Most of the observational claims in cosmology are based on the assumption that the universe is isotropic and homogeneous so they essentially test different types of Friedmann models. This also refers to recent observations of supernovae Ia, which, within the framework of Friedmann cosmologies give strong support to negative pressure matter and also weaken the age conflict. In this essay we drop...

K 〈x, y〉 dy = ‖x‖ By ‖·‖ we denote the standard Euclidean norm. The notion of isotropic position was extensively studied by V. Milman and A. Pajor [M-P]. Note that our definition is consistent with [K-L-S]. The normalization in [M-P] is slightly different. If the information about the body K is uncomplete it is impossible to bring it exactly to the isotropic position. So, the definition of the ...

A phenomenology of isotropic magnetohydrodynamic (MHD) turbulence subject to both rotation and applied magnetic field is presented. It is assumed that the triple correlation decay time is the shortest between the eddy turn-over time and the ones associated to the rotating frequency and the Alfvén wave period. For Pm=1 it leads to four kinds of piecewise spectra, depending on four parameters: in...

In this treatment method laser radiation, which is guided from a co-axially expanding liquid jet-stream, locally initiates on a metal surface a thermochemical etching reaction, which leads to selective material removal. Time-resolved measurements of the electrical potential were correlated with the specific processing parameters to identify conditions for stable and enhanced chemical etching re...

The change of signature of a metric is explained using simple examples and methods. The Klein-Gordon field on a signature-changing background is discussed, and it is shown how the approach of Dray et al. can be corrected to ensure that the KleinGordon equation holds. Isotropic cosmologies are discussed, and it is shown how the approach of Ellis et al. can be corrected to ensure that the Einstei...

A new class of systems of strongly singular integrodifferential equations is examined, which emerges in the study of the bridged interface crack growth, e.g., in fiber stitched layered composites. This work generalizes the asymptotic analysis of strongly singular integral equations by Willis and Nemat-Nasser [Quart. Appl. Math., 48 (1990), pp. 741–753]. Singular perturbation solutions up to the...

Some conventional machining methods have been developed to machine microelectrodes. However, these methods still require too much time and too many resources. This paper uses electrochemical etching as an alternative method for the simple and cheap fabrication of microelectrodes. Electrochemical etching is usually considered an appropriate method of producing sharp probes. However, it is possib...

A finely layered medium behaves as a homogeneous anisotropic medium at long wavelengths. When each layer is a transversely isotropic viscoelastic (TIV) medium, attenuation anisotropy can be described by a generalization of Backus averaging to the lossy case. We introduce a method to compute the complex and frequency-dependent stiffnesses of the equivalent viscoelastic, homogeneous, transversely...

In 1,2 or 3 dimensions a scalar wave excited by a non-negative source in a viscoelastic medium with a non-negative relaxation spectrum or a Newtonian response or both combined inherits the sign of the source. The key assumption is a constitutive relation which involves the sum of a Newtonian viscosity term and a memory term with a completely monotone relaxation kernel. In higher-dimensional spa...

molecular tumbling causes that anisotropy of nuclear interaction now plays dominant role in the appearance of NMR spectra. Frankly speaking the NMR signals are very broad and spectra become featureless. In general missing isotropic tumbling leads to severe broadening of the detected signals. The lack of resolution, however; does not mean the absence of structure information, it rather reflects ...