Sentence examples for has singularity from inspiring English sources

The fractional differential equation with Riemann-Stieltjes integral conditions considered in Theorem 3.1 is singular, that is, (f t,u,v)) has singularity at (t=0) or (t=1) and (v=0), and (g t,v)) has singularity at (t=0) or (t=1) and (v=0), which generalizes and improves the known results for continuous functions in [16, 27 29].

In BVP (4.21), note that (a(t)) is singular at (t=0) and (t=1), that is to say, the nonlinearity has singularity at (t=0) and (t=1).

In particular, we consider that (f t,u,v)) has singularity at (t=0) or 1 and (v=0), (g t,v)) has singularity at (t=0) or 1 and (v=0).

However, contrary to the Caputo-Fabrizio derivative in this paper, the Caputo-Katugampola fractional derivative has singularity for (t =tau ).

In Example 4.1, the nonlinearity term f has singularity at (t=0) and (t=frac{1}{2}).

Note that (1.1) is indispensable because we envisage examples in which K : X × X → [ 0, ∞ ] has singularity at the diagonal.

The powerful side of our method is that it can easily compute solutions even if the equation has singularities.

One can see from Equation 5 that the effective dielectric function has singularities at ω = 0 and ω = ΩTO.

The behaviour of Vandermonde matrices is different when the density of ω has singularities and depends on the density growth rates near the singularities points.

(3.35) As in the one-population model, the Perron eigenvalue has singularities, reflecting the possible breakdown of the Perron–Frobenius theorem in the thermodynamic limit.

Since f is well-defined on its domain y, neither the real-valued f nor any of its sub-expressions f i has singularities in its respective domain y i induced by y.