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101.
102.
In this paper, we prove a uniqueness theorem for a free boundary problem which is given in the form of a variational inequality. This free boundary problem arises as the limit of an equation that serves as a basic model in population biology. Apart from the interest in the problem itself, the techniques used in this paper, which are based on the regularity theory of variational inequalities and of harmonic functions, are of independent interest, and may have other applications.
103.
This paper presents a variational inequality (VI) approach to the problem of minimizing a sum of p-norms. First the original problem is reformulated as an equivalent linear VI. Then an improved extra-gradient method is presented
to solve the linear VI. Applications to the problem of p-norm Steiner Minimum Trees (SMT) shows that the proposed method is effective. Comparison with the general extra-gradient
method is also provided to show the improvements of the new method. 相似文献
104.
本文对广义风险过程中的渐近方差作了非参数估计,得出并证明了两个定理,为广义风险过程中破产概率的区间估计作了理论准备. 相似文献
105.
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Summary Equilibrium equations and stability conditions for the simple deformable elastic body are derived by means of considering
a minimum of the static energy principle. The energy is supposed to be sum of the volume (elastic) and the surface terms.
The ability to change relative positions of different material particles is taken into account, and appropriate natural definitions
of the first and second variations of the energy are introduced and calculated explicitly. Considering the case of negligible
magnitude of the surface tension, we establish that an equilibrium state of a nonhydrostatically stressed simple elastic body
(of any physically reasonable elastic energy potential and of any symmetry) possessing any small smooth part of free surface
is always unstable with respect to relative transfer of the material particles along the surface. Surface tension suppresses
the mentioned instability with respect to sufficiently short disturbances of the boundary surface and thus can probably provide
local smoothness of the equilibrium shape of the crystal. We derive explicit formulas for critical wavelength for the simplest
models of the internal and surface energies and for the simplest equilibrium configurations. We also formulate the simplest
problem of mathematical physics, revealing peculiarities and difficulties of the problem of equilibrium shape of elastic crystals,
and discuss possible manifestations of the above-mentioned instability in the problems of crystal growth, materials science,
fracture, physical chemistry, and low-temperature physics. 相似文献
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