Sentence examples for and has a singularity from inspiring English sources

and has a singularity at x = 0.

Levi [3] considered (1.1), where the potential V satisfies a superquadratic growth and has a singularity.

At the end of the interface, as shown in Figure 2, it is known that the interface stress σ ij (ij = rr, θθ, rθ) goes to infinity at the edge of the joint and has a singularity of σ ij  ∝ 1/r1 − λ when a a-2β) > 0.

In this paper, we are concerned with the existence of periodic solutions of singular Rayleigh equations x"+fbigl t, x'bigr)+g(x)=p t), (1.1) where (g: (0, +infty tomathbf{R}) is continuous and has a singularity at the origin, (f: mathbf{R^{2}}tomathbf{R^{2}}) is continuous and 2π periodic with respect to the first variable t, (p: mathbf{R}tomathbf{R}) is continuous and 2π periodic.

} t in(- infty, +infty), and g has a singularity of attractive type, if lim_{xrightarrow0^ g t,x =+infty, quad text{uniformly for a.e.

The normal derivative of u reads ϕ (x, y ) = (cos cos + sin sin sin cos − cos sin ⋅ ν (x, y ) ⋅ τ ⋅ r τ − 1 and has a generic singularity at the origin.

Since the potential in Theorem 16.7 of Ambrosetti and Coti Zelati has a singularity, but the potential in Theorem 1.3 has no singularity, the two theorems are essentially different.

Wang and Ma [14] first studied the resonant singular equation x"+frac{1}{4}n^{2}x+g(x)=p t), (1.2) where g has a singularity and satisfies lim_{xrightarrowinfty}g(x)=g(+infty).

If (b<0) then (H K)) has a singularity and there is still a root to (H K =1/K).

Mark Zuckerberg has a singularity of focus, and has had it from the start.

where λ is a real parameter and q is real-valued function which has a singularity in (a, b).