Biorthogonal system - Wikipedia
网页In mathematics, a biorthogonal system is a pair of indexed families of vectors ~ ~ such that ~, ~ =,, where and form a pair of topological vector spaces that are in duality, , is a bilinear mapping and , is the Kronecker delta.
Bioorthogonal chemistry - Wikipedia
网页The term bioorthogonal chemistry refers to any chemical reaction that can occur inside of living systems without interfering with native biochemical processes. [1][2][3] The term was coined by Carolyn R. Bertozzi in 2003. [4][5] Since its introduction, the concept of the bioorthogonal reaction has enabled the study of biomolecules such as ...
Bioorthogonal chemistry - Nature Reviews Methods Primers
网页2021年4月15日 · Bioorthogonal chemistry represents a class of high-yielding chemical reactions that proceed rapidly and selectively in biological environments without side reactions towards endogenous functional...
Bioorthogonal Chemistry and Its Applications
网页2021年11月30日 · Bioorthogonal chemistry is a set of methods using the chemistry of non-native functional groups to explore and understand biology in living organisms. In this review, we summarize the most common reactions used in bioorthogonal methods, their relative advantages and disadvantages, and their frequency of occurrence in the …
Biorthogonal system - Encyclopedia of Mathematics
网页2014年1月12日 · Biorthogonal system. A pair of sets $\ {a_t\}$ and $\ {\xi_t\}$, $t \in T$, of elements of a topological vector space $X$ and the dual (topological) space $X^*$, respectively, which satisfies the conditions $$ \xi_t (a_s) = \langle \xi_t, a_s \rangle = 0 $$ if $t \ne s$ and $\ne 0$ if $t=s$ (here, $\langle {\cdot}, {\cdot} \rangle$ is the ...
网页Abstract. Fundamental to the study of bases in a separable Hilbert space H is the. notion of a biorthogonal system. Two sequences {fn} and { g„} of elements from H are said to be biorthogonal if (f„, gm) = 8^,. A complete sequence that possesses a biorthogonal sequence is called exact.
Developing bioorthogonal probes to span a spectrum of reactivities - Nature
网页2020年7月21日 · Bioorthogonal chemistries enable researchers to interrogate biomolecules in living systems. These reactions are highly selective and biocompatible, and can be performed in many complex ...
Bioorthogonal chemistry - PMC - National Center for …
网页Bioorthogonal chemistry encompasses a class of high-yielding rapid and selective chemical reactions that proceed in biological environments, with little or no reactivity towards endogenous functional groups.
Bioorthogonal Chemistry—Introduction and Overview [corrected]
网页Bioorthogonal chemistry has emerged as a new powerful tool that facilitates the study of structure and function of biomolecules in their native environment.
In Vivo Applications of Bioorthogonal Reactions: Chemistry and ...
网页2023年1月19日 · Bioorthogonal chemistry involves selective biocompatible reactions between functional groups that are not normally present in biology. It has been used to probe biomolecules in living systems, and has advanced biomedical strategies such as diagnostics and therapeutics.
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