Sentence examples for in a class of functions from inspiring English sources
This enables us to seek for the optimum in a class of functions and their derivatives instead of a class of shapes.
Hence, due to the analysis performed in [11, 12] we need to study, in a general multidimensional geometry, existence and multiplicity for the elliptic equation (1.4) in a class of functions properly decaying at infinity (in fact exponentially), lim_{|x| rightarrowinfty} u(x)=0.
(1.2) In particular, Sun [23] used a class of functions Y defined in the sequel to establish several Kamenev-type (see [25]) oscillation criteria for (1.2).
A numerical experiment for a class of functions in known Sobolev smoothness classes gives L2 errors for the fully discrete needlet approximation that are almost identical to those for the original semidiscrete needlet approximation.
In [8], by employing a class of function and a generalized Riccati transformation technique, Rogovchenko and Tuncay studied the oscillation of (1.10).
A sensitivity shaping problem is formulated as an approximation problem to the desired frequency response with a function in a class of sensitivity functions with a degree bound.
It is proved that the operator of a boundary value problem of heat conductivity in an infinite angular domain in a class of growing functions is Noetherian with an index which is equal to minus one.
After ward, we utilized the normalized generalized Tremblay operator in a class of analytic functions ( mathcal {A}(m)), with subclasses ( mathcal {S}(m), mathcal {S}_{lambda }^(m)) and ( mathcal {K}_{lambda }(m)) in the open unit disk.
We prove the Hyers-Ulam stability of a 2-dimensional quadratic functional equation in a class of vector variable functions in Banach modules over a unital -algebra.
For this parabolic system, they proved the existence of solution in a class of classically differentiable functions both with respect to time and space under appropriate regularity conditions.
