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A function that is absolutely monotonic on [,) can be extended to a function that is not only analytic on the real line but is even the restriction of an entire function to the real line. The big Bernshtein theorem : A function f ( x ) {\displaystyle f(x)} that is absolutely monotonic on ( − ∞ , 0 ] {\displaystyle (-\infty ,0]} can be ...
In organic chemistry, functionality is often used as a synonym for functional group. For example, a hydroxyl group can also be called a HO-function. [1] [2] Functionalisation means the introduction of functional groups, for example the functionalisation of a surface [3] (e.g. silanization for the specific modification of the adhesion of a surface)
Ab initio quantum chemistry methods are a class of computational chemistry techniques based on quantum chemistry that aim to solve the electronic Schrödinger equation. [1] Ab initio means "from first principles" or "from the beginning", meaning using only physical constants [ 2 ] and the positions and number of electrons in the system as input.
Where the Negishi coupling is rarely used in industrial chemistry, a result of the aforementioned water and oxygen sensitivity, it finds wide use in the field of natural products total synthesis. The increased reactivity relative to other cross-coupling reactions makes the Negishi coupling ideal for joining complex intermediates in the ...
The standard state of a material (pure substance, mixture or solution) is a reference point used to calculate its properties under different conditions.A degree sign (°) or a superscript Plimsoll symbol (⦵) is used to designate a thermodynamic quantity in the standard state, such as change in enthalpy (ΔH°), change in entropy (ΔS°), or change in Gibbs free energy (ΔG°).
The Fourier transform of a periodic function cannot be defined using the integral formula directly. In order for integral in Eq.1 to be defined the function must be absolutely integrable. Instead it is common to use Fourier series. It is possible to extend the definition to include periodic functions by viewing them as tempered distributions.
"Double bagging", the practice of using two condoms at once, is not an extra-effective method of birth control; instead such use is more likely to cause condom breakage due to friction between the condoms. [382] It is not possible to get pregnant from semen released in a commercial swimming pool without penetration.
The hidden subgroup problem is especially important in the theory of quantum computing for the following reasons.. Shor's algorithm for factoring and for finding discrete logarithms (as well as several of its extensions) relies on the ability of quantum computers to solve the HSP for finite abelian groups.