Dual models for p-form mimetic gravity and their connection to perfect fluids consisting of (p+1)-branes

We propose an approach that allows one to reformulate $n$-dimensional $p$-form mimetic gravity (including usual mimetic gravity as particular case $p = 0$) as nonlinear $(n-p-1)$-form electrodynamics via electric-magnetic duality. The resulting dual Lagrangian density is just the square root of the ordinary quadratic Lagrangian density of $(n-p-1)$-form electrodynamics. By applying field transformation in the action, we show that for the arbitrary $p$ this dual theory transforms into the $(p+1)$-brane fluid: the model of the stack of the parallel $(p+1)$-branes foliating physical spacetime. As the structure of the field transformations depends on $p$, the sets of solutions in these models are related differently. We prove, that for $p = 0$ and $p = n-2$ dual mimetic models describe usual particle fluid with the potential flow and to the $(n-1)$-brane fluid respectively. For other values of $p$ not all mimetic solutions behave like that, in general, so we restrict ourselves only to the case $n = 4$, $p = 1$. In this case, we show, that mimetic formulation is dual to the well-known Nielsen-Olesen theory of "dual strings" and discuss the criterion indicating whether its solutions behave like string fluid.Comment: 12 page

Aspects of geometric calculation of the planetary gear train with intermediate rollers. Part 1

The paper presents the geometric calculation of the planetary gear train with intermediate rollers, where the number of intermediate rollers is greater or less than that of the teeth in the annular gear by one, the profile surface of the annular gear teeth being the same. The gear ratio is changed by both a value and a sign

Load analysis of the planetary gear train with intermediate rollers. Part 2

The paper presents the load analysis of the planetary gear train with intermediate rollers based on solving a statically indeterminate problem including contact area problems

Application of the calculation method for calculating an economically justified land tax

The article considers the mechanism used to calculate the land tax. caused by the overestimation by the state of the cadastral value of land plots used as a tax base, which leads to the problem of economically unreasonable taxation for taxpayers. The directions for improving the mechanism of land tax calculation and changing the practice of taxation have been formed. The analysis of normative legal base, taxation practice, statistical data, economic publications devoted to the mechanism of land tax assessment has been carried out. The article contains judgments of the continuous presence of a significant overestimation of the tax base for the land tax in the tax system of Russia, which leads to the unreliable definition of the taxpayer’s tax liability. It is concluded that in case of disagreement of an organization or an individual with the amount of tax base, its revision is carried out within the framework of tax relations using the principle of economic feasibility and equality of taxation and calculation method developed by economic science to protect taxpayer’s rights