Differential Chow Form for Projective Differential Variety

In this paper, a generic intersection theorem in projective differential algebraic geometry is presented. Precisely, the intersection of an irreducible projective differential variety of dimension d>0 and order h with a generic projective differential hyperplane is shown to be an irreducible projective differential variety of dimension d-1 and order h. Based on the generic intersection theorem, the Chow form for an irreducible projective differential variety is defined and most of the properties of the differential Chow form in affine differential case are established for its projective differential counterpart. Finally, we apply the differential Chow form to a result of linear dependence over projective varieties given by Kolchin.Comment: 17 page

The critical role of the boundary layer thickness for the Initiation of aeolian sediment transport

Here, we propose a conceptual framework of Aeolian sediment transport initiation that includes the role of turbulence. Upon increasing the wind shear stress τ above a threshold value τ′t , particles resting at the bed surface begin to rock in their pockets because the largest turbulent fluctuations of the instantaneous wind velocity above its mean value u¯ induce fluid torques that exceed resisting torques. Upon a slight further increase of τ , rocking turns into a rolling regime (i.e., rolling threshold τt≃τ′t ) provided that the ratio between the integral time scale Ti∝δ/u¯ (where δ is the boundary layer thickness) and the time Te∝√d/[(1−1/s)g] required for entrainment (where d is the particle diameter and s the particle–air–density ratio) is sufficiently large. Rolling then evolves into mean-wind-sustained saltation transport provided that the mean wind is able to compensate energy losses from particle-bed rebounds. However, when Ti/Te is too small, the threshold ratio scales as τt/τ′t∝Te/Ti∝sd2/δ2 , consistent with experiments. Because δ/d controls Ti/Te and the relative amplitude of turbulent wind velocity fluctuations, we qualitatively predict that Aeolian sediment transport in natural atmospheres can be initiated under weaker (potentially much weaker) winds than in wind tunnels, consistent with indirect observational evidence on Earth and Mars

A New Phase Transition Related to the Black Hole's Topological Charge

The topological charge $\epsilon$ of AdS black hole is introduced in Ref.[1,2], where a complete thermodynamic first law is obtained. In this paper, we investigate a new phase transition related to the topological charge in Einstein-Maxwell theory. Firstly, we derive the explicit solutions corresponding to the divergence of specific heat $C_{\epsilon}$ and determine the phase transition critical point. Secondly, the $T-r$ curve and $T-S$ curve are investigated and they exhibit an interesting van der Waals system's behavior. Critical physical quantities are also obtained which are consistent with those derived from the specific heat analysis. Thirdly, a van der Waals system's swallow tail behavior is observed when $\epsilon>\epsilon_{c}$ in the $F-T$ graph. What's more, the analytic phase transition coexistence lines are obtained by using the Maxwell equal area law and free energy analysis, the results of which are consistent with each other.Comment: 11 pages, 5 figure

Attractive Interaction between Vortex and Anti-vortex in Holographic Superfluid

Annihilation process of a pair of vortices in holographic superfluid is numerically simulated. The process is found to consist of two stages which are amazingly separated by vortex size $2r$. The separation distance $\delta(t)$ between vortex and anti-vortex as a function of time is well fitted by $\alpha (t_{0}-t)^{n}$, where the scaling exponent $n=1/2$ for $\delta (t)>2r$, and $n=2/5$ for $\delta(t)<2r$. Then the approaching velocity and acceleration as functions of time and as functions of separation distance are obtained. Thus the attractive force between vortex and anti-vortex is derived as $f(\delta)\propto 1/\delta^{3}$ for the first stage, and $f(\delta)\propto 1/\delta^{4}$ for the second stage. In the end, we explained why the annihilation rate of vortices in turbulent superfluid system obeys the two-body decay law when the vortex density is low.Comment: 14 pages, 5 figure

The Photometric Investigation of V921 Her using the Lunar-based Ultraviolet Telescope of Chang'e-3 mission

The light curve of V921 Her in ultraviolet band observed by the Lunar-based Ultraviolet Telescope (LUT) is analyzed by the Wilson-Devinney code. Our solutions conclude that V921 Her is an early type marginal contact binary system with an additional close-in component. The binary system is under poor thermal contact with a temperature difference of nearly $700K$ between the two components. The close-in component contributes about $19\,\%$ of the total luminosity in the triple system. Combining the radial velocity study together with our photometric solutions, the mass of the primary star and secondary one are calculated to be $M_1 = 1.784(\pm0.055)M_\odot$, $M_2 = 0.403(\pm0.012)M_\odot$. The evolutionary scenario of V921 Her is discussed. All times of light minimum of V921 Her available in the bibliography are taken into account and the $O - C$ curve is analyzed for the first time. The most probable fitting results are discussed in the paper, which also confirm the existence of a third component ($P_3=10.2$ year) around the binary system. The period of V921 Her is also undergoing a continuously rapid increase at a rate of $dP/dt=+2.79\times{10^{-7}}day\cdot year^{-1}$, which may due to mass transfer from the less massive component to the more massive one

Effects of vitamins and trace-elements supplementation on milk production in dairy cows: A review

During the past decade, significant advances were made in understanding the effects of vitamins and trace-elements supplement on milk production of dairy cows. This work discussed the effects of vitamins and trace-elements supplementation on milk production of dairy cows. Studies have indicated that vitamin A (VA) and β-carotene (BC) supplementation have some effects on udder health and milk yield in dairy cows whose intake is below 110 IU/kg BW/day. If low quality forage is fed, supplementation of VA should be considered. Supplementation of B-vitamin has important effects on milk production and could increase milk yield and milk component production. The effect of vitamin E (VE) and selenium (Se) supplementation on the milk yield and milk components are not unified due to the optimum dose, route and timing of VE administration in lactational dairy cows. Zinc (Zn) supplementation increases lactation performance and reduces milk somatic cell count (SCC) in most studies. Limited research has indicated that copper (Cu) supplementation could reduce milk SCC. Before deciding to supplement vitamins and trace-minerals indicated earlier for the improvement of milk production of lactational cows, farmers should have their animals fed with tested and evaluated rations to be sure of the levels of supplementation which may be warranted.Keywords: Vitamin, trace-element, dairy cow, milk productio

Decoupling of economic growth from CO₂ emissions in Yangtze River Economic Belt cities

Cities play significant roles in mitigating global climate change and formulating low carbon roadmaps. As the first regional strategy that prioritizes green development, the Yangtze River Economic Belt (YREB) is an economic circle along the Yangtze River, stringing up 11 provinces and municipalities from west to east of China. The huge regional heterogeneity in terms of economic development, size, and structure in YREB cities need differentiated emission reduction strategies and low-carbon development pathways. This study compiled the CO2 emission inventories of 85 cities in the YREB for the first time and explored the decoupling of economic growth from CO2 emissions at the city level. The results show that CO2 emissions of YREB cities increased at an annual average rate of 5.1% from 2005 to 2017, and 85 YREB cities emitted 44% of national total CO2 emissions and contributed 41% of national GDP in 2017. 61% of cities dominated by high-tech and service industry achieved decoupling between economic development and emissions before 2009 and are moving forward to a stronger decoupling state. 25% of cities achieved decoupling after 2009 and these post-decoupling cities took the heavy industry and light industry as their leading industries. Resource-based cities with slow economic development and high CO2 emissions changed from decoupling to negative decoupling or coupling. The proposed differentiated low-carbon development pathways for YREB cities could provide references for cities at different stages to achieve decoupling of GDP from CO2 emissions and emission reduction goals