This paper studies the asymptotic behavior of solutions for a nonlinear convection diffusion reaction equation in R^n.Firstly,the global existence and uniqueness of classical solutions for small initial data are established.Then,we obtain the L^(p),2≤p≤+∞decay rate of solutions.The approach is based on detailed analysis of the Green function of the linearized equation with the technique of long wave-short wave decomposition and the Fourier analysis.
Dietz, Marko
Machill, Susanne
Hoffmann, Herbert C.
Schmidtke, Knut
Background and aims Nitrate leaching from intensively cropped soils represents a huge environmental problem. In order to diversify the range of nitrogen management strategies, this investigation is focused on the effects of ribwort plantain, Plantago lanceolata L., and its allelochemicals on soil N mineralization. Methods High-performance liquid chromatography was used in this study for phytochemical analysis of the major allelochemicals aucubin, catalpol, and verbascoside. Soil incubation experiments demonstrated a significant suppression of soil N mineralization caused by the incorporation of the iridoid glycoside (IG) aucubin, leaf material of two varieties (P. lanceolata cv. Libor and cv. Arterner), and an aqueous extract of P. lanceolata leaves. Results Throughout the growing season, the two varieties conspicuously differed in aucubin and verbascoside contents as well as in leaf dry weight. In soil incubation experiments, incorporated leaf material of both varieties affected long-term low soil nitrate concentrations. Experimental aucubin application resulted in an inhibitory effect on soil N mineralization. This was not true for the IG catalpol. Furthermore, we observed a negative relationship between IG concentrations and inorganic soil nitrogen concentrations when the soil was incubated with aqueous P. lanceolata leaf extract of different concentrations. Conclusion This study enforced the hypothesis that allelochemicals of P. lanceolata have an active role in a suppression effect on soil N mineralization. Further research may be necessary to investigate the specific effects of P. lanceolata allelochemicals on the nitrogen cycle.
Let A =3D (a(k, m))(k, m) (>=3D 0) be a non-negative matrix and Delta(n) be the forward difference operator of order n for n =3D 1, 2, .... Denote by parallel to A parallel to(p, Delta n) the infimum of those U, satisfying the following inequality: (Sigma(infinity)(k=3D0)vertical bar Sigma(n)(j=3D0)Sigma(infinity)(m=3D0)(-1)(j)((n)(j))a(k+j,m)x(m)vertical bar(p)) <=3D U (Sigma(infinity)(j=3D0)vertical bar x(j)vertical bar(p))((p) over bar), where x is an element of l(p) and p >=3D 1. This paper is focused on the problem of finding parallel to A parallel to(p,Delta n), where A is a matrix operator from l(p) into l(p)(Delta(n)). In particular, we apply our results to well known matrix operators such as Copson, Hilbert, and Norlund.
We present a practical entanglement classification scheme for pure state in form of 2 x L x M x N under the stochastic local operation and classical communication (SLOCC), where every inequivalent class of the entangled quantum states may be sorted out according to its standard form and the corresponding transformation matrix. This provides a practical method for determining the interconverting matrix between two SLOCC equivalent entangled states, and classification examples for some 2 x 4 x M x N systems are also presented.
We show that the generating function of all correlators with N twisted and L untwisted states, i.e. the Reggeon vertex for magnetized branes on R-2 can be computed once the correlator of N nonexcited twisted states and the corresponding Green function are known and we give an explicit expression as a functional of these objects.
It was recently proposed that the leading singularities of the S-Matrix of N = 4 super Yang-Mills theory arise as the residues of a contour integral over a Grassmannian manifold, with space-time locality encoded through residue theorems generalizing Cauchy's theorem to more than one variable. We provide a method to identify the residue corresponding to any leading singularity, and we carry this out explicitly for all leading singularities at tree level and one-loop. We also give several examples at higher loops, including all generic two-loop leading singularities and an interesting four-loop object. As an example we consider a 12-pt N(4)MHV leading singularity at two loops that has a kinematic structure involving double square roots. Our analysis results in a simple picture for how the topological structure of loop graphs is reflected in various substructures within the Grassmannian.
Ay?egül Gündüza
Nurten Uzun Adatepea
Meral E. K?z?ltana
Derya Karadeniza
Ömer Uysalb
Various investigations have revealed a widespread and somewhat controversial pattern of cerebral, cerebellar and brainstem involvement in the pathophysiology of restless legs syndrome (RLS). However, several studies which investigated functional or structural aspects indicated cortical involvement in RLS. In this study, we aimed to analyze circadian changes of cortical excitability in idiopathic RLS patients by means of transcranial magnetic stimulation (TMS). Eleven idiopathic RLS patients and eight healthy age and sex matched subjects were investigated using single-pulse TMS and motor nerve conduction studies during early afternoon when there were no symptoms and late at night (22:00-23:00) when the symptoms reappeared. Central motor conduction time, latencies and amplitudes of scalp and cervical motor evoked potentials, resting and active motor thresholds, and cortical silent period were measured. Measured parameters were similar between RLS patients and healthy subjects during the daytime. At night, cortical silent periods tended to shorten, and motor thresholds tended to decrease in the RLS group, whereas in controls they tended to increase.At night, active motor-threshold measurements were significantly lower in the RLS group (28.5 ± 6.2% vs 40.4 ± 8.4%, p = 0.006). Therefore, we propose that in patients with RLS, conduction along the motor corticospinal axons is normal, with the possible loss of subcortical inhibition at nighttime.
Disclosed is an L order N times digital extracting filter, including a plurality of alternately cascaded accumulator groups and 2 times extractors, wherein L, N and M are natural numbers, N = 2M, an output signal of the 2 times extractor is a signal formed by extracting a value from every other value of an input signal thereof, and L stages of accumulators cascade to form an accumulator group, wherein the output signal end of a previous stage of accumulator is connected to the input signal end of a subsequent stage of accumulator. As compared to a cascade integrator comb extracting filter, the digital extracting filter in the present utility model can solve the stability problem of the cascade integrator comb extracting filter on the basis of realizing the performance of the cascade integrator comb extracting filter.