Lippold's "Full Moon" (1949 50) and "Sun" (1953 56; commissioned by the Metropolitan Museum of Art, New York City, to hang in its room of Persian carpets) show an intuition of a basic regularity, precise order, and completeness that underlies the universe.
Depending on the precise situation and on the regularity required of the solution, boundary conditions at just one or both endpoints of the free surface need to be imposed.
Hairer has found a new approach, called the theory of regularity structures, which gives precise mathematical meaning to a broad class of stochastic PDEs and their solutions.
We will obtain both the precise behavior of the norm Cp and the sharp regularity assumptions on the functions f and g (i.e., the exponent bp) that make this inequality possible.
Estimating depth from binocular disparity is extremely precise, and the cue does not depend on statistical regularities in the environment.
Meanwhile, recent achievements on controlling template regularity and internal structure clearly demonstrate their potency for the precise integration of nanomaterials with high degree of freedom[17, 26 28].
This regularity of a characteristic spectrum is called further as 3-regular heterogeneity, or 3-regularity.
These regularity criteria are based on local Lp regularity or on wavelet coefficients and give a precise information on pointwise behavior.
We need to make precise the sense of solutions that we will handle here and distinguish two types of solutions, according to the regularity of f.
Although this precise methodology has never been employed in the study of nucleolar organizers for prostate cancer, the increasing size and regularity of the nucleoli are a long-standing subjective observation in these tumors [ 4, 5, 39].
