Help


[permalink] [id link]
+
Page "Gauss–Bonnet theorem" ¶ 8
from Wikipedia
Edit
Promote Demote Fragment Fix

Some Related Sentences

Note and for
Note, 6 and 8 lock levers don't require holes for contacts.
Note extent of these interests and how available they will be for the public to enjoy.
Note that we need not know the value of p, for the experiment to be binomial.
Most European domestic power supplies run at 230 V, so the current drawn by a particular European appliance ( in Europe ) will be less than for an equivalent American one ( in the United States ).< ref group =" Note "> The formula for power is given by
Note that any model of ZF ¬ C is also a model of ZF, so for each of the following statements, there exists a model of ZF in which that statement is true.
( Note that by designating cardinal directions for 1 ,-1,, and, complex numbers such as are considered constructible.
Examples of algebraic integers are,, and ( Note, therefore, that the algebraic integers constitute a proper superset of the integers, as the latter are the roots of monic polynomials for all
Note electrode naming for diodes is always based on the direction of the forward current ( that of the arrow, in which the current flows " most easily "), even for types such as Zener diodes or solar cells where the current of interest is the reverse current.
Note: in a galvanic cell, contrary to what occurs in an electrolytic cell, no anions flow to the anode, the internal current being entirely accounted for by the cations flowing away from it ( cf drawing ).
Note that this expression is not well-defined for all time series or processes, because the variance may be zero ( for a constant process ) or infinite.
In 2004, she accorded three stars to chef Jean-Georges Vongerichten ’ s Spice Market restaurant after Vongerichten gave her book Cooking for Mr. Latte a positive blurb ; the Times spotlighted the incident with an Editor ’ s Note.
In 2007, the Times printed another Editor ’ s Note after Hesser published a review of Vegetable Garden by Patricia Wells without disclosing that in 1999, Wells had contributed a jacket blurb for Hesser ’ s book The Cook and the Garden.
( Note that K is the SI unit for temperature ( kelvin ) and should not be confused with k, the SI prefix for kilo.
Note that a locally finite Borel measure automatically satisfies μ ( C ) < ∞ for every compact set C.
Note that if we regard the product as a vector space, then B is not a linear transformation of vector spaces ( unless or ) because, for example.
Note that the associative property does not hold for expressions that include non-linear operators, such as the antilinear time reversal operator in physics.
Note: Major destination for Cubans trying to migrate to the United States
Note: Concentrations of Cr ( VI ) in US municipal drinking water supplies reported by EWG are within likely, natural background levels for the areas tested and not necessarily indicative of industrial pollution ( CalEPA Fact Sheet ), as asserted by EWG.
Note: in Greek, the term for " consul " is " ypatos ", which translates as " supreme one ", and hence does not necessarily imply a joint office.
Note that the points must all be different numbers for them to count towards the fire bet.
Note that for any fixed w the function f ( x ) = F ( w x ) is computable ; thus the universality property states that all computable functions of one variable can be obtained in this fashion.

Note and orientable
Note that PGL ( n, F ) and PSL ( n, F ) are equal if and only if every element of F has an n < sup > th </ sup > root in F. As an example, note that but this corresponds to the real projective line being orientable, and the projective special linear group only being the orientation-preserving transformations.
( Note, however, that the cases where S has boundary or is not orientable are definitely still of interest.

Note and compact
) Note that the same set of points would not have, as an accumulation point, any point of the open unit interval ; hence that space cannot be compact.
Note that, in a metric space, every compact subset is closed and bounded.
Note that neither of these statements implies the other, since there are complete metric spaces which are not locally compact ( the irrational numbers with the metric defined below ; also, any Banach space of infinite dimension ), and there are locally compact Hausdorff space which are not metrizable ( for instance, any uncountable product of non-trivial compact Hausdorff spaces is such ; also, several function spaces used in Functional Analysis ; the uncountable Fort space ).
Note that one formulation of AC is that the Cartesian product of a family of nonempty sets is nonempty ; but since the empty set is most certainly compact, the proof cannot proceed along such straightforward lines.
Note that on a compact geometry, not every straight line comes back to its starting point.
Note that Leonardo, in his notebooks, cited red, yellow, green and blue ( along with white and black ) as the " painter's primaries ", though he may not have had a specific palette in mind ; but replacing the cyan paint with a deep blue paint ( such as ultramarine blue ), and adding a green paint, greatly improves the saturation of both purple and green mixtures in a compact four paint selection, and allows a dark neutral or black to be mixed directly, using only red and green.
Note that the classification by mass ( high, intermediate, low ) refers to the optically visible donor, not to the compact X-ray emitting accretor.
Note that A is unital if and only if X is compact, in which case C < sub > 0 </ sub >( X ) is equal to C ( X ), the algebra of all continuous complex-valued functions on X.
Note that this proof of existence of stellar black holes is not entirely observational but relies on theory: We can think of no other object for these massive compact systems in stellar binaries besides a black hole.
Note that if a linear operator is compact, then it is easy to see that it is bounded, and hence continuous.
Note that A. Connes also proved that the von Neumann group algebra of any connected locally compact group is hyperfinite, so the last condition no longer applies in the case of locally compact groups.
Note, that the mean width can be defined for any body ( that is compact ), but it is most
Note: " A Month of Sundays " appeared on the cassette and compact disc versions of the album but was not included on the LP format.
Note that any compact, connected, oriented surface with nonempty boundary in Euclidean 3-space is the Seifert surface associated to its boundary link.
Note that it suffices to prove the result for a small interval I = (− ε, ε ), since if ψ ( t ) is a smooth bump function with compact support in (− ε, ε ) equal identically to 1 near 0, then ψ ( t ) ⋅ F ( t, x ) gives a solution on R × U. Similarly using a smooth partition of unity on R < sup > n </ sup > subordinate to a covering by open balls with centres at δ ⋅ Z < sup > n </ sup >, it can be assumed that all the f < sub > m </ sub > have compact support in some fixed closed ball C. For each m, let
Note that there were two other Farina-styled car lines launched by BMC at the same time — the compact Austin A40 Farina and large Wolseley 6 / 99 / Austin A99 Westminster and derivatives.
Note that, even though a compact surface with a point removed and the same surface with a disc removed are topologically the same, a complex structure on the surface behaves very differently around a point and around a removed disc.
Note that, as profinite groups are compact, the open subgroups are exactly the subgroups of finite index, so that the discrete quotient group is always finite.

2.598 seconds.