscript figures; LaTex, uses emulateapj.sty; to Appear in the Astrophysical Journal, Feb. 20, 1999, Vol. 51

Approximate perturbed direct homotopy reduction method: infinite series reductions to two perturbed mKdV equations

An approximate perturbed direct homotopy reduction method is proposed and applied to two perturbed modified Korteweg-de Vries (mKdV) equations with fourth order dispersion and second order dissipation. The similarity reduction equations are derived to arbitrary orders. The method is valid not only for single soliton solution but also for the Painlev\'e II waves and periodic waves expressed by Jacobi elliptic functions for both fourth order dispersion and second order dissipation. The method is valid also for strong perturbations.Comment: 8 pages, 1 figur

Improved statistical learning abilities in adult bilinguals

Using multiple languages may confer distinct advantages in cognitive control, yet it is unclear whether bilingualism is associated with better implicit statistical learning, a core cognitive ability underlying language. We tested bilingual adults on a challenging task requiring simultaneous learning of two miniature grammars characterized by different statistics. We found that participants learned each grammar significantly better than chance and both grammars equally well. Crucially, a validated continuous measure of bilingual dominance predicted accuracy scores for both artificial grammars in a generalized linear model. The study thus demonstrates the first graded advantage in learning novel statistical relations in adult bilinguals

Metoda za optimizaciju tehničkih parametara liofilizacije

Vacuum freeze-drying is a technique that makes a material dehydrate at low temperature and low pressure, and it has many merits. A control system is designed and developed based on a certain area freeze-drying machine. A test by the control system is done to optimize the freeze-drying technical parameters. According to the test results, by the method of quadratic orthogonal experiment, the key parameters, including duration, temperature and vacuum of freeze-drying, are analysed and optimized. The test proves the optimized parameters valid for certain vacuum freeze-drying machines and certain bacterins. Furthermore, the optimized parameters show that the vacuum freeze-drying method is useful for any area vacuum freeze-drying machine and any bacterin.Liofilizacija u vakuumu postupak je koji dehidrira materijal pri niskoj temperaturi i niskom tlaku, što ima mnogo prednosti. Kontrolni sustav dizajniran je i razvijen za određeni uređaj za liofilizaciju. Kako bi se optimizirali tehnički parametri liofilizacije, provedeno je ispitivanje od strane nadzornog sustava. Prema rezultatima, metodom kvadratnog ortogonalnog eksperimenta, analizirani su i optimizirani ključni parametri uključujući trajanje, temperaturu i razinu vakuuma liofilizacije. Ispitivanje dokazuje da optimizirani parametri vrijede za određene uređaje za liofilizaciju i određene bakterine. Dodatno, optimizirani parametri pokazuju da je liofilizacija upotrebljiva za bilo koji uređaj za liofilizaciju u vakuumu i bilo koji bakterin

Hyperbolicity Measures "Democracy" in Real-World Networks

We analyze the hyperbolicity of real-world networks, a geometric quantity that measures if a space is negatively curved. In our interpretation, a network with small hyperbolicity is "aristocratic", because it contains a small set of vertices involved in many shortest paths, so that few elements "connect" the systems, while a network with large hyperbolicity has a more "democratic" structure with a larger number of crucial elements. We prove mathematically the soundness of this interpretation, and we derive its consequences by analyzing a large dataset of real-world networks. We confirm and improve previous results on hyperbolicity, and we analyze them in the light of our interpretation. Moreover, we study (for the first time in our knowledge) the hyperbolicity of the neighborhood of a given vertex. This allows to define an "influence area" for the vertices in the graph. We show that the influence area of the highest degree vertex is small in what we define "local" networks, like most social or peer-to-peer networks. On the other hand, if the network is built in order to reach a "global" goal, as in metabolic networks or autonomous system networks, the influence area is much larger, and it can contain up to half the vertices in the graph. In conclusion, our newly introduced approach allows to distinguish the topology and the structure of various complex networks

Chronic thoracic hemisection spinal cord injury in adult rats induces a progressive decline in transmission from uninjured fibers to lumbar motoneurons

Although most spinal cord injuries are anatomically incomplete, only limited functional recovery has been observed in people and rats with partial lesions. To address why surviving fibers cannot mediate more complete recovery, we evaluated the physiological and anatomical status of spared fibers after unilateral hemisection (HX) of thoracic spinal cord in adult rats. We made intracellular and extracellular recordings at L5 (below HX) in response to electrical stimulation of contralateral white matter above (T6) and below (L1) HX. Responses from T6 displayed reduced amplitude, increased latency and elevated stimulus threshold in the fibers across from HX, beginning 1-2 weeks after HX. Ultrastructural analysis revealed demyelination of intact axons contralateral to the HX, with a time course similar to the conduction changes. Behavioral studies indicated partial recovery which arrested when conduction deficits began. These findings suggest a chronic pathological state in intact fibers and necessity for prompt treatment to minimize it

Film Edge Nonlocal Spin Valves

Spintronics is a new paradigm for integrated digital electronics. Recently established as a niche for nonvolatile magnetic random access memory (MRAM), it offers new functionality while demonstrating low power and high speed performance. However, to reach high density spintronic technology must make a transition to the nanometer scale. Prototype devices are presently made using a planar geometry and have an area determined by the lithographic feature size, currently about 100 nm. Here we present a new nonplanar geometry in which one lateral dimension is given by a film thickness, the order of 10 nm. With this new approach, cell sizes can shrink by an order of magnitude. The geometry is demonstrated with a nonlocal spin valve, where we study devices with an injector/detector separation much less than the spin diffusion length.Comment: 10 pages, 3 figure

Ultrafast Hole Trapping and Relaxation Dynamics in p-Type CuS Nanodisks

CuS nanocrystals are potential materials for developing low-cost solar energy conversion devices. Understanding the underlying dynamics of photoinduced carriers in CuS nanocrystals is essential to improve their performance in these devices. In this work, we investigated the photoinduced hole dynamics in CuS nanodisks (NDs) using the combination of transient optical (OTA) and X-ray (XTA) absorption spectroscopy. OTA results show that the broad transient absorption in the visible region is attributed to the photoinduced hot and trapped holes. The hole trapping process occurs on a subpicosecond time scale, followed by carrier recombination (~100 ps). The nature of the hole trapping sites, revealed by XTA, is characteristic of S or organic ligands on the surface of CuS NDs. These results not only suggest the possibility to control the hole dynamics by tuning the surface chemistry of CuS but also represent the first time observation of hole dynamics in semiconductor nanocrystals using XTA