mathematics, a differential field K is differentially closed if every finite system of differential equations with a solution in some differential field extending...

and differential topology, a closed form is a differential form α whose exterior derivative is zero (dα = 0); and an exact form is a differential form...

theory – Study of Galois symmetry groups of differential fields Differentially closed field Differential graded algebra – Algebraic structure in homological...

Pseudoelementary class Strength (mathematical logic) Differentially closed field Exponential field Ax–Grothendieck theorem Ax–Kochen theorem Peano axioms...

donor advised charity Dichlorofluorescein, a fluorescent dye Differentially closed fields L-dopachrome isomerase, also called dopachrome conversion factor...

mathematics, differential topology is the field dealing with the topological properties and smooth properties of smooth manifolds. In this sense differential topology...

and model-theoretic algebra, and in particular the theory of differentially closed fields. Wood graduated in 1966 from Randolph-Macon Woman's College,...

In mathematics, differential Galois theory is the field that studies extensions of differential fields. Whereas algebraic Galois theory studies extensions...

linear differential equations (see Holonomic function). As, in general, the solutions of a differential equation cannot be expressed by a closed-form expression...

closed form of a solution is a solution in radicals; that is, a closed-form expression for which the allowed functions are only nth-roots and field operations...

groups). The theory of non-abelian free groups. The theory of differentially closed fields of characteristic p. When p = 0 {\displaystyle p=0} , the theory...

theory of differentially closed fields (DCF) is the theory of differentially perfect fields with axioms saying that if f and g are differential polynomials...

Instead, the magnetic field of a material is attributed to a dipole, and the net outflow of the magnetic field through a closed surface is zero. Magnetic...

In differential geometry, a one-form (or covector field) on a differentiable manifold is a differential form of degree one, that is, a smooth section of...

of modern differential geometry during the 18th and 19th centuries. Since the late 19th century, differential geometry has grown into a field concerned...

1-vector field. Nor can one meaningfully go from a 1-vector field to a 2-vector field to a 3-vector field (4 → 6 → 4), as taking the differential twice yields...

pullback. Differential forms are part of the field of differential geometry, influenced by linear algebra. Although the notion of a differential is quite...

needed] Example: Nullstellensatz for algebraically closed fields and for differentially closed fields.[clarification needed] Cylindrical algebraic decomposition...

is how they enter differential equations. Specific mathematical fields include geometry and analytical mechanics. Scientific fields include much of physics...

states that elementary antiderivatives, if they exist, are in the same differential field as the function, plus possibly a finite number of applications of...

the resulting electric field. In its integral form, it states that the flux of the electric field out of an arbitrary closed surface is proportional...

condition for a closed differential form to be exact (while an exact form is necessarily closed). Precisely, it states that every closed p-form on an open...

types of fields, such as real closed fields or exponential fields (which are equipped with an exponential function exp : F → F×). For fields that are...

based on the existence of differential forms with prescribed properties. On any smooth manifold, every exact form is closed, but the converse may fail...

The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of the International Mathematical...

Hopf. The Euler characteristic of a closed surface is a purely topological concept, whereas the index of a vector field is purely analytic. Thus, this theorem...

constructed as physical fields, due to their finite propagation speed and causal nature when a simplified physical model of an isolated closed system is set [clarification...

Algebraic function Closed-form expression Differential Galois theory Elementary function arithmetic Liouville's theorem (differential algebra) Tarski's...

applications to representation theory, differential geometry, quantum statistical mechanics, quantum information, and quantum field theory. Operator algebras can...

reference tracking performance. A common closed-loop controller architecture is the PID controller. The field of control theory can be divided into two...