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Excel maintains 15 figures in its numbers, but they are not always accurate; mathematically, the bottom line should be the same as the top line, in 'fp-math' the step '1 + 1/9000' leads to a rounding up as the first bit of the 14 bit tail '10111000110010' of the mantissa falling off the table when adding 1 is a '1', this up-rounding is not undone when subtracting the 1 again, since there is no ...
In mathematics, the local trace formula (Arthur 1991) is a local analogue of the Arthur–Selberg trace formula that describes the character of the representation of G(F) on the discrete part of L 2 (G(F)), for G a reductive algebraic group over a local field F.
In mathematics, the Arthur–Selberg trace formula is a generalization of the Selberg trace formula from the group SL 2 to arbitrary reductive groups over global fields, developed by James Arthur in a long series of papers from 1974 to 2003.
An indoor location tracking map on a mobile phone. Mobile phone tracking is a process for identifying the location of a mobile phone, whether stationary or moving. . Localization may be affected by a number of technologies, such as the multilateration of radio signals between (several) cell towers of the network and the phone or by simply
In analytic number theory, the Petersson trace formula is a kind of orthogonality relation between coefficients of a holomorphic modular form. It is a specialization of the more general Kuznetsov trace formula. In its simplest form the Petersson trace formula is as follows.
Trace formula may refer to: Arthur–Selberg trace formula , also known as invariant trace formula, Jacquet's relative trace formula, simple trace formula, stable trace formula Grothendieck trace formula , an analogue in algebraic geometry of the Lefschetz fixed-point theorem in algebraic topology , used to express the Hasse–Weil zeta function .
While the usual trace formula studies the harmonic analysis on G, the relative trace formula is a tool for studying the harmonic analysis on the symmetric space /. For an overview and numerous applications Cogdell, J.W. and I. Piatetski-Shapiro, The arithmetic and spectral analysis of Poincaré series , volume 13 of Perspectives in mathematics .
In mathematics, specifically functional analysis, a trace-class operator is a linear operator for which a trace may be defined, such that the trace is a finite number independent of the choice of basis used to compute the trace. This trace of trace-class operators generalizes the trace of matrices studied in linear algebra.