where ψ y,z,t) is a differentiable function; j, k, m, and l are integers; u0 x,y,z,t) is a special solution of Equation 2; f is a function to be determined later.
Let (H=L^{2}((a,b);mathbb{R})) and consider the Fredholm integral equation of the first kind int_{a}^{b}k t,s f(s),ds=g(t),quad tin[a,b], (1) where (k(cdot,cdot)) and g are known functions, and f is the unknown function to be determined.
Consider Fredholm integral equation with logarithmic kernel: begin{aligned} u(x -int _0^1 ln |x -intlpha u(y),mathrm{{d}}y=f(x)quad 0le xle 1 end{aligned} (1)where (f in L^2 [0,1]) is known function and u is unknown function to be determined.
We consider the functional equation sum_{i=0}^{n-1} fbigl Xcdot sigma_{i} (Y) bigr)=f(X f Y) for all (X, Y in G^{n}), where (f: G^{n} rightarrowmathbb {R}) is the unknown function to be determined, and (sigma_{i} (X)=(x_{i+1},x_{i+2}, ldots, x_{n}, x_{1}, x_{2}, ldots, x_{i} )).
The solution to this problem may be written in the form begin{aligned} varphi(mathbf{x})= int_{partialOmega}K_{ast1}(mathbf{x},mathbf {y},kappa),d sigma_{y}varphi_{1}(mathbf{y}), end{aligned} (4.9) where (varphi_{1}(mathbf{y})) is a Hölder continuous function to be determined on ∂Ω.
Thus, consideration of the pathophysiological role of V-A decoupling allows the true pathogenic mechanism of acute heart failure in a patient with normal LV systolic function to be determined.
where c is an arbitrary constant, h y,z,t) are functions to be determined later.
For naturalists the relevant biological processes are departures from good human functioning, to be determined by the relevant science.
The configuration of the four transducers enabled dependent discriminating functions to be determined directly from the quadratic terms of the TOFs, without the need for previous geometric transformations.
where Ω is a bounded open domain in R n with a smooth boundary ∂ Ω. a > 0 and m, p ≥ 2 are real numbers, and f i : R 2 → R ( i = 1, 2 ) are given functions to be determined later.
where u 1 ( t ), u 2 ( t ), u 3 ( t ) and u 4 ( t ) are control functions to be determined for achieving synchronization between two systems (29) and (30).
