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equivalent

1. Maths
a. having a particular property in common; equal
b. (of two equations or inequalities) having the same set of solutions
c. (of two sets) having the same cardinal number
2. Maths Logic (of two propositions) having an equivalence between them
Collins Discovery Encyclopedia, 1st edition © HarperCollins Publishers 2005
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Equivalent

 

The equivalent of an element is the weight, expressed in carbon mass units, that will combine with or replace one atomic weight of hydrogen or one-half atomic weight of oxygen.

The equivalent of an acid is equal to the acid’s molecular weight divided by its alkalinity (number of hydrogen ions).

The equivalent of a base is equal to the base’s molecular weight divided by its acidity (number of hydroxyl groups).

The equivalent of a salt is equal to the molecular weight of the salt divided by the sum of the charges of the cations or anions forming the salt.

In oxidation-reduction reactions, the equivalent of an oxidizing agent is equal to the quotient obtained as a result of dividing the agent’s molecular weight by the number of electrons obtained by the atom or atoms of the reduced element. The equivalent may vary, depending on the number of electrons accepted by the oxidizing agent.

The concept of equivalent is widely used in the stoichiometric calculations of chemical reactions.

S. A. POGODIN

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.
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Linear scan voltammograms (LSVs) (or equivalently cathodic part of cyclic voltammograms) were selected for simulation.
We note that t(1) = 0; therefore in order to demonstrate the inequality t(x) [less than or equal to] 0 on [0,1], we have to establish that t'(x) [greater than or equal to] 0 on [0,1] or equivalently
Transparency is a state in which the cost of information (computing, processing, communicating, searching, coordinating, and monitoring) is approaching zero or, equivalently, in which cheap connectivity is so abundant and easy, it's nearly infinite.
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However, the Commission stresses the need to further harmonise and strengthen member states' approaches to ensure that fraud is fought equivalently across the EU.
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He made many conjectures, among them was flyping conjecture which states that the number of crossings is the same for any reduced projection of an alternating knot or equivalently "Two reduced alternating knots are equivalent iff they can be converted into one another by flypes" The conjecture was proved by Menasco and Thistlewaite [3,4] by using Jones Polynomial.
In 2001, the existence of left-handed materials (LHMs) was experimentally verified by Smith and co-workers by using a split-ring resonator and a thin wire [5]; in 2002, the composite right/left-handed transmission line (CRLH-TL) was first proposed by Caloz and Itoh, this structure provides left-handed (LH) and right-handed (RH) characteristics at low and high frequency bands respectively [2]; in 2006, the equivalently model of D-CRLH-TL was proposed by Caloz, according to the equivalently model of CRLH-TL [3].
Case 1: [b.sub.1] (or [C.sub.v1]) is infinite and [b.sub.2] (or [C.sub.v2]) approaches zero, i.e., the end of the transmission line loaded by varactor ([C.sub.v1]) is equivalently shorted and another end loaded by varactor ([C.sub.v2]) is equivalently open, as shown in Figure 1(b).
Therefore, it is much necessary to equivalently characterize these problems with other approaches or forms in order to find other efficient solutions.