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Its Euler characteristic is 0, by the product property. More generally, any compact parallelizable manifold, including any compact Lie group, has Euler characteristic 0. [13] The Euler characteristic of any closed odd-dimensional manifold is also 0. [14] The case for orientable examples is a corollary of Poincaré duality.
Thus the Euler class is a generalization of the Euler characteristic to vector bundles other than tangent bundles. In turn, the Euler class is the archetype for other characteristic classes of vector bundles, in that each "top" characteristic class equals the Euler class, as follows. Modding out by 2 induces a map
Homology theory can be said to start with the Euler polyhedron formula, or Euler characteristic. [16] This was followed by Riemann 's definition of genus and n -fold connectedness numerical invariants in 1857 and Betti 's proof in 1871 of the independence of "homology numbers" from the choice of basis.
Charge transfer coefficient, and symmetry factor (symbols α and β, respectively) are two related parameters used in description of the kinetics of electrochemical reactions. They appear in the Butler–Volmer equation and related expressions. The symmetry factor and the charge transfer coefficient are dimensionless. [1]
The SI unit of quantity of electric charge is the coulomb (symbol: C). The coulomb is defined as the quantity of charge that passes through the cross section of an electrical conductor carrying one ampere for one second. [6] This unit was proposed in 1946 and ratified in 1948. [6] The lowercase symbol q is
Under certain conditions, some battery chemistries are at risk of thermal runaway, leading to cell rupture or combustion. As thermal runaway is determined not only by cell chemistry but also cell size, cell design and charge, only the worst-case values are reflected here. [64]
Charge quantization is the principle that the charge of any object is an integer multiple of the elementary charge. Thus, an object's charge can be exactly 0 e, or exactly 1 e, −1 e, 2 e, etc., but not 1 / 2 e, or −3.8 e, etc. (There may be exceptions to this statement, depending on how "object" is defined; see below.)
Example charging graph. On the left: per-cell quantities. On the right: example values for a 40 Ah, 6-cell (12 V) battery. Note: schematic illustration; not based on actual measurements. IUoU is a DIN-designation [1] (DIN 41773) for a lead-acid battery charging procedure that is also known as 3-stage charging, 3-phase charging, or 3-step charging.