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The non-orientable genus, demigenus, or Euler genus of a connected, non-orientable closed surface is a positive integer representing the number of cross-caps attached to a sphere. Alternatively, it can be defined for a closed surface in terms of the Euler characteristic χ, via the relationship χ = 2 − k , where k is the non-orientable genus.
The genus (sometimes called the demigenus or Euler genus) of a connected non-orientable closed surface is a positive integer representing the number of cross-caps attached to a sphere. Alternatively, it can be defined for a closed surface in terms of the Euler characteristic χ, via the relationship χ = 2 − g, where g is the non-orientable ...
This equation, stated by Euler in 1758, [2] is known as Euler's polyhedron formula. [3] It corresponds to the Euler characteristic of the sphere (i.e. = ), and applies identically to spherical polyhedra. An illustration of the formula on all Platonic polyhedra is given below.
File:Lagrangian vs Eulerian [further explanation needed] Eulerian perspective of fluid velocity versus Lagrangian depiction of strain. In classical field theories , the Lagrangian specification of the flow field is a way of looking at fluid motion where the observer follows an individual fluid parcel as it moves through space and time.
3 and each rational prime congruent to 1 mod 3 are equal to the norm x 2 − xy + y 2 of an Eisenstein integer x + ωy. Thus, such a prime may be factored as ( x + ωy )( x + ω 2 y ) , and these factors are Eisenstein primes: they are precisely the Eisenstein integers whose norm is a rational prime.
Spending online on Monday in the United States is expected to reach $13.2 billion, 6% more than on Cyber Monday a year earlier, according to preliminary estimates from Adobe Inc. That outlay would ...
In calculating the Euler characteristic of S′ we notice the loss of e P − 1 copies of P above π(P) (that is, in the inverse image of π(P)). Now let us choose triangulations of S and S′ with vertices at the branch and ramification points, respectively, and use these to compute the Euler characteristics.
From January 2008 to December 2012, if you bought shares in companies when Dennis H. Reilley joined the board, and sold them when he left, you would have a -17.6 percent return on your investment, compared to a -2.8 percent return from the S&P 500.
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