PHIn chemistry, pH (piːˈeɪtʃ ), also referred to as acidity, historically denotes "potential of hydrogen" (or "power of hydrogen"). It is a scale used to specify the acidity or basicity of an aqueous solution. Acidic solutions (solutions with higher concentrations of hydrogen () ions) are measured to have lower pH values than basic or alkaline solutions. The pH scale is logarithmic and inversely indicates the activity of hydrogen ions in the solution. where [H+] is the equilibrium molar concentration (mol/L) of H+ in the solution.
Error functionIn mathematics, the error function (also called the Gauss error function), often denoted by erf, is a complex function of a complex variable defined as: Some authors define without the factor of . This nonelementary integral is a sigmoid function that occurs often in probability, statistics, and partial differential equations. In many of these applications, the function argument is a real number. If the function argument is real, then the function value is also real.
Gamma functionIn mathematics, the gamma function (represented by Γ, the capital letter gamma from the Greek alphabet) is one commonly used extension of the factorial function to complex numbers. The gamma function is defined for all complex numbers except the non-positive integers. For every positive integer n, Derived by Daniel Bernoulli, for complex numbers with a positive real part, the gamma function is defined via a convergent improper integral: The gamma function then is defined as the analytic continuation of this integral function to a meromorphic function that is holomorphic in the whole complex plane except zero and the negative integers, where the function has simple poles.
Nucleic acid double helixIn molecular biology, the term double helix refers to the structure formed by double-stranded molecules of nucleic acids such as DNA. The double helical structure of a nucleic acid complex arises as a consequence of its secondary structure, and is a fundamental component in determining its tertiary structure. The term entered popular culture with the publication in 1968 of The Double Helix: A Personal Account of the Discovery of the Structure of DNA by James Watson.
Transcendental functionIn mathematics, a transcendental function is an analytic function that does not satisfy a polynomial equation, in contrast to an algebraic function. In other words, a transcendental function "transcends" algebra in that it cannot be expressed algebraically. Examples of transcendental functions include the exponential function, the logarithm, and the trigonometric functions. Formally, an analytic function f (z) of one real or complex variable z is transcendental if it is algebraically independent of that variable.
Function (mathematics)In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function. Functions were originally the idealization of how a varying quantity depends on another quantity. For example, the position of a planet is a function of time. Historically, the concept was elaborated with the infinitesimal calculus at the end of the 17th century, and, until the 19th century, the functions that were considered were differentiable (that is, they had a high degree of regularity).
Multivalued functionIn mathematics, a multivalued function, also called multifunction and many-valued function, is a set-valued function with continuity properties that allow considering it locally as an ordinary function. Multivalued functions arise commonly in applications of the implicit function theorem, since this theorem can be viewed as asserting the existence of a multivalued function. In particular, the inverse function of a differentiable function is a multivalued function, and is single-valued only when the original function is monotonic.
PH indicatorA pH indicator is a halochromic chemical compound added in small amounts to a solution so the pH (acidity or basicity) of the solution can be determined visually or spectroscopically by changes in absorption and/or emission properties. Hence, a pH indicator is a chemical detector for hydronium ions (H3O+) or hydrogen ions (H+) in the Arrhenius model. Normally, the indicator causes the color of the solution to change depending on the pH. Indicators can also show change in other physical properties; for example, olfactory indicators show change in their odor.
Nucleic acid tertiary structureNucleic acid tertiary structure is the three-dimensional shape of a nucleic acid polymer. RNA and DNA molecules are capable of diverse functions ranging from molecular recognition to catalysis. Such functions require a precise three-dimensional structure. While such structures are diverse and seemingly complex, they are composed of recurring, easily recognizable tertiary structural motifs that serve as molecular building blocks. Some of the most common motifs for RNA and DNA tertiary structure are described below, but this information is based on a limited number of solved structures.
Beta functionIn mathematics, the beta function, also called the Euler integral of the first kind, is a special function that is closely related to the gamma function and to binomial coefficients. It is defined by the integral for complex number inputs such that . The beta function was studied by Leonhard Euler and Adrien-Marie Legendre and was given its name by Jacques Binet; its symbol Β is a Greek capital beta. The beta function is symmetric, meaning that for all inputs and .
