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Formal Market
Formal, formality, informal or informality imply the complying with, or not complying with, some set of requirements (forms, in Ancient Greek). They may refer to: Dress code and events * Formal wear, attire for formal events * Semi-formal attire, attire for semi-formal events * Informal attire, more controlled attire than casual but less than formal * Formal (university), official university dinner, ball or other event * School formal, official school dinner, ball or other event Logic and mathematics *Formal logic, or mathematical logic ** Informal logic, the complement, whose definition and scope is contentious *Formal fallacy, reasoning of invalid structure ** Informal fallacy, the complement *Informal mathematics, also called naïve mathematics *Formal cause, Aristotle's intrinsic, determining cause *Formal power series, a generalization of power series without requiring convergence, used in combinatorics *Formal calculation, a calculation which is systematic, but without a r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Set Theory
Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly concerned with those that are relevant to mathematics as a whole. The modern study of set theory was initiated by the German mathematicians Richard Dedekind and Georg Cantor in the 1870s. In particular, Georg Cantor is commonly considered the founder of set theory. The non-formalized systems investigated during this early stage go under the name of '' naive set theory''. After the discovery of paradoxes within naive set theory (such as Russell's paradox, Cantor's paradox and the Burali-Forti paradox) various axiomatic systems were proposed in the early twentieth century, of which Zermelo–Fraenkel set theory (with or without the axiom of choice) is still the best-known and most studied. Set theory is commonly employed as a foundational ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formal Derivative
In mathematics, the formal derivative is an operation on elements of a polynomial ring or a ring of formal power series that mimics the form of the derivative from calculus. Though they appear similar, the algebraic advantage of a formal derivative is that it does not rely on the notion of a limit, which is in general impossible to define for a ring. Many of the properties of the derivative are true of the formal derivative, but some, especially those that make numerical statements, are not. Formal differentiation is used in algebra to test for multiple roots of a polynomial. Definition The definition of formal derivative is as follows: fix a ring ''R'' (not necessarily commutative) and let ''A'' = ''R'' 'x''be the ring of polynomials over ''R''. Then the formal derivative is an operation on elements of ''A'', where if :f(x)\,=\,a_n x^n + \cdots + a_1 x + a_0, then its formal derivative is :f'(x)\,=\,Df(x) = n a_n x^ + \cdots + 2 a_2 x + a_1, just as for polynomials over th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dimethoxymethane
Dimethoxymethane, also called methylal, is a colorless flammable liquid with a low boiling point, low viscosity and excellent dissolving power. It has a chloroform-like odor and a pungent taste. It is the dimethyl acetal of formaldehyde. Dimethoxymethane is soluble in three parts water and miscible with most common organic solvents. Synthesis and structure It can be manufactured by oxidation of methanol or by the reaction of formaldehyde with methanol. In aqueous acid, it is hydrolyzed back to formaldehyde and methanol. Due to the anomeric effect, dimethoxymethane has a preference toward the ''gauche'' conformation with respect to each of the C–O bonds, instead of the ''anti'' conformation. Since there are two C–O bonds, the most stable conformation is ''gauche''-''gauche'', which is around 7 kcal/mol more stable than the ''anti''-''anti'' conformation, while the ''gauche''-''anti'' and ''anti-gauche'' are intermediate in energy. Since it is one of the smallest molecules ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ketal
In organic chemistry, an acetal is a functional group with the connectivity . Here, the R groups can be organic fragments (a carbon atom, with arbitrary other atoms attached to that) or hydrogen, while the R' groups must be organic fragments not hydrogen. The two R' groups can be equivalent to each other (a "symmetric acetal") or not (a "mixed acetal"). Acetals are formed from and convertible to aldehydes or ketones and have the same oxidation state at the central carbon, but have substantially different chemical stability and reactivity as compared to the analogous carbonyl compounds. The central carbon atom has four bonds to it, and is therefore saturated and has tetrahedral geometry. The term ketal is sometimes used to identify structures associated with ketones (both R groups organic fragments rather than hydrogen) rather than aldehydes and, historically, the term acetal was used specifically for the aldehyde-related cases (having at least one hydrogen in place of an R on t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Acetal
In organic chemistry, an acetal is a functional group with the connectivity . Here, the R groups can be organic fragments (a carbon atom, with arbitrary other atoms attached to that) or hydrogen, while the R' groups must be organic fragments not hydrogen. The two R' groups can be equivalent to each other (a "symmetric acetal") or not (a "mixed acetal"). Acetals are formed from and convertible to aldehydes or ketones and have the same oxidation state at the central carbon, but have substantially different chemical stability and reactivity as compared to the analogous carbonyl compounds. The central carbon atom has four bonds to it, and is therefore saturated and has tetrahedral geometry. The term ketal is sometimes used to identify structures associated with ketones (both R groups organic fragments rather than hydrogen) rather than aldehydes and, historically, the term acetal was used specifically for the aldehyde-related cases (having at least one hydrogen in place of an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formal Concentration
Molar concentration (also called molarity, amount concentration or substance concentration) is a measure of the concentration of a chemical species, in particular of a solute in a Solution (chemistry), solution, in terms of amount of substance per unit volume of solution. In chemistry, the most commonly used unit for molarity is the number of Mole (unit), moles per liter, having the unit symbol mol/L or Mole (unit), mol/Decimetre, dm3 in SI unit. A solution with a concentration of 1 mol/L is said to be 1 molar, commonly designated as 1 M. Definition Molar concentration or molarity is most commonly expressed in units of moles of solute per litre of Solution (chemistry), solution. For use in broader applications, it is defined as amount of substance of solute per unit volume of solution, or per unit volume available to the species, represented by lowercase c: :c = \frac = \frac = \frac. Here, n is the amount of the solute in moles, N is the number of particle number ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
