Sharif Digital Repository

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  

Aromatic aldehydes and ketones are readily acetalized or ketalized under microwave irradiation in the presence of water as a solvent  

A four-step synthetic strategy was applied to achieve novel methacrylic monomers. 5-Norbornene-2,2-dimethanol was prepared from a Diels–Alder reaction of cyclopentadiene and acrolein, followed by the treatment of the adduct with an HCHO/KOH/MeOH solution. The resulting 1,3-diol (1) was then acetalized with different aromatic aldehydes having OH groups on the ring to produce four spiroacetal derivatives. The reaction of methacryloyl chloride with the phenolic derivatives led to four new methacrylic monomers that were identified spectrochemically (mass, FTIR, 1H-NMR, and 13C-NMR spectroscopy). Free radical solution polymerization was used to prepare novel spiroacetal–norbornene containing... 

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... 

A combination of silica chloride and wet SiO2 was used as an effective deacetalizating agent for the conversion of acetals to their corresponding carbonyl derivatives under mild and heterogeneous condition