A singular solution ys(x) of an ordinary differential equation is a solution that is singular or one for which the initial value problem (also called...

(mathematics) Hyperbolic growth Movable singularity Pathological (mathematics) Regular singularity Singular solution "Singularities, Zeros, and Poles". mathfaculty...

Schwarzschild solution with 0 ≤ r < rs, which contains the singularity at r = 0, is completely separated from the outer patch by the singularity at r = rs...

conditions'. A singular solution is a solution that cannot be obtained by assigning definite values to the arbitrary constants in the general solution. In the...

largest to smallest singular values) is infinite for a truly singular matrix. An infinite condition number means any numerical solution is unstable: arbitrarily...

one solution y ( x ) {\displaystyle y(x)} , the so-called singular solution, whose graph is the envelope of the graphs of the general solutions. The...

In mathematics, singularity theory studies spaces that are almost manifolds, but not quite. A string can serve as an example of a one-dimensional manifold...

In linear algebra, the singular value decomposition (SVD) is a factorization of a real or complex matrix into a rotation, followed by a rescaling followed...

satisfied; in algebraic equations, the possible number of solutions is decreased. Singular perturbation theory is a rich and ongoing area of exploration...

Singular they, along with its inflected or derivative forms, them, their, theirs, and themselves (also themself and theirself), is a gender-neutral third-person...

of the universe near the initial gravitational singularity, described by an anisotropic, chaotic solution of the Einstein field equation of gravitation...

A gravitational singularity, spacetime singularity, or simply singularity, is a theoretical condition in which gravity is predicted to be so intense that...

x^{4}{\frac {d^{2}\psi }{dx^{2}}}=e^{-\psi }} The equation has a singular solution given by e − ψ s = 2 x 2 , or − ψ s = 2 ln ⁡ x + ln ⁡ 2 {\displaystyle...

a regular singular point, where the growth of solutions is bounded (in any small sector) by an algebraic function, and an irregular singular point, where...

geometry, a singular point on a curve is one where the curve is not given by a smooth embedding of a parameter. The precise definition of a singular point depends...

the given system in such a way that any singular solution of the original system becomes a general solution of the new system. Although Cartan showed...

Hideo Yoshihara, along with some input from Busemann, later used a singular solution of Tricomi's equations to analytically solve the behavior of transonic...

be a black hole and will instead be a naked singularity. Although the Kerr solution appears to be singular at the roots of ⁠ Δ = 0 {\displaystyle \Delta...

Einstein proposed that the field equations would determine the path of a singular solution, like a black hole, to be a geodesic. Both physicists and philosophers...

named after the mathematician George Chrystal, who discussed the singular solution of this equation in 1896. The equation reads as ( d y d x ) 2 + A...

Riemann–Roch theorem Riemann surface Road curve Sato–Tate conjecture secant Singular solution Sinuosity Slope Space curve Spinode Square wheel Subtangent Tacnode...

1 {\displaystyle k=n-1} , singularities occur only for n ≥ 8 {\displaystyle n\geq 8} . An example of such singular solution of the Plateau problem is...

From a physical point of view, a gravitational instanton is a non-singular solution of the vacuum Einstein equations with positive-definite, as opposed...

In physics and astronomy, the Reissner–Nordström metric is a static solution to the Einstein–Maxwell field equations, which corresponds to the gravitational...

Brendle and Richard Schoen. Following the possibility that the singularities of solutions of the Ricci flow could identify the topological data predicted...

continuing work to uncover the geometric and analytic properties of singularities of the Ricci flow equation and related systems of differential equations...

Recurrence plot Limit cycle Initial value problem Clairaut's equation Singular solution Poincaré–Bendixson theorem Riccati equations Functional differential...

that if α ∈ R n {\displaystyle \alpha \in \mathbb {R} ^{n}} is a non-singular solution of the system f 1 ( x 1 , … , x n , e x 1 , … , e x n ) = … = f n...

problem caused by singular solutions. The theorem computes certain constants that must satisfy an inequality in order that there be a solution. Let ( M , I...

1007/s10958-005-0350-5. S2CID 122382003. Bryson, Arthur E. Jr.; Ho, Yu-Chi (1969). "Singular Solutions of Optimization and Control Problems". Applied Optimal Control. Waltham:...