Spin structureIn differential geometry, a spin structure on an orientable Riemannian manifold (M, g) allows one to define associated spinor bundles, giving rise to the notion of a spinor in differential geometry. Spin structures have wide applications to mathematical physics, in particular to quantum field theory where they are an essential ingredient in the definition of any theory with uncharged fermions. They are also of purely mathematical interest in differential geometry, algebraic topology, and K theory.
DendrimerDendrimers are highly ordered, branched polymeric molecules. Synonymous terms for dendrimer include arborols and cascade molecules. Typically, dendrimers are symmetric about the core, and often adopt a spherical three-dimensional morphology. The word dendron is also encountered frequently. A dendron usually contains a single chemically addressable group called the focal point or core. The difference between dendrons and dendrimers is illustrated in the top figure, but the terms are typically encountered interchangeably.
TautomerTautomers (ˈtɔːtəmɚ ) are structural isomers (constitutional isomers) of chemical compounds that readily interconvert. The chemical reaction interconverting the two is called tautomerization. This conversion commonly results from the relocation of a hydrogen atom within the compound. The phenomenon of tautomerization is called tautomerism, also called desmotropism. Tautomerism is for example relevant to the behavior of amino acids and nucleic acids, two of the fundamental building blocks of life.
Crown etherIn organic chemistry, crown ethers are cyclic chemical compounds that consist of a ring containing several ether groups (). The most common crown ethers are cyclic oligomers of ethylene oxide, the repeating unit being ethyleneoxy, i.e., . Important members of this series are the tetramer (n = 4), the pentamer (n = 5), and the hexamer (n = 6). The term "crown" refers to the resemblance between the structure of a crown ether bound to a cation, and a crown sitting on a person's head.
Bridging ligandIn coordination chemistry, a bridging ligand is a ligand that connects two or more atoms, usually metal ions. The ligand may be atomic or polyatomic. Virtually all complex organic compounds can serve as bridging ligands, so the term is usually restricted to small ligands such as pseudohalides or to ligands that are specifically designed to link two metals. In naming a complex wherein a single atom bridges two metals, the bridging ligand is preceded by the Greek letter mu, μ, with a subscript number denoting the number of metals bound to the bridging ligand.
Stille reactionThe Stille reaction is a chemical reaction widely used in organic synthesis. The reaction involves the coupling of two organic groups, one of which is carried as an organotin compound (also known as organostannanes). A variety of organic electrophiles provide the other coupling partner. The Stille reaction is one of many palladium-catalyzed coupling reactions. Allyl, alkenyl, aryl, benzyl,acyl halides (Cl, Br, I), pseudohalides (OTf, OPO(OR)2), OAc The R1 group attached to the trialkyltin is normally sp2-hybridized, including vinyl, and aryl groups.
PeptidePeptides are short chains of amino acids linked by peptide bonds. A polypeptide is a longer, continuous, unbranched peptide chain. Polypeptides which have a molecular mass of 10,000 Da or more are called proteins. Chains of fewer than twenty amino acids are called oligopeptides, and include dipeptides, tripeptides, and tetrapeptides. Peptides fall under the broad chemical classes of biological polymers and oligomers, alongside nucleic acids, oligosaccharides, polysaccharides, and others.
MacromoleculeA macromolecule is a very large molecule important to biological processes, such as a protein or nucleic acid. It is composed of thousands of covalently bonded atoms. Many macromolecules are polymers of smaller molecules called monomers. The most common macromolecules in biochemistry are biopolymers (nucleic acids, proteins, and carbohydrates) and large non-polymeric molecules such as lipids, nanogels and macrocycles. Synthetic fibers and experimental materials such as carbon nanotubes are also examples of macromolecules.
Complex geometryIn mathematics, complex geometry is the study of geometric structures and constructions arising out of, or described by, the complex numbers. In particular, complex geometry is concerned with the study of spaces such as complex manifolds and complex algebraic varieties, functions of several complex variables, and holomorphic constructions such as holomorphic vector bundles and coherent sheaves. Application of transcendental methods to algebraic geometry falls in this category, together with more geometric aspects of complex analysis.
Complex manifoldIn differential geometry and complex geometry, a complex manifold is a manifold with an atlas of charts to the open unit disc in , such that the transition maps are holomorphic. The term complex manifold is variously used to mean a complex manifold in the sense above (which can be specified as an integrable complex manifold), and an almost complex manifold. Since holomorphic functions are much more rigid than smooth functions, the theories of smooth and complex manifolds have very different flavors: compact complex manifolds are much closer to algebraic varieties than to differentiable manifolds.
