By suitable approximation of the "minimum" function we then obtain from Corollary 4.1 the following analogue of Theorem 1.4.
Let F ∈ C ( S n − 1 ) be a non-constant even function, such that: F ( u ) ≥ 0 if f ( u ) < 0, and F ( u ) = 0 if f ( u ) ≥ 0. By suitable approximation of the function F with spherical harmonics, we can find a nonnegative even function G ∈ H n and an even function H ∈ H n such that 〈 f, G 〉 < 0, and G = H ∗ g. (4.6).
We have shown that by a suitable approximation of J ( H ~, H ), it is possible to solve this type of problem for several interesting applications such as standard MIMO channel estimation, L-optimality criterion, MMSE channel equalization, and ZF precoding.
In Section 3, we show that the stochastic Feynman-Kac functional defined by V t,x)= int_{0}^{t} int_{{mathbb {R}}}deltabigl(W^{x}_{t-r}-y bigr)B dr,dy) (1.5) is well defined and exponentially integrable by using a suitable approximation of the Dirac delta function under some suitable conditions.
In other words, we have chosen a C 2 uniform approximation of the truncation ( v − V R ) + / ( V F − V R ) with x + = max ( x, 0 ) obtained by integrating twice a smooth suitable approximation of the δ ( V − V R ) / ( V F − V R ).
Therefore, the common practice is to choose a suitable approximation of the ideal compensator.
Using a suitable approximation of the grid velocities evaluated at the locations in time prescribed by the specific ODE time integrator, a GCL compliant scheme can be constructed which retains the design temporal accuracy of the underlying ODE time integrator.
For this model to produce a suitable approximation of reality, the supply-constrained sectors must correspond to tradable goods.
We chose 1300 m as the nearest suitable approximation of a sprint distance to obtain a sufficient number of performances data.
For failure probability estimates of large structural systems, the numerical expensive evaluations of the limit state function have to be replaced by suitable approximations.
Ernst Mach's notion of the economy of thought is related to the demand of manageability, which is important especially in the engineering sciences and other applied sciences: for example, a mathematical equation can be made "simpler" by suitable approximations, so that it can be solved by a computer.
