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...gy group, which he also showed to be isomorphic to the ordinary [[homology groups]] of the manifold ''M''. ...phism between the Floer homology group HF(''M'') and the ordinary homology groups ''H''(''M'') is canonical. Therefore, for any "good" Hamiltonian path ''H'' ...

# All [[functional groups]] on a branch unit are equally reactive ...ally create a polymer gel. Since [[steric hindrance]] effects prevent each functional group from being equally reactive and intramolecular reactions do occur, th ...

...ing monomers carrying arbitrary numbers and types of reactive [[functional groups]]. === One type of functional groups === ...

...a graphical method of determining the number and nature of the functional groups on an enzyme that are necessary for its catalytic activity. ...graphical method for the determination of the number and type of essential groups ...

...ar, as an abstract group (without topology) it is also the [[Direct sum of groups|direct sum]] (in the usual way) of the family <math>H_i.</math> ...nd only if the [[Extension of a topological group|extension of topological groups]] ...

...the [[Lie group–Lie algebra correspondence]] and its variant for algebraic groups in the characteristic zero; for example, this approach taken in {{harv|Jant ...stribution'' ''f'' supported at ''x''<nowiki>''</nowiki> is a ''k''-linear functional on ''A'' such that <math>f(I_x^n) = 0</math> for some ''n''. (Note: the def ...

...-functions satisfy a number of analytic properties, including an important functional equation. ...coefficients of appropriately chosen Eisenstein series and satisfy a crude functional equation involving a product of partial ''L''-functions. ...

...n number theory|Additive function|additive functions on the reals|Cauchy's functional equation}} ...] is additive. When the domain is the [[real number]]s, this is [[Cauchy's functional equation]]. For a specific case of this definition, see [[additive polynomi ...

...logical vector spaces over the normed fields of real or complex numbers in functional analysis."<ref name="exact" /> *Topological vector spaces appearing in functional analysis are typically not linearly topologized (since subspaces do not for ...

...ver <math>\mathbb{C}</math> equipped with a [[Unital map|unital]] [[linear functional]] <math>\phi:A\to\mathbb{C}</math>. As an example, one could take, for a p ...of a (discrete) [[Group (mathematics)|group]] <math>\Gamma</math> with the functional <math>\phi</math> given by the group trace <math>\phi (g) = \delta_{g=e},g\ ...

...mathematical-society/volume-76/issue-3/Harmonic-analysis-on-semisimple-Lie-groups/bams/1183531812.pdf }} ...0.1016/0022-1236(75)90034-8 | mr=0399356 | year=1975 | journal=Journal of Functional Analysis | volume=19 | pages=104–204| doi-access= }} ...

...size and (2) there are no intramolecular reactions between the functional groups on the same molecule.<ref>{{cite journal |last1=Stockmayer |first1=Walter H ...d and unreacted, that are part of branched units, to the total number of A groups in the mixture is defined as <math>\rho</math>. This will lead to the follo ...

{{Short description|Organosulfur compound with two –SH groups}} {{About|compounds with two SH functional groups||dithiole}} ...

...th> is a tensor product of the representations <math>\pi_v</math> of local groups. ...ion as a meromorphic function of all complex <math>s</math>, and satisfy a functional equation ...

In [[functional analysis]], a discipline within mathematics, a [[Locally convex topological ...https://arxiv.org/pdf/1412.1497.pdf "On topological spaces and topological groups with certain local countable networks] (2014)</ref> ...

...ical group|topological abelian groups]], the category of condensed abelian groups is an [[abelian category]], which allows for the use of tools from [[homolo ..., a ''condensed group'', ''condensed ring'', etc. is defined as a sheaf of groups, rings etc. on this site. ...

...orem is a key tool in one of the quickest proofs of amenability of abelian groups. *{{Conway A Course in Functional Analysis|edition=2}} ...

...finite [[Field (mathematics)|field]] ''k'' is a [[polynomial]] in [[linear functional]]s with coefficients in ''k''; i.e., it can be written as *[[Claudio Procesi]] (2007) ''Lie Groups: an approach through invariants and representation'', Springer, {{isbn|9780 ...

...ine hydroxyl value traditionally involves acetylation of the free hydroxyl groups of the substance with [[acetic anhydride]] in [[pyridine]] solvent. After c ...ge (wt. %) of hydroxyl groups in units of the mass of hydroxide functional groups in grams per 100 grams of substance. The conversion between hydroxyl value ...

...am Karrass, Donald Solitar, ''Combinatorial group theory. Presentations of groups in terms of generators and relations'', Reprint of the 1976 second edition, ...ng co-Hopfian is not a [[quasi-isometry]] invariant for finitely generated groups.<ref name=COR/> ...