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We describe the main results obtained in a joint work with Athanasopoulos and Caffarelli on the regularity of viscosity solutions and of their free boundaries for a rather general class of parabolic phase transition problems.
      
It also has the ability to conveniently incorporate boundaries and creases into a smooth limit shape of models.
      
As a result, the boundaries between the surface crystals become a little larger with prolonging the period of ageing time.
      
With increasing the amount of salt, there was hardly influence on the growth rate along c-axis, whereas an obvious decline was observed in the growth rate along either a-axis or b-axis, which enlarges the boundaries between the surface crystals.
      
The use of a temperature as high as 473 K produces a membrane composed of bar-like crystals with larger boundaries.
      
A nonlinear equation that is satisfied by the optimal exercise boundaries of the perpetual Bermudan option is found.
      
With the reduction of the parameter combination, the intergranular phase γ-(Fe, Ni) is formed in the grain boundaries of Ni-Al intermetallic matrix instead of the intergranular phase α-Fe, and large amount of intermetallics are obtained.
      
It is found that route B can get a high angle grain boundaries distribution in the workpiece than other routes.
      
The effect of NbC precipitates on suppressing recrystallization has been widely investigated, mostly focusing on the Zener pinning of NbC on grain boundaries.
      
Solutions for a completely saturated porous elastic solid with impeded boundaries
      
With this model, the design of concrete production system is placed in the whole system and tested with related dynamic impactions and interactions under complicated boundaries.
      
Phase portraits of the variable-structure systems which define the boundaries of the integral funnels were constructed.
      
For the zero solution of the difference equation x(n) = ax(n - m) + bx(n - k) with arbitrary delays k, m, the formulas of the stability domain boundaries were derived.
      
It is shown that an appropriate variational problem with unfastened boundaries is equivalent to the discovery of a chain of subspaces, which is generated by a polynomial in an isometric operator in an abstract Hilbert space.
      
A mathematical model for determination of the layer boundaries in the horizontal well-boring systems was considered, and a method to resolve it on the basis of the A.N.
      
On Extreme Disentanglement of Clutters in the Polesskii Estimates of the Boundaries of Combinatorial Reliability of Random Binar
      
Consideration was given to the so-called "Polesskii estimates" which define new, more accurate reliability boundaries of the random binary systems as compared with the classical Esary-Proshan estimates.
      
The results of comparing the Polesskii estimates with other possible lines to attack the approachment of the boundaries of combinatorial reliability of the random binary systems were presented.
      
Morphological characteristics of the prototype wing pattern can be used in lepidopteran population studies as markers of population groups and interpopulation boundaries.
      
Significant differences in the conditions of particle localization at the boundaries between polymer phases and between two low-molecular-weight liquids arising from the specific features of polymer adsorption were demonstrated.
      
 

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