called the Pfaffian polynomial. The value of this polynomial, when applied to the entries of a skew-symmetric matrix, is called the Pfaffian of that matrix...

In mathematics, Pfaffian functions are a certain class of functions whose derivative can be written in terms of the original function. They were originally...

In dynamics, a Pfaffian constraint is a way to describe a dynamical system in the form: ∑ s = 1 n A r s d u s + A r d t = 0 ; r = 1 , … , L {\displaystyle...

In graph theory, a Pfaffian orientation of an undirected graph assigns a direction to each edge, so that certain cycles (the "even central cycles") have...

a constraint equation in Pfaffian form, whether the constraint is holonomic or nonholonomic depends on whether the Pfaffian form is integrable. See Universal...

A Pfaffian system is specified by 1-forms alone, but the theory includes other types of example of differential system. To elaborate, a Pfaffian system...

noted for his work on partial differential equations of the first order Pfaffian systems, as they are now called, which became part of the theory of differential...

convert the problem into a Pfaffian computation of a skew-symmetric matrix derived from a planar embedding of the graph. The Pfaffian of this matrix is then...

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...

define its Pfaffian closure, which is again an o-minimal structure. (The Pfaffian closure of a structure is, in particular, closed under Pfaffian chains where...

time and the coordinates but not on the momenta) Nonholonomic constraints Pfaffian constraint Scleronomic constraint (not depending on time) Rheonomic constraint...

dimension. Karpinski–Macintyre theorem, a bound on the VC dimension of general Pfaffian formulas. Vapnik, V. N.; Chervonenkis, A. Ya. (1971). "On the Uniform Convergence...

language. Frobenius' original version of the theorem was stated in terms of Pfaffian systems, which today can be translated into the language of differential...

time and the coordinates but not on the momenta) and Nonholonomic system Pfaffian constraints Scleronomic constraints (not depending on time) and rheonomic...

In other words, a nonholonomic constraint is nonintegrable: 261  and in Pfaffian form: ∑ i = 1 n a s , i d q i + a s , t d t = 0         ( s = 1 , 2 , …...

Pfaff, German mathematician Concepts named after him include the Pfaffian, Pfaffian functions, and the Pfaff problem 29491 Pfaff, a main-belt asteroid...

{\displaystyle \det(A)=\operatorname {Pf} (A)^{2}.} This polynomial is called the Pfaffian of A {\displaystyle A} and is denoted Pf ⁡ ( A ) {\displaystyle \operatorname...

Antihermitian matrix Positive-definite, positive-semidefinite matrix Pfaffian Projection Spectral theorem Perron–Frobenius theorem List of matrices Diagonal...

by Catalan, Spottiswoode, Glaisher, and Scott; skew determinants and Pfaffians, in connection with the theory of orthogonal transformation, by Cayley;...

functions are the Pfaffian functions. In particular the theory of the real ordered field with restricted, totally defined Pfaffian functions is model...

algebraic combinations of many transcendental functions, the so-called Pfaffian functions. Sturm's theorem – Counting polynomial roots in an interval Rational...

Systems, Springer Verlag, New York, 1991. Alekseevskii, D.V. (2001) [1994], "Pfaffian problem", Encyclopedia of Mathematics, EMS Press R. Bryant, "Nine Lectures...

Investigations on the Foundations of Thermodynamics, which made use of Pfaffian systems and the concept of adiabatic accessibility, a notion that was introduced...

Rote, G. (2001). "Division-free algorithms for the determinant and the pfaffian: algebraic and combinatorial approaches" (PDF). Computational discrete...

always +1 for any field. One way to see this is through the use of the Pfaffian and the identity Pf ( M T Ω M ) = det ( M ) Pf ( Ω ) . {\displaystyle...

graphs arise in statistical mechanics in the theory of ice-type models. A Pfaffian orientation has the property that certain even-length cycles in the graph...

Photon Factory, a synchrotron located at KEK in Tsukuba, Japan pf(A), the Pfaffian of a matrix A Phenylphosphine, an organophosphorus compound Plasmodium...

)={\frac {1}{(2\pi )^{n}}}\operatorname {Pf} (\Omega ).} where we have the Pfaffian Pf ⁡ ( Ω ) {\displaystyle \operatorname {Pf} (\Omega )} . Here M {\displaystyle...

Grassmann integral of a free Fermi field is a high-dimensional determinant or Pfaffian, which defines the new type of Gaussian integration appropriate for Fermi...

_{n}}} where Pf ⁡ ( A ) {\displaystyle \operatorname {Pf} (A)} is the Pfaffian of ⁠ A {\displaystyle A} ⁠ and C = ( n 2 i ) {\textstyle {\mathcal {C}}={\binom...