Displaying similar documents to “Some counterpart inequalities for a functional associated with Jensen's inequality.”

Conditions for periodic vibrations in a symmetric n-string

Claude Gauthier (2008)

Open Mathematics

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A symmetric N-string is a network of N ≥ 2 sections of string tied together at one common mobile extremity. In their equilibrium position, the sections of string form N angles of 2π/N at their junction point. Considering the initial and boundary value problem for small-amplitude oscillations perpendicular to the plane of the N-string at rest, we obtain conditions under which the solution will be periodic with an integral period.

An asymptotic approximation of Wallis’ sequence

Vito Lampret (2012)

Open Mathematics

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An asymptotic approximation of Wallis’ sequence W(n) = Πk=1n 4k 2/(4k 2 − 1) obtained on the base of Stirling’s factorial formula is presented. As a consequence, several accurate new estimates of Wallis’ ratios w(n) = Πk=1n(2k−1)/(2k) are given. Also, an asymptotic approximation of π in terms of Wallis’ sequence W(n) is obtained, together with several double inequalities such as, for example, W ( n ) · ( a n + b n ) < π < W ( n ) · ( a n + b n ' ) with a n = 2 + 1 2 n + 1 + 2 3 ( 2 n + 1 ) 2 - 1 3 n ( 2 n + 1 ) ' b n = 2 33 ( n + 1 ) 2 ' b n ' 1 13 n 2 ' n ∈ ℕ .

Poisson sampling for spectral estimation in periodically correlated processes

Vincent Monsan (1994)

Applicationes Mathematicae

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We study estimation problems for periodically correlated, non gaussian processes. We estimate the correlation functions and the spectral densities from continuous-time samples. From a random time sample, we construct three types of estimators for the spectral densities and we prove their consistency.

Differential geometry of grassmannians and the Plücker map

Sasha Anan’in, Carlos Grossi (2012)

Open Mathematics

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Using the Plücker map between grassmannians, we study basic aspects of classic grassmannian geometries. For ‘hyperbolic’ grassmannian geometries, we prove some facts (for instance, that the Plücker map is a minimal isometric embedding) that were previously known in the ‘elliptic’ case.