Search results

...is, at present, less accurate than [[Kohn–Sham equations|Kohn–Sham density functional theory]] models, but has the advantage of being fast, so that it can be app ...orrelation|correlation]] energy. The lack of the true exchange–correlation functional is a well known problem in DFT, and there exists a huge variety of approach ...

...erator''' is a [[linear operator]] on a [[Banach space]] whose [[Spectrum (functional analysis)|spectrum]] in an [[Open set|open]] [[Circular sector|sector]] in ...d [[Parabolic partial differential equation|parabolic partial differential equations]]. ...

...algebra]] but concerned with difference equations rather than differential equations. As an independent subject it was initiated by [[Joseph Ritt]] and his stud == Algebraic difference equations == ...

...ions, but are at least a local extremum of the left side of the Yang–Mills equations. While Yang–Mills connections can be viewed as a non-linear generalization == Bi-Yang–Mills action functional == ...

...his problem. Solutions are precisely the critical points for the [[energy functional]] More generally, given a suitable functional ''J'', the associated Nehari manifold is defined as the set of functions '' ...

...Maximum principles and applications|series=Series in Partial Differential Equations and Applications|publisher=World Scientific Publishing Co. Pte. Ltd.|locati {{Functional analysis}} ...

...of a predator, the population dynamics are described by the following two equations: ...idence is often lacking on both functional responses and the importance of functional responses for population dynamics, there is no need to strongly favor one l ...

In [[mathematics]] – specifically, in [[functional analysis]] – a '''Bochner-measurable function''' taking values in a [ ...le = Monotone operators in Banach space and nonlinear partial differential equations ...

...<ref name=":0">{{Cite book|title=Applied Theory of Functional Differential Equations|last1=Kolmanovskii|first1=V.| last2=Myshkis| first2=A.| publisher=Kluwer Ac ...ore applicable than [[Ordinary differential equation|ordinary differential equations (ODE)]], in which future behavior only implicitly depends on the past. ...

{{about|certain differential equations|certain functional equations named after Abel|Abel equation}} ...near ODEs (Abel's Nonlinear ODEs of the First Kind and Relative Degenerate Equations) | journal=International Journal of Mathematics and Mathematical Sciences | ...

...–Lax–Milgram theorem''' (or simply '''Lions's theorem''') is a result in [[functional analysis]] with applications in the study of [[partial differential equatio * (existence of a "weak inverse") for each [[continuous linear functional]] ''f''&nbsp;&isin;&nbsp;''V''^&lowast;, there is an element ''h' ...

...minimizing the functional one may compute the best image segmentation. The functional was proposed by mathematicians [[David Mumford]] and Jayant Shah in 1989.<r == Definition of the Mumford–Shah functional == ...

== Graph Ginzburg–Landau functional == ...'V'' and edge weights <math>\omega_{i,j}</math>, the graph Ginzburg–Landau functional of a map <math>u:V\to \mathbb{R}</math> is given by ...

...tical point (mathematics)|critical points]] of the Yang–Mills-Higgs action functional, which are determined by a vanishing first [[derivative]] of a [[Calculus o ...'' is given by:<ref name=":10">{{cite web |title=Lecture 3: The Yang–Mills equations |url=https://empg.maths.ed.ac.uk/Activities/GT/Lect3.pdf |access-date=2024- ...

...iological assumptions and providing a [[Qualitative theory of differential equations|qualitative analysis]] of population dynamics.<ref name="Sigmund1936">{{cit ...ian]] [[physicist]] [[Vito Volterra]], who had developed his predator-prey equations based on observations of fish populations in the [[Adriatic Sea]] during [[ ...

...d position (e.g. time, in [[Heat equation|heat]] or [[Wave equation|wave]] equations) and all the others are put together, an ordinary "differential" equation w ...her abstract differential equations amounts (by e.g. reduction to a set of equations of the first order) to the study of this equation. ...

...math>F</math>'''-YM equations''') are a generalization of the [[Yang–Mills equations]]. Its solutions are called <math>F</math>'''-Yang–Mills connections''' (or == F-Yang–Mills action functional == ...

...icant contributions to [[analysis]], [[algebra]], [[geometry]], [[integral equations]] and many other fields that pertain to his interests. ...eering and technology. The third volume involves integral equations and [[functional analysis]] that deal "with the theory of operators". ...

.../math>: indeed, every <math>x \in \ell^\infty</math> defines a continuous functional on the space <math>\ell^1</math> of absolutely summable sequences by compon ...n <math>(0,\ldots,0,1,0,\ldots)</math> we see that every continuous linear functional on <math>\ell^1</math> arises in this way. i.e. ...

...regular solutions to [[Elliptic operator|elliptic]] [[partial differential equations]]. ...2=Trudinger|authorlink2=Neil Trudinger|title=Elliptic Partial Differential Equations of Second Order|publisher=Springer|publication-place=New York|year=1983|isb ...