alternating sum造句

• We then multiply the character by an alternating sum of exponentials.
• The alternating sum over the torsion groups of the factor rings corresponding to the subvarieties.
• The "'Euler characteristic "'can then be defined as the alternating sum
• That is, the boundary of a singular simplex is the alternating sum of restrictions to its faces.
• In this setting, Morse theory gives a set of inequalities for alternating sums of Betti numbers in terms of a corresponding alternating sum of the number of index:
• In this setting, Morse theory gives a set of inequalities for alternating sums of Betti numbers in terms of a corresponding alternating sum of the number of index:
• If one is interested, as is usually the case, in just one summand within the alternating sum, further arguments such as vanishing theorems must be brought to bear.
• In practice, this presents no particular problem, as long as one avoids the fatal trap of replacing alternating sums of ?" by the wedge symbol, with one exception.
• More generally, one can define the Euler characteristic of any chain complex to be the alternating sum of the ranks of the homology groups of the chain complex, assuming that all these ranks are finite.
• Random walk theory might even be usefully employed ( Is the absolute alternating sum at least 11 ? ), which is a little cute . talk ) 16 : 22, 11 December 2010 ( UTC)
• However, this equivalent form applies only to a crease pattern on a flat piece of paper, whereas the alternating sum form of the condition remains valid for crease patterns on conical sheets of paper with nonzero defect at the vertex.
• In Hirzebruch's formulation, the Hirzebruch Riemann Roch theorem, the theorem became a statement about Euler characteristics : The Euler characteristic of a vector bundle on an algebraic variety ( which is the alternating sum of the dimensions of its cohomology groups ) equals the Euler characteristic of the trivial bundle plus a correction factor coming from characteristic classes of the vector bundle.
• This Dirichlet series is the alternating sum corresponding to the Dirichlet series expansion of the Riemann zeta function, " & zeta; " ( s ) & mdash; and for this reason the Dirichlet eta function is also known as the "'alternating zeta function "', also denoted " & zeta; " * ( s ).
• The affine curve " X " is generalized to a " T " " F " bundle over a " Deligne Lusztig variety " where " T " is a maximal torus of " G ", and instead of using just the first cohomology group they use an alternating sum of  !-adic cohomology groups with compact support to construct virtual representations.
• Essentially I need to find a simplicial complex ( http : / / en . wikipedia . org / wiki / Simplicial _ complex ) such that the alternating sum of the characters for the homology groups \ sum (-1 ) ^ i h _ i, where h _ i is a character for the homology group H _ i ( http : / / en . wikipedia . org / wiki / Simplicial _ homology, better explained http : / / www . math . hmc . edu / % 7Esu / pcmi / projects / simplicial _ module / simplicial _ pcmi . pdf ) of the characters gives the character