Normal forms for real quadratic forms

We investigate the non-diagonal normal forms of a quadratic form on , in particular for n = 3. For this case it is shown that the set of normal forms is the closure of a 5-dimensional submanifold in the 6-dimensional Grassmannian of 2-dimensional subspaces of . Received: 27 June 2008     

Chaotic Motion Generated by Delayed Negative Feedback Part II: Construction of Nonlinearities

We construct a smooth function g* : IR ? IR with such that the equation has a slowly oscillating periodic solution y, and a slowly oscillating solution z* whose phase curve is homoclinic with respect to the orbit o of y in the space C = C⁰([1,0],IR). For an associated Poincaré map we obtain a transversal homoclinic loop. The proof of transversality employs a criterion which uses oscillation properties of solutions of variational equations. The main result is that the trajectories (ψn)^∞_-∞ of the Poincaré map in a neighbourhood of the homoclinic loop form a hyperbolic set on which the motion is chaotic.     

Implicit peer methods for large stiff ODE systems

Implicit two-step peer methods are introduced for the solution of large stiff systems. Although these methods compute s-stage approximations in each time step one-by-one like diagonally-implicit Runge-Kutta methods the order of all stages is the same due to the two-step structure. The nonlinear stage equations are solved by an inexact Newton method using the Krylov solver FOM (Arnoldi??s method). The methods are zero-stable for arbitrary step size sequences. We construct different methods having order p=s in the multi-implicit case and order p=s?1 in the singly-implicit case with arbitrary step sizes and s??5. Numerical tests in Matlab for several semi-discretized partial differential equations show the efficiency of the methods compared to other Krylov codes.     

Cluster-tilted algebras are Gorenstein and stably Calabi-Yau

We prove that in a 2-Calabi-Yau triangulated category, each cluster tilting subcategory is Gorenstein with all its finitely generated projectives of injective dimension at most one. We show that the stable category of its Cohen-Macaulay modules is 3-Calabi-Yau. We deduce in particular that cluster-tilted algebras are Gorenstein of dimension at most one, and hereditary if they are of finite global dimension. Our results also apply to the stable (!) endomorphism rings of maximal rigid modules of [Christof Geiß, Bernard Leclerc, Jan Schröer, Rigid modules over preprojective algebras, arXiv: math.RT/0503324, Invent. Math., in press]. In addition, we prove a general result about relative 3-Calabi-Yau duality over non-stable endomorphism rings. This strengthens and generalizes the Ext-group symmetries obtained in [Christof Geiß, Bernard Leclerc, Jan Schröer, Rigid modules over preprojective algebras, arXiv: math.RT/0503324, Invent. Math., in press] for simple modules. Finally, we generalize the results on relative Calabi-Yau duality from 2-Calabi-Yau to d-Calabi-Yau categories. We show how to produce many examples of d-cluster tilted algebras.     

Benchmark results in vector atmospheric radiative transfer

In this paper seven vector radiative transfer codes are inter-compared for the case of underlying black surface. They include three techniques based on the discrete ordinate method (DOM), two Monte-Carlo methods, the successive orders scattering method, and a modified doubling-adding technique. It was found that all codes give very similar results. Therefore, we were able to produce benchmark results for the Stokes parameters both for reflected and transmitted light in the cases of molecular, aerosol and cloudy multiply scattering media. It was assumed that the single scattering albedo is equal to one. Benchmark results have been provided by several studies before, including Coulson et al. [22], Garcia and Siewert [7], [8], Wauben and Hovenier [10], and Natraj et al. [11] among others. However, the case of the elongated phase functions such as for a cloud and with a high angular resolution is presented here for the first time. Also in difference with other studies, we make inter-comparisons using several codes for the same input dataset, which enables us to quantify the corresponding errors more accurately.     

Characterization of the perceived sound of trauma-induced tinnitus in gerbils

Tinnitus often develops following inner ear pathologies, like acoustic trauma. Therefore, an acoustic trauma model of tinnitus in gerbils was established using a modulated acoustic startle response. Cochlear trauma evoked by exposure to narrow-band noise at 10 kHz was assessed by auditory brainstem responses (ABR) and distortion product otoacoustic emissions (DPOAE). Threshold shift amounted to about 25 dB at frequencies >?10 kHz. Induction of a phantom-noise perception was documented by an acoustic startle response paradigm. A reduction of the gap-prepulse inhibition of acoustic startle (GPIAS) was taken as evidence for tinnitus at the behavioral level. Three to five weeks after trauma the ABR and DPOAE thresholds were back to normal. At that time, a reduction of GPIAS in the frequency range 16-20 kHz indicated a phantom noise perception. Seven weeks post trauma the tinnitus-affected frequency range became narrow and shifted to the center-trauma frequency at 10 kHz. Taken together, by investigating frequency-dependent effects in detail, this study in gerbils found trauma-evoked tinnitus developing in the frequency range bordering the low frequency slope of the induced noise trauma. This supports the theory of lateral inhibition as the physiological basis of tinnitus.     

Dynamic-range compression affects the lateral position of sounds

Dynamic-range compression acting independently at each ear in a bilateral hearing-aid or cochlear-implant fitting can alter interaural level differences (ILDs) potentially affecting spatial perception. The influence of compression on the lateral position of sounds was studied in normal-hearing listeners using virtual acoustic stimuli. In a lateralization task, listeners indicated the leftmost and rightmost extents of the auditory event and reported whether they heard (1) a single, stationary image, (2) a moving/gradually broadening image, or (3) a split image. Fast-acting compression significantly affected the perceived position of high-pass sounds. For sounds with abrupt onsets and offsets, compression shifted the entire image to a more central position. For sounds containing gradual onsets and offsets, including speech, compression increased the occurrence of moving and split images by up to 57 percentage points and increased the perceived lateral extent of the auditory event. The severity of the effects was reduced when undisturbed low-frequency binaural cues were made available. At high frequencies, listeners gave increased weight to ILDs relative to interaural time differences carried in the envelope when compression caused ILDs to change dynamically at low rates, although individual differences were apparent. Specific conditions are identified in which compression is likely to affect spatial perception.     

Coexistence of magnetic fluctuations and superconductivity in the pnictide high temperature superconductor SmFeAsO1-xFx measured by muon spin rotation

Muon spin rotation experiments were performed on the pnictide high temperature superconductor SmFeAsO1-xFx with x=0.18 and 0.3. We observed an unusual enhancement of slow spin fluctuations in the vicinity of the superconducting transition which suggests that the spin fluctuations contribute to the formation of an unconventional superconducting state. An estimate of the in-plane penetration depth lambda ab(0)=190(5) nm was obtained, which confirms that the pnictide superconductors obey an Uemura-style relationship between Tc and lambda ab(0);(-2).