Pointwise convergenceIn mathematics, pointwise convergence is one of various senses in which a sequence of functions can converge to a particular function. It is weaker than uniform convergence, to which it is often compared. Suppose that is a set and is a topological space, such as the real or complex numbers or a metric space, for example. A net or sequence of functions all having the same domain and codomain is said to converge pointwise to a given function often written as if (and only if) The function is said to be the pointwise limit function of the Sometimes, authors use the term bounded pointwise convergence when there is a constant such that .
DNADeoxyribonucleic acid (diːˈɒksᵻˌraɪboʊnjuːˌkliːᵻk,_-ˌkleɪ-; DNA) is a polymer composed of two polynucleotide chains that coil around each other to form a double helix. The polymer carries genetic instructions for the development, functioning, growth and reproduction of all known organisms and many viruses. DNA and ribonucleic acid (RNA) are nucleic acids. Alongside proteins, lipids and complex carbohydrates (polysaccharides), nucleic acids are one of the four major types of macromolecules that are essential for all known forms of life.
Uniform convergenceIn the mathematical field of analysis, uniform convergence is a mode of convergence of functions stronger than pointwise convergence. A sequence of functions converges uniformly to a limiting function on a set as the function domain if, given any arbitrarily small positive number , a number can be found such that each of the functions differs from by no more than at every point in .
Small moleculeIn molecular biology and pharmacology, a small molecule or micromolecule is a low molecular weight (≤ 1000 daltons) organic compound that may regulate a biological process, with a size on the order of 1 nm. Many drugs are small molecules; the terms are equivalent in the literature. Larger structures such as nucleic acids and proteins, and many polysaccharides are not small molecules, although their constituent monomers (ribo- or deoxyribonucleotides, amino acids, and monosaccharides, respectively) are often considered small molecules.
Limit of a sequenceAs the positive integer becomes larger and larger, the value becomes arbitrarily close to . We say that "the limit of the sequence equals ." In mathematics, the limit of a sequence is the value that the terms of a sequence "tend to", and is often denoted using the symbol (e.g., ). If such a limit exists, the sequence is called convergent. A sequence that does not converge is said to be divergent. The limit of a sequence is said to be the fundamental notion on which the whole of mathematical analysis ultimately rests.
XenobiologyXenobiology (XB) is a subfield of synthetic biology, the study of synthesizing and manipulating biological devices and systems. The name "xenobiology" derives from the Greek word xenos, which means "stranger, alien". Xenobiology is a form of biology that is not (yet) familiar to science and is not found in nature. In practice, it describes novel biological systems and biochemistries that differ from the canonical DNA–RNA-20 amino acid system (see central dogma of molecular biology).
Monotone convergence theoremIn the mathematical field of real analysis, the monotone convergence theorem is any of a number of related theorems proving the convergence of monotonic sequences (sequences that are non-decreasing or non-increasing) that are also bounded. Informally, the theorems state that if a sequence is increasing and bounded above by a supremum, then the sequence will converge to the supremum; in the same way, if a sequence is decreasing and is bounded below by an infimum, it will converge to the infimum.
Expanded genetic codeAn expanded genetic code is an artificially modified genetic code in which one or more specific codons have been re-allocated to encode an amino acid that is not among the 22 common naturally-encoded proteinogenic amino acids. The key prerequisites to expand the genetic code are: the non-standard amino acid to encode, an unused codon to adopt, a tRNA that recognises this codon, and a tRNA synthetase that recognises only that tRNA and only the non-standard amino acid.
DeoxyribozymeDeoxyribozymes, also called DNA enzymes, DNAzymes, or catalytic DNA, are DNA oligonucleotides that are capable of performing a specific chemical reaction, often but not always catalytic. This is similar to the action of other biological enzymes, such as proteins or ribozymes (enzymes composed of RNA). However, in contrast to the abundance of protein enzymes in biological systems and the discovery of biological ribozymes in the 1980s, there is only little evidence for naturally occurring deoxyribozymes.
SequenceIn mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members (also called elements, or terms). The number of elements (possibly infinite) is called the length of the sequence. Unlike a set, the same elements can appear multiple times at different positions in a sequence, and unlike a set, the order does matter. Formally, a sequence can be defined as a function from natural numbers (the positions of elements in the sequence) to the elements at each position.
