Results 1 - 10 of 3403
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[en] In this work, we determine the critical exponent for a weakly coupled system of semilinear wave equations with distinct scale-invariant lower-order terms, when these terms make both equations in some sense “parabolic-like.” For the blow-up result, the test functions method is applied, while for the global existence (in time) results, we use – estimates with additional regularity.
[en] The main goal of the adaptive local strategy consists in reducing the complexity of computational problems. We propose a new approach to curve approximation and smoothing based on 4-point transformations or Discrete Projective Transform (DPT). In the framework of DPT, the variable point is related to three data points (accompanying points ). The variable y -ordinate is expressed via the convolution of accompanying y -ordinates and weight functions that are defined as cross-ratio functions of four x -coordinates. DPT has some attractive properties (natural norming, scale invariance, threefold symmetry, and “4-point” orthogonality ), which are useful in designing new algorithms. Diverse methods and algorithms based on DPT have been developed.
[en] Utilizing the inherent scale-invariance of Maxwell's Equations, classical electrodynamics is incorporated into the theory of scale-invariant gravity. In this incorporation the gravitational constant G is shown to transform like β-2(β is the gauge function), the generalized Lorentz Force Law is derived, the electric charge is shown to be invariant under gauge transformation, and matter creation is shown to be a necessity. In all nontrivial gauges a modified version of QED is obtained. The deviation from standard QED, however, is shown to be beyond the range of experimental detection when G α β-2. (orig.)
[en] The results of seismic investigations based on methods of the theory of nonequilibrium processes and self-similarity theory have shown that a shallow earthquake can be treated as a critical transition that occurs during the evolution of a non-equilibrium seismogenic system and is preceded by phenomena such as the scale invariance of spatiotemporal seismic structures. The implication is that seismicity can be interpreted as a purely multifractal process. Modeling the focal domain as a fractal cluster of microcracks allows formulating the prognostic signatures of earthquakes actually observed in seismic data. Seismic scaling permits monitoring the state of a seismogenic system as it approaches instability. (reviews of topical problems)
[en] The present theories of galaxy formation are reviewed. The relation between peculiar velocities and the correlation function of galaxies points to the possibility that galaxies do not form uniformly everywhere. Scale invariant properties of the cluster-cluster correlations are discussed. Comparing the correlation functions in a dimensionless way, galaxies appear to be stronger clustered, in contrast with the comparison of the dimensional amplitudes of the correlation functions. Theoretical implications of several observations as Lyman-α clouds, correlations of faint galaxies are discussed. None of the present theories of galaxy formation can account for all facts in a natural way. 29 references
[en] We advance scale-invariance arguments for systems that are governed (or approximated) by a q-Gaussian distribution, i.e., a power law distribution with exponent Q=1/(1-q); q element of R. The ensuing line of reasoning is then compared with that applying for Gaussian distributions, with emphasis on dimensional considerations. In particular, a Gaussian system may be part of a larger system that is not Gaussian, but, if the larger system is spherically invariant, then it is necessarily Gaussian again. We show that this result extends to q-Gaussian systems via elliptic invariance. The problem of estimating the appropriate value for the Tsallis' parameter q is revisited. A kinetic application is also provided
[en] Scale-invariant running couplings are constructed for several quarks being decoupled together, without reference to intermediate thresholds. The result is a multi-scale generalization of the renormalization group without the discontinuities caused by having just a single running coupling. The method is applicable to any order
[en] The simple parton model leads to the Bjorken scaling law only for rather large values of the transfer. For small values, the scale invariance is broken by a purely kinematical effect which is shown to depend on: (1+(4M2x2/Q2))sup(1/2)-1, M being the mass of the target nucleon. Thus, one has to consider: ν>=5M (5GeV) and: Q2>=10M2x (9GeV/c)2 for the whole x range) if it is demanded that scaling holds within 10% to error
[en] The ratio RK,AA'=AFKA'(x,Q2)/A'FKA(x,Q2) (K=2,3) of structure functions of A and A' nuclei at x → 0.1 in the rescaling model is considered. A simple parametrization for RK,AA' compatible with its behaviour at x ∼ 0.1 is proposed. The parametrization slightly depends on Q2 and well agrees with experimental data in the 0.2≤x≤0.7 region