11 research outputs found

    On some inflation model based on the past price dynamics

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    The paper describes a model of a price movement path formed upon the past dynamics, following from a couple of assumptions. A system of delayed differential equations has been built and the properties of solutions analyzed. At the end, the main conclusions drawn from the model are presented.inflation, economic system, a delay vector, a price movement path

    On the supercritically diffusive magneto-geostrophic equations

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    We address the well-posedness theory for the magento-geostrophic equation, namely an active scalar equation in which the divergence-free drift velocity is one derivative more singular than the active scalar. In the presence of supercritical fractional diffusion given by (-\Delta)^\gamma, where 0<\gamma<1, we discover that for \gamma>1/2 the equations are locally well-posed, while for \gamma<1/2 they are ill-posed, in the sense that there is no Lipschitz solution map. The main reason for the striking loss of regularity when \gamma goes below 1/2 is that the constitutive law used to obtain the velocity from the active scalar is given by an unbounded Fourier multiplier which is both even and anisotropic. Lastly, we note that the anisotropy of the constitutive law for the velocity may be explored in order to obtain an improvement in the regularity of the solutions when the initial data and the force have thin Fourier support, i.e. they are supported on a plane in frequency space. In particular, for such well-prepared data one may prove the local existence and uniqueness of solutions for all values of \gamma \in (0,1).Comment: 24 page

    Strong [CII] emission at high redshift

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    We report the detection of the [CII]157.74um fine-structure line in the lensed galaxy BRI 0952-0115 at z=4.43, using the APEX telescope. This is the first detection of the [CII] line in a source with L_FIR < 10^13 L_sun at high redshift. The line is very strong compared to previous [CII] detections at high-z (a factor of 5-8 higher in flux), partly due to the lensing amplification. The L_[CII]/L_FIR ratio is 10^-2.9, which is higher than observed in local galaxies with similar infrared luminosities. Together with previous observations of [CII] at high redshift, our result suggests that the [CII] emission in high redshift galaxies is enhanced relative to local galaxies of the same infrared luminosity. This finding may result from selection effects of the few current observations of [CII] at high redshift, and in particular the fact that non detections may have not been published (although the few published upper limits are still consistent with the [CII] enhancement scenario). If the trend is confirmed with larger samples, it would indicate that high-z galaxies are characterized by different physical conditions with respect to their local counterparts. Regardless of the physical origin of the trend, this effect would increase the potential of the [CII]158um line to search and characterize high-z sources.Comment: Accepted for publication in A&A Letters, 5 pages, 2 figure

    On the second iterate for active scalar equations

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    We consider an iterative resolution scheme for a broad class of active scalar equations with a fractional power \gamma of the Laplacian and focus our attention on the second iterate. The main objective of our work is to analyze boundedness properties of the resulting bilinear operator, especially in the super-critical regime. Our results are two-fold: we prove continuity of the bilinear operator in BMO^{1-2\gamma} - a fractional analogue of the Koch-Tataru space; for equations with an even symbol we show that the B^{-\gamma}_{\infty,q} -regularity, where q > 2, is in a sense a minimal necessary requirement on the solution.Comment: This paper has been withdrawn by the author due to a crucial error in Section 3.

    Toxic Metal Contamination Treatment with Microbes

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    Glass-ionomer Cements in Restorative Dentistry: A Critical Appraisal

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