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1.
《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2021,38(5):1337-1371
In this paper we consider minimizers of the functional where is a bounded open set and where are the first k eigenvalues on Ω of an operator in divergence form with Dirichlet boundary condition and with Hölder continuous coefficients. We prove that the optimal sets have finite perimeter and that their free boundary is composed of a regular part, which is locally the graph of a -regular function, and a singular part, which is empty if , discrete if and of Hausdorff dimension at most if , for some . 相似文献
2.
《Arabian Journal of Chemistry》2022,15(6):103805
In this research work, selenium dioxide (SeO2) nanorods have been prepared by a solvothermal method in which a strong reducing agent (NaBH4) was used to reduce precursor salt into SeO2 nanorods. X-ray diffraction (XRD) technique was applied to observe the crystal structure which confirmed its tetragonal geometry. Moreover, morphology and particle size were studied by scanning electron microscopy (SEM). SEM fully described the 1-dimensional morphology of SeO2 nanorods which then arranged themselves to create a 3-dimensional flower-like structure with an average particle size of 50 nm. Also, the catalytic activity of SeO2 nanorods as diesel-additive was studied by defining different parameters such as fire and flash points, calorific value, cloud and pour points, specific gravity, and kinematic viscosity. Subsequently, SeO2 nanorods proved to be an excellent diesel additive due to higher total heat content and lower value of kinematic viscosity which enhances the better performance of the diesel engine. 相似文献
3.
Transformation hydrodynamics and the corresponding metamaterials have been proposed as a means to exclude the drag force acting on an object. Here, we report a strategy to deploy the hydrodynamic cloaks in a more practical manner by assembling different-shaped cloaking parts. Our strategy is to first model a square-shaped cloak and a carpet cloak and then combine them to conceal a more complex-shaped space in the three-dimensional hydrodynamic flow. With the derivation of transformation hydrodynamics, the coordinate transformations for each hydrodynamic cloaking are demonstrated with the calculated viscosity tensors. The pressure and velocity fields of the square, triangular (carpet), and exemplary three-dimensional house-shaped cloaks are numerically simulated, thus showing a cloaking effect and reduced drag. This study suggests an efficient way of cloaking complex architectures from fluid-dynamic forces. 相似文献
4.
In this paper, we discuss the viscosity solutions of the weakly coupled systems of fully nonlinear second-order degenerate parabolic equations and their Cauchy-Dirichlet problem. We prove the existence, uniqueness and continuity of viscosity solution by combining Perron's method with the technique of coupled solutions. The results here generalize those in Proc. London Math. Soc. 63 (1991) 212-240 and Comm. Partial Differential Equations 16 (1991) 1095-1128. 相似文献
5.
Somyot Plubtieng Rattanaporn Punpaeng 《Journal of Mathematical Analysis and Applications》2007,336(1):455-469
In this paper, we introduce two iterative schemes by the general iterative method for finding a common element of the set of an equilibrium problem and the set of fixed points of a nonexpansive mapping in a Hilbert space. Then, we prove two strong convergence theorems for nonexpansive mappings to solve a unique solution of the variational inequality which is the optimality condition for the minimization problem. These results extended and improved the corresponding results of Marino and Xu [G. Marino, H.K. Xu, A general iterative method for nonexpansive mapping in Hilbert spaces, J. Math. Anal. Appl. 318 (2006) 43-52], S. Takahashi and W. Takahashi [S. Takahashi, W. Takahashi, Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces, J. Math. Anal. Appl. 331 (1) (2007) 506-515], and many others. 相似文献
6.
Recently, the authors have proposed a new necessary and sufficient condition for turnpike optimality in calculus of variations
with singular Euler equation. The method is based on a characterization of the value function and generalizes the well known
method based on the Green theorem. Furthermore, it allows the optimality of a competition between several turnpikes to be
characterized. For a class of such problems not enjoying the turnpike property, we give an explicit formula for the value
function and show how to characterize the optimal solution as the limiting solution of a family of perturbed problems satisfying
the turnpike property. The considered problems are scalar with infinite horizon. 相似文献
7.
C. Baumgarten B. Braun G. Court G. Ciullo P. Ferretti G. Graw W. Haeberli M. Henoch R. Hertenberger N. Koch H. Kolster P. Lenisa A. Nass S.P. Pod'yachev D. Reggiani K. Rith M.C. Simani E. Steffens J. Stewart T. Wise 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2002,18(1):37-49
The use of storage cells has become a standard technique for internal gas targets in conjunction with high energy storage
rings. In case of spin-polarized hydrogen and deuterium gas targets the interaction of the injected atoms with the walls of
the storage cell can lead to depolarization and recombination. Thus the number of wall collisions of the atoms in the target
gas is important for modeling the processes of spin relaxation and recombination. It is shown in this article that the diffusion
process of rarefied gases in long tubes or storage cells can be described with the help of the one-dimensional diffusion equation.
Mathematical methods are presented that allow one to calculate collision age distributions (CAD) and their moments analytically.
These methods provide a better understanding of the different aspects of diffusion than Monte Carlo calculations. Additionally
it is shown that measurements of the atomic density or polarization of a gas sample taken from the center of the tube allow
one to determine the possible range of the corresponding density weighted average values along the tube. The calculations
are applied to the storage cell geometry of the HERMES internal polarized hydrogen and deuterium gas target.
Received 9 July 2001 and Received in final form 18 September 2001 相似文献
8.
J. Teixeira 《Il Nuovo Cimento D》1994,16(9):1433-1437
Summary The dynamics of water molecules occupying very small volumes can be probed by incoherent quasi-elastic neutron scattering.
We summarise some results obtained with wet samples of porous silica and hydrated proteins. The movements of the molecules
in the vicinity of the substrate are extremely reduced as compared to those of bulk water at the same temperature. Almost
only rotational movements subsist and the local diffusion is of the order of that observed in deeply supercooled water.
Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994. 相似文献
9.
Blends of polyarylate of bisphenol A, PAr, with two commercial main chain liquid crystalline polymers, Vectra A950 and Vectra B950, are studied. From dynamic viscoelastic measurements it is deduced that both systems (PAr/Vectra A950 and PAr/Vectra B950) are immiscible and scanning electron microscopy (SEM) micrographs show the presence of spherical domains of the liquid crystalline polymer when PAr constitutes the matrix. Extrusion capillary measurements reveal that, under conditions of temperature and shear rate similar to those of processing, the viscosity is reduced to approximately 10% of its value when the content of liquid crystalline polymer is only 20%. This great improvement of the rheological properties is observed in both PAr/Vectra A950 and PAr/Vectra B950 blends. The effect of draw ratio on Young's modulus for different compositions is also analyzed, pointing out the reinforcing action of both liquid crystalline polymers on polyarylate: for instance, 20% of Vectra B950 in the blend gives rise to a 700% increase of the modulus of fibres prepared at a draw ratio of 50. SEM of the extrudates reveals that the spherical domains are elongated at the entrance of the capillary giving rise to a microfibrillar morphology which is related to the excellent rheological and mechanical properties of the blends. 相似文献
10.
The solvability of a class of forward-backward stochastic differential equations (SDEs for short) over an arbitrarily prescribed time duration is studied. The authors design a stochastic relaxed control problem, with both drift and difftusion all being controlled, so that the solvability problem is converted to a problem of finding the nodal set of the viscosity solution to a certain Hamilton-Jacobi-Bellman equation. This method overcomes the fatal difficulty encountered in the traditional contraction mapping approach to the existence theorem of such SDEs. 相似文献