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For an evolution of metrics (M, g t ) there is a t-smooth family of embeddings e t : M→ R N inducing g t , but in general there is no family of embeddings extending a given initial embedding e. We give an example of this phenomenon when g t is the evolution of g under the Ricci flow. We show that there are embeddings e inducing g which do not admit of t-smooth extensions to e t inducing g t for any t> 0. We also find hypersurfaces of dim > 2 that will not remain a hypersurface under Ricci flow for any positive time. © 2019, Springer Nature B.V  

We prove the optimal W2,∞ regularity for variational problems with convex gradient constraints. We do not assume any regularity of the constraints; so the constraints can be nonsmooth, and they need not be strictly convex. When the domain is smooth enough, we show that the optimal regularity holds up to the boundary. In this process, we also characterize the set of singular points of the viscosity solutions to some Hamilton-Jacobi equations. Furthermore, we obtain an explicit formula for the second derivative of these viscosity solutions; and we show that the second derivatives satisfy a monotonicity property. © 2021 Elsevier Inc  

We prove the optimal W2,∞ regularity for fully nonlinear elliptic equations with convex gradient constraints. We do not assume any regularity about the constraints; so the constraints need not be C1 or strictly convex. We also show that the optimal regularity holds up to the boundary. Our approach is to show that these elliptic equations with gradient constraints are related to some fully nonlinear double obstacle problems. Then we prove the optimal W2,∞ regularity for the double obstacle problems. In this process, we also employ the monotonicity property for the second derivative of obstacles, which we have obtained in a previous work. © 2021 Elsevier Inc  

In this study, plasmonic properties of transition metal atoms (Sc-Zn, Pd, Pt) adsorbed on various sites of graphene sheets were investigated before and after CO adsorption by density functional theory (DFT). To this aim, Electron Energy Loss Spectroscopy (EELS) of these systems were obtained by periodic DFT. The results indicated that the highest in-plane plasmon peaks undergo blue shifts after CO adsorption, in such a way that Co–graphene system demonstrates the highest blue shift of 2.42 eV from Visible to UV region. Also, out-of-plane plasmons do not exhibit significant sensitivity to CO adsorption. For deeper understanding of electronic structure of metal-graphene systems, appropriate... 

How do we enter into empathic relations with inanimate objects (IO)? Do we indirectly infer that they possess mental states, or directly perceive them as mental things? In recent years these questions have been addressed by a number of authors. Some argue in favor of an indirect approach that involves mediatory procedures; others defend a direct approach that postulates no intermediate. In this paper I argue on the side of the latter. I show that Simulation Theory (ST), one of the most elaborated versions of the indirect approach, does not have the capacity to account for our empathy with IO. Investigating ST paves the way for criticizing a special kind of indirect theory, namely Imaginative... 

A general regularity was found based on an effective pair potential of Lennard-Jones LJ (12, 6), for both dense, nonmetallic and nonionic fluids and solids according to which (Z-1) v2 linearly varies with respect to ρ2 for each isotherm, and this equation of state (EoS I) is known as LIR. However, despite the fact that Ne is a simple spherical species, unexpectedly, its solid and liquid phases both show a significant deviation from EoS I. In this work, we have investigated the accuracy of the EoS I for other systems, including quantum light molecules, such as D 2, H 2 and He, in both fluid and solid states at different temperatures. Like Ne, we have noticed that these systems do not well... 

In this study the bioleaching of a low-grade uranium ore containing 480 ppm uranium has been reported. The studies involved extraction of uranium using Acidithiobacillus ferrooxidans derived from the uranium mine samples. The maximum specific growth rate (μ max) and doubling time (t d) were obtained 0.08 h-1 and 8.66 h, respectively. Parameters such as Fe2+ concentration, particle size, temperature and pH were optimized. The effect of pulp density (PD) was also studied. Maximum uranium bio-dissolution of 100 ± 5 % was achieved under the conditions of pH 2.0, 5 % PD and 35 °C in 48 h with the particles of d 80 = 100 μm. The optimum concentration of supplementary Fe2+ was dependent to the PD.... 

Complex product systems (CoPS) industries largely contribute to industrial development, economic growth and creation of national wealth in both developed and developing economies. CoPS also show a number of specific characteristics as a distinctive category of industrial products in comparison with mass-produced consumer goods. These aspects have attracted the attention of scholars to study CoPS over the last two decades, resulting in a fairly extensive body of literature on the subject. However, there is a further need to connect research findings in this area, to illustrate a macro view of the development in the field, explore common themes, and identify possible paths into the future.... 

For the first time, Dysprosium was extracted by the novel method of emulsion liquid membrane in a pulsed packed column in a continuous process. Emulsion liquid membrane (ELM) was comprised of D2EHPA (di-2-ethylhexylphosphoric acid) as carrier and Span 80 (Polysorbate 80) as the surfactant in kerosene as the diluent and nitric acid as internal phase. In this work, the packed column was characterized from a hydrodynamic point of view including flooding condition and holdup at flooding points. Operational parameters affecting the flooding points, such as pulsation intensity and flow rate of continuous and dispersed phases have been studied. It was found that increase in pulsation intensity up...