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Closed-Form Summation Formulae

2017
Closed-form summation formulae provide a compact means of describing different types of spectra. By combining a limited number of sinusoids, we can generate complex waveforms with many harmonic or inharmonic partials. In this chapter, we will look at various formulae, and their implementation and application, from band-limited pulse oscillators to ...
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A Closed-Form Formula for Pricing Variance Swaps on Commodities

Vietnam Journal of Mathematics, 2016
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Weraprasertsakun, Anurak, Rujivan, Sanae
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On formulas in closed form for van vleck expansions

International Journal of Quantum Chemistry, 1972
AbstractCanonical transformations have been widely used to simplify Hamiltonians and other operators. In molecular and in solid state theory, the so‐called Van Vieck expansion is usually employed for this purpose while in theories of particles interacting with fields a combination of canonical transformations in closed form with Van Vleck type ...
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A Closed-Form Formula for Calculating Bond Duration

Financial Analysts Journal, 1984
(1984). A Closed-Form Formula for Calculating Bond Duration. Financial Analysts Journal: Vol. 40, No. 3, pp. 76-78.
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A closed-form formula for GPS GDOP computation

GPS Solutions, 2008
Geometric dilution of precision (GDOP) is often used for selecting good satellites to meet the desired positioning precision. An efficient closed-form formula for GDOP has been developed when exactly four satellites are used. It has been proved that increasing the number of satellites for positioning will always reduce the GDOP.
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A closed form network connectivity formula one-dimensional MANETs

2004 IEEE International Conference on Communications (IEEE Cat. No.04CH37577), 2004
In this paper, a closed form network connectivity formula for a one-dimensional mobile ad hoc network (MANET) is developed. Precisely, we derive the probability that a MANET is fully connected given a certain number of nodes randomly and uniformly placed along a path between a source and destination pair.
Foh, CH, Lee, B-S
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Derivation of the Closed-Form Solution to the Mori Formula

Journal of the Physical Society of Japan, 1997
Summary: The closed-form solution to the memory function in the generalized Langevin equation (Mori formula), obtained as a series expansion in terms of the projection operator, is rederived without use of the expansion method. The procedure for approximation of the closed-form solution is briefly mentioned.
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CLOSED FORM FORMULAS FOR EXOTIC OPTIONS AND THEIR LIFETIME DISTRIBUTION

International Journal of Theoretical and Applied Finance, 1999
We first recall the well-known expression of the price of barrier options, and compute double barrier options by the mean of the iterated mirror principle. The formula for double barriers provides an intraday volatility estimator from the information of high-low-close prices. Then we give explicit formulas for the probability distribution function and
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Closed-Form Formulae for European Options Under Three-Factor Models

Communications in Mathematics and Statistics, 2019
The author derives new closed-form valuations to European options under three-factor hybrid models that include stochastic interest rates and stochastic volatility and incorporate a nonzero covariance structure between factors. The idea is to cleverly use the empirically proven 3/2 stochastic volatility model with a time-dependent drift in which one is
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Mwanaute's Closed-Form Formula for RSA 𝑑

This resource presents a closed-form formula, referred to as “Mwanaute’s Closed-Form Formula,” for computing the RSA private exponent ddd given the public exponent eee and prime factors ppp and qqq. Unlike standard methods that require the Extended Euclidean Algorithm, this formula allows direct computation in constant time using basic arithmetic ...
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