Search results

...number]] in a [[Domain (mathematical analysis)|domain]] <math>R\subseteq \Complex</math>. The operator <math>\bar{\partial}</math> is called the DBAR operato The DBAR operator is nothing other than the complex conjugate of the operator ...

...al geometry|discrete dynamical systems|Exponential map (discrete dynamical systems)}} * [[exponential map (Lie theory)]] from a Lie algebra to a Lie group, ...

{{Short description|Complex three dimensional gauge theory}} ...ns form]]s which appear in the [[action (physics)|action]] of Chern–Simons theory.<ref>{{cite journal ...

...e synchronous state in a [[dynamical system]] consisting of many identical systems which are coupled together, such as the [[Kuramoto model]]. The master stability function is now defined as the function which maps the complex number <math> \gamma </math> to the greatest [[Lyapunov exponent]] of the e ...

...be the loop [[transfer function]] and ''S'' be the [[Sensitivity (control systems)|sensitivity function]]. where <math>p_k</math> are the [[Pole (complex analysis)|poles]] of ''L'' in the right half plane (unstable poles). ...

...f the field is the [[complex numbers]] <math>\mathbb{C},</math> then the [[complex projective line]] <math>\mathbf P^1(\mathbb{C})</math> is one-dimensional w ...action of ''T''.<ref>[[Peter Lancaster]] & Miron Tismenetsky (1985) ''The Theory of Matrices'', second edition, page 147, Academic Press {{ISBN|0-12-435560- ...

...dratic function|two]], is a simple and accessible demonstration of [[chaos theory|chaos]] in [[dynamical system]]s. It can be constructed by performing the f # Choose any [[complex number]] on the [[unit circle]] whose [[Complex_number#Polar_complex_plane| ...

...nce involves functions of a [[motor variable]] where arguments are [[split-complex number]]s. In [[mathematical physics]], there are hypercomplex systems called [[Clifford algebra]]s. The study of functions with arguments from a ...

{{Short description|Theorem in dynamical systems theory}} ...behavior]] in dynamical systems, and [[bifurcation theory]]. Conley index theory formed the basis for development of [[Floer homology]]. ...

...AKNS system is a pair of two partial [[differential equation]]s for two [[complex-valued function]]s ''p'' and ''q'' of 2 variables ''t'' and ''x'': If ''p'' and ''q'' are [[complex conjugate]]s this reduces to the [[nonlinear Schrödinger equation]]. ...

...ght|thumb|300px|[[Domain colouring]] plot of <math>\exp(z)-z</math> in the complex plane. Black points represent the zeroes of the function.]] ...]] which are about solvability of (systems of) polynomial equations in the complex numbers. ...

...ket engines]], etc.<ref name="williams">Williams, F. A. (2018). Combustion theory. CRC Press.</ref><ref>Clavin, P., & Searby, G. (2016). Combustion waves and ...Roy. Inst. Proc., 8, 536-542.</ref><ref>Rayleigh, J. W. S. B. (1896). The theory of sound (Vol. 2). Macmillan.</ref> In simple terms, Rayleigh criterion sta ...

...For this reason, they are difficult to find and have no general existence theory, not even locally. == Complex analysis == ...

name =Complex inverse Wishart Distribution| *<math>\mathcal{C}\Gamma_p</math> is the complex [[multivariate gamma function]] ...

...c mapping]], or a [[semigroup]] of mappings, of the [[unit disk]] in the [[complex numbers]] into itself. Let ''D'' be the [[unit disk]] in the complex numbers. Let {{mvar|f}} be a [[holomorphic function]] mapping ''D'' into it ...

[[File:Independence complex.svg|thumb|350px|The '''independence complex''' of ''G'']] ...g subsets), formed by the sets of vertices in the [[Independent set (graph theory)|independent sets]] of ''G''. Any subset of an independent set is itself a ...

...ial Parameter Space Detail PSP Rays.png|right|thumb|Parameter plane of the complex exponential family f(z)=exp(z)+c with 8 [[External ray|external ( parameter In the theory of [[dynamical system]]s, the '''exponential map''' can be used as the [[Dy ...

...hd1.html | author=Judit Csima | title=Investigations on Simple Eco-Grammar Systems | institution=[[Eötvös Loránd University]] | year=2002 }}</ref> ...rs, but emptiness of the common language is generally undecidable for more complex grammars.|date=February 2022}} ...

{{short description|Gauge theory providing unifying formalism for integrable systems}} ...hic''' or '''semi-topological Chern–Simons theory''', is a [[quantum field theory]] initially defined by [[Nikita Nekrasov]],<ref name="nekrasov">{{cite thes ...

...onfiguration.<ref>{{cite journal|last1=Racah|first1=Giulio|title=Theory of Complex Spectra. III|journal=Phys. Rev.|date=1943|volume=63|issue=9–10 |page=367|do ...e journal|last1=Isacker|first1=P. Van|title=Seniority in quantum many-body systems|journal=Symmetries in Nature: Symposium in Memoriam Marcos Moshinsky|series ...