Search results
Results from the WOW.Com Content Network
In mathematics, the Pell numbers are an infinite sequence of integers, known since ancient times, that comprise the denominators of the closest rational approximations to the square root of 2. This sequence of approximations begins 1 / 1 , 3 / 2 , 7 / 5 , 17 / 12 , and 41 / 29 , so the sequence of Pell ...
Amyloid beta (Aβ, Abeta or beta-amyloid) denotes peptides of 36–43 amino acids that are the main component of the amyloid plaques found in the brains of people with Alzheimer's disease. [2] The peptides derive from the amyloid-beta precursor protein (APP), which is cleaved by beta secretase and gamma secretase to yield Aβ in a cholesterol ...
The notions of completely and absolutely monotone function/sequence play an important role in several areas of mathematics. For example, in classical analysis they occur in the proof of the positivity of integrals involving Bessel functions or the positivity of Cesàro means of certain Jacobi series. [ 6 ]
Thomae's function: is a function that is continuous at all irrational numbers and discontinuous at all rational numbers. It is also a modification of Dirichlet function and sometimes called Riemann function. Kronecker delta function: is a function of two variables, usually integers, which is 1 if they are equal, and 0 otherwise.
The American Invitational Mathematics Examination (AIME) is a selective 15-question, 3-hour test given since 1983 to those who rank in the top 5% on the AMC 12 high school mathematics examination (formerly known as the AHSME), and starting in 2010, those who rank in the top 2.5% on the AMC 10. Two different versions of the test are administered ...
Fundamental sequences arise in some settings of definitions of large countable ordinals, definitions of hierarchies of fast-growing functions, and proof theory.Bachmann defined a hierarchy of functions in 1950, providing a system of names for ordinals up to what is now known as the Bachmann–Howard ordinal, by defining fundamental sequences for namable ordinals below . [9]
For a direct sum this is clear, as one can inject from or project to the summands. For a left split sequence, the map t × r: B → A × C gives an isomorphism, so B is a direct sum (3.), and thus inverting the isomorphism and composing with the natural injection C → A × C gives an injection C → B splitting r (2.).
Amyloid-beta precursor protein (APP) is an integral membrane protein expressed in many tissues and concentrated in the synapses of neurons. It functions as a cell surface receptor [ 5 ] and has been implicated as a regulator of synapse formation , [ 6 ] neural plasticity , [ 7 ] antimicrobial activity, [ 8 ] and iron export . [ 9 ]